Corpus Methods for Semantics. Quantitative studies in polysemy and synonymy

Corpus Methods for Semantics

Human Cognitive Processing (HCP)

Cognitive Foundations of Language Structure and Use This book series is a forum for interdisciplinary research on the grammatical structure, semantic organization, and communicative function of language(s), and their anchoring in human cognitive faculties. For an overview of all books published in this series, please see http://benjamins.com/catalog/hcp

Editors Klaus-Uwe Panther

Nanjing Normal University & University of Hamburg

Linda L. Thornburg

Nanjing Normal University

Editorial Board Bogusław Bierwiaczonek

Jan Dlugosz University, Czestochowa, Poland / Higher School of Labour Safety Management, Katowice

Mario Brdar

Josip Juraj Strossmayer University, Croatia

Barbara Dancygier

University of British Columbia

N.J. Enfield

Max Planck Institute for Psycholinguistics, Nijmegen & Radboud University Nijmegen

Elisabeth Engberg-Pedersen University of Copenhagen

Ad Foolen

Radboud University Nijmegen

Raymond W. Gibbs, Jr.

University of California at Santa Cruz

Rachel Giora

Tel Aviv University

Elżbieta Górska

University of Warsaw

Martin Hilpert

University of Neuchâtel

Zoltán Kövecses

Eötvös Loránd University, Hungary

Teenie Matlock

University of California at Merced

Carita Paradis

Lund University

Günter Radden

University of Hamburg

Francisco José Ruiz de Mendoza Ibáñez University of La Rioja

Doris Schönefeld

University of Leipzig

Debra Ziegeler

University of Paris III

Volume 43 Corpus Methods for Semantics. Quantitative studies in polysemy and synonymy Edited by Dylan Glynn and Justyna A. Robinson

Corpus Methods for Semantics Quantitative studies in polysemy and synonymy Edited by

Dylan Glynn University of Paris VIII

Justyna A. Robinson University of Sussex

John Benjamins Publishing Company Amsterdamâ•›/â•›Philadelphia

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TM

The paper used in this publication meets the minimum requirements of the╯American National Standard for Information Sciences – Permanence of Paper for Printed Library Materials, ansi z39.48-1984.

Library of Congress Cataloging-in-Publication Data Corpus Methods for Semantics : Quantitative studies in polysemy and synonymy / Edited by Dylan Glynn and Justyna A. Robinson. p. cm. (Human Cognitive Processing, issn 1387-6724 ; v. 43) Includes bibliographical references and index. 1. Semantics. 2. Cognitive grammar. 3. Computational linguistics. 4. Polysemy. 5.  Corpora (Linguistics) I. Glynn, Dylan. II. Robinson, Justyna A. P325.C595 2014 401’.43--dc23 isbn 978 90 272 2397 5 (Hb ; alk. paper) isbn 978 90 272 7033 7 (Eb)

2014004752

© 2014 – John Benjamins B.V. No part of this book may be reproduced in any form, by print, photoprint, microfilm, or any other means, without written permission from the publisher. John Benjamins Publishing Co. · P.O. Box 36224 · 1020 me Amsterdam · The Netherlands John Benjamins North America · P.O. Box 27519 · Philadelphia pa 19118-0519 · usa

Table of contents

Contributors Outline

vii 1

Section 1.╇ Polysemy and synonymy Polysemy and synonymy: Cognitive theory and corpus method Dylan Glynn Competing ‘transfer’ constructions in Dutch: The case of ont-verbs Martine Delorge, Koen Plevoets, and Timothy Colleman Rethinking constructional polysemy: The case of the English conative construction Florent Perek Quantifying polysemy in Cognitive Sociolinguistics Justyna A. Robinson The many uses of run: Corpus methods and Socio-Cognitive Semantics Dylan Glynn

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61 87 117

Visualizing distances in a set of near-synonyms: Rather, quite, fairly, and pretty Guillaume Desagulier

145

A case for the multifactorial assessment of learner language: The uses of may and can in French-English interlanguage Sandra C. Deshors and Stefan Th. Gries

179

Dutch causative constructions: Quantification of meaning and meaning of quantification Natalia Levshina, Dirk Geeraerts, and Dirk Speelman

205

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The semasiological structure of Polish myśleć ‘to think’: A study in verb-prefix semantics Małgorzata Fabiszak, Anna Hebda, Iwona Kokorniak, and Karolina Krawczak

223

A multifactorial corpus analysis of grammatical synonymy: The Estonian adessive and adposition peal ‘on’ Jane Klavan

253

A diachronic corpus-based multivariate analysis of “I think that” vs. “I think zero” Christopher Shank, Koen Plevoets, and Hubert Cuyckens

279

Section 2.╇ Statistical techniques Techniques and tools: Corpus methods and statistics for semantics Dylan Glynn

307

Statistics in R: First steps Joost van de Weijer and Dylan Glynn

343

Frequency tables: Tests, effect sizes, and explorations Stefan Th. Gries

365

Collostructional analysis: Measuring associations between constructions and lexical elements Martin Hilpert

391

Cluster analysis: Finding structure in linguistic data Dagmar Divjak and Nick Fieller

405

Correspondence analysis: Exploring data and identifying patterns Dylan Glynn

443

Logistic regression: A confirmatory technique for comparisons in corpus linguistics Dirk Speelman

487

Name index

535

Subject index

541

Contributors

Timothy Colleman Ghent University [email protected]

Dylan Glynn University of Paris VIII [email protected]

Hubert Cuyckens University of Leuven [email protected]

Stefan Th. Gries University of California, Santa Barbara [email protected]

Sandra Deshors New Mexico State University [email protected]

Anna Hebda Adam Mickiewicz University, Poznań [email protected]

Martine Delorge Ghent University [email protected]

Martin Hilpert University of Neuchâtel [email protected]

Guillaume Desagulier Université Paris 8 Vincennes Staint Denis Université Paris Ouest Nanterre La Défense UMR 7114 MoDyCo [email protected]

Jane Klavan University of Tartu [email protected]

Dagmar Divjak University of Sheffield [email protected]

Karolina Krawczak Adam Mickiewicz University, Poznań [email protected]

Małgorzata Fabiszak Adam Mickiewicz University, Poznań [email protected]

Natlia Levshina Université catholique de Louvain [email protected]

Nick Fieller University of Sheffield [email protected]

Florent Perek University of Freiburg [email protected]

Dirk Geeraerts University of Leuven [email protected]

Koen Plevoets Ghent University [email protected]

Iwona Kokorniak Adam Mickiewicz University, Poznań [email protected]

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Justyna A. Robinson University of Sussex [email protected]

Dirk Speelman University of Leuven [email protected]

Christopher Shank Bangor University [email protected]

Joost van de Weijer Lund University [email protected]

Outline

1. Aim of the volume It could be argued that Cognitive Linguistics is undergoing a paradigm shift. Originally, the field sought to show the inadequacies of earlier models of language and the theories of linguistic structure based upon them. Today, the emphasis has changed to testing the various theories about how language works (Geeraerts 2006; Gries and Stefanowitsch 2006; Stefanowitsch and Gries 2006; Gonzalez-Marquez et al. 2008; Glynn and Fischer 2010). This has brought analytical methods, based on observable and quantifiable data, to the fore. In the light of these developments, this volume systematises, reviews, and promotes a range of research techniques and theoretical perspectives that currently inform work across the field of linguistics, with a particular focus on Cognitive Semantics. More precisely, the aim of this book is twofold: i. Didactic: To broaden the understanding and application of the state-of-the-art corpus linguistic techniques for the study of conceptual structure in Cognitive Semantics. Scientific: To advance the state-of-the-art of those techniques through a collecii. tion of studies applied to the description of the conceptual structures of polysemy and synonymy. This publication grew out of the belief that there exists a strong desire in the research community to understand and learn how quantitative corpus methods work and how to apply them to research questions that are basic to the cognitive project. Instead of a rift between linguists using corpus data and those using traditional introspective analysis, constructive communication between the methodologies should be encouraged. Both the descriptive research and the explanations of the statistical techniques included in this book seek to promote such communication. The chapters that describe the statistical techniques are written to help linguists using traditional methods both understand how these new methods work and how to apply them. The research chapters, in turn, showcase the methods described. Their aim is not only to advance corpus-driven quantitative research in Cognitive Semantics, but also to promote the possibilities that these methodologies offer. Observational data and quantitative corpus-driven methods cannot inform all research questions. However, it is hoped that this volume will advance the current state-of-the-art in their use as well as promote their application in the broader linguistic research community.

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2. Structure and summary The book divides into two sections. The first section begins with eleven chapters, arranged according to their object of study. These chapters begin with an overview of the field in “Polysemy and synonymy: Corpus method and cognitive theory” (Glynn). This chapter includes the analytical justification for approaching both lexis and morpho-syntax in terms of polysemy and synonymy as well as a justification of extending the traditional uses of the terms to cover any variation or similarity in use. The analytical chapters begin with morpho-syntactic polysemy, move to lexical polysemy, then on to lexical synonymy, and finally turn to morpho-syntactic synonymy. Beginning with research on the polysemy of morpho-syntactic semantics, the first descriptive chapter, “Competing ‘transfer’ constructions in Dutch” (Delorge, Plevoets, and Colleman), considers the polysemy of a morpheme-based construction. The ontprefix in Dutch combines with a range of verbs to express dispossession. Using correspondence analysis, the study seeks to capture the lexical semantic morpho-syntactic interplay associated with the construction. The next chapter, “Rethinking constructional polysemy” (Perek), also examines a grammatical construction. The syntactically encoded conative construction in English combines with a range of lexemes. Through the application of collostructional analysis, the author attempts the task of teasing out and identifying the semantic variation associated with the construction. Turning to lexical semantics, “Quantifying polysemy in cognitive sociolinguistics” (Robinson) examines the usage of polysemous adjectives in a community of speakers from South Yorkshire, UK. The study applies cluster analysis, logistic regression, and decision tree analysis in order to examine the extent to which individual conceptualisations are non-random and can be related to the socio-demographic characteristics of the speaker. “The many uses of run” (Glynn) is a repeat analysis of Gries’ (2006) study. Employing a combination of cluster analysis, correspondence analysis and logistic regression, it confirms Gries’ findings but argues that sociolinguistic dimensions should be included in the study of polysemy. Remaining with lexical semantics, but focusing on near-synonymy, “Visualizing distances in a set of near-synonyms” (Desagulier) examines rather, quite, fairly, and pretty in English, combining collostructional analysis and multivariate statistics such as correspondence analysis and cluster analysis. “The uses of may and can in French-English interlanguage” (Deshors and Gries) treats a lexical alternation in first language and second language use. With the use of cluster analysis and logistic regression, the authors seek to identify not only the relationship in use between may and can, but to compare this with French native speakers using English. Moving towards morpho-syntactic semantics, “Dutch causative constructions” (Levshina, Geeraerts, and Speelman) examines a lexeme-based grammatical construction alternation. Focusing on the expression of causation in Dutch, the study employs logistic regression analysis to determine both the semantic and extralinguistic factors

Outline 3

that determine the choice and difference in conceptualisation between the two constructions. The next study, “The semasiological structure of Polish myśleć ‘to think’” (Fabiszak, Hebda, Kokorniak, and Krawczak) continues to move from lexical to syntactic semantics with an analysis of the near-synonymy of a set of prefix-verb combinations. The study combines introspective methods and usage-feature analysis, examined with cluster analysis, correspondence analysis and logistic regression. “A multifactorial analysis of grammatical synonymy” (Klavan) studies a lexical-morphological alternation. Employing logistic regression, the study attempts to determine the conceptual differences that motivate speakers’ choice of a preposition over a grammatical case to express the spatial relation of on in Estonian. “A diachronic corpus-based multivariate analysis of ‘I think that’ vs. ‘I think zero’” (Shank, Plevoets, and Cuyckens) is an analysis of well-known complementiser alternation in English. Logistic regression is used to test a wide range of language factors proposed in the literature to motivate the omission of the complementiser. The second section consists of seven chapters that explain some of the tools and methods for quantitative corpus-driven research. It is designed to introduce the application and interpretation of the statistical methods used in the first section for researchers completely new to the field. It also serves as a ‘cookbook’, or is a quick reference, for intermediate users of the statistical techniques and the programming environment R. The first chapter, “Techniques and tools: Corpus methods and statistics for semantics” (Glynn), is an overview of the field. It examines two corpus methods that are commonly used in Cognitive Semantics and summarises many of statistical techniques currently used in the field. The second chapter introduces the statistical environment of R, used throughout the book (van de Weijer and Glynn). Readers with no experience in R will find this chapter useful when applying the techniques described in the previous chapters to data analysis. The following chapter, “Frequency tables: Tests, effect sizes, and explorations” (Gries), covers many of the essential and basic analytical concepts and how to apply them in R. Building on the statistical basics, the next chapter, “Collostructional analysis: Measuring associations between constructions and lexical elements” (Hilpert), explains the application of collostructional analysis, one of the most popular quantitative techniques in Cognitive Linguistics. This family of techniques are used to quantify the degree of association between linguistic forms. The next three chapters each consider a different multivariate statistical technique. The three techniques in question have proven popular in recent Cognitive Linguistic research. The chapter “Cluster analysis: Finding structure in linguistic data” (Divjak and Fieller), focuses on a method for sorting a given set of phenomena, such as lexemes, constructions, or senses, into categories of similar and dissimilar, relative to some other set(s) of linguistic phenomena such as meanings, argument types, case marking, and so forth. This is followed by the chapter “Correspondence analysis: Exploring data and identifying patterns” (Glynn), which considers a technique similar

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to cluster analysis, but one that looks for correlations between different phenomena rather than categorising them. It is useful for identifying structure in complex multidimensional data. The third chapter on multivariate techniques, “Logistic regression: A confirmatory technique for variant comparison in corpus linguistics” (Speelman), considers an advanced form of statistical modelling. Logistic regression is a powerful and popular tool in the social sciences, including Cognitive Linguistics. As a confirmatory technique, regression analysis represents a level of statistical analysis that is more complex than the previous techniques covered. This chapter charts the basics of its application, interpretation and verification. Where the first section represents a broad, yet coherent, picture of the cutting edge in the application of these techniques, the second section seeks to offer an introduction to the different statistical techniques employed in corpus-driven semantics. Focusing on the study of polysemy and synonymy of both lexical morpho-syntactic forms, these empirical analyses represent the vanguard of corpus-driven Cognitive Linguistics. 

The editors

References Geeraerts, D. (2006). Methodology in Cognitive Linguistics. In G. Kristiansen, M. Achard, R. Dirven, & F. J. Ruiz de Mendoza Ibañez (Eds.), Cognitive Linguistics: Current applications and future perspectives (pp. 21–50). Berlin & New York: Mouton de Gruyter. Glynn, D., & Fischer, K. (Eds.). (2010). Quantitative Cognitive Semantics: Corpus-driven approaches. Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110226423 Gonzalez-Marquez, M., Mittelberg, I., Coulson, S., & Michael S. (Eds.). (2008). Methods in Cognitive Linguistics. Amsterdam & Philedelphia: John Benjmains. Gries, St. Th. (2006). Corpus-based methods and Cognitive Semantics: The many senses of to run. In St. Th. Gries, & A. Stefanowitsch (Eds.), Corpora in Cognitive Linguistics: Corpus-based approaches to syntax and lexis (pp. 57–99). Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110197709 Gries, St. Th., & Stefanowitsch, A. (Eds.). (2006). Corpora in Cognitive Linguistics: Corpus-based approaches to syntax and lexis. Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110197709 Stefanowitsch, A., & Gries, St. Th. (Eds.). (2006). Corpus-based approaches to metaphor and metonymy. Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110199895

Section 1

Polysemy and synonymy

Polysemy and synonymy Cognitive theory and corpus method Dylan Glynn

University of Paris VIII

This chapter introduces the field of polysemy and synonymy studies from a Cognitive Linguistic perspective. Firstly, the discussion explains and defines the object of research, showing that the study of semantic relations, traditionally restricted to the description of lexical semantics, needs to be extended to include all formal structures, including morpho-syntax. Secondly, given the theoretical assumptions of Cognitive Linguistics, it is argued that quantitative corpus-driven methods are essential for the description of semantic structures. Lastly, the chapter charts the development of Cognitive Semantic research in polysemy and synonymy and demonstrates how the current corpus-driven research in the field is inherently linked to the traditions of radial network analysis and prototype semantics. It is argued that instead of an empirical revolution (as has been suggested in recent commentaries), the current trends in the use of observational data are a natural extension of the Cognitive Semantic research tradition. Keywords: Cognitive Linguistics, corpus linguistics, polysemy, prototype semantics, quantification, radial network analysis, synonymy

1. Introduction: Theory and method The idea of ‘corpus semantics’, just like the possibility of ‘quantifying meaning’, is not self-evident. This introduction to the field of corpus-driven Cognitive Semantics attempts to explain how semantic analysis can, and indeed, should, turn to corpus methods. It also explains why quantitative techniques are needed in this endeavour. Assuming the Usage-Based Model (Hopper 1987; Langacker 1987), how can we identify and explain the semantic structuring of language empirically? Post-Generativist and post-Structuralist approaches to language avoid positing, a priori, analytical constructs to explain the structuring of language, rather treating it holistically as a dynamic and varied result of use. However, without a structurally independent langue or an ‘ideal’ speaker’s competence, against what predictive model can we test

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our hypotheses or attempt to falsify our claims about language structure? Without constructs such as langue and ideal competence, linguistic research, whether Functional or Cognitive, must adopt an inductive, sample-based, methodology. To these ends, experimental techniques for the analysis of semantics have been developed, yet corpus methods remain poorly represented within the field. Moreover, the theory of Cognitive Linguistics recognises no internal language modules, such as syntax, lexis, semantics or pragmatics. From a non-modular perspective, the study of meaning must account for the integration of all these components of language structure and do so simultaneously in a functionally and conceptually plausible manner. Corpus-driven methods, and multivariate statistics more specifically, are perfectly suited for such a task. A usage-based semantics, therefore, must take two fundamental steps. Firstly, it must adopt inductive research methods. Whether elicited through experimentation, extracted from electronic corpora, or collated from questionnaires and field research, generalisations based on samples of data present the only possibility for hypothesis testing. Importantly, acknowledging this fact entails validating sample-based results through statistical confirmation. Secondly, it must develop corpus-driven semantic analysis. If we are to account holistically for the integrated complexity of the various dimensions of language structure, it is essential that we examine natural contextualised language production. Samples of natural language large enough to permit inductively valid claims are what we term corpora. Here again, statistics comes to the fore, though for a different reason. If we are to identify structure, sensitive to its usage context, multivariate statistics is a powerful, if not essential, tool due to the sheer complexity of the data. The aim of this book is both to introduce quantitative corpus-driven semantic methodology to the broader research community and to advance the state-of-theart. The methods in focus are those that are especially applicable to the lexical and constructional semantic relations of similarity and difference. Linguistic forms are used in different ways, and capturing this semasiological variation is what we term the study of polysemy. Likewise, speakers choose between different linguistic forms to express similar concepts. Explaining this onomasiological variation is what we term the study of synonymy. The reader should be aware that the term polysemy is not restricted to ‘true’ polysemy, where distinct referents are indicated by a single form. Instead, meaning is understood from a usage-based perspective, where any systematic variation in use represents semasiological structure. In the same vein, synonymy is not restricted to absolute similarity since, from a Cognitive Linguistic perspective, one assumes that any variation in form is motivated by some variation in use and that ‘true’ synonymy is rare, if it exists at all. Lastly, it must be added that the term semantics is used to indicate encyclopaedic semantics and pragmatics, as opposed to linguistic semantics in its narrow sense.



Polysemy and synonymy

Moreover, the term corpus methodology should be understood to indicate research that is corpus-driven, as opposed to corpus-exemplified (q.v. Tummers et al. 2005). Where corpus-exemplified research identifies occurrences to explain or support a theory of language structure, corpus-driven research examines large samples of natural language in order to test theories about language structure (often previously proposed a priori in corpus-exemplified research). In this, we focus on quantitative techniques, and, more specifically, statistical methods for the exploration of data and the falsification or confirmation of quantitatively testable hypotheses. We begin by developing operational definitions of polysemy and synonymy (Section 2). The discussion then demonstrates, given the above definitions, why we need corpus methodology (Section 3). Finally, we consider the argument that the quantitative corpus tradition and the prototype-based Cognitive Semantic tradition are not only analytically compatible, but, in fact, are inherently entwined. It is argued that the introspection-based research in prototype structuring of linguistic categories and the results of the radial network tradition should be understood as the theoretical modelling of semantic structure, an essential first step in empirical research (Section 4).

2. Polysemy and synonymy: Definition, object and operationalisation Given the linguistic heritage of the 20th century, it is upon us to begin with two simple questions. Firstly, what exactly constitutes polysemous and synonymous semantic relations in usage-based semantics? Secondly, is it theoretically and analytically possible to speak of the polysemy and synonymy of a syntactic construction? This section answers each question in turn. In doing so, the discussion will offer operational definitions of the concepts ‘polysemy’ and ‘synonymy’ and will justify extending the study of such relations to morpho-syntax. With meaning defined as encyclopaedic and with all form being semantically motivated, how do we understand the notions of polysemy (difference in sense of a form) and synonymy (similarity in sense between forms)? Given a traditional understanding of the terms, usage-based approaches, such as Cognitive Linguistics or Functional Linguistics, are not interested in polysemy or synonymy per se. Much of what cognitivists and functionalists examine would be called ‘semantic vagueness’, ‘word fields’ or ‘syntactic alternation’ in other theoretical paradigms. Moreover, for Structuralism, which holds a distinction between the langue and its use, our position, that the meaning of a word can be operationalised as its use, is nonsense. For Generativism, which argues for an autonomous formal system, examining the semantic structure of syntactic patterns is equally nonsense. In Structuralist terms, polysemy was identified using the definitional test and/ or the ambiguity test. These tests were designed to distinguish polysemous relations from vague relations, on the one hand, and from a monosemic form, on the other (for

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further discussion, see Geeraerts 1993a). This modular understanding of semantic structure assumes two theoretical constructs – firstly, the notion of truth conditional semantics and, secondly, the notion of semantic categories determined by necessary and sufficient conditions. The same assumptions determined the definition of synonymy – any two lexemes were considered synonymous if replacing one lexeme with the other did not change the ‘truth semantic’ meaning of the phrase (Lyons 1968:â•›428). Cognitive Linguistics categorically refutes both assumptions.1 Indeed, cognitive-functional approaches to meaning do not recognise the notion of necessary and sufficient conditions nor any strict division between linguistic semantics and context pragmatics. Without such assumptions, the meaning of the terms polysemy and synonymy can be loosened and defined as: Polysemy – different concepts-functions of a form Synonymy – different forms for a concept-function Note that these definitions of polysemy and synonymy do not exclude taxonomic relations such as hyponymy and hyperonymy (for polysemy) or basic level, superordinate and subordinate relations (for synonymy). The definitions need to include these relations because, in a given situation-context, a given form may be used at different levels of specificity (‘vertical’ polysemy), just as a choice is made between different words signifying different levels of specificity (‘vertical’ synonymy). Such a broad understanding of semantic relations could be more accurately described as semasiological and onomasiological variation (Geeraerts 1993b; Grondelaers and Geeraerts 2003). Nevertheless, we will continue with the terms polysemy and synonymy since they enjoy wider currency.

1. See Geeraerts (1987, 1993a, 1994) and Tuggy (1993) for a more detailed explanation of the theoretical questions at stake here. For a summary of the questions that led to the original debates on truth conditional semantics and necessary and sufficient conditions, see Verschueren (1981) and Lakoff (1982). Footnote 10 lists the principal works that established Cognitive Linguistics’ position on these questions. The contemporary Anglo-Saxon Structuralist position is summarised in Cruse (2000) and Murphy (2003). The aforementioned debates largely ignored the contemporary French, German and Russian traditions. Examples of current French Structuralist research on semantic relations include Rastier’s (1987, 1991, 2011) context sensitive approach and Victorri and Fuchs’s (1996) construal sensitive framework. The German Structuralist understanding of semantic relations lies close to the Anglo-Saxon tradition (q.v. Coșeriu 1980; Kastovsky 1982; Lutzeier 1985; and Lipka 1992). The Leibnizian tradition of semantic primitives, important to the Moscow school of semantics, is represented by Apresjan (1974, 2000), Wierzbicka (1985, 1996), and Mel’čuk (1989). From a Leibnizian functional perspective, Wierzbicka (1989, 1990) offers responses to issues raised in Verscheuren (1981) and Lakoff (1982). Geeraerts (1999b) offers, in turn, responses to Wierzbicka.



Polysemy and synonymy

Can we now justify applying the notions of polysemy (semasiological variation of a single form) and synonymy (onomasiological variation between more than one form) to the study of grammar? If we assume that all form is conceptually or functionally motivated and if we agree that, in the study of polysemy and synonymy, we are effectively studying variation in concept-function relative to form and variation in form relative to concept-function, then this must necessarily be extended to non-lexical meaning and form. Therefore, in blunt terms, the study of polysemy and synonymy includes the study of schematic forms and their meanings such as those typical of syntax and prosody just as much as it does the study of words and morphemes. We can, therefore, identify our object of study more precise terms: Polysemy – the functional-conceptual variation of any symbolic form Synonymy – the functional-conceptual relation between any symbolic forms2 This is a simple statement about an object of study that many linguists would take as obvious, yet others take as ludicrous. The division is a result of the fact that even if we accept that all formal structure is motivated, there certainly exist different types of form just as there exist different types of meaning. Phonological, gestural, syntactic, morphological and lexical forms all tend to possess different characteristics. There is no doubt in this – the referential meaning of a lexeme like chair is far from the intersubjective meaning of a request implicature, and these two ‘types’ of meaning differ from the abstract relational meaning of the Transitive Construction. Notwithstanding the belief that such linguistic devices are inextricably interwoven structurally, the characteristics of these different types of form and meaning, just as the tools needed to describe them, differ profoundly. If we accept that, analytically (as opposed to theoretically), such differences exist, then we can distinguish different lines of research. Given this, it is still possible to speak of lexical research or syntactic research as long as this is seen as an analytical emphasis, not an object of study. In order to avoid conjuring the theoretical modules of earlier theories of language, we can term the different lines of research – schematic 2. This definition would also cover antonymy. Although it may seem a little far-fetched to consider antonymy as a synonymy relation, this is merely a result of the terminology. Ideally, onomasiological structure would be a better term than synonymy, but the term is not established in the Anglo-Saxon tradition and would, therefore, add considerable terminological weight to the discussion. Nevertheless, it must be noted that antonymy should not be seen as an antonym (in a non-technical sense) for synonymy. It is well known from the study of lexical fields and, more recently, word space modelling in computational linguistics, that antonyms are, in fact, closely related to each other semantically and, therefore, are relatively synonymous. For example, hate is much closer in meaning to love than car or run. Generally, antonyms are synonyms semantically opposed by one culturally or perceptually salient feature. Therefore, in fact, antonymy is an antonym to synonymy, in other words, very close in its meaning. See Jones (2002:â•›51) and Murphy (2003:â•›37) for examples of the issue at hand.

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and concrete. Such distinctions are abstract enough to avoid leading us into the trap of modularising language structures, while also being transparent enough to help us easily differentiate between lines of research and the tools they necessitate. Therefore, although semantic structure and its relations exist equally for morpho-syntax and lexis, the kind of semantics typically associated with lexical forms is of a much more concrete nature than that of more schematic formal structures. This is, of course, a tendency, but an important one because the different kinds of formal structure and the semantics associated with them may warrant different analytical techniques. For these practical purposes, let us identify four objects of study: Polysemy – Concrete meaning – Schematic meaning Synonymy – Concrete form – Schematic form Seen in these terms, Lakoff ’s (1987) analysis of over is a study of concrete, or non-schematic, polysemy, but his study of the Deictic Construction is schematic polysemy. On the other side of the coin, Lakoff ’s (1987) analysis of anger is concrete (non-schematic) synonymy and the analysis of the Dative alternation by Goldberg (2002) is an instance of schematic synonymy. Regardless of whether we speak of words or syntax, the analytical object of the relations between different yet functionally-conceptually similar forms versus the relations between different functions-concepts of a single form should be evident. A few further examples should demonstrate the distinction and its value for identifying the fundamental objects of study for all usage-based linguistics. By way of example for schematic polysemy, consider Halliday’s (1967) study of the English Transitive Construction, Langacker’s (1982) analysis of the English Passive Construction or Bondarko’s (1983) analysis of the Perfective Aspect. For concrete polysemy, take Culioli’s (1990) analysis of the French lexeme donc ‘so, thus’ or Fillmore’s (2000) lexeme crawl. For synonymy, the same diversity exists. At the schematic level, we have Givón’s (1982) evidential markers, Halliday’s (1985) English Grammatical Conjunctions, Talmy’s (1988) Causative Constructions, Culioli’s (1990) English Negation Constructions, and Langacker’s (1991) English Nominal Constructions.3 Obviously, the lexical research is equally diverse: from Fillmore’s (1977) buy-sell frame, the 3. Seen from this perspective, the entire tradition of conceptual analysis (Wierzbicka 1985; Lakoff 1987; Stepanov 1997; Vorkachev 2004; and Bartmiński 2008 inter alia) is based upon synonymy. Such research begins with a concept and examines what words or expressions are available for its linguistic representation. On the grammatical front, a similar notion holds. Understood in these terms, Talmy’s (1988) Force Dynamics or Langacker’s Causative Constructions (1991:â•›408–411) are essentially onomasiological fields of near-synonymous forms. Of course, regardless of whether it is lexis or syntax, in order to understand the relationship between these different forms, we must investigate each form semasiologically, that is, its



Polysemy and synonymy

lexical field of say-speak by Dirven et al. (1982), and Lehrer’s (1982) study on adjectives for the description of wine to the full swath of conceptual metaphor and metonymy studies. Indeed, in usage-based linguistics, most descriptive linguistic studies can be classified as one of these four lines of research. Despite the fact that a wide and varied range of linguistic analyses can be understood as the study of polysemy or synonymy, not all research can be characterised by this typology. Within both the Functional and Cognitive paradigms, there exist objects of study that are not readily characterised in this manner. Such research lies beyond the realm of polysemy and synonymy. Within Cognitive Linguistics, ad hoc, or non-entrenched, categorisation typical of conceptual integration (Fauconnier and Turner 1998), just as with the entire field of language processing, are beyond the purview of polysemy and synonymy research. Within Functional Linguistics, the detailed, context dependent analysis of conversation or the wide-ranging research on the characteristics of genre, register, and stylistics seem to lie outside the realm of semantic relations per se. This is not to say that such research, both the cognitive and the functional, does not inform the study of semantic relations, but it is distinct from this object of study. Having established the importance and limits of these two objects of study – the conceptual-functional structure of the form and the forms available to express a concept-function – we can now ask how best to operationalise these notions? In other words, how can we define the object of study in a measurable way?4 With no langue or independent syntax against which we can test hypotheses, what exactly are we analysing in the study of semantic relations? How can we falsify or verify results? We need an operationalisation of the object of study that either offers stability to the system or a means of capturing the dynamic nature of that system. The answer lies in Langacker’s (1987:â•›59–60) theory of the entrenched form-meaning pair.5 The theory of entrenchment can provide a frequency-based operationalisation of grammaticality – the more often a form-meaning pair is used, the more automated its processing becomes and the more ‘grammatically acceptable’ it is according to the speaker’s intuition.6

polysemy. Bondarko (1991) argues convincingly that the semasiological–onomasiological divide is fundamental to any theory of conceptually or functionally motivated language. 4. For a discussion on the importance of operationalisation in language science, see Stefanowitsch (2010). 5. See also Givón’s (2005:â•›48ff.) more detailed investigation into what he terms automated processing in the attention system. The idea of form-function mapping is extended to include perceptual and conceptual issues such as prototype structure. 6. The theory of entrenchment is based on the notion of automisation, a widely accepted theory in psychology. Schneider and Shiffrin (1977) and Shiffrin and Schneider (1977) were the first to develop the hypothesis.

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Generalised across a speech community, that is the ensemble of individual speakers’ linguistic knowledge, we have an operationalisation of grammar. If we accept these hypotheses and assume that through repeated contextualised use, the relation between a concept-function and a form becomes stable, then we have an identifiable object of study. At a theoretical level, therefore, the study of semantic relations is the study of variation of entrenched form-meaning pairs: Polysemy – entrenched functional-conceptual variation of a schematic or non-schematic form Synonymy – entrenched functional-conceptual relation between schematic and non-schematic forms It is important to note that Langacker’s theory of entrenchment is determined by relative frequency of use. This can be re-stated as an operational definition: the degree of entrenchment is determined by the frequency of association of a given form and a given use of that form. Of course, what constitutes ‘a form’ and ‘a use’ is open to debate, but the notion of entrenchment per se is operationalised in a way that permits quantified analysis of semantic structure – the aim of this volume. The relative frequency of a form-meaning pair determines its entrenchment in a speaker’s knowledge. This, when extended to an entire speech community, means that the frequency of a form-meaning pair in language can indicate the degree of its stability in the intersubjective system of language.7 Therefore: Polysemy and synonymy can be measured in terms of the relative frequency of association of form and meaning Given this understanding of semantic relations, questions as diverse as prototype effects and sociolinguistic variation are neatly explained by a single principle. This claim deserves a brief explanation. A central question for the study of polysemy is: which ‘senses’ are more ‘central’, or more prototypical, than others. A similar question exists in synonymy studies: which forms are more basic taxonomically (as in basic-level terms, Lakoff 1987)? Both the concept of prototype meaning and basic-level form can be operationalised in terms of frequency. Although it is not claimed that frequency alone can explain prototype or taxonomic structure, it is, nonetheless, one important operationalisation of these phenomena (see Arppe et al. 2010). The operationalised definition is straightforward: the more frequent a given meaning, the more ‘typical’ it is categorically. This is a frequency-based understanding of prototypicality. The same can be 7. Even if this operationalisation of entrenchment is adequate, which is questionable (see Note 8), this does not, in turn, entail that corpora are representative of frequency of use. Given the dynamic complexity of language, it is a reasonable argument that no corpus will be truly representative for the foreseeable future.



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posited, mutatis mutandis, of basic level categories in taxonomic structure: if for polysemy, typicality is operationalised as the most frequent concept-function (relative to a form), for synonymy, basicness is operationalised as the most frequent form (relative to a concept-function). Therefore, for synonymy, the more frequent a form, the more basic it is taxonomically. Importantly, this frequency-based understanding of the system integrates the varied and dynamic nature of language into our model of semantic relations. For a usage-based understanding of language, the system is emergent and entirely dependent on context – context of situation, context of speaker, context of time, context of region. A given form-meaning pair will be more frequent in one city than another, in one register than another, for one gender more than another, and at one period of time more than another. Relative frequency, at a theoretical level, eloquently incorporates this complexity into the object of study. Therefore, the operationalisation – context-sensitive frequency-based typicality – simultaneously captures semantic structure both categorically (prototype effects) and taxonomically (basic-level effects) but also relative to social variation. Lastly, it must be stressed that this frequency-based approach to entrenchment is only an operational definition. Other operationalisations of the relationship between form and meaning may be equally valid. Despite Langacker’s concern with frequency, something that holds well for corpus linguists, perceptual and conceptual salience surely also have a hand in the learning process, and therefore in entrenchment. Langacker’s explanation of entrenchment assumes that all input has the same ‘weight’ in or ‘impact’ upon the system. This, it would seem, is a simplification. There is no reason to suppose that every occurrence of, or exposure to, language events has the same value in the process of entrenchment. The implications, especially for prototype and taxonomic structures are far reaching. We must suppose, therefore, that the frequency-based account of language cannot give us the full picture. It does, however, offer an operationalised and quantifiable object of study, one that will permit the testing of hypotheses, the verification of results, and one that will provide clear benchmarks for the comparison of results, using other methodologies and other operationalisations.8

3. Complexity and sampling: The need for quantification Why are quantitative corpus methods needed for a cognitive approach to polysemy and synonymy? There are two answers to that question. The first answer takes us back to our object of study and the second, to our model of language. 8. The possibility of using frequency as an operationalisation is central to a diverse range of discussions in usage-based linguistics. Schmid (2000, 2010), Tomasello (2003), Bybee (2007) and Geeraerts (2010a) are examples of research that consider this possibility.

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The first reason we need quantitative techniques can be summarised as a question of complexity. We defined our object of study as “relative frequency of association of form and meaning”. The discussion has, thus far, ignored an important issue – what constitutes a given form and what constitutes a given meaning? We have stated that a form is any form and that meaning is anything we know of the world. In fact, both the terms ‘form’ and ‘meaning’ are entirely misleading. All forms exist in a formal context and are, therefore, composite. Theoretically, one should not speak of a form but of a composite form. Similarly, meaning is situated contextually and therefore one should not speak of a meaning as a reified sense, but as an intersubjective result of communication.9 The importance and implications of these two points cannot be underestimated. Formal structure is complex. Even the simplest utterance is a composite form at some level. Moreover, dialect and sociolect variation means that even phonetic components can be indicative of usage variation. Prosody, syntax, morphology, lexis and even gesture, all come together in effectively every utterance as composite forms. Since it is a fundamental tenet of Cognitive Linguistics that language must be analysed holistically, we must treat forms as composite structures, always. If formal structure is complex from a cognitive perspective, meaning is more so. Even lexical meaning cannot be divided into discrete senses. It is a dynamic, context dependent, multi-dimensional and intersubjective social phenomenon. Geeraerts’ (1993a) and Kilgarriff ’s (1997) studies on polysemy and word meanings mark important milestones in the study of semantic relations. Their work shows that lexical senses, just like any functionally or conceptually determined category, cannot be assumed to be discrete or reifiable. Arriving at this point, both theoretically and descriptively, was a long road. Via theoretical research on prototype structures (Geeraerts 1993a; Zlatev 2003), on the one hand, and via corpus research in lexicology (Kilgarriff 1997; Glynn 2010b) on the other, the proposal that a reified and discrete understanding of semantic structure, including individuated senses, will not produce adequate descriptions of that structure has gained currency. Encyclopaedic semantics entails that all of sociolinguistic structure is included in the semantic analysis. The situation context, the gender, the age, the socio-economic class, the geographical region, and the social status are all dimensions of language use, dimensions of world knowledge in how to use language, how to communicate successfully. This world knowledge must, therefore, be integrated into semantic analysis. The result is a complex multidimensional ‘form’ coupled with a complex multidimensional ‘meaning’. It may be possible, using intuition and introspection, to consider

9. It is not the point of this discussion to enter into the debates on sign and communication theory. Suffice it is to say that any sign theory to which a Cognitive Linguist would ascribe would also see meaning as a result of a communicative act and not an inherent objectifiable phenomenon.



Polysemy and synonymy

Table 1.╇ Variation in the results of introspection-based polysemy analysis Lexeme

Senses identified

Study

over (English)

6 basic senses, 21 sub-senses 17 senses 9 of Lakoff ’s sub-senses as 1 sense 3 basic senses, > 40 sub-senses 6 basic senses, 12 senses sub-senses 3 basic senses 1 basic sense, 15 senses sub-senses 13 senses 3 basic senses, 11 sub-senses 3 basic senses, 8 sub-senses 3 basic senses, inconclusive sub-senses 3 basic senses, 14 sub-senses 5 basic senses, 8 sub-senses

Lakoff (1987) Taylor (1989a) Vandeloise (1990) Deane (1993a, 2006) Dewell (1994) Kreitzer (1997) Tyler and Evans (2003) Cuyckens (1991) Geeraerts (1992) Bellavia (1996) Dewell (1996) Meex (2001) Liamkina (2007)

over (Dutch) über (German)

all of these dimensions, but to understand how they all interact, or how they could all interact, is an effectively impossible feat. Quantifying the analysis permits the use of multivariate statistics, which is designed for modelling and capturing structure in precisely this kind of complex system. The second reason we need to develop quantitative methods for the study of semantic relations lies in the model of language propounded by Cognitive Linguistics. Both the Structuralist and Generativist traditions assumed models of language that permitted the falsification of claims made about its structure. Necessary and sufficient conditions, for establishing semantic categories, and grammatical acceptability tests, for checking proposed grammatical rules, both allow an analyst to falsify hypotheses. What possibility does Cognitive Linguistics have for falsifying propositions made about language structure? How can we test for the descriptive or explanatory adequacy of a conceptual metaphor or a reference-point construction? Neither makes any predictions that can be falsified. The lexical polysemy studies of early Cognitive Semantics were excellent examples of this problem. Lakoff (1987) proposed 21 senses for the lexeme over, but his work was challenged (see Table 1). Although this, it would seem, is good scientific procedure – a study proposes a given number of senses, the results are challenged – there is, ultimately, no way of resolving the issue because there is no way of disproving his original analysis. Table 1 lists the different proposals of the number of senses for over in English, Dutch and German. This debate could effectively continue ad nauseum, since using one’s intuition to determine a category, especially a category that can have both a fuzzy boundary and better or worse exemplars, has no possibility for falsification. It is, ultimately, a matter of opinion.

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In earlier theoretical paradigms, truth conditional semantics and predictive rules could be tested using deductive proofs. Usage-based research has no such options. A counter example, even many, does not contradict a proposal about relative structure. From our perspective, linguistic structure is emergent; it is dynamic and varied. However, a quantification of the study of semantic relations permits inductive research. The only way to test our hypotheses is to take a sample of natural language use or a sample of elicited language use and make generalisations based on that sample. Once we speak in terms of samples and populations, then we speak of inductive research, and, in brief, statistics. Statistical analysis gives us the probability that a given finding in a given sample is not chance, it gives the possibility of modelling the variation in our data and testing the accuracy of analyses by using these models to predict language use. Quite simply, moving towards quantification and statistical analysis appears inevitable for all usage-based language research.

4. Modelling meaning. Multidimensional patterns and prototype effects How does the usage-based approach contribute to the prototype structure and radial network tradition of polysemy and synonymy in Cognitive Semantics? The study of both (vague) polysemy and (near) synonymy has a long tradition in Cognitive Linguistics. Indeed, many of the seminal works were devoted to such questions. This section places quantitative corpus-driven research, such as that presented in the current volume, in Gries and Stefanowitsch (2006) and Glynn and Fischer (2010), in this ‘historical’ context. At the end of the last century, what was often called the ‘network’ or ‘radial category’ approach to meaning included a wide range of polysemy and synonymy studies of especially spatial prepositions and grammatical cases. These forms were particularly interesting because they linked the theoretical research on perception-based construal and image schemata with the culturally determined lexico-grammatical structure. The aim of this research was to model prototype structure and encyclopaedic semantics. In effect, presented with the boundless considerations of encyclopaedic semantics as well as relative categorisation due to prototype effects on structure, theoretically and analytically, much of the work can be seen as an attempt to identify order in what is an immensely varied and complex system. While theoretical models such as Frame Semantics (Fillmore 1985) and Idealised Cognitive Models (Lakoff 1987) were proposed in an attempt to identify structure in encyclopaedic semantics and the prototype effects in language, radial network analysis, in its various guises (Barthélemy 1991; Rice 1993; Geeraerts 1995), was essentially a representational formalism designed to visualise and summarise systematicity in semantic complexity. This formalism was used, to various extents, by different authors, but the principle



Polysemy and synonymy

of (i) employing encyclopaedic semantic features (ii) without the notion of necessary and sufficient conditions for category membership (iii) in order to distinguish senses and relate forms, underlies all radial network research. The theoretical research on semantics and categorisation began with Fillmore (1975, 1977) and Lakoff (1975, 1977). Although theoretical discussion on these topics continues to this day, the field was established by Verschueren (1981), Fillmore (1985), Vandeloise (1986), Geeraerts (1987), and Lakoff (1987).10 The application of these theories in descriptive analysis blossomed into what was termed the radial network approach. Early case studies included Lindner (1983), Brugman (1983a, 1984), Rudzka-Ostyn (1983, 1989), Hawkins (1985), Vandeloise (1986), Janda (1986, 1990), Norvig and Lakoff (1987), and Taylor (1988). This line of research proved so popular that the mainstay of Cognitive Semantics in 1990s could be argued to be based upon it. A string of anthologies largely devoted to the application of the method include Geeraerts (1989), Tsohatzidis (1990), Dubois (1991), Lehrer and Kittay (1992), Zelinsky-Wibbelt (1993), Schwarz (1994), Dirven and Vanparys (1995), Taylor and MacLaury (1995), Pütz and Dirven (1996), Ravin and Leacock (2000), Cuyckens and Zawada (2001), Cuyckens and Radden (2002), Nerlich et al. (2003), Cuyckens et al. (2003), and Rakova et al. (2007). At first sight, this highly abstracted and introspective research tradition would seem distinct from, even at odds with, the bottom up approach of corpus-driven methodology. However, upon closer inspection, we see that the very origins of corpus-driven, indeed, quantitative corpus-driven, semantic research lie in the radial network studies. The contemporary methodology directly inherits from and builds upon this tradition. For both the study of synonymy and polysemy, many of the earliest studies were entirely empirical. Moreover, as we will see below, the two approaches are theoretically linked. Let us, however, begin with an overview of the radial network research. For the practical concerns of brevity, it is impossible to offer even a snippet of this immense field. However, Table 2 offers a selection of studies, chosen to represent the depth and variation of the radial network approach to semasiological structure. The object of study, its general part of speech or grammatical category, whether this is schematic or concrete in form, as well as the method of analysis and reference аrе listed. It must be stressed that the distinction between schematic and concrete forms is only designed to show tendencies and no theoretical distinction is intended. The decision as to what to include is based on a subjective evaluation of the impact of the study and the author upon the field, as well the extent of the study, priority being given to monographs. 10. Beyond these early studies, the following research represents key points in the discussion on semantics and categorisation in Cognitive Semantics: Deane (1988), Geeraerts (1988, 1989, 1993a, 1997), Taylor (1989a), Wierzbicka (1989, 1990), Vandeloise (1990), Kleiber (1990, 1999), Lehrer (1990a, 1990b), Dunbar (1991, 2001), Tuggy (1993, 1999), and Croft (1998). Recent discussion includes Tyler and Evans (2003), Zlatev (2003) and Evans (2005, 2006).

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Table 2.╇ Prototype-encyclopaedic analysis of polysemy in Cognitive Semantics Object

Form

Schematicity Method

Reference

lie (English) talk, say, tell, speak (English) over (English) on the go Cx. (English) up, out (English) idea (English) kind of Cx. (English) uit (Dutch), wy (Polish) spatial preps. (English) za-, pere-, do-, ot- (Russian) spatial preps. (French) over (English) let alone Cx. (English) down (English) tall (English) ask (English) Genitive (English) Dative (Czech) vers (Dutch) Middle Voice Cx. (French) Resultative Cx. (English) Dative (Polish) over (Dutch) Ditransitive Cx. (English) in (Dutch) Instrumental (Russian) at, on, in (English) ‘give’ (Mandarin) at, by, to (English) (a)round (English) Genitive (Polish) in (English) Instrumental (Polish) off (English) op (Dutch) over (English) answer, respond (English) door, langs (Dutch) Caused-Motion Cx. (English) at, on, in (English) Dative (Polish) over (English) figure out (English)

verb verb prep. constr. particle noun constr. prep. prep. prefix prep. prep. constr. prep. adj. verb case case adj. constr. constr. case prep. constr. prep. case prep. verb prep. prep. case prep. case prep. prep. prep. verb prep. constr. prep. case prep. verb

concrete concrete concrete schematic concrete concrete schematic concrete concrete concrete concrete concrete schematic concrete schematic concrete schematic schematic concrete schematic schematic schematic concrete schematic concrete schematic concrete concrete concrete concrete schematic concrete schematic concrete concrete concrete concrete concrete schematic concrete schematic concrete concrete

Coleman and Kay (1981) Dirven et al. (1982) Brugman (1983a) Brugman (1983b) Lindner (1983) Brugman (1984) Kay (1984) Rudzka-Ostyn (1985) Herskovits (1986, 1988) Janda (1986) Vandeloise (1986) Lakoff (1987) Fillmore et al. (1988) Schulze (1988) Dirven and Taylor (1988) Rudzka-Ostyn (1989) Taylor (1989b) Janda (1990, 1993) Geeraerts (1990) Melis (1990) Goldberg (1991, 1995) Rudzka-Ostyn (1992, 1996) Geeraerts (1992) Goldberg (1992, 1995) Cuyckens (1993) Janda (1993) Rice (1993) Newman (1993) Deane (1993b) Schulze (1993) Rudzka-Ostyn (1994, 2000) Vandeloise (1994) Dąbrowska (1994) Schulze (1994) Cuyckens (1994) Dewel (1994) Rudzka-Ostyn (1995) Cuyckens (1995) Goldberg (1995) Sandra and Rice (1995) Dąbrowska (1997) Kreitzer (1997) Morgan (1997)

elicitation observation introspection introspection introspection introspection introspection introspection introspection introspection introspection introspection introspection introspection elicitation observation introspection introspection introspection observation introspection introspection introspection introspection introspection introspection introspection introspection introspection introspection introspection introspection introspection introspection introspection introspection observation introspection introspection elicitation introspection introspection introspection



Polysemy and synonymy

Table 2.╇ (continued) Object

Form

Schematicity Method

Reference

at, on, in (English) Causative Cx. (English) Dative (Dutch) straight (English) on (English) to, for (English) What’s X doing Y Cx. (Engl.) crawl (English)

prep constr. constr. adj. prep. prep. constr. verb

concrete schematic schematic concrete concrete concrete schematic concrete

Cuyckens et al. (1997) Lemmens (1998) Geeraerts (1998) Cienki (1998) Rice et al. (1999) Rice (1999) Kay and Fillmore (1999) Fillmore (2000)

elicitation observation introspection introspection elicitation observation introspection introspection

Research in synonymy, though it received less attention and possibly produced less in terms of quantity, was equally important in the development of Cognitive Semantics. Studies such as Fillmore (1977), Lehrer (1982), Dirven et al. (1982), Janda (1986), and later Schmid (1993), Geeraerts et al. (1994), and Rudzka-Ostyn (1995) represent seminal work in the field. Table 3 offers a summary of Cognitive Linguistic case studies in synonymy, again up until the turn of the century. There is some redundancy with Table 2 because what may be a set of individual case studies on polysemy were also combined to present a study in near-synonymy. Again, the table is designed to offer an overview and is no way complete. It should be noted that although there was less work on synonymy per se, the conceptual metaphor studies, which were extremely numerous at the time, are, in effect, synonymy studies. Although such research was primarily interested in figurative lexemes, they remain, nonetheless, studies of near-synonymy (as noted by Kittay and Lehrer 1981 at the time). There was much discussion about what constitutes a source domain and/or target domain and whether certain expressions were in fact examples of the concept in question. From a lexical semantic point of view, these questions are, of course, questions of near-synonymy. Expressions such as to have the hots versus to be head over heels were said to profile different aspects of the target domain, in other words, they were near-synonyms. In order to appreciate the trends and heritage of contemporary methods in Cognitive Semantic research, it is helpful to make a quantified summary of the research output.11 Since, for reasons of space, full coverage of this research history is impossible, only the results of the investigation are presented. A survey of 126 studies was conducted from roughly the beginning of the Cognitive Linguistic research community with the publication of Paprotté and Dirven’s (1985) anthology The Ubiquity of

11. See Geeraerts (2005; 2006b), Croft (2009) and Glynn (2010c) for other discussions on methodological trends in Cognitive Linguistics.

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Table 3.╇ Prototype-encyclopaedic analysis of synonymy in Cognitive Semantics Object

Form

Schema- Method ticity

Reference

buy (English) speak (English) wine terms (English) trade names (English) za-, pere-, do-, ot- (Russian) Deictic Cx. (English) risk (English) house (English) start – begin (English) clothing terms (Dutch) see (English) contact (English) answer (English) up – down (English) front – back (English) Perfectivisers (Polish) run (English) por – para (Spanish) liegen – stehen (German) epistemic modifiers (Dutch) causatives (French) negation (English) kill (English) verb particle Cxs (English) beer terms (Dutch, French) football terms (Dutch) anaphoric nouns (English)

verb verb adj. nouns prefix constr. verb noun verb noun verb verb verb prep. prep. prefix verb prep. verb verb constr. various. verb constr. noun noun noun

concrete concrete concrete concrete schematic schematic concrete concrete concrete concrete concrete concrete concrete concrete concrete schematic concrete concrete concrete concrete schematic concrete concrete schematic concrete concrete concrete

Fillmore (1977) Dirven et al. (1982) Lehrer (1982) Vorlat (1985) Janda (1986) Lakoff (1987) Fillmore and Atkins (1992) Schmid (1993) Schmid (1993) Geeraerts et al. (1994) Atkins (1994) Dirven (1994) Rudzka-Ostyn (1995) Boers (1996) Boers (1996) Dąbrowska (1996) Taylor (1996) Delbeque (1996) Bornetto (1996) Sanders and Spooren (1996) Archard (1996) Lewandowska-Tomaszczyk (1996) Lemmens (1998) Gries (1999) Geeraerts (1999a) Geeraerts et al. (1999) Schmid (2000)

introspection observation elicitation observation introspection introspective observation elicitation observation observation observation introspection observation introspection introspection introspection introspection introspection introspection introspection introspection introspection observation observation observation observation observation

Metaphor to the turn of the century, where the field becomes extremely diverse and empirical methods begin to become the norm. In order to operationalise the criterion of what constitutes ‘cognitive’ research in the field, the survey is restricted to three publication avenues. Only full articles that addressed polysemy or synonymy in the three following kinds of sources are considered: The official journal of the International Cognitive Linguistics Association, Cognitive Linguistics, between 1990 and 1999. ii. Five foundational anthologies within the paradigm, three of which are proceedings of the first three conferences of the International Cognitive Linguistics Society (Rudzka-Ostyn and Geiger 1993; de Stadler and Eyrich 1993; and Casad i.



Polysemy and synonymy

1996) and two of which predate the society but, at the time, were constitutive of the community (Paprotté and Dirven 1985 and Rudzka-Ostyn 1988). iii. Nine anthologies largely devoted to the Cognitive Linguistic research on polysemy and synonymy, published between 1989 and 1996 (Geeraerts 1989; Tsohatzidis 1990; Dubois 1991; Rauh 1991; Lehrer and Kittay 1992; Zelinsky-Â�Wibbelt 1993; Schwarz 1994; Taylor and MacLaury 1995; and Pütz and Dirven 1996). Monographs are not included since it is difficult to gauge the impact and importance they contributed to the field but also because they often contain multiple case studies. Another issue is how to determine what constitutes an example of the radial network approach to semantic relations. This is determined using the three-part definition offered above: employing encyclopaedic semantic features, without the notion of necessary and sufficient conditions for category membership, in order to distinguish senses or relate forms. Each of the 126 studies are categorised for year of publication, type of publication and author. The object of study for each study is also categorised as: – schematic vs. concrete (lexemes vs. constructions/grammatical categories) – polysemy vs. synonymy – linguistic phenomenon (actual form(s) under investigation) – language Lastly, the studies are categorised for their method of analysis. Three kinds of method are distinguished: introspection, observation, and elicitation. Two of these methods are further distinguished. For observational data (corpus based) methods, three methods are distinguished: – corpus-driven with statistical verification – corpus-driven with raw counts – corpus-illustrated (introspection exemplified with natural data) For elicited methods, another three methods are distinguished: – quantified direct elicitation (questionnaires etc.) with raw counts – quantified direct elicitation with statistical verification – experimental elicitation with statistical verification Distinguishing introspective, experimental and observational methods is unproblematic, save when a study uses more than one method, as in Dirven and Taylor (1988). In this case, for instance, the study is categorised as elicited, since these data feature more prominently than the corpus data in the analysis. The most striking result is just how balanced and broad the range of studies is. Although obviously Eurocentric, a surprisingly wide range of languages is considered (in total 30 different languages, with English making up 36% of the studies). Moreover,

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18 16 14 12

Concrete

10

Schematic

8

Polysemy Synonymy

6 4 2 0 1985 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999

Figure 1.╇ Object of study in Cognitive Semantics, 1985–1999

despite the predilection for spatial prepositions, particles, and morphemes, these parts of speech represent ‘only’ 18 (14%) of the studies. Although 14% represents a sizable proportion of the research, considering that the approach is often termed preposition research and considering that two of the anthologies were devoted to prepositions and another two to spatial representation, this figure is not as overwhelming as one might expect. However, the best indicator of the diversity of the research is found if we take a more coarse-grained perspective and consider schematic vs. concrete and synonymous and vs. polysemous objects of study. Figure 1 represents the numbers of such studies over the 15-year period. We see here how evenly dispersed the four different objects of study are over the period. Only in 1993 do we see a divergence, where the number of studies examining schematic forms such as grammatical constructions and grammatical categories drop when other objects of study remain steady or increase in number. Indeed, divided in this manner, not even the analysis of concrete instances of polysemy, such as prepositions, is even vaguely dominant. Although this tells us nothing of the methodological heritage, it is important to note that radial network analysis was not restricted to polysemy studies of spatial prepositions, and that the diverse range of lexical and grammatical analysis of both near-synonymy and vague-polysemy visible today is directly descendent from this tradition. Turning to the methodological trends, we see an important and consistent presence of empirical studies, even if the use of introspection dominates. Figure 2 depicts these trends. Two levels of granularity are summarised in a single plot: a simple distinction between empirical and introspective as well as a breakdown of empirical into elicited and observational. Figure 2 shows how empirical methods followed the trends in introspective studies and were, although less common, far from irrelevant. The



Polysemy and synonymy

18 16 14 12

Empirical

10

Introspection

8

Observation

6

Elicitation

4 2 0

1985 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999

Figure 2.╇ Method of study in Cognitive Semantics, 1985–1999

exception to this is, again, 1993, where we see a large number of introspective studies and no published observation or elicitation-based research in the sample. At a more fine-grained level, there is a striking lack of statistical sophistication in the observation-based research. In the sample of studies, only a single corpus analysis, Gries (1999), showed any sophistication, the entire body of corpus-driven research being restricted to raw counts. Although we know this was not completely the case since studies outside the narrow range under consideration employed statistical techniques from the beginning of the research paradigm, the relative trend is clear – the use of statistical techniques to consider results of corpus-driven research was not the norm. The use of statistical techniques for elicited data, however, was more common, though far from typical and appearing quite late in the sample, Schulze (1991), Chaffin (1992), and Myers (1994) being the earliest instances. Although based on a limited sample of 126 studies from the official journal and a selection of anthologies, the survey hopefully demonstrates that the semantic tradition within Cognitive Linguistics is not restricted to prepositional studies nor is its methodology overwhelmingly introspective. Perhaps the image that Cognitive Linguistics is exclusively orientated towards introspective methodology results from the most widely known theoretical works that founded the paradigm. Certainly the seminal publications of Fillmore (1985), Talmy (1985), Lakoff (1987), and Langacker (1987) restrict themselves to introspective investigation. The importance of these theoretical and foundational works notwithstanding, we see above that the research community as a whole always included significant methodological diversity. Quantitative corpus-driven methods are, therefore, not a new turn or a new direction, but the natural development of an existing tradition. The rich descriptive heritage summarised in Tables 2 and 3 represents the Cognitive Semantic approach to polysemy and synonymy research. This volume continues the tradition, but instead of turning to prototype set theory as the analytical framework to capture the complexity of semantic relations, the corpus-driven research presented

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here uses multivariate statistical modelling and collocation association measures. Does this mean that we have done away with radial network analysis, prototype category structure and fuzzy set structure? It would be possible to dismiss the introspective radial network analyses of the early period of Cognitive Linguistics as little more than exercises in prototype set theory. After all, it has been shown that the method of analysis was largely ad hoc (Sandra and Rice 1995) and the last decade has seen few important studies employing the approach. Indeed, some in the empirical research community would seek to distance themselves from such a research tradition.12 However, to turn our back on this tradition or seek to demonstrate the superiority of the current methodology would do injustice to this previous research. Firstly, it is precisely this research tradition that freed the study of semantic relations from the notions of discrete senses and context independent semantics. Radial network studies were the first and essential step towards this realisation – both theoretically and analytically. Theoretically, it set the stage for an understanding of semantics as emergent structure and, analytically, it produced the idea of understanding meaning as a network of interacting factors. On both fronts, the corpus-driven and experimental study of semantic relations is a direct heir to radial network research. Indeed, within the tradition, as early as Geeraerts (1993a:â•›260), the idea that we need to move away from a reified and mono-dimensional understanding of meaning was being overtly mooted.13 Secondly, such studies are an essential step in empirical research. They represent hypothetical models of language structure, based on careful and systematic introspection-based analysis of language. Rather than ignore, or worse still, dismiss such theoretical research, empirical analysis needs to treat it as foundational. The results of introspection-based research are theoretical models, models that are, most likely, reasonably accurate descriptions of language structure. The new generation of experimental and observational linguistic analysis needs to test the accuracy and explanatory power of those models, modifying them where needed. Seen in this light, the configuration of the argument-structure of the verbs of ‘buying and selling’ by 12. There is much discussion about an empirical turn/revolution in Cognitive Linguistics (Geeraerts 2006b, 2010b; Levshina 2011; Klavan 2012 inter alios). Indeed, certain authors have expressed concerns about “empirical imperialism” (Lampert and Lampert 2010; Schmid 2010), a term coined by Geeraerts (2006a). Some of the discussion on the topic (Stefanowitsch 2008; Fischer 2010) represents the ‘turn’ as a break from the past and indeed Gries (forthc.) considers corpus-driven and experimentation-based research in polysemy as an entirely different discipline from research using prototype set theory. Whether it is a result of the gradual emergence of empiricism or a radical methodological revolution, there is little doubt that the analytical landscape of Cognitive Semantics has changed substantially over the last 25 years. 13. This line of thinking is not as radical as one might expect. Lehrer and Lehrer (1994) and Victorri and Fuchs (1996) represent further examples of early discussions on how a non-reified understanding of semantic structure needs to be developed.



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Fillmore (1977), the schema specifications in Lakoff ’s (1987) study of over, or the image-schematic grammatical features of Janda’s (1993) study of the Dative are theoretical models and it is our task to test their descriptive accuracy and improve them. There are, of course, differences between the corpus-driven quantitative research and the introspection-based radial network studies. No matter how large a corpus, found data will always be biased towards what is common rather than what is possible. Introspection is a vital methodology for proposing hypotheses about what is possible in a language. It follows that a lack of corpus evidence of a given form-meaning pair does not mean it is not possible or does not occur. This is simply because even the largest corpus in the world is but a microscopic fraction of actual language use. This difference affects the results profoundly. Corpus-driven research is exclusively frequency-based, and this, in turn, will prioritise typical structures over less typical structures. It is for this reason that it would be difficult to simply carry out a corpus-driven study on over and compare the results with Lakoff ’s (1987) results. A corpus-driven study may or may not confirm parts of the network analysis, but it is unlikely that it would paint the same picture anymore than lack of confirmation would negate his hypothesis. This is simply because only the most frequent usage patterns, or schema configurations to use Lakoff ’s terminology, would be found. Another apparent difference would be the lack of interest in prototype effects. In the corpus-driven research, what has become of the analytical apparatus – prototype categorisation and fuzzy sets? Although there is little overt reference to such notions, the results of multifactorial analysis and collocation analysis are, in fact, structured as fuzzy-bounded prototype categories. Since the results are based upon relative frequency, they are, therefore, necessarily ‘prototype’ structured (at least if we accept a frequency-based operationalisation of prototypicality) and are not discrete. Moreover, multifactorial feature analysis identifies ‘meanings’ as tendencies, where a tendency is a multidimensional pattern of use. This, quite literally, produces networks of different uses – a frequency-based and complex multidimensional network of sense relations. The radial network analysis produced prototype maps of meaning upon one ‘semantic’ dimension where the ‘nodes’ were discrete reified senses. Today, multifactorial feature analysis produces multidimensional networks of usage patterns that can be interpreted as emergent language structure. The difference between the two is a natural progression, not a methodological schism. We can, therefore, deduce that, despite important differences, there is a direct line of descent in the methodology from the radial network approach described above to the contemporary corpus-driven research represented by studies such as Gries (2003, 2006), Heylen (2005), Divjak and Gries (2006), Divjak (2006, 2010a, 2010b), Wulff (2006), Gronderlaers et al. (2007, 2008), Wulff et al. (2007), Janda and Solovyev (2009), Hilpert (2008), Gilquin (2009), Glynn (2009, 2010a, 2010b, 2014a, 2014b, forthc.), Speelman and Geeraerts (2010), Krawczak and Kokorniak (2012), Krawczak (2014a, 2014b), and the research in this volume. Armed with contemporary corpus-driven

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methods, the task ahead of us now is, arguably, to return to the research questions that gave rise to Cognitive Semantics in an effort to understand the conceptual and functional structures that motivate language. Although contemporary quantitative research may be gaining descriptive adequacy, our ultimate goal remains explanatory adequacy.

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Competing ‘transfer’ constructions in Dutch The case of ont-verbs Martine Delorge, Koen Plevoets, and Timothy Colleman Ghent University

This paper zooms in on the semantic relations between the constructions of “possessional transfer” (i.e. constructions used to encode events of possessional transfer) in Dutch by zooming in on a specific morphological class of dispossession verbs, viz. verbs with the prefix ont- ‘away’, such as ontnemen ‘take away’, ontfutselen ‘fish out of ’, onttrekken ‘extract, withdraw’, ontheffen ‘relieve’, etc. A database with several thousand attested ont-examples from various corpora of present-day written Dutch will serve as the starting point for an investigation of their constructional possibilities and preferences: the ont-verbs will be shown to cluster into a number of subclasses in terms of alternation possibilities. In addition, a comparison of these present-day Dutch results with data from a diachronic corpus of 19th century Dutch will reveal a number of lexico-grammatical shifts: the use of the double object construction and (especially) of the aan-dative with ont-verbs is more heavily constrained now than it was in earlier stages of the language. Keywords: aan-dative, alternations, dispossession verbs, Dutch, ont-verbs

1. Introduction1 As shown in (1) to (5) below, the grammar of present-day Dutch includes several different argument structure constructions that can be used for the encoding of three-participant events of ‘possessional transfer’. The constructions in (1) and (2) have received by far the most linguistic attention, since they constitute the wellknown dative alternation: (1) exemplifies the double object construction in which 1. All three authors are associated with the BOF/GOA research project on ‘Meaning in-between structure and the lexicon’ in the Linguistics department at Ghent University. We would like to thank the editors as well as two anonymous referees for their helpful comments and suggestions. The usual disclaimers apply.

40 Martine Delorge, Koen Plevoets, and Timothy Colleman

the verb is combined with a subject and two bare NP objects, (2) exemplifies the socalled aan-dative, in which the theme is coded as a direct object but the recipient is marked with the preposition aan (cognate with on, but relevantly similar to to). Existing studies of these constructions and their semantic relations include Van Belle and Van Langendonck (1996), Janssen (1997), Geeraerts (1998), Colleman (2009a) and Colleman and De Clerck (2009). In addition to the aan-dative, there are a number of structurally similar constructions formed with other prepositions that can also be used to encode certain subtypes of ‘possessional transfer’ events. One of these is the construction in (3), in which the preposition van marks the source of the transfer in a ‘dispossession’ event. At first sight, the example in (4) – which also denotes an event of dispossession – exemplifies the very same construction. However, there is a crucial difference in the linking of argument roles between (3) and (4): in the latter clause, the direct object codes the possessional source, and van marks the theme. In terms of the distinction between the basic types of ditransitive alignment put forward in typological research by Haspelmath (2005) and Malchukov and colleagues (2010), the constructions in (2) and (3) represent indirective alignment (i.e. the theme is coded like the monotransitive patient; i.e. as a bare NP object, and the recipient/possessor is coded differently) but the construction in (4) represents secundative alignment (i.e. the recipient/possessor argument is coded like the monotransitive patient while the theme gets special marking). The met-construction in (5) is also secundative, but it denotes a fairly prototypical event of ‘caused possession’ rather than ‘dispossession’. (1) De man heeft de vrouw een boek gegeven. ‘The man has given the woman a book.’ (2) De man heeft een boek aan de vrouw gegeven. ‘The man has given a book to the woman.’ (3) De man heeft een boek gestolen van de vrouw. ‘The man has stolen a book from the woman.’ (4) De man heeft de vrouw beroofd van al haar boeken. ‘The man has robbed the woman of all her books.’ (5) De man heeft de vrouw begiftigd met een boek. ‘The man presented the woman with a book.’ In terms of constructional polysemy, the first two constructions cover a wider region in semantic space than the latter three. While the instances in (1) and (2) denote events of ‘caused possession’ with agent, theme and recipient participants, both the double object construction and the aan-dative can also be used to encode events of dispossession with agent, theme and (human) source participants, albeit with rather limited lexical possibilities (see Geeraerts 1998 and Colleman & De Clerck 2009 for examples and further discussion). (6) and (7) present examples with the dispossession verb ontnemen ‘take away’.



Competing ‘transfer’ constructions in Dutch

(6) De man heeft de vrouw een boek ontnomen. ‘The man has taken a book from the woman.’ (lit. has away-taken the woman a book) (7) De man heeft een boek aan de vrouw ontnomen. ‘The man has taken a book from the woman.’ The van-constructions in (3) and (4), by contrast, are limited to events of dispossession, whereas the met-construction in (5) is limited to a handful of infrequent and formal verbs of giving and cannot be used to encode the reverse orientation of transfer.2

2. Introducing the Dutch ont-verbs In this paper we will try to shed more light on the synchronic and diachronic semantic relations between the argument structure constructions introduced in section 1 by zooming in on a specific morphological class of dispossession verbs, viz. complex verbs with the prefix ont- ‘away’. While the ont-verbs are not particularly frequent in everyday language, they nevertheless constitute an interesting class in that many of them are found in several of the above constructions. Moreover, even though, semantically, ont-verbs of dispossession seem to form a rather homogeneous class at first sight, they nevertheless display very different constructional preferences. As such, a quantitative investigation of the degree of attraction between these ont-verbs and the argument structure constructions in question can shed more light on the issue of constructional competition between constructions with partly overlapping semantic ranges: how do the constructions illustrated in section 1 divide up the semantic domain of ‘dispossession’, which is itself a sub-domain of ‘possessional transfer’? Moreover, since we will not only look into the constructional preferences of the selected ont-verbs in present-day data, but also in data from a corpus of 19th century Dutch, it can also be investigated whether the semantic relation between the ‘dispossession’ constructions in question has changed in the course of the last century and a half. As such, the present study adds to the growing body of diachronic investigations of constructional semantics (see, e.g., Barðdal 2007 and Colleman & De Clerck 2011 for earlier studies). The following 15 ont-verbs were selected for the case study, listed in alphabetical order: ontdoen ‘strip’, ontfutselen ‘filch, fish out of ’, ontheffen ‘release’, ontlenen ‘take, derive, borrow’, ontladen ‘unload, be released’, ontlasten ‘relieve’, ontlokken ‘elicit

2. There is a single lexical exception in the case of the construction in (4): next to a set of verbs of dispossession, this pattern also accommodates the giving verb voorzien ‘provide’, as in Ze voorzagen hem van voedsel (‘They provided him with food’). Most probably, this is a calque of the French pattern pourvoir quelqu’un de quelque chose.

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(from)’, ontnemen ‘take away’, ontroven ‘steal away’, ontrukken ‘snatch (away)’, ontstelen ‘steal away’, onttrekken ‘withdraw, take away, derive’, ontvreemden ‘steal, thieve’, ontworstelen ‘tear, wrest from’ and ontwringen ‘wrench from’. These verbs were chosen on the basis of (i) their semantic status as (prototypical) dispossession verbs and (ii) frequency considerations. Semantically, ditransitive ont-verbs belong to two categories, good examples of which are ontnemen ‘take away from’ and ontzeggen ‘deny’, respectively. Whereas ontnemen denotes an event of dispossession, as in (6) and (7) above, ontzeggen instead denotes a blocked ‘caused possession’ event, as in (8). Put differently, ontnemen and ontzeggen are verbs of taking and not-giving, respectively. In terms of Colleman’s (2009b) multidimensional analysis of the semantic structure of the Dutch double object construction, the examples in (6) and (8) represent distinct subsenses of the construction, departing from the core ‘caused reception’ meaning along the semantic dimensions of ‘orientation of the transfer’ and ‘polarity of the transfer’, respectively. (8) Ze hebben vrouwen lange tijd het stemrecht ontzegd. ‘For a long time, they denied women the right to vote.’ In this case study, we focus on ont-verbs of the ‘dispossession’ type. The verbs under investigation select agent, theme and possessional source participants. Note that this is not to say that they occur exclusively in three-argument constructions: on the contrary, several of them occur far more often in two-argument constructions without an expressed source (see below). In terms of Goldbergian construction grammar, the selected verbs select a possessional source participant, but this participant need not be lexically profiled – though it is for the most prototypical members of the category, such as ontnemen (‘take away’) or ontfutselen (‘filch, fish out of ’) (for further details on the notion of lexical profiling, see Goldberg 1995:â•›43–48). The formation of dispossession verbs with the prefix ont- is not a productive word-formation pattern anymore, but dictionaries include quite a lot of examples, many of which are highly infrequent in present-day language (e.g. ontsjacheren ‘to barter sth. away from s.o.’ or ontschaken ‘to take s.o. away from s.o. by abduction’, to give but two examples). In order to avoid the selection of all too infrequent verbs for the case study, we only selected verbs which are included in the CELEX lexical database of Dutch. In addition, preference was given to verbs with a CELEX frequency of at least 3 occurrences per one million words of running text.3 However, this frequency criterion was applied liberally: an exception was made for a number of infrequent verbs that we wanted to include in the investigation for semantic reasons, such as ontroven and ontstelen, the verb bases of which are the semantically prototypical and highly frequent dispossession verbs roven ‘rob’ and stelen ‘steal’. 3. The CELEX frequency was checked using the WordGen tool developed by Wouter Duyck and colleagues (Duyck et al. 2004).



Competing ‘transfer’ constructions in Dutch

3. Methodology of the case study A database consisting of several thousands of attested ont-examples from various corpora of present-day written Dutch serves as the starting point for an investigation of the constructional flexibility of these verbs: the newspaper component of the present-day CONDIV-corpus, the 27 and 38 Million Words Corpora of the Dutch Institute for Lexicology (INL) and the Twente Nieuws Corpus (TNC). The selected corpora all represent relatively formal genres of written Dutch (newspapers, magazines, fictional and non-fictional prose, etc.). All forms of the 15 test verbs were automatically retrieved from the corpora, and the results were manually filtered and labelled according to syntactic construction. We used more than one corpus in order to be able to retrieve enough examples of the selected verbs to make well-grounded judgements about their constructional behaviour. After all, some of the verbs from the selection, as already mentioned, are quite infrequent. The different corpora are similar enough in their contents to justify combining them together. Section 4 presents and discusses the main findings from the synchronic investigation. In addition, we compared the present-day Dutch results with data from a corpus of 19th-century Dutch in order to investigate possible lexicogrammatical shifts. The diachronic part of the study is based on a corpus consisting of 50 volumes from the periodical De Gids (1850-1899). De Gids (‘The Guide’) was an influential literary and general cultural journal, and as such represents formal written Dutch. The results of the diachronic investigation are presented in Section 5.

4. The results of the present-day investigation 4.1

Overall distribution

As was noted in Section 2 above, the overall aim of the investigation is to investigate the constructional competition between the various Dutch argument structure constructions that can be used to encode ‘dispossession’ events, through an identification of the constructional preferences of a sample of ont-verbs in (a) present-day data and (b) 19th century data. Table 1 presents the results of the synchronic part of the corpus investigation. We distinguish six different three-argument constructions, four of which have already been introduced in Section 1: the double object construction (DOC), the aan-dative, and two constructions with van, which are labeled van-I (“indirective”) and van-S (“secundative”), respectively. The remaining constructions distinguished in the table are two fairly infrequent indirective patterns in which the (possessional) source argument is marked with the prepositions bij ‘at’ and uit ‘out (of)’, respectively. In addition, most of the investigated verbs occur in other constructions, too, i.e. in various two-argument constructions. In five cases, two-participant

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constructions even account for the large majority of occurrences, viz. with ontvreemden ‘steal, thieve’, ontworstelen ‘wrest from’, onttrekken ‘withdraw, take away’, ontlasten ‘relieve’, and ontladen ‘unload’. In fact, the verb ontladen turned out to display just a single three-argument instance in the corpus data, from a total of 331 occurrences, viz. a single instance of the secundative van-construction. Because of this sparsity of data, this verb is excluded from further discussion. The rather frequent occurrence of verbs of dispossession in structures without a possessional source object is not very surprising. Newman (1996:â•›57) has already observed that “there is no giver necessarily present in the base of take […] There is only one person necessarily involved in the characterization of the basic meaning of TAKE”. As shown in Delorge (2010), simplex verbs of dispossession, such as stelen ‘steal’, roven ‘rob’, etc. typically display the same characteristic.4 In the remainder of this section, we remove the monotransitive and other two-argument constructions from consideration and focus on the distribution of the three-argument constructions. The distribution of the 14 remaining ont-verbs over the 6 three-argument constructions distinguished in Table 1 is statistically significant (χ² = 46741.05, df = 65, p < 2.2e-16). Table 4 in the Appendix lists the Pearson residuals. The Cramér’s V effect size is 0.7125667, which suggests a strong association. Note that effect sizes tend to increase with the number of rows and columns, however, and that there are quite a lot of cells with an expected frequency of less than 5, which reduces the value of the chi-square test. This is why we turn to an exploratory statistical tool in the next sub-section.

4.2

Four clusters of ont-verbs

As a first observation, it can be seen from the frequencies in Table 1 that there is a nearly complete lexical split between the secundative van-construction on the one hand and the other five three-argument constructions included in the table on the other. While many verbs occur in both the DOC and several of the indirective constructions in the corpus data, the secundative construction is associated with a number of verbs that occur in this three-argument construction (virtually) exclusively, viz. ontlasten ‘relieve’, ontdoen ‘strip’, and ontheffen ‘release’ (in addition, ontladen ‘unload’ was also attested in this construction only, see Section 4.1). Corpus examples are listed in (9) to (11). As can be seen from these examples, the theme of ontheffen and 4. It should be noted that constructions with a reflexive pronoun, such as the ontworstelen example in (i) below, were included in the rest category, too, as they do not contain three arguments. (i) Een deel van de Otavalo-Indianen probeert zich aan die armoede te ontworstelen. [TNC] ‘Part of the Otavalo Indians try to wrest themselves out of that poverty.’



Competing ‘transfer’ constructions in Dutch

Table 1.╇ Observed frequencies in the present-day data Verb ontdoen ontfutselen ontheffen ontlasten ontlenen ontlokken ontnemen ontroven ontrukken ontstelen onttrekken ontvreemden ontworstelen ontwringen Total

Three-argument constructions DOC

aan

0 458 0 0 0 587 3993 2 6 104 2 8 7 11 5178

0 146 5 0 6087 342 207 3 189 3 2248 3 26 11 9270

van-I van-S 0 19 0 0 2 23 15 0 0 0 7 33 0 0 99

2575 0 697 111 0 0 0 0 0 0 0 0 0 0 3383

uit

bij

Total

0 4 0 0 17 2 2 0 7 0 46 298 1 0 377

0 1 0 0 4 53 3 0 0 0 0 43 0 0 104

2575 628 702 111 6110 1007 4220 5 202 107 2303 385 34 22 18411

Other cxs

Total

1888 28 321 956 65 256 270 0 7 3 3562 653 859 1 8869

4463 656 1023 1067 6175 1263 4490 5 209 110 5865 1038 893 23 27280

ontlasten is typically an abstract entity, such as a task or duty. In the case of ontdoen, the lexical possibilities are wider. None of these verbs is a very prototypical representative of the class of ‘dispossession’ verbs semantically, unlike some of the other verbs which will be discussed below. Ontlasten and ontheffen imply a positive effect on the original possessor, who is relieved of something conceptualized as a burden – needless to say, in prototypical dispossession events, the transfer has a negative effect on the original possessor. As for ontdoen, this denotes an event of physical removal or separation rather than actual dispossession: typically, as in (11), the object NP does not refer to a human participant.5 (9) Inmiddels zijn creatieve oplossingen gevonden om hen te ontlasten van hun zware taak. [TNC] ‘In the meantime, creative solutions have been found to relieve them of their heavy task.’

5. The object NP can refer to a human participant, as in (ii) below. However, even such instances seem to denote an event of physical removal rather than of actual dispossession. (ii) Het Hof van Cassatie achtte het onmogelijk dat de man de 18-jarige van haar broek had kunnen ontdoen als zij zich daar tegen had verzet. [TNC] ‘The court of cassation judged that it would have been impossible for the man to strip the 18-year-old of her pants if she had offered resistance.’

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(10) De bisschop onthief haar van haar functie. [TNC] ‘The bishop released her from office.’ (11) Met snijbranders ontdoen de slopers de molens van hun wieken. [TNC] With cutting torches, the demolishers are stripping the mills of their sails.’ Returning to the syntactic possibilities, ontheffen is the only one of these verbs that is also attested in another three-argument construction, viz. the indirective aan-construction, but only very sporadically so (a mere 5 out of 1023 corpus instances). Conversely, none of the remaining 11 ont-verbs are attested in the secundative van-construction a single time. This situation is reminiscent of the lexical split found with verbs of giving, where the secundative pattern is also limited to a handful of verbs that are not eligible for use in the DOC or the aan-dative, including begiftigen, as in (5) above (see Delorge & De Clerck 2007). Most of the remaining 11 verbs are used in the DOC as well as in several indirective constructions. However, a manual inspection of the frequencies in Table 1 (and of the Pearson residuals in Table A) suggests that they cluster into a number of classes with distinct constructional preferences. We used an exploratory statistical technique, viz. Correspondence Analysis (CA), to visualize such associations in the data: see the plot in Figure 1, in which the constructions are represented in capitals and the verbs in lower case (on CA, see Greenacre 2007, as well as the articles by Glynn in the present volume). The eigenvalues for the first two dimensions are 53.8% and 44.33%, respectively, indicating that the analysis presented in Figure 1 explains 98.13% of the variation (inertia). The table used to produce the correspondence analysis includes many small cells, and so the numerical summary of the analysis is included in the Appendix, Table 5. To assure a reasonable degree of accuracy in the analysis, the quality score (qlt) should be over 500. A figure of 500 indicates that 50% of the inertia for that data point lies off principle axes and therefore that points are less accurately displayed in the plot (see Glynn, this volume, and Greenacre 2007 for more details). The remainder of this sub-section interprets the visualization in Figure 1. The only outlier among the 11 verbs is ontvreemden ‘steal, thieve’, which is grouped with the uit-construction on the right-hand side of the plot. Indeed, ontvreemden is the only verb which is combined with a uit-phrase in the majority of its three-participant uses. Unlike the “secundative” verbs discussed above, ontvreemden, which is a hyponym of stelen ‘steal’, denotes a prototypical dispossession event involving a human possessor: if something is stolen, it is by definition stolen from someone. However, ontvreemden differs from ontnemen ‘take away from’ and other verbs to be discussed below in that this human possessor participant is not lexically profiled: in the majority of instances, the possessor role is not expressed. In fact, this is a characteristic ontvreemden shares with its hypernym (see Goldberg’s 1995:â•›45–46 semantic discussion of English steal and the frequency data for Dutch stelen in Delorge 2010). The uit-construction differs from the other three-argument constructions in Table 1 in that the PP refers to a locational source rather than to a possessional source. In (12),



Competing ‘transfer’ constructions in Dutch

Correspondence analysis graph ontstelen ontnemen DOC

Dimension1 (53.80%)

1.0

ontfutselen ontlokken

0.5

VAN.I BIJ

ontwringen ontroven

0.0

ontvreemden UIT

ontworstelen

–0.5 AAN ontrukken onttrekken ontlenen

0

1

2

3

4

5

Dimension2 (44.33%)

Figure 1.╇ Correspondence analysis of the present-day data (without the secundative construction)

for instance, the jewellery store is the place where the necklace was stolen, though this of course refers indirectly to the person from whom it was stolen, viz. the jeweller. While this is a pattern typically found with ontvreemden, the van-example in (13) shows that the verb does also occur in three-argument constructions with a genuine possessional source argument. (12) Fadiga ontvreemdde het collier, met een waarde van 300 euro, zondag uit een juwelierszaak. [TNC] ‘On Sunday, Fadiga stole the necklace worth 300 € from a jewelry store.’ (13) Muijtstege had de twee wel vaker financieel geholpen en ze hadden ook al eerder geld van hem ontvreemd. [TNC] ‘Muijtstege had given financial help to the two [petty criminals] before, and they had stolen money from him before as well.’ On the left-hand side, we find a kind of cline of verbs positioned in-between the DOC and the aan-dative. Starting at the top, the two verbs that are most closely associated with the DOC are ontnemen ‘take away from’ and ontstelen ‘steal away from’. Indeed, these are found with double object syntax in the large majority of their instances across the four corpora: the DOC accounts for 88.9% of the ontnemen instances in the database and for 94.5% of the ontstelen instances. Good examples of this are shown in (14) and (15).

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(14) Verder mag de leiding verslaafden hun paspoort en geld niet meer ontnemen. [TNC] ‘Furthermore, the leaders are no longer allowed to dispossess addicts of their passports and money.’ (lit. to away-take addicts their passport and money) (15) 10000 frank kan de miljoenen niet vervangen die de staat mij ontstolen heeft. [CONDIV] ‘10,000 francs cannot replace the millions that the state has stolen from me.’ (lit. that the state has me away-stolen) In both cases, the observed preference for the DOC can be straightforwardly linked to the verbs’ lexical semantics. The verb bases nemen ‘take’ and stelen ‘steal’ are among the most prototypical simplex verbs of taking away. Similarly, their prefixed variants ontnemen and ontstelen denote prototypical dispossession events in which a human participant is deprived of an item in his/her possession, typically by another human participant. This item need not be a concrete object – it is in (14), but not, or less so, in (15) – but, in any event, there was a fairly prototypical possession relation between the indirect and direct object referents before the event, which is broken by instigation of the subject referent. Note that, unlike many of the other verbs in Table 1, ontnemen and ontstelen occur in two-argument constructions in only a small fraction of their instances (6% and 2.7%, respectively): these are typical three-participant verbs, with a lexically profiled possessional source participant. Van Belle and Van Langendonck (1996:â•›245) have also observed the preference of ontnemen for the double object construction, albeit on an introspective basis. They ascribe this to the factor [+/– involvement], which, in their account, is one of the two major semantic determinants of the dative alternation in Dutch, next to [+/– (material) transfer]. Ontnemen lexicalizes a transfer of possession which has a fundamental effect on the original possessor, and the same applies to ontstelen: the ‘transfer’ events denoted in (14) and (15) above (negatively) affect the indirect object referent, i.e. the loss of the direct object referent has clear consequences for the indirect object and his/her further actions. Since the DOC is hypothesized to highlight the relationship between the direct and the indirect object referents, the lexical semantics of verbs such as ontnemen and ontstelen tallies well with the constructional semantics of the double object construction (cf. De Schutter 1974:â•›205; Verhagen 1986 and Colleman 2009b; inter alia). According to Van Belle and Van Langendonck (1996:â•›245), the only reason why verbs such as ontnemen can appear in the aan-dative at all, despite their strong lexical focus on the affectedness of the possessional source participant, is that there is also a ‘caused motion’ event involved: the theme moves from the domain of possession of the source to that of the agent. An often advanced semantic explanation for the dative alternation posits that the aan-structure emphasizes the spatial aspects of the denoted transfer scene, i.e. the movement of the theme along a path from the agent participant towards the recipient participant (or, in this case, from the source participant



Competing ‘transfer’ constructions in Dutch

Table 2.╇ DOC and aan-frequencies in instances with concrete vs. abstract themes theme = concrete entity theme = abstract entity Total

DOC

aan

Total

â•⁄411 2786 3197

â•⁄19 110 129

â•⁄430 2896 3326

toward the agent participant) (see, e.g. Goldberg 1992 and Langacker 1991 for similar semantic hypotheses about the English to-dative, and Colleman & De Clerck 2009 for further discussion). This would seem to suggest that material transfers generally prefer the aan-construction, or, at least, that the proportion of aan-instances to DOC instances is larger when the theme is a concrete object than when it is some kind of abstract commodity. The ontnemen data, however, show that no significant difference can be attested between cases with a concrete theme on the one hand, and cases with an abstract theme on the other hand; see the distribution in Table 2 (χ² = 0.386, df = 1, p = 0.5342).6 This warns us against an all too literal interpretation of the ‘caused motion’ hypothesis: even when the theme is a concrete entity which undergoes a spatial transfer as it changes ownership, the DOC is still the preferred construction in the large majority of cases. The general semantic hypothesis put forward in Colleman (2009b) is that the aan-dative highlights the changing agent-theme relationship, whereas the DOC highlights all three participants and their interrelations, including the recipient participant. We leave it to future research to test the validity of this hypothesis in a more systematic way for verbs with a possessional source rather than a recipient, but, in any event, ontnemen and ontstelen fit the picture, with their strong lexical focus on the affectedness of the possessor participant. As we move from the top to the bottom of the left-hand side in Figure 1, the lexical preferences shift towards the aan-dative. Ontfutselen ‘filch, fish out of ’ and ontlokken ‘elicit from’ are the only two remaining verbs for which the DOC is the most frequently attested construction in the database (accounting for 69.8% and 46.5% of all occurrences, respectively). There is a twofold reason why they are positioned lower in the plot than ontnemen and ontstelen: (i) because their proportion of aan-examples is relatively higher (22% and 27%, respectively, as opposed to less than 5% for both ontnemen and ontstelen) and (ii) because they are the only verbs, next to ontvreemden ‘steal’, which are found in the indirective van-construction (in the case of ontfutselen) or in the bij-construction (in the case of ontlokken) somewhat more than sporadically, though it should be stressed that such uses still account for only a small fraction of

6. The frequencies in Table 2 do not add up to the overall frequencies of the DOC and aan-dative with ontnemen listed in Table 1, as a good number of cases were not straightforwardly classifiable into either concrete or abstract categories but represented various in-between uses.

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their total number of occurrences. We will briefly return to the constructions with van and bij at the end of this sub-section. Still further down, in the lower-left corner, are those verbs which occur with aan in the majority of their (three-argument) uses. The verbs associated most closely with the aan-dative are ontlenen ‘take, derive, borrow’, onttrekken ‘withdraw from, derive’, ontrukken ‘snatch away, pull away’ and ontworstelen ‘wrest from’: this construction accounts for 99.6%, 97.6%, 93.6% and 76.5% of the overall number of three-argument instances, respectively. The first thing to observe is that these verbs cover a much wider region in semantic space than just ‘possessional transfer’: typical examples are shown in (16) to (19) below, none of which involves a human possessor participant that is ‘dispossessed’ of something in the strict sense of the word: rather, these instances denote various kinds of (metaphorical) ‘separation’ or ‘withdrawal’ events. (16) Of Jeroen Bosch inspiratie ontleende aan al dat water in de stad, is niet bekend. [TNC] ‘Whether Hieronymus Bosch derived inspiration from all that water in the town is unknown.’ (17) Tegenwoordig is [dat] de meest gebruikte methode om geur aan natuurlijke producten te onttrekken. [TNC] ‘Presently, that is the most usual method for extracting the odour of natural products.’ (18) Bourguiba mag zijn land hebben ontrukt aan de Franse overheersing, hij was niettemin een francofiel. [TNC] ‘Bourguiba may have wrenched his country from French rule, he was a francophile nonetheless.’ (19) Dat spoort met een tendens om de VS te ontworstelen aan internationale afspraken. [CONDIV] ‘That confirms a tendency to wrestle the USA out of international agreements.’ Many occurrences of onttrekken and ontrukken, especially, are more or less fixed expressions, such as iets aan de vergetelheid onttrekken/ontrukken ‘to save something from oblivion’ or iets aan het zicht onttrekken ‘to hide something from sight’. This is the case in more than 50% of the ontrukken examples and 26.6% of the onttrekken examples. Again, such examples are not prototypical instances of dispossession events. Still, the aan-construction can be used to express events with a human deprivee, too: see (20) and (21) for examples of ontrukken and onttrekken. (20) In het holst van de nacht ontrukten zwaarbewapende Amerikaanse immigratieagenten een verschrikt Cubaans jongetje van zes aan luid lamenterende verwanten. [TNC] ‘In the middle of the night, heavily armed American immigration agents snatched a startled Cuban boy of six from loudly lamenting family members.’



Competing ‘transfer’ constructions in Dutch

(21) De partij vraagt voorts aan procureur-generaal Van Oudenhove om alle Vlaams Blok-dossiers aan Dejemeppe te onttrekken. [CONDIV] ‘Furthermore, the party asks attorney general Van Oudenhove to withdraw all cases related to the Vlaams Blok from Dejemeppe.’ Only in such cases is the DOC a (marked) option as well, hence the low frequencies in the DOC column in Table 1. (22) is one of the few DOC clauses attested with ontworstelen, for instance: in this case, the verb is used in its literal, compositional sense ‘wrest from’, and the relation between the object referents is one of fairly prototypical possession. (22) Ik dacht aan de talloze keren dat ik in de supermarkt had moeten wachten omdat moeders vooraan in de rij hun gillende broedsel vergeefs een reep chocola probeerden te ontworstelen. [TNC] ‘I thought of the many occasions when I had found myself waiting in the supermarket because mothers at the front of the row fruitlessly try tried to wrest away a chocolate bar from their yelling brood.’ For a final observation, the constructions with bij and van can be seen to occupy an isolated position in the middle of Figure 1. Indeed, none of the verbs under investigation is particularly attracted to these constructions. The verbs with the relatively highest frequencies of indirective van-instances are ontvreemden ‘steal’ and ontfutselen ‘filch, fish out of ’, but even in these cases, the van-construction only accounts for about 3% of the occurrences. See (13) above for an example with ontvreemden and (23) below for one with ontfutselen. (23) Ze moeten 80.000 frank boete betalen omdat ze geld en andere goederen hebben ontfutseld van enkele gasten. [CONDIV] ‘They have to pay an 80,000 francs fine because they have filched money and other goods from a number of guests.’ In this regard, the ont-verbs differ from the pattern attested with simplex verbs of dispossession, for with stelen ‘steal’, nemen ‘take’, etc., the human possessor participant is marked with van in present-day Dutch (as in (3) above, see Delorge 2010 for details). It is sometimes suggested that it would be natural for ont-verbs of dispossession to substitute the “default” source preposition van for aan (e.g. Schermer-Vermeer 1991:â•›216–217). However, our data show that, so far, the van-construction has not really caught on with these verbs, at least not in formal registers of written Dutch. The “top verbs” of the bij-construction are ontvreemden ‘steal’, again, and ontlokken ‘elicit (from)’, but, similarly to the van-construction, this construction with bij accounts for only a small fraction of occurrences in both cases (in-between 4 and 5%). An ontlokken example is shown in (24). Again, such examples do not denote prototypical dispossession.

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(24) Alleen het bootje met daarop Sint en zijn pieten die sinterklaasliedjes zongen, ontlokte applaus bij het publiek. [TNC] ‘Only the boat on which the saint and his servants were singing St-Nicholas songs drew applause from the public.’ To summarize, we can distinguish four clusters of ont-verbs in the present-day data: a set of verbs that are (virtually) exclusively used in the secundative van-construction: ontlasten ‘relieve’, ontdoen ‘strip’, ontheffen ‘release’ (and ontladen ‘unload’); ii. the verb ontvreemden ‘steal’, which marks the source participant with uit, bij, or van, if it is expressed at all; iii. a set of verbs with a strong lexical preference for the double object construction, most notably ontnemen ‘take away from’ and ontstelen ‘steal away from’; iv. a set of verbs with a strong lexical preference for the aan-construction, most notably ontlenen ‘take, derive, borrow’, onttrekken ‘withdraw, derive’, ontrukken ‘snatch away’ and ontworstelen ‘wrest, wrench away’. i.

There is a cline from (iii) to (iv), with verbs such as ontfutselen ‘filch, fish out of ’, ontroven ‘rob from’ and ontwringen ‘wrench from’ occupying intermediate positions. The next section explores the constructional preferences of ont-verbs in an older sub-stage of the Dutch language.

5. A diachronic perspective An important trend in construction grammar is the growth of interest in issues of diachronic and synchronic language variation in the syntax and semantics of schematic constructions – see Colleman and De Clerck (2011) for references and discussion. In this section, we will explore a number of differences and similarities in the constructional behaviour of the selected ont-verbs between present-day Dutch and 19th-century Dutch, as represented by a 50-year sample of the corpus De Gids (1850–1899). First, Table 3 presents the distribution of the 14 verbs under investigation over the six three-argument constructions in the 19th-century data – ontladen ‘unload’ was left out again. This distribution is statistically significant (χ² = 5659.828, df = 65, p-value < 2.2e-16). Table 6 in the Appendix lists the Pearson residuals, and the Cramér’s V effect size is 0.5195202. The data show that the virtually complete lexical split between the secundative construction on the one hand and the other three-argument constructions on the other was already present in the 19th century: the three verbs attested in the secundative van-construction are not attested in any of the other three-argument constructions, with the exception of ontheffen ‘release’, which has a small number of aan and DOC examples. Conversely, the other 11 verbs do not enter into the secundative construction.



Competing ‘transfer’ constructions in Dutch

Table 3.╇ Observed frequencies in the 19th-century data Verb ontdoen ontfutselen ontheffen ontlasten ontlenen ontlokken ontnemen ontroven ontrukken ontstelen onttrekken ontvreemden ontworstelen ontwringen Total

Three-argument constructions DOC

aan

0 30 2 0 9 179 1023 29 113 78 7 4 4 43 1521

0 11 4 0 873 144 697 11 287 13 39 5 6 41 2131

van-I van-S 0 0 0 0 34 0 0 0 0 0 0 4 0 2 40

89 0 304 30 0 0 0 0 0 0 0 0 0 0 423

uit

bij

Total

0 0 0 0 74 2 0 0 0 0 0 1 0 0 77

0 0 0 0 0 2 0 0 0 0 0 0 0 0 2

89 41 310 30 990 327 1720 40 400 91 46 14 10 86 4194

Other cxs

Total

87 3 23 67 12 17 57 0 32 2 52 17 87 16 472

176 44 333 97 1002 344 1777 40 432 93 98 31 97 102 4666

Figure 2, below, shows the plot from a Correspondence Analysis of the observed frequencies of these remaining 11 verbs in the DOC and the four indirective constructions. The two-dimensional analysis accounts for 96.65% of the inertia (Dim. 1: 72.95%, Dim. 2: 23.7%). Again, the numerical output is supplied in the Appendix, Table 7. We will not explore this distribution to the same degree of detail as in the previous section, but we will focus on the relation between the DOC and the aan-dative, the two constructions involved in the dative alternation. A difference with the visualization in Figure 1 is that, in Figure 2, the DOC and the aan-construction occupy less extreme positions in the cluster of points on the left-hand side of the plot: the distance between the two constructions is smaller than in Figure 1. This suggests that in the 19th-century data, there is more overlap in their distributions over the 11 verbs than in the present-day data. In order to further test this, we conducted two-by-two comparisons of the observed DOC and aan-dative frequencies of the 11 non-secundative verbs in 19th-century vs. present-day language. In six cases, this revealed a significant shift. Three verbs display a significantly stronger preference for the DOC in the present-day data compared to the 19th-century data: ontnemen (χ²  = 1194.934, df  =  1, p  < 2.2e-16; OR = 0.07611464), ontstelen (χ² = 8.7284, df = 1, p = 0.003133; OR = 0.1744933) and ontlokken (χ² = 6.0898, df = 1, p = 0.0136; OR = 0.7244433). The odds ratios (ORs) are included as a measure of the effect size: the effect is stronger for ontnemen and ontstelen than for ontlokken (the more the OR differs from 1, the stronger the effect). Three other verbs display the reverse tendency, i.e. they have a significantly stronger

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Correspondence analysis graph UIT

1.5

1.0 Dimension1 (87.61%)

54

0.5

0.0

–0.5

–1.0

VAN

ontlenen

ontvreemden

onttrekken AAN onturkken ontheffen ontworstelenontwringen ontlokken ontnemen BIJ ontfutselen DOC ontroven ontstelen

0

0.5 1 1.5 Dimension2 (8.948%)

2

2.5

Figure 2.╇ Correspondence analysis of the 19th C data (without secundative construction)

preference for the aan-dative in the present-day data compared to the older data: ontlenen (Fisher Exact p = 8.038e-09; OR = Infinite), onttrekken (Fisher Exact p = 2.828e11; OR = 198.7147) and ontrukken (χ² = 51.9195, df = 1, p-value = 5.782e-13; OR = 12.36263).7 In this case, the odds ratios are larger than 1 because the effect is reversed: the odds for the aan-dative are larger in the present-day data than in the old data. The remaining five verbs do not display a significant diachronic shift: the distribution attested with ontwringen, for instance, is remarkably constant, with a proportion of DOC to aan-dative instances of (about) 1:1 in both periods. The diachronic shifts observed in individual verbs can be seen as indicators of a tendency towards polarization or constructional specialization: in those verbs which already displayed a strong preference for one of the two alternating constructions in the 19th-century data, this lexical preference has become even stronger in the present-day data. That is, ontnemen, ontstelen and (to a somewhat lesser extent) ontlokken have become even more closely associated with the DOC, whereas ontlenen, onttrekken, and ontrukken have become even more closely associated with the aan-construction. All in all, there seem to be few verbs left in this morphological class which can be said to alternate more or less freely. An interesting follow-up question for further 7. In the case of ontlenen and onttrekken, we used the Fisher Exact test rather than the Pearson chi-square test because at least one of the cells in the 2-by-2 table had an expected frequency of less than 5.



Competing ‘transfer’ constructions in Dutch

diachronic research into the Dutch dative alternation is whether this polarization tendency observed for ont-verbs is also found in other ditransitive verb classes.

6. Conclusion Whereas the large majority of existing studies on the grammatical encoding of ‘possessional transfer’ events in Dutch – or English, for that matter – deal with verbs of giving, either primarily or exclusively, the present study has focused on verbs lexicalizing the reverse direction of transfer, i.e. verbs of dispossession. More specifically, we have presented a corpus-based case study of a specific morphological class of dispossession verbs, viz. prefixed verbs with ont- ‘away’. Starting with the frequency data included in a database with over 18,000 three-argument examples from four corpora of present-day written Dutch, we have distinguished four clusters of ont-verbs according to their constructional preferences. These are (i) verbs which are (virtually) exclusively found in the secundative van-construction, (ii) verbs with a preference for indirective constructions with uit, bij, or van, or for two-argument constructions without a source participant, (iii) verbs with a strong lexical preference for the double object construction, and (iv) verbs with a strong lexical preference for the aan-dative. These clusters provide valuable information about the semantic relations between the argument structure constructions at stake. As for the distinction between clusters (iii) and (iv), for instance, we have observed that, compared to the verbs strongly attracted to the aan-dative in cluster (iv), the verbs with a strong attraction to the DOC in cluster (iii) denote more prototypical events of dispossession in which a human original possessor is (strongly) negatively affected by the transfer. This suggests that the DOC is the preferred construction for the encoding of scenes in which the source of the transfer is a prototypical human deprivee – a finding which is in line with a general hypothesis known from the literature on the dative alternation with verbs denoting a possessional transfer in the canonical direction (i.e., verbs of giving and the like), viz. that compared to the aan-dative, the DOC highlights the affectedness of the indirect object referent. We have not found corroborating evidence, however, for another wellknown hypothesis about verbs of giving, viz. that the use of the aan-dative highlights the spatial aspects of the scene: in clauses with ont-verbs, it does not seem to matter for the choice between the DOC and the aan-dative whether or not the theme actually moves along a spatiotemporal path as it changes ownership. Furthermore, we have also observed that there is a cline from verbs with a strong DOC preference to verbs with a strong aan-preference, with a number of verbs occupying intermediate positions. This is different for the secundative van-construction, in that there is a nearly complete lexical split between this construction on the one hand and the other five constructions included in the table on the other: the secundative construction is frequently found with a number of ont-verbs which hardly occur in the DOC or in any

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of the investigated indirective constructions. Semantically, these verbs depart from prototypical ‘dispossession’ in that they imply a positive rather than negative effect on the original possessor, who is relieved of something conceptualized as a burden, or denote an event of physical removal or separation. The secundative construction, it turns out, is hardly an option for the encoding of more protypical ‘dispossession’ events with a human possessional source maleficially affected by the subject’s action. The indirective constructions with van, bij, and uit, finally, account for a small fraction of the ont-examples only; ontvreemden ‘steal’ is the only verb in the data with a preference for one of these constructions, namely for the locative construction with uit – it remains to be investigated how exactly simplex verbs of dispossession such as stelen ‘steal’ or roven ‘rob’ behave with respect to these various indirective constructions. The most interesting finding from the diachronic part of the investigation is that the relation between the DOC and the aan-dative seems to characterized by an interesting tendency of polarization or semantic specialization: the lexical preferences displayed in the 19th-century data tend to become even stronger in the present-day language.

References Barðdal, J. (2007). The semantic and lexical range of the ditransitive construction in the history of (North) Germanic. Functions of Language, 14, 9–30. DOI: 10.1075/fol.14.1.03bar Colleman, T. (2006). De Nederlandse datiefalternantie: Een constructioneel en corpusgebaseerd onderzoek [The Dutch dative alternation. A constructionist and corpus-based investigation]. Unpublished Ph. D. dissertation, Ghent University. Colleman, T. (2009a). The semantic range of the Dutch double object construction: A collostructional perspective. Constructions and Frames, 1, 190–220. DOI: 10.1075/cf.1.2.02col Colleman, T. (2009b). Verb disposition in argument structure alternations: A corpus study of the Dutch dative alternation. Language Sciences, 31, 593–611. DOI: 10.1016/j.langsci. 2008.01.001 Colleman, T., & De Clerck, B. (2009). Caused motion? The semantics of the English to-dative and the Dutch aan-dative. Cognitive Linguistics, 20, 5–42. DOI: 10.1515/COGL.2009.002 Colleman, T., & De Clerck, B. (2011). Constructional semantics on the move: On semantic specialization in the English double object construction. Cognitive Linguistics, 22, 183–210. DOI: 10.1515/cogl.2011.008 Delorge, M., & De Clerck, B. (2007). A contrastive and corpus-based study of English and Dutch provide-verbs. Phrasis, 48, 121–142. Delorge, M. (2010). De relatie tussen betekenis en structuur bij privatieve en receptieve werkwoorden in het Nederlands [The relation between meaning and structure in verbs of dispossession and reception in Dutch]. Unpublished Ph. D dissertation, Ghent University. De Schutter, G. (1974). De Nederlandse zin: Poging tot beschrijving van zijn structuur [The Dutch clause: An attempt at describing its structure]. Brugge: De Tempel.



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Duyck, W., Desmet, T., Verbeke, L., & Brysbaert, M. (2004). WordGen: A tool for word selection and nonword generation in Dutch, English, German, and French. Behavior Research Methods, Instruments, & Computers, 36, 488–499. DOI: 10.3758/BF03195595 Geeraerts, D. (1998). The semantic structure of the indirect object in Dutch. In W. Van Langendonck & W. Van Belle (Eds), The Dative. Volume 2. Theoretical and contrastive studies (pp. 185–210). Amsterdam & Philadelphia: John Benjamins. Goldberg, A. E. (1992). The inherent semantics of argument structure: The case of the English ditransitive. Cognitive Linguistics, 3, 37–74. DOI: 10.1515/cogl.1992.3.1.37 Goldberg, A. E. (1995). Constructions: A construction grammar approach to argument structure. Chicago: University of Chicago Press. Greenacre, M. (2007). Correspondence analysis in practice (2nd ed.). Boca Raton: Chapman & Hall/CRC. DOI: 10.1201/9781420011234 Haspelmath, M. (2005). Argument marking in ditransitive alignment types. Linguistic Discovery, 3, 1–21. DOI: 10.1349/PS1.1537-0852.A.280 Janssen, T. (1997). Giving in Dutch: An intra-lexematical and inter-lexematical description. In J. Newman (Ed.), The Linguistics of Giving (pp. 267–306). Amsterdam & Philadelphia: John Benjamins. Langacker, R. W. (1991). Concept, image, and symbol: The cognitive basis of grammar. Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110857733 Malchukov, A., Haspelmath, M., & Comrie, B. (2010). Studies in ditransitive constructions: A comparative handbook. Berlin & New York: Mouton de Gruyter. Newman, J. (1996). Give. A Cognitive Linguistic study. Berlin: Mouton de Gruyter. Schermer-Vermeer, I. (1991). Substantiële versus formele taalbeschrijving: Het indirect object in het Nederlands [Substantial versus formal language analysis: The indirect object in Dutch]. Amsterdam: University of Amsterdam, Dutch Department. Van Belle, W., & Van Langendonck, W. (1996). The indirect object in Dutch: In W. Van Belle & W. Van Langendonck (Eds.), The dative. Volume I: Descriptive studies (pp. 217–250). Amsterdam & Philadelphia: John Benjamins. DOI: 10.1075/cagral.2 Verhagen, A. (1986). Linguistic theory and the function of word order in Dutch. Dordrecht: Foris.

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Appendix Table 4.╇ Pearson’s residuals of the χ² of Table 1 ontdoen ontfutselen ontheffen ontlasten ontlenen ontlokken ontnemen ontroven ontrukken ontstelen onttrekken ontvreemden ontworstelen ontwringen

DOC

aan

van-I

van-S

uit

bij

–26.9111 â•⁄21.17231 –14.0511 â•⁄–5.58732 –41.4537 â•⁄18.05141 â•⁄81.45388 â•⁄â•⁄0.50072 â•⁄–6.7413 â•⁄13.47256 –25.3715 â•⁄–9.63693 â•⁄–0.82861 â•⁄â•⁄1.93476

–36.0072 â•⁄–9.57147 –18.5346 â•⁄–7.47589 â•⁄54.27883 â•⁄–7.32894 –41.6047 â•⁄â•⁄0.304086 â•⁄â•⁄8.65564 â•⁄–6.93123 â•⁄31.96341 –13.7075 â•⁄â•⁄2.146425 â•⁄–0.02316

–3.72107 â•⁄8.501756 –1.94289 –0.77257 –5.38299 â•⁄7.557048 –1.61472 –0.16397 –1.04221 –0.75853 –1.52988 21.49648 –0.42758 –0.34395

â•⁄96.62736 –10.7422 â•⁄50.01195 â•⁄20.06194 –33.5068 –13.6028 –27.8464 â•⁄–0.95851 â•⁄–6.09239 â•⁄–4.43409 –20.5712 â•⁄–8.4109 â•⁄–2.49949 â•⁄–2.01059

â•⁄–7.2614 â•⁄–2.47057 â•⁄–3.79141 â•⁄–1.50763 â•⁄–9.66559 â•⁄–4.10051 â•⁄–9.08068 â•⁄–0.31998 â•⁄â•⁄1.40804 â•⁄–1.48021 â•⁄–0.16867 103.3261 â•⁄â•⁄0.364079 â•⁄–0.67119

–3.81388 –1.35253 –1.99135 –0.79184 –5.19401 19.83698 –4.26796 –0.16806 –1.0682 –0.77745 –3.60682 27.68344 –0.43825 –0.35252

Table 5.╇ Numerical output of the correspondence analysis of the present-day data > Principal inertias (eigenvalues): dim 1 2 3 4

value % cum% 0.828914 53.8 53.8 0.683026 44.3 98.1 0.025129 1.6 99.8 0.003653 0.2 100.0 -------- ----Total: 1.540722 100.0 Rows: 1 2 3 4 5 6 7 8 9 10 11

| | | | | | | | | | |

scree plot ************************* ********************* *

name mass qlt inr k=1 ontf | 42 896 21 | -829 ontln | 407 1000 161 | 760 ontlk | 67 492 28 | -563 ontn | 281 995 292 | -1252 ontrv | 0 917 0 | -87 ontrk | 13 982 4 | 679 onts | 7 990 8 | -1301 ontt | 153 996 56 | 745 ontv | 26 1000 429 | 38 ontwrs| 2 901 0 | 308 ontwrn| 1 957 0 | -299

cor 891 946 486 978 158 981 972 987 0 898 686

ctr 35 283 26 531 0 7 15 103 0 0 0

k=2 cor ctr | 59 5 0 | | 181 53 19 | | -60 5 0 | | 163 17 11 | | 191 759 0 | | -10 0 0 | | 177 18 0 | | 71 9 1 | | -5078 1000 968 | | 17 3 0 | | 188 271 0 |



Competing ‘transfer’ constructions in Dutch

Table 5.╇ (continued) Columns: name mass qlt 1 | DOC | 345 1000 2 | AAN | 617 1000 3 | VANI| 7 824 4 | UIT | 25 995 5 | BIJ | 7 698

inr 348 204 22 383 43

k=1 | -1239 | 694 | -438 | 165 | -314

cor 986 946 37 1 10

ctr 638 358 2 1 1

k=2 cor | 146 14 | 166 54 | -2011 787 | -4835 994 | -2562 687

ctr 11 25 39 859 67

| | | | |

Table 6.╇ Pearson residuals of the χ² on Table 3 ontdoen ontfutselen ontheffen ontlasten ontlenen ontlokken ontnemen ontroven ontrukken ontstelen onttrekken ontvreemden ontworstelen ontwringen

DOC

aan

van-I

van-S

uit

bij

â•⁄–5.68127 â•⁄â•⁄3.923941 –10.4144 â•⁄–3.29846 –18.4732 â•⁄â•⁄5.547325 â•⁄15.98458 â•⁄â•⁄3.805351 â•⁄–2.66221 â•⁄â•⁄7.832866 â•⁄–2.37058 â•⁄–0.47808 â•⁄â•⁄0.196071 â•⁄â•⁄2.114915

â•⁄–6.72469 â•⁄–2.15422 –12.2317 â•⁄–3.90425 â•⁄16.49591 â•⁄–1.71846 â•⁄–5.9854 â•⁄–2.06827 â•⁄â•⁄5.875097 â•⁄–4.88802 â•⁄â•⁄3.232374 â•⁄–0.79243 â•⁄â•⁄0.407667 â•⁄–0.40802

–0.92132 –0.62533 –1.71948 –0.5349 â•⁄7.992057 –1.766 –4.05023 –0.61765 –1.9532 –0.93162 –0.66236 10.58121 –0.30883 â•⁄1.302676

â•⁄26.70959 â•⁄–2.03352 â•⁄48.77557 â•⁄15.50718 â•⁄–9.99249 â•⁄–5.74288 –13.171 â•⁄–2.00857 â•⁄–6.35164 â•⁄–3.02954 â•⁄–2.15395 â•⁄–1.18828 â•⁄–1.00428 â•⁄–2.94514

–1.27828 –0.86761 –2.38568 –0.74215 13.094 –1.63397 –5.61947 –0.85696 –2.70995 –1.29256 –0.91899 â•⁄1.46546 –0.42848 –1.25655

–0.20601 –0.13983 –0.38449 –0.11961 –0.6871 â•⁄4.66983 –0.90566 –0.13811 –0.43675 –0.20832 –0.14811 –0.08171 –0.06906 –0.20251

Table 7.╇ Numerical output of the correspondence analysis of the 19th-century data Principal inertias (eigenvalues): dim 1 2 3 4

value 0.319872 0.032668 0.007285 0.005248 -------Total: 0.365073

% 87.6 8.9 2.0 1.4 ----100.0

cum% 87.6 96.6 98.6 100.0

scree plot ************************* **

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60 Martine Delorge, Koen Plevoets, and Timothy Colleman

Table 7.╇ (continued) Rows: 1 2 3 4 5 6 7 8 9 10 11 12

| | | | | | | | | | | |

name ontf | onth | ontln | ontlk | ontn | ontrv | ontrk | onts | ontt | ontv | ontwrs| ontwrn|

mass 11 2 263 87 456 11 106 24 12 4 3 23

Columns: name mass qlt 1 | DOC | 403 999 2 | AAN | 565 995 3 | VAN | 11 979 4 | UIT | 20 895 5 | BIJ | 1 31

qlt 981 693 996 647 993 982 749 970 830 941 691 789 inr 470 239 132 144 15

inr 14 0 547 38 209 13 32 57 11 75 0 5

| | | | |

k=1 -658 69 870 -320 -408 -646 162 -887 400 828 -52 -192

| | | | | | | | | | | |

k=1 -649 383 1437 1483 -566

cor 991 951 454 856 30

cor 952 77 995 646 993 954 241 917 485 93 82 503 ctr 531 259 69 140 1

ctr k=2 15 | -116 0 | 195 622 | -26 28 | 15 237 | -9 14 | -110 9 | 235 59 | -214 6 | 337 8 | -2501 0 | 143 3 | -144 k=2 | -59 | 82 | -1547 | -317 | 82

cor 8 44 525 39 1

cor 29 616 1 1 0 28 508 53 344 848 609 285 ctr 43 117 777 63 0

ctr 4 2 6 1 1 4 179 34 42 711 2 15

| | | | |

| | | | | | | | | | | |

Rethinking constructional polysemy The case of the English conative construction Florent Perek

Freiburg Institute for Advanced Studies and Université Lille 3

This chapter examines the conative construction, e.g., I kicked at the ball, using collexeme analysis. Previous studies report that strong collexemes of a construction provide an indication of its central meaning, from which polysemic extensions are derived. However, the conative construction does not seem to attract a particular kind of verb that could be used to characterize its central meaning. To address this problem, a variant of collexeme analysis is suggested that consists in splitting the verbal distribution into semantic classes and consider “verb-class-specific” constructions independently. For the three classes tested, the most significant collexemes are found to be verbs whose inherent meaning contains the semantic contribution of the construction in that class. Hence, the most attracted collexemes do provide an indication of the constructional meaning, albeit specific to each verb class. Keywords: collexeme analysis, semantic classes, verb-class-specific constructions

1. Introduction1 In constructional approaches to grammar, argument structures are taken to be symbolic pairings of a syntactic structure with a schematic meaning independent of the verbs instantiating them (cf. Goldberg 1995, 2006). For example, the ditransitive construction (e.g., John built the children a new merry-go-round) is a pairing of the double-object syntactic pattern with a core meaning of ‘caused possession’. An increasingly large body of evidence from experiments (Goldberg et al. 2004) and corpus 1. This chapter is based on material presented at the 4th International Conference of the German Cognitive Linguistics Association on October 8th 2010 in Bremen. I would like to thank the audience of my talk for their interest and comments. I am also indebted to Dylan Glynn, Adele Goldberg and Martin Hilpert for their comments on earlier versions of this chapter.

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studies (Stefanowitsch and Gries 2003) suggests that there is a close relation between constructional meaning and constructional usage, in that the meaning of a construction closely corresponds to the meaning of the elements that typically occur in it. In the case of argument structure constructions, this means that the meaning of verbs occurring in a given syntactic pattern determines to a large extent the meaning that will be associated with this syntactic pattern. Along the same lines, previous corpus-based studies on the interaction of syntax and lexis using the method of collostructional analysis show that “strong collexemes of a construction provide a good indicator of its meaning” (Stefanowitsch and Gries 2003:â•›227); for example, the ditransitive is biased towards verbs lexicalizing its core meaning of caused possession, such as give. Collexeme analysis is thus considered as a valid approach to the analysis of constructional meaning. This chapter presents an attempt to use collostructional analysis to describe the meaning of the conative construction, in which a typically transitive verb is followed not by a direct object, but by a prepositional phrase headed by at (e.g., The waiter wiped at the counter). As shown by the literature review presented in Section 2, previous research indicates that the meaning of the conative construction is difficult to grasp with a single semantic generalization that would be both accurate and maximally general, which points to a polysemy analysis. Along the lines of Stefanowitsch and Gries (2003), Section 3 considers whether collostructional analysis can inform a polysemy analysis of the conative construction by identifying its central meaning(s), from which other meanings could be derived. However, a collexeme analysis of the construction reveals that no single verb type clearly stands out as prototypical, as is the case with previously studied constructions. These results challenge the claim that collexeme analysis is a good way to characterize the meaning of the construction from the verbs that most prominently occur in it. In Section 4, a solution to this problem is presented that restores the relation between constructional meaning and verbal use. Drawing on an earlier proposal by Croft (2003) that constructional polysemy is better viewed as generalizations over several semantic classes of verbs rather than extensions from a prototype, a slightly different implementation of collexeme analysis is suggested, whose basic idea is to split the verbal distribution into semantic classes and consider each of these thus-defined “verb-class-specific” constructions independently. The method is applied to three classes of verbs: verbs of striking, verbs of cutting and verbs of pulling. In each class tested, the most significant collexemes are verbs whose meaning inherently contains precisely those aspects of meaning that are arguably contributed by the construction when it is used with other verbs. Hence, the most attracted collexemes do provide an indication of the constructional meaning, albeit specific to each verb class. The conclusion of this study is two-fold. At the theoretical level, it shows that the polysemy of the conative construction is better seen not as a unified network, but rather as a conglomerate that can be explained by local lexical generalizations



Rethinking constructional polysemy

over classes of verbs. Such clusters of low-level generalizations are arguably, at least in this case, a more psychologically valid mental representation of constructional meaning than general schemata deriving from prototypical verbs. At the methodological level, this study shows that looking at the level of verb classes is a useful adaptation of collexeme analysis that can appropriately deal with cases which would otherwise yield results that are difficult to interpret. It allows us to see more clearly what the semantic contribution of a grammatical construction is, albeit for each semantic class separately.

2. The conative construction The conative construction is most naturally discussed with reference to the conative alternation, whereby the direct object of a transitive verb is realized as a prepositional phrase headed by the preposition at, as in John shot at the burglar. As we will see in this section, the meaning contributed by this syntactic construction is highly variable, which makes a maximally general semantic characterization of the construction challenging, if possible at all. One of the most cited semantic characterizations of the construction is that of Levin (1993), who suggests that the construction “describes an ‘attempted’ action without specifying whether the action was actually carried out”. Pinker’s (1989:â•›104) description, viz. “the subject is trying to affect the oblique object but may or may not be succeeding”, basically refers to the same idea while further specifying the origin of the “attempted action” interpretation, namely that the conative variant lacks the entailment that the referent of the at-phrase is affected by whatever activity the agent is engaged in. Finally, Goldberg (1995:â•›63–64) formulates a construction grammar account of the construction based on these earlier observations, in which she posits that the central meaning contributed by the construction is roughly ‘x directs action at y’, and accounts for the “attempted action” interpretation reported by Levin and Pinker by stipulating that in such cases “the verb designates the intended result of the act denoted by the construction”. The common idea behind all three analyses is the notion that the conative counterpart leaves the affectedness of the at-phrase referent unspecified, whereas it is strongly (if not necessarily) implied by the transitive variant. More recent work on the conative construction shows that this characterization is not by itself sufficient to account for the interpretation of all conative sentences. As Van der Leek (1996:â•›367) notes, “the conative does not, in its own right, guarantee an intended result reading when featuring otherwise transitive verbs”. Both Van der Leek (1996) and Broccias (2001) note that many conative sentences do entail that the patient is affected, albeit to a lesser extent than the transitive counterpart. Verbs of ingestion provide a good example thereof. Indeed, such expressions as James Bond sipped at his Martini do entail that at least some of the designated substance was

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ingested; what they prevent is a holistic interpretation where the whole substance would be consumed. Non-affectedness thus cannot be a relevant reading for verbs of ingestion, which rather involve a ‘bit-by-bit’ interpretation. Van der Leek (1996:â•›367) also notes that “usage of verbs of ingestion in the conative often seems to be motivated by a desire to signal that no real attempt is (or even can be) made to carry out the action to completion”. Example (1) (taken from Van der Leek 1996:â•›367, originally from the Longman Dictionary of Contemporary English) exemplifies such a case: (1) [Sandy was] sipping at her drink just to be polite Sentence (1) explicitly specifies the actual goal of the sipping (to be polite), and thus entails that Sandy has no real intention to consume the whole drink. In other words, the conative construction can be found in cases where there is apparently no intention on behalf of the agent to affect the target, and hence where actual affectedness is not only unlikely but also (and more importantly) irrelevant. Subscribing to a constructional approach whereby clausal meaning results from the fusion of a verb’s meaning with an abstract schema conveyed by the syntactic construction, Broccias (2001) presents a new analysis of the conative construction. To account for instances not covered by the “attempted action” generalization and to tackle several other issues with previous studies, Broccias argues that the conative construction conveys either one of three schemas: the allative schema, the ablative schema, and the allative/ablative schema, which combines aspects of the first two. The allative schema is described in purely locative terms as involving translational motion towards a target with which contact is not necessarily made, which more or less corresponds to the aforementioned analyses in terms of “attempted action”; note, for example, that Pinker (1989) describes the output of his conative lexical rule in a similar locative fashion as ‘X goes towards X acting-on Y’. This is also reminiscent of Goldberg’s description of the construction’s central meaning in terms of “directed-action”. Broccias’ ablative schema, contrary to the former one, does imply that contact is made but does not bring about the intended effect and is open to repetition; this schema is involved, for example, with verbs of ingestion, as mentioned earlier. It should be clear from the previous discussion that the semantic contribution of the conative construction is highly variable, and is, if anything, difficult to grasp with a single generalization. What could stand as the common motivation behind all these uses is the very abstract notion that the conative construction moves the focus to what the agent is doing, regardless of whatever effect this action brings about. This proposal echoes Dixon’s (1991:â•›280) analysis, who notes that “the emphasis is not on the effect of the activity on some specific object […] but rather on the subject’s engaging in the activity”. While this account seems reasonable at first blush, such an abstract characterization must still go a long way towards the actual semantic contribution with individual verbs, leaving a heavy burden to processes of meaning construction. In addition, such a general meaning could not account for why some verbs (such as



Rethinking constructional polysemy

break and bend) cannot occur in this construction, since a priori any verb meaning involving an agent subject could, in theory, undergo a focus on the agent’s activity. Thus, the syntactic frame [NP V at NP] more likely corresponds to several different abstract schemas. Whether or not these schemas can be related in a polysemic network is a matter of debate, but it seems to be a reasonable position. Indeed, the various semantic contributions sketched above can be shown to share family resemblances, which gives credence to a polysemy analysis. For example, both the ‘intended-result’ and ‘bit-by-bit’ readings share the notion that, whatever else is going on in the sentence, there is in both cases some goal which is not reached by the agent: bringing about a result on the second entity for the former, and leading an incrementally unfolding event to its completion in the latter. In the next section, the polysemy of the conative construction is examined on the basis of corpus data. Specifically, it is proposed that the central meaning (or meanings) of the construction can be identified from an examination of its verbal distribution, using the method of collexeme analysis.

3. A collexeme analysis of the conative construction Previous discussions of constructional polysemy consider that a construction gains additional meanings through semantic extensions from a central meaning. For example, the central meaning of the ditransitive construction is ‘actual change of possession’, as instantiated by, e.g., the verb give. Several semantic extensions are derived from this central meaning, such as ‘enabled change of possession’ (as with, e.g., allow) or ‘intended change of possession’ (as with many verbs of creation, e.g. bake). All these meanings are related in that they all share the notion of some change of possession, but ‘actual transfer’ is the prototypical meaning since it is both concrete and “basic to human experience”, according to Goldberg’s (1995:â•›39) scene encoding hypothesis. How do we identify the central meaning of a construction? In quantitative corpus linguistics, it has been proposed that the verbal distribution of a construction reveals a great deal about its meaning. More precisely, the most frequent verbs occurring in a construction would be those instantiating its central meaning. This section presents an attempt to identify the central meaning of the conative construction on the basis of its verbal usage, using the method of collexeme analysis. Collexeme analysis is one of the specific implementations of the more general method of collostructional analysis suited to the identification of the central meaning of a construction. This section starts with an outline of what the method consists in (cf. Hilpert’s contribution (this volume, 391–404) for a more thorough introduction). Drawing on previous research, it is then shown how this method is useful for the study of grammatical constructions. The remainder of this section presents a collexeme analysis of the conative construction.

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Table 1.╇ Contingency table for collexeme analysis Lexeme L Other lexemes

3.1

Construction C

Other constructions

F(L in C) F(other L in C)

F(L in other C) F(other L in other C)

Collexeme analysis

Collexeme analysis was first introduced by Stefanowitsch and Gries (2003) as “an extension of collocational analysis specifically geared to investigating the interaction of lexemes and the grammatical structures associated with them” (ibid.:â•›209). Collexeme analysis is concerned with the words occurring in a given slot of a chosen construction, and more particularly with “determining the degree to which particular slots in a grammatical structure prefer, or are restricted to, a particular set or semantic class of lexical items” (ibid.:â•›211). The method starts with the identification of a particular construction in a corpus, and of a particular slot of that construction that can be filled with different lexical items. For each lexeme occurring in the slot, the following contingency table must be calculated, as in Table 1. This contingency table is then submitted to a distributional statistic (often the Fisher-exact test2) to calculate the collostruction strength of the lexeme. This value gives an index of the degree of statistical association between the lexeme and the construction, given their frequency of co-occurrence, the frequency of the lexeme elsewhere, and the frequency of other lexemes in the construction. The verbs in the distribution are then ranked according to their collostruction strength. The final step (interpretation) consists in using this ordered list of collexemes to inform a description of the meaning of the grammatical construction, which is essentially guided by the theoretical assumptions of the constructional approach. In construction grammar, the occurrence of a lexeme in a construction is to a large extent determined by the degree of semantic compatibility (cf. Goldberg 1995) between the meaning of the lexeme and that of the construction (or more precisely, the meaning assigned by the construction to the particular slot under study). In collexeme analysis, collostruction strength is assumed to correlate with semantic compatibility: lexemes are more attracted to some constructional slot (i.e. occur in that slot more often than expected) if they are more semantically compatible with the slot. It thus follows that the strongest collexemes of a construction, as the most semantically compatible lexemes, are a potential source of information about the meaning of the construction. 2. Despite the wide range of available distributional statistics, Stefanowitsch and Gries (2003:â•›218) argue that the Fisher exact test is a perfect choice for collostructional analysis: it “neither makes any distributional assumptions, nor does it require any particular sample size”.



Rethinking constructional polysemy

The task of the analyst is thus to track down the origin of semantic compatibility from the lexical semantics of these collexemes, so as to deduce a characterization of the constructional meaning. Stefanowitsch and Gries (2003) illustrate their claims with a few case studies showing the usefulness of the method for the description of grammatical constructions. Two of these are of particular interest for us here: the into-causative construction (Subj V Obj into V-ing) and the famous ditransitive construction (Subj V Obj1 Obj2). For the into-causative, Stefanowitsch and Gries (2003) looked at the first verb slot of the construction and found that the top collexemes are verbs “instantiating the two major sub-senses of the construction, namely ‘trickery’ (as exemplified by trick/fool […]) and ‘force’ (as exemplified by coerce/force […])” (p. 226), while verbs instantiating senses of the construction that are intuitively less central (such as ‘verbal coercion’ and ‘persuasion through a positive or negative stimulus’) appear much further down the list. As to the ditransitive construction, the verb give turns out to be by far its strongest collexeme, which is to be expected given the principle of semantic compatibility: among the many ways in which a verb can be compatible with a construction, give and the ditransitive exemplify the optimal case where there is semantic identity. In other words, since the verb give is maximally compatible with the ditransitive construction, it comes as no surprise that it is its strongest collexeme. Yet, the authors argue that, contrary to what happens with the into-causative construction, the basic ‘transfer’ sense of the ditransitive is not overwhelmingly dominant in the collexemes of the construction, in that there are relatively few significant collexemes instantiating the central sense in the whole list (6 out of 30, 10 including metaphorical uses such as tell, show and teach). Rather, the high diversity of verbs provides, according to Stefanowitsch and Gries , evidence for the polysemy analysis of the construction put forward by Goldberg. It is indeed true that instances of the central sense are a minority among the collexemes in terms of the number of types, but these few types are clearly clustered towards the top of the list: at least four of them (eight including the metaphorical uses) are among the top ten collexemes. Thus, for both constructions, there seems to be a strong tendency for the top collexemes to instantiate the most central meaning(s). Both case studies thus present evidence that collexeme analysis is a valid quantitative method to profile the meaning of constructions from their prominent verbal collocates. As Stefanowitsch and Gries (2003:â•›227) conclude, “strong collexemes of a construction provide a good indicator of its meaning”. Therefore, the method should be helpful in identifying the elusive meaning of the conative construction.

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3.2

Data collection

The verbal distribution of the conative construction was extracted from the prose fiction part of the BNC, containing about 16 million words in 431 texts primarily drawn from novels. The choice of this corpus was neither arbitrary nor unmotivated. Intuitively, the conative construction seems to convey a complex descriptive function which makes it more at home in narrative genres, and probably not to be found so frequently in spontaneous spoken language. The latter intuition is actually borne out by an earlier attempt at finding conative sentences in the conversation part of the corpus, revealing that the construction is extremely rare in that register (only 17 tokens in 4 million words). The corpus was queried for all verbs followed by the preposition at (with an optional intervening adverb) in the same sentence, with the exclusion of frequent verbs that cannot support a conative reading and for which at can only be used in a purely locative sense (e.g. be, stay, live, arrive, etc.).3 The resulting set of sentences was manually annotated to select only conative sentences, which were defined according to two criteria: (1) the verb has to be transitive, and (2) the interpretation of the sentences has to fall somehow into one of those described in the previous section. Sentences with coordinated verbs were duplicated in the dataset (one duplicate per verb). This yielded a final set of 2,563 instances, distributed over 159 verb types.

3.3

Results

The collostruction strength of each verb in the construction was computed by Coll.analysis 3, an R program written and kindly provided by Stefan Gries, with the Fisher exact test as a distributional statistic.4 Following Stefanowitsch and Gries (2005), Coll.analysis applies a log transformation to the p-values yielded by the Fisher exact test, and changes the sign to a plus if the association is one of attraction (i.e. the actual verb’s frequency exceeds the expected frequency) and to a minus in case of repulsion (i.e. the actual verb’s frequency is below the expected frequency). This gives a more readable value than the p-values, often expressed in powers of ten. A collostruction strength above 1.301 means that the verb is significantly attracted to the construction; a collostruction strength below –1.301 means that the verb is significantly repelled by

3. The Corpus Query Processor program, part of the Corpus Workbench suite developed at the University of Stuttgart (http://cwb.sourceforge.net/), was used to query the corpus. The corpus was assembled from the XML version of the BNC with a script that parsed all texts of the corpus and copied only those with the “prose-fiction” genre attribute. Another script then converted the corpus into a format readable by CQP. 4. Available at: http://www.linguistics.ucsb.edu/faculty/stgries/teaching/groningen/.



Rethinking constructional polysemy

Table 2.╇ The thirty strongest collexemes of the conative construction in BNC-prose-fiction Rank Verb

f(conative:all) coll.strength Rank Verb

f(conative:all) coll.strength

â•⁄1 â•⁄2 â•⁄3 â•⁄4 â•⁄5 â•⁄6 â•⁄7 â•⁄8 â•⁄9 10 11 12 13 14 15

226:661 179:823 â•⁄72:166 â•⁄53:156 â•⁄43:97 â•⁄73:643 â•⁄36:121 â•⁄71:689 â•⁄29:87 â•⁄31:107 â•⁄44:300 â•⁄91:1363 â•⁄36:291 â•⁄76:1217 â•⁄22:140

29:263 43:567 24:180 18:112 13:56 35:524 17:149 â•⁄9:32 â•⁄8:26 26:364 35:656 17:190 51:1186 11:112 23:466

tug clutch dab claw gnaw sniff nibble sip peck nag pluck tear stab grab hack

209.92 127.13 â•⁄75.74 â•⁄49.14 â•⁄46.02 â•⁄32.05 â•⁄31.26 â•⁄28.56 â•⁄26.95 â•⁄26.62 â•⁄24.13 â•⁄22.51 â•⁄17.41 â•⁄17.29 â•⁄13.08

16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

hammer snatch jab scrabble paw scratch slash swipe niggle poke suck prod kick lap strain

12.87 12.86 12.58 11 10.23 â•⁄9.13 â•⁄8.07 â•⁄8.07 â•⁄7.58 â•⁄7.55 â•⁄6.7 â•⁄6.52 â•⁄6.44 â•⁄4.82 â•⁄4.13

the construction. As noted above, the verbs at the top of the distribution ordered by collostruction strength provide an indication of the constructional meaning. The thirty strongest collexemes of the conative construction are reported in Table 2. As it turns out, the construction attracts a great variety of verbs. Almost all verb classes allowed in the construction are represented in that list: verbs of pulling (tug, pluck), verbs of seizing and holding (clutch, claw, grab, snatch), verbs of hitting and touching (dab, claw, peck, stab, hammer, jab, paw, swipe, poke, prod, kick), verbs of ingestion (gnaw, nibble, sip, peck, suck, lap), verbs of cutting (tear, hack, slash), etc. This result is not surprising in itself, as constructions are often associated with several related senses, and therefore several classes of verbs. Again, this points to a polysemy analysis, as indeed the collexemes presented in Table 2 arguably instantiate different senses of the construction. For example, assuming Broccias’ (2001) distinctions (cf. Section 2), clutch, stab and kick mostly instantiate the allative schema, while nibble, hack and suck rather instantiate the ablative schema. While it is, a priori, not problematic that the construction attracts different classes of verbs, the list of collexemes is, however, not particularly helpful in characterizing the construction’s meaning. Moreover, contrary to what happens in the case studies reviewed above, there does not seem to be a class of verbs that the construction attracts in particular. The list presents alternations of very different types of verbs, and no particular class seems to be more strongly attracted than the others. For example, the five most attracted collexemes exemplify precisely five different verb classes: tug (verb of pulling), clutch (verb of seizing/holding), dab (verb of touching/hitting), claw

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(verb of hitting or seizing/touching) and gnaw (verb of eating/chewing). Moreover, these verbs exemplify various semantic aspects of the construction: tug at entails no change of location and an inherent repetition of the attempt, clutch at and claw at entail either missed contact or prolonged exertion of a force, dab at entails little or no affectedness, gnaw at entails no completion. Thus, contrary to what Stefanowitsch and Gries (2003) found with the ditransitive construction, collexeme analysis is not helpful in identifying one (or more) particular sense of the conative construction which would be central and from which the other senses would be derived. As a matter of fact, there need not be an identifiable verb class corresponding to each constructional sense: since the senses of the conative construction are so highly abstract, they are liable to be combined with a great variety of verbs from different semantic classes. Hence, it is not particularly surprising that the collexeme list of the conative construction (or probably of any abstract construction) is not as easily interpretable as that of the ditransitive construction. As one reviewer suggests, this might be because the semantics of the conative construction is less directly related to basic bodily experience than that of the ditransitive or of the caused-motion construction; as such, it is less likely to correspond to patterns of lexicalization in the language in general. This means that collexeme analysis in its present form would not be able to identify the senses of many constructions, at least not as neatly as those of the ditransitive construction (for example).

3.4

Towards a solution

In the face of such results, this chapter suggests another approach based on a refinement of collexeme analysis, which might be more informative in the case of the conative construction, and probably many other constructions. This approach is motivated by an earlier proposal by Croft (2003), who criticizes the concept of constructional polysemy, and thus the related notion of a “central” meaning. According to Croft, the very concept of constructional polysemy is problematic in several respects. The main problem can be roughly summarized as follows: how can a construction be considered truly polysemous if its meaning in context only depends on the verb it is instantiated with? In the case of the ditransitive construction, Croft (ibid.:â•›55) notes that “each semantic class is associated with only one sense of the ditransitive construction”. This seems to be in part semantically motivated: for example, the fact that the modal extension (‘conditions of satisfaction imply that X causes Y to have Z’) is the only one occurring with promise (for instance) is expected since it is the only extension whose specifications do not conflict with the meaning of the verb. However, why the extension ‘X intends that Y have Z’ is the only one compatible with verbs of creation appears to be completely arbitrary, since there is nothing in the verb’s meaning that blatantly conflicts with a number of the other extensions, whose instantiation with the verb would thus make perfect sense.



Rethinking constructional polysemy

A polysemic analysis of the conative construction runs into exactly the same problem: while there can be several different readings of a single conative sentence, not all interpretations are equally available in all instances. For example, in no case would conative sentences with verbs of ingestion mean ‘X moves towards Y in order to ingest Y’. Conversely, verbs of rubbing could never be used in the conative construction to convey the meaning ‘X rubs a part of Y and goes towards having Y totally rubbed’, let alone an allative interpretation (i.e. ‘X goes towards Y to rub Y’).5 Sometimes the unavailability of some readings is straightforwardly explained by intrinsic properties of the verbs themselves: for example, the impossibility of an incremental reading with semelfactives such as hit and kick can be explained by the aspectual properties of these verbs and more particularly the absence of an incremental theme. However, there are still perfectly sensible combinations that, nonetheless, are disallowed, which would not be the case if the construction was truly polysemous. Croft suggests that such cases are more appropriately accounted for not by considering the construction as genuinely polysemous, but by treating it as several “verb-class-specific constructions”, i.e. lower-level generalizations of a constructional meaning over a clearly delimited semantic verb class, instantiated only with verbs of that class. The remainder of this chapter presents evidence that this view might also be more appropriate for the conative construction. As observed in Table 2, no particular meaning stands out in the whole distribution of the construction. However, if we look again at Table 2 by focusing on verbs from a specific semantic field, a clearer picture emerges. A class that is fairly easy to delimit is that of verbs of eating. Table 3 reports the distribution of verbs of eating in the conative construction (the significantly attracted and significantly repelled collexemes appear on a gray background). Table 3.╇ Verbs of eating in the conative construction Verb

f(conative:all)

coll.strength

nibble peck suck lick gulp gobble munch pick eat

36:121 29:87 35:656 20:488 â•⁄9:267 â•⁄1:60 â•⁄1:84 79:4678 12:4089

â•⁄31.26 â•⁄26.95 â•⁄â•⁄6.7 â•⁄â•⁄2.68 â•⁄â•⁄1.07 â•⁄–0.18 â•⁄–0.3 â•⁄–1.1 –21.53

5. Conative uses of rub and other similar verbs (wipe, brush, …) do receive a form of “non-affectedness” interpretation which is not ‘X tries to rub Y’ but rather corresponds to a scenario in which some entity remains unaffected; this entity might be mentioned (as in rub at the stain) or might remain implicit or unspecified (as in rub at the counter, which most likely entails that the agent’s goal is to clean the counter and that this goal is not achieved).

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The most strongly attracted verb in that class, nibble, denotes an event of eating where only a small amount of some substance is ingested, and is therefore inherently compatible with the “bit-by-bit” reading supported by the construction. In fact, this verb is similar to give in the ditransitive construction: assuming a more specific eating-conative construction instantiated by verbs of eating only and whose meaning would be ‘eat in a bit-by-bit fashion’, the meaning of nibble is identical to the meaning of that construction, which largely motivates the prominent occurrence of that verb in the construction. The other significantly attracted collexemes also support the ‘bit-by-bit’ interpretation. Peck typically refers to how birds eat, by moving their beak forward repeatedly; in the conative construction, it is also frequently used to refer to people eating only a small amount of their meal. Suck and lick are not purely verbs of eating but rather describe a kind of action that an agent performs on another entity; when they are used to describe events of eating (as they very often are in the corpus), both typically refer to a slow and gradual means of ingestion through the progressive dissolution of a substance. Finally, the sole collexeme repelled by the construction is eat; this again reflects the semantic preferences of the construction, as eat is a maximally neutral verb of ingestion which is more commonly used to denote total consumption and lends itself less easily to a ‘bit-by-bit’ interpretation.6 This simple example shows that focusing on a particular class of verbs clearly captures what the semantic contribution of the construction is for this particular class. Thus, a collexeme analysis at the level of individual verb classes seems to be a promising approach. The next section elaborates on this proposal and presents a version of collexeme analysis based on semantic classes.

4. A collexeme analysis of verb-class-specific constructions In the previous section, it was found that a collexeme analysis performed on the whole distribution of the conative construction is not very helpful in characterizing its constructional meaning and does not clearly support a polysemy analysis either. 6. As Dylan Glynn notes in a review of an earlier version of this chapter, it is somehow unexpected that pick does not appear among the attracted collexemes of the construction, let alone that it almost reaches the threshold of repulsion, since pick at indeed seems to be a prime example of the ‘bit-by-bit’ reading induced by the construction. This result is explained by the fact that the verb pick is highly polysemous and at the same time highly frequent, and that it is not primarily a verb of eating: in fact, it probably occurs in this sense in the conative construction only. This asymmetry in the semantic distribution of pick thus appears to obscure its contribution to our understanding of the meaning of the construction. The general issue of the relation between frequency of verb forms and frequency of verb senses is taken up again in Section 4.1.2.



Rethinking constructional polysemy

It was observed that a clearer picture emerges if we look only at verbs from a specific semantic class (in that case, verbs of eating): the meaning of the strongest collexemes clearly reflects the semantic contribution of the construction for this semantic class. This section outlines a more principled and systematic formulation of this approach and then presents its application to three classes of verbs: verbs of cutting, verbs of pulling and verbs of striking.

4.1

Method

This section first explains how verbs in this study were classified into semantic classes. It then turns to some statistical issues posed by the present approach.

4.1.1 Determining verb classes The present approach first requires that the verbs from the distribution of the conative construction are sorted into several classes. Of course, a given verb form can correspond to several meanings, and these meanings can belong to different semantic classes. For example, in Table 2, peck and pick can function as verbs of eating but also as verbs of striking (albeit more rarely). However, the frequencies obtained from the corpus are frequencies of verb forms, not of verb meanings, and thus some of these frequencies may actually be distributed over several semantic classes. All instances of a verb form cannot just be assigned to a single class or be counted in several classes simultaneously: it must be determined for each token to which semantic class it belongs. For the example of verb-class-specific collexeme analysis presented in the last section, the field of verbs of eating was relatively easy to select from the whole distribution. However, it might not be so easy to identify, on the sole basis of intuition, the verb classes found in the distribution and the semantic class each verb token belongs to. To facilitate this process, an external lexicographic source was relied on: WordNet (Fellbaum 1998), a lexical database of the English language which was created and is being maintained at the Cognitive Science Laboratory of Princeton University. It groups English words into sets of synonyms (called synsets) and provides lists of the various meanings of each word form that can be looked up to perform semantic annotation. Starting with an established list of sense distinctions, instead of building it during the annotation process, is not only convenient, it also allows the achievement of a crucial feature of empirical studies of meaning: overt operationalization (cf. Glynn 2010), in the sense that the analytical criteria are overtly identified. This makes the analysis falsifiable, since it enables it to be repeated on the same data or on another dataset (e.g. for the purpose of comparison). The list of verb senses could be drawn from any dictionary, but WordNet presents another useful feature for this approach: it records relations between synsets such as

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hyponymy, hyperonymy, part-whole relations, entailments, etc. Of particular interest to us, the relations of hyponymy (and conversely, hyperonymy) connect the synsets into a type hierarchy, which can be used to define verb classes: a verb class includes the verbs of a given synset and all of its hypernyms, i.e. verbs whose meaning includes (and often, elaborates) the meaning of the synset. Hence, co-hyponyms belong to the same class. In sum, WordNet can be used both to annotate for verb senses and to define verb classes on the basis of the annotated data and hyponymy/hyperonymy relations between senses recorded in the database. It has been noted elsewhere that WordNet sense distinctions are somehow arbitrary and sometimes so fine-grained that it is practically impossible to apply the classification to naturally occurring examples (not to mention the theoretical vacuity and actual impracticability of the very notion of sharp sense boundaries, cf. Kilgarriff 1997; Glynn 2010). While this is true in many cases, in the context of this study it is often unproblematic to ignore some sense distinctions as long as they do not extend over different verb classes. For example, drag has two senses in WordNet that may apply to conative uses of the verb: (i) ‘pull, as against a resistance’ and (ii) ‘draw slowly or heavily’. It is not clear from the glosses what the semantic difference is supposed to be, and if anything it is very subtle and therefore not easily applicable to the annotation of examples in context. This distinction can, however, be ignored, since both senses have pull as their direct hyperonym: they can thus be conflated into a single entry, drag, subsumed by the class of verbs of pulling. Even though the fine-grained sense distinctions posited in WordNet might not always be well-grounded, the coarser-grained distinctions imposed by verb classes are more reliable and more easily noticeable. This strategy thus avoids the pitfalls of drawing strict sense boundaries. The original dataset was manually annotated for WordNet senses with the help of an interactive program.7 As it turns out, while some verbs are highly polysemic according to WordNet’s classification, the conative construction is usually restricted to one or two senses of these verbs, and most verbs can belong to only one semantic class when they occur in the construction. The verb sense distribution was built by calculating the frequency of each word sense in the construction. Each verb sense in this distribution was then annotated with the synset ID of its direct hyperonym, or with its own synset ID if the verb sense is a hyperonym of other verbs in the distribution. This ID identifies both the class to which the verb belongs, and the most general verb (i.e. hyperonym) of that class. In the case of classes subsumed by another class, which can be diagnosed by the hyperonym of one class being a member of another class, the lower class was merged into the higher one. As a last step, in each class, senses of the

7. This tool was written in Java and uses the JWNL API to read the WordNet 3.0 files (http:// sourceforge.net/projects/jwordnet/), downloaded from the website (http://wordnet.princeton. edu/wordnet/download/).



Rethinking constructional polysemy

same verb form were collapsed into one cell summing all frequencies of the verb form. With this method, maximally large and distinctive verb classes were obtained.

4.1.2 Statistical matters In the collexeme analysis of verbs of ingestion in Section 3.4, verbs were just filtered out on the basis of their belonging to the semantic class under study. However, if the verb-class-specific constructions hypothesis is taken seriously, a collexeme analysis of a specific semantic class only makes sense if the collostruct under consideration is not the general construction but a more specific one taking only verbs of this semantic class, and since such constructions have a lower frequency than the more general one, the actual collostruction strength values could be slightly different, hence changing the significance of some collexemes and possibly the order of the collexeme list. The frequency of a verb-class-specific construction is obtained by summing the frequency of all verb senses in the class. There is, however, still one missing set of frequencies: the frequency of each verb sense in other constructions. Unfortunately, except with a semantically annotated corpus, there is no easy way to determine this frequency, as it is practically intractable to manually annotate the whole corpus for verb senses. It must be acknowledged that this is an inherent weakness of this approach. However, as serious as it might be, this problem can be attenuated using two methods. First, in each verb class, only those verb senses that were by far the most frequent instance of their verb form are kept in the analysis. For example, catch occurs only seven times as a verb of striking in the conative construction versus fifty times in other senses (mainly as a verb of seizing); it was thus removed from the list of verbs of striking and does not appear in Table 5. The rationale behind this decision is that a verb form occurring clearly less prominently in a given verb-class-specific construction than in the other ones should be a weak collexeme of the construction anyway and is not likely to tell us much about the constructional meaning.8 Second, the overall frequency of the verb form was used for each verb sense, which makes the assumption that every occurrence of each verb form in the corpus has the meaning that the verb has in the conative construction. This is, of course, surely false for polysemous verbs, though not overly problematic for this study since it will merely downplay the collostruction strength of verbs. Indeed, the frequency of a verb sense is at least as high as the frequency of the verb form, and for polysemous forms it is a priori lower. The approximate collostruction strength calculated with the frequency of the verb form will thus be lower than the theoretical collostruction strength that would be calculated with the frequency of the verb sense, thus probably narrowing the range of significant collexemes. As it turns out, this 8. The deleted verbs include: scrape, scratch and slash for the cutting-conative construction, catch, pick, tweak and twitch for the pulling-conative construction, and catch, jab, peck, pick and poke for the striking-conative construction.

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possible downplaying of the attraction of the verbs to the construction does not prevent the identification of a number of interesting collexemes in each class.

4.2

Results

This section reports the collexeme analysis performed on the cutting-conative, pulling-conative and striking-conative constructions, defined as elaborations of the conative construction instantiated, respectively, by verbs of cutting, verbs of pulling and verbs of striking.

4.2.1 Verbs of cutting Events of cutting involve an agent moving a suitable instrument over the surface of an object, and causing a rupture in the physical integrity of that object as a result. With verbs of cutting, the conative construction does not support the allative interpretation (or at least not literally): contact is necessarily made between some instrument and the referent of the at-phrase, but this contact does not bring about the effect that the transitive use of the verb would entail: the cutting either fails entirely, or is too minimal for one to consider that the object is indeed cut. Hence, conative uses of verbs of cutting often convey the implicature that the action performed to do the cutting is repeated. Table 4 presents the collexemes of the cutting-conative construction. The analysis reveals three significantly attracted collexemes: hack, saw and chip. All three collexemes are particularly suited to the semantic contribution of the cutting-conative construction. The lexemes hack and saw are inherently repetitive: an event of hacking or sawing always consists of several identical actions. Moreover, a single movement (a stroke of a hacking tool or of a saw) generally does not by itself bring about the intended effect on the patient, e.g. cutting something to bits or sawing a piece of wood apart; the Table 4.╇ Collexemes of the cutting-conative construction Verb

f(conative:all)

coll.strength

WordNet gloss

hack saw chip chisel snip chop slice nick cut

22:140 â•⁄6:74 â•⁄4:93 â•⁄2:39 â•⁄2:54 â•⁄3:174 â•⁄3:237 â•⁄2:163 â•⁄4:3075

â•⁄19.76 â•⁄â•⁄3.69 â•⁄â•⁄1.63 â•⁄â•⁄1.11 â•⁄â•⁄0.87 â•⁄â•⁄0.47 â•⁄â•⁄0.27 â•⁄â•⁄0.23 –22.71

cut with a hacking tool cut with a saw break a small piece off from carve with a chisel sever or remove by pinching or snipping cut into pieces make a clean cut through cut a nick into separate with or as if with an instrument



Rethinking constructional polysemy

movement must be repeated until the desired effect is obtained. Hence hack and saw naturally support the semantic contribution of the cutting-conative construction in their conceptual semantics, i.e. both ‘no-significant-effect’ and ‘repetition’. The item chip inherently features only one of these two aspects. In any event of chipping, only a small piece of the patient is broken off, and chip does not in any case support a truly holistic interpretation, i.e. an object that is chipped is only minimally affected and keeps its overall physical integrity, compared to what happens with true verbs of change of state like break. Events of chipping must be repeated if the patient is to be considered significantly affected. The only significantly repelled collexeme in the list is cut. Its repulsion can be explained by its status as a maximally neutral verb of cutting (and indeed the hyperonym of the whole class), which thus does not carry any semantic elaboration that would promote its use in the conative construction. In addition, cut lends itself to a holistic interpretation to a much larger extent than the attracted collexemes.

4.2.2 Verbs of pulling Events of pulling consist in an agent exerting a force on a patient, usually in order to move the patient towards self or to affect it in some other way (e.g. open a door). The effect on the patient is not an inherent feature of these verbs, but is rather a frequent implicature of their transitive use. The conative construction prevents this implicature of change of location/state, thus bringing the interpretation towards an ‘attempted action’ reading. Such uses also easily allow an interpretation of repeated actions, since a single iteration of pulling does not bring about a significant effect. Table 5 lists the collexemes of the pulling-conative construction. The construction has two significantly attracted collexemes: tug and pluck. According to the Oxford English Dictionary, tug applies to events where the puller puts a lot of energy in the pulling, or exerts a force during an extended period. Hence, tug focuses on the effort the agent puts into the act of pulling, and not so much on the dynamics of the event itself, i.e. whether the patient is set in motion or not. Table 5.╇ Collexemes of the pulling-conative construction Verb

f(conative:all)

coll.strength

WordNet gloss

tug pluck wrench yank haul jerk drag pull

226:661 â•⁄42:300 â•⁄12:314 â•⁄â•⁄1:122 â•⁄â•⁄5:411 â•⁄â•⁄8:717 â•⁄25:1528 138:6024

153.73 â•⁄10.31 â•⁄–0.49 â•⁄–1.64 â•⁄–3.9 â•⁄–7.02 –10.49 –38.41

pull hard pull or pull out sharply twist or pull violently or suddenly pull, or move with a sudden movement draw slowly or heavily pull, or move with a sudden movement draw slowly or heavily apply force so as to cause motion towards the source of the motion

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Pluck as a verb of pulling is often used to refer to the removal of some object from where it grows, e.g. fruit, plants, hair, or feathers. To overcome the inherent resistance of the ground to which the object is attached (e.g. skin, branch, earth), acts of plucking frequently involve a sharp and sudden pull so as to abruptly separate the object from its ground (as alluded to by WordNet’s gloss). The more general use of this verb to refer to other kinds of pulling keeps this ‘sharp and sudden’ aspect. Due to their short duration, acts of plucking are particularly prone to repetition. As indicated earlier, the repelled collexemes may have slightly overestimated repulsion scores; thus, the values of the five repelled collexemes (yank, haul, jerk, drag and pull) have to be interpreted with caution. However, the last two (drag and pull) provide some interesting insight into the construction’s meaning. Drag is more appropriately described as a verb of accompanied motion (i.e. where both agent and theme move along the same path, like bring) rather than a pure verb of pulling: it strongly presupposes the motion of the patient, which makes it at odds with the conative construction. Pull is, of course, the hyperonym of the semantic class, i.e., it is arguably the most neutral verb of pulling. Since it has no inherent semantic traits that particularly favor the conative reading(s), its appearance as a repelled collexeme is expected.

4.2.3 Verbs of striking Verbs of striking represent the largest of the three semantic classes under study. It comprises verbs that have either hit or strike as their hyperonym in WordNet. Events of striking consist in an agent performing some movement in the direction of a patient, aiming at forceful contact with the patient, usually with the intention of affecting it in some way (doing it harm or damage). In the conative construction, verbs of striking typically assume an allative interpretation: some effort is directed towards a goal (here, bringing about an effect on the patient) that is not reached. Table 6 lists the collexemes of the striking-conative construction. The significantly attracted collexemes include dab, hammer, swipe, buffet, kick, pummel and swat, and all of these verbs feature one or more particular semantic traits favored by the construction.9 The verb dab, by far the strongest collexeme, is categorized by WordNet as a verb of striking, though it is a very peculiar one. Contrary to more typical members, dabbing involves little energy and is normally not aimed at affecting the target, or at least not negatively. Rather, typical instances of dabbing include using a cloth to gather and remove a substance (like blood or tears) from a surface, or gently applying a substance

9. Table 5 also lists buffet as a significant collexeme. However, it is a very rare verb in our reasonably large corpus, occurring only twice, yet each time in the conative construction, which probably explains why it reaches the significance threshold. Since its rarity makes it a poor candidate as a relevant and telling collexeme of the construction, it was removed from the discussion.



Rethinking constructional polysemy

Table 6.╇ Collexemes of the striking-conative construction Verb

f(conative:all) coll.strength

dab hammer swipe buffet kick pummel swat batter slap

71:166 29:263 â•⁄9:32 â•⁄2:2 51:1186 â•⁄4:31 â•⁄3:27 â•⁄7:161 16:510

â•⁄66.44 â•⁄â•⁄9.56 â•⁄â•⁄6.81 â•⁄â•⁄3.1 â•⁄â•⁄2.89 â•⁄â•⁄1.98 â•⁄â•⁄1.41 â•⁄â•⁄0.78 â•⁄â•⁄0.44

tap lash whack scuff whip bat bash punch pound

24:802 â•⁄8:265 â•⁄1:37 â•⁄1:44 â•⁄9:350 â•⁄1:71 â•⁄1:85 â•⁄5:278 â•⁄4:245

â•⁄â•⁄0.4 â•⁄â•⁄0.33 â•⁄–0.14 â•⁄–0.19 â•⁄–0.32 â•⁄–0.39 â•⁄–0.51 â•⁄–0.69 â•⁄–0.75

thump

â•⁄4:322

â•⁄–1.31

hook beat bang smash pat strike

â•⁄2:228 27:1372 â•⁄8:602 â•⁄4:421 â•⁄6:545 34:1990

â•⁄–1.37 â•⁄–1.62 â•⁄–1.96 â•⁄–2.14 â•⁄–2.3 â•⁄–3.39

hit

â•⁄7:2007

–17.96

WordNet gloss hit lightly beat with or as if with a hammer strike with a swiping motion strike against forcefully strike with the foot strike, usually with the fist hit swiftly with a violent blow strike against forcefully hit with something flat, like a paddle or the open hand strike lightly strike as if by whipping hit hard poke at with the foot or toe strike as if by whipping strike with, or as if with a bat hit hard deliver a quick blow to hit hard with the hand, fist, or some heavy instrument hit hard with the hand, fist, or some heavy instrument hit with a hook hit repeatedly strike violently hit hard hit lightly deliver a sharp blow, as with the hand, fist, or weapon deal a blow to, either with the hand or with an instrument

on a surface (e.g. for medical or cosmetic purposes). This typical lack of affectedness of the patient in an act of dabbing is in line with the meaning of ‘non-effective action’ that the conative construction is often claimed to convey. The verb hammer originally refers to an act of hitting involving a hammer or a similar tool as instrument; in that restricted use, typical things that can be hammered include nails, metal sheets and other metallic goods. If anything, this use of hammer typically entails repetition, i.e., just as with hack in Section 4.2.1, any event of hammering normally involves multiple blows on the patient, since a single blow does

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not suffice in affecting the patient in the intended way. For example, nails are rarely properly hammered into a wall with a single blow, but rather inserted only partly, and the hammering must be repeated as many times as necessary. Similarly, a sheet of metal can never be shaped into any appropriate form with a single blow; it has to be worked until the intended shape is arrived at. Of course, the verb in its modern use is not restricted to describe exclusively acts of striking with a hammer, but the aspects of ‘minimal effect’ and ‘repetition’ found in the original meaning of the verb arguably subsist (as comfirmed by modern dictionaries), and the instrumental component is echoed by the notion of a forceful and violent striking usually accompanied by loud noise (which many dictionaries gloss as ‘as if with a hammer’). The verbs swipe, kick and swat are similar cases in that they refer to a precisely defined shape of motion in space. In other words, what makes an event of swiping, kicking or swatting, is, above all, a particular movement performed by the agent, respectively a swinging blow10 (of the arm or of an instrument), an outward motion of the foot, and the motion of a flat surface (an open hand or an instrument with the appropriate shape) through the air so that the surface hits a target (often an insect, crushing it). This makes these verbs agent-centered, i.e., they focus on describing what the agent is doing rather than the effects that its action may have. In addition, kick specifies the body part involved (a leg), further reinforcing its agent-centered character. Strikingly, there turn out to be much fewer verbs with a focus on the shape of motion among the other (i.e. non-attracted) collexemes. Possible candidates include lash, whip, slap and possibly punch; however, the shape evoked by the former two is due to the kind of instrument used rather than the action performed itself, and the latter two less obviously refer to a fully described shape. The other verbs rather focus on the manner of impact or on its effects. It thus seems that this semantic property (‘precisely defined shape’) is highly correlated with the striking-conative construction. Finally, pummel combines aspects of hammer and of the agent-centered verbs. It is slightly agent-focused since it refers to a particular body part (the fists). But more importantly, it is inherently repetitive, as all consulted dictionaries indicate: pummeling consists of a succession of small blows, most often dealt with the fists. As for the repelled collexemes, the usual cautioning remarks apply. Let us, however, note that, just like with the cutting- and pulling-conative constructions, the maximally neutral verbs hit and strike are, as expected, the most repelled collexemes of the striking-conative construction.

10. As a confirmation of this analysis, the OED notes that swipe is chiefly used in the context of cricket.



4.3

Rethinking constructional polysemy

Discussion

As should be clear from the preceding discussion, Stefanowitsch and Gries’ (2003) claims about the relation between the collexemes attracted to a construction and that construction’s meaning are clearly borne out for these three verb-class-specific instantiations of the conative construction. Namely, the attracted collexemes all prominently profile in their inherent semantics one or more semantic trait(s) that the construction contributes by itself when it occurs with other verbs. The semantic generalizations that each collexeme supports are reported in Table 7. The collexeme list clearly exemplifies the principle of semantic compatibility and how this principle bears on usage; namely, verbs with a meaning that lends itself particularly well to the interpretation sanctioned by the construction are “attracted” by it: they are much more frequent in that construction than chance would predict. Conversely, the hyperonym of the semantic class is the most repelled collexeme in each case, which the principle of semantic compatibility also predicts since such verbs are supposedly the most neutral verbs in their class, and thus do not profile any particular semantic trait that would attract them to the construction. In conclusion, it seems possible to characterize the meaning of the conative construction, or more precisely, the meaning the construction contributes when it Table 7.╇ Semantic generalizations supported by the collexemes of verb-class-specific constructions Verb-class-specific Construction

Collexemes

Semantic generalization(s)

cutting-conative

hack saw

event consisting of several identical movements with a minimal individual effect; hence it is inherently unbounded and repetitive

chip

minimal effect; no holistic interpretation

tug

focus on the effort (energy and duration) that the agent puts into the action rather than its effects

pluck

idem, plus a short duration which makes it prone to repetition

dab

lowly energetic; patient often not directly affected

hammer

inherently consists of several repeated blows; a single blow does not produce a sufficient effect

swipe kick swat

agent-centered: they profile a precisely defined motion that the agent performs, as well as information on the entity set in motion

pummel

profiles a body part (fists), inherently repetitive

pulling-conative

striking-conative

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combines with verbs of each semantic class under study, simply by attending to the salient semantic properties of the collexemes in each class. Of course, these collexemes do not lexicalize one of the meanings of the conative construction per se, as is the case with give and the ditransitive construction. But there is still arguably some abstract semantic quality shared between the collexemes and the constructional meaning as it occurs with other verbs. Such a semantic characterization would be much more difficult (if possible at all) to arrive at by looking at the entire distribution, i.e. at the level of the general construction vs. the more specific verb-class-specific constructions. The methodological and theoretical implications of this finding are elaborated on in the concluding words of the next section.

5. Conclusion As the first large-scale corpus-based investigation of the conative construction, this study contributes to the documentation of the construction’s usage. Its initial goal was to see what the verbs most frequently used with the construction could tell us about its meaning, drawing on the method of collexeme analysis. As it turns out, a collexeme analysis of the construction based on data from the prose-fiction part of the BNC fails to highlight its central meaning(s), since there does not seem to be a particular kind of verb that the construction attracts. Hence, while the collexeme list is not totally at odds with the meaning of the construction as it has been characterized introspectively, in this case collexeme analysis does not seem to be helpful in characterizing it precisely. To solve this problem, a different kind of analysis was proposed. Instead of considering the conative construction as a whole, the focus was shifted to verb-class-specific constructions, i.e. elaborations of a construction instantiated by verbs from a specific semantic class. A collexeme analysis was performed on three verb-class-specific constructions, respectively instantiated by verbs of cutting, verbs of pulling and verbs of striking, identified on the basis of the lexical database WordNet. The collexemes of each of these lower-level constructions feature in their inherent meaning the semantic traits that are characteristic of verbs of that class when they occur in the construction. In other words, collexeme analysis profiles the constructional meaning much better at the level of each verb class than at the most general level. Of course, it does not mean that collexeme analysis is ineffective for the conative construction taken as a whole; it is just not particularly telling. The collexemes found for the overarching construction are attracted because they are more compatible with the constructional meaning. But the conative construction is so multifaceted when taken at the most general level that it is much easier to understand why these verbs are collexemes and what this tells us about the meaning of the construction if we go down to the level of verb classes.



Rethinking constructional polysemy

On the theoretical side, these results shed some light on the nature of constructional generalizations. Namely, a long-standing debate in constructional approaches to grammar is concerned with which level of generalization best reflects speakers’ knowledge of constructions. In the case of argument structure, earlier constructional approaches (cf. Fillmore and Kay ms.; Goldberg 1995) sought to cast the broadest generalizations possible by positing one single very abstract meaning accounting for all instances of the construction, either directly or through an extension of the constructional meaning. However, more recent research questions this commitment and emphasizes the importance of lower levels of generalizations to appropriately account for the distribution and meaning of constructions; see, for example, Boas’ (2003) concept of “mini-constructions” to account for English resultatives, and of course Croft’s (2003) proposal for “verb-class-specific constructions” (cf. also Fillmore 2001; Glynn 2004). Of course, the debate “general vs. local” might appear null and void in a truly constructional account, in which both abstract schemas and their various elaborations can be stored at any level of generality. But if a number of local generalizations alone account for what appears at first sight to be a single general construction, this casts the question of whether the overarching construction is needed at all, all the more so if the local generalizations provide a better account in terms of accuracy and coverage. This is precisely what happens with the conative construction: to the extent that speakers attend to frequently occurring verbs in some syntactic context, and use that information to “get a ‘fix’ on the construction’s meaning” (Goldberg 2006:â•›92), they can usefully exploit this lexical semantic information only at the level of verb-class-specific-constructions. Under this view, a verb appears to be a collexeme of the general construction only because it is, first and foremost, a collexeme of a verb-class-specific construction. In sum, the results of this study suggest a different view of the polysemy of the conative construction, which can plausibly be extended to other constructions. The various meanings of the conative construction are better seen not as a network of related senses, but as a cluster of low-level generalizations over similar verb meanings, in line with Croft’s (2003) proposal. As a reviewer points out, it thus would seem as if we are actually dealing with a case of constructional homonymy, i.e. several constructions sharing the same form but conveying different meanings. However, the possibility that these verb-class-specific constructions might be, at least to some extent, unified under a higher-level generalization should not be entirely rejected. The fact that low-level generalizations can determine the semantic contribution of the syntactic pattern for verbs of the semantic class does not exclude the possibility of cross-generalizations between different classes. First, if several distinct verb classes receive the same semantic contribution (which is plausible, since the conative construction conveys a wide yet still limited range of meanings), they could form a single higher generalization, which in turn could be used to produce new combinations. Second, patterns of analogy between different classes might well play a major role in determining the distribution and in helping speakers get at the correct

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interpretation, forming generalizations of intermediate scope. The generalizations accounting for the conative construction could well be centered on a few classes first, from which an abstract meaning could be extracted and applied to other verbs and classes. Such a scenario is probably necessary to explain the inclusion of “orphans”, i.e. verbs whose semantic class does not have any other representative in the distribution. Obviously, there is still much to learn about the workings of constructional generalizations. I hope, however, to have presented in this chapter a promising application of collexeme analysis to understand the mechanisms of constructional abstraction and the possible underlying representations on the basis of corpus data.

References Boas, H. (2003). A constructional approach to resultatives. Stanford: CSLI Publications. Broccias, C. (2001). Allative and ablative at-constructions. In M. Andronis, C. Ball, H. Elston, & S. Neuvel (Eds.), CLS 37: The main session: Papers from the 37th meeting of the Chicago linguistic society. Volume 1 (pp. 67–82). Chicago: Chicago Linguistic Society. Croft, W. (2003). Lexical rules vs. constructions: A false dichotomy. In H. Cuyckens, T. Berg, R.  Dirven, & K. Panther (Eds.), Motivation in language: Studies in honour of Günter Radden (pp. 49–68). Amsterdam: John Benjamins. Dixon, R. (1991). A new approach to English grammar: On semantic principles. Oxford: Clarendon Press. Fellbaum, C. (1998) (Ed.). WordNet: An electronic lexical database. Cambridge, MA: MIT Press. Fillmore, C., & Kay, P. (MS). Construction Grammar (course reader). University of California, Berkeley. Fillmore, C. (2001). Mini-grammars of some time-when expressions in English. In J. Bybee, & M. Noonan (Eds.), Complex sentences in grammar and discourse: Essays in honor of Sandra A. Thompson (pp. 31–60). Amsterdam: John Benjamins. Glynn, D. (2004). Constructions at the crossroads: The place of construction grammar between field and frame. Annual Review of Cognitive Linguistics, 2, 197–233. DOI: 10.1075/arcl.2.07gly Glynn, D. (2010). Testing the hypothesis: Objectivity and verification in usage-based cognitive semantics. In D. Glynn, & K. Fischer (Eds.), Quantitative cognitive semantics: Corpus-driven approaches (pp. 239–270). Berlin: Mouton de Gruyter. DOI: 10.1515/9783110226423 Goldberg, A. (1995). Constructions: A construction grammar approach to argument structure. Chicago: University of Chicago Press. Goldberg, A. (2006). Constructions at work: The nature of generalization in language. Oxford: Oxford University Press. Goldberg, A., Casenhiser, D., & Sethuraman, N. (2004). Learning argument structure generalizations. Cognitive Linguistics, 15(3), 289–316. DOI: 10.1515/cogl.2004.011 Kilgarriff, A. (1997). I don’t believe in word senses. Computers and the Humanities, 31(2), 91– 113. DOI: 10.1023/A:1000583911091 Levin, B. (1993). English verb classes and alternations. Chicago: Chicago University Press. Pinker, S. (1989). Learnability and cognition: The acquisition of argument structure. Cambridge, MA: MIT Press.



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Stefanowitsch, A., & Gries, St. Th. (2003). Collostructions: Investigating the interaction between words and constructions. International Journal of Corpus Linguistics, 8(2), 209–243. DOI: 10.1075/ijcl.8.2.03ste Stefanowitsch, A., & Gries, St. Th. (2005). Covarying collexemes. Corpus Linguistics and Linguistic Theory, 1(1), 1–43. DOI: 10.1515/cllt.2005.1.1.1 Van der Leek, F. (1996). The English conative construction: A compositional account. In L. Dobrin, K. Singer, & L. McNair (Eds.), CLS 32: The main session: Papers from the 32th meeting of the Chicago linguistic society (pp. 363–378). Chicago: Chicago Linguistic Society.

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Quantifying polysemy in Cognitive Sociolinguistics Justyna A. Robinson University of Sussex

This chapter uses various statistical techniques to explore the extralinguistic grounding of individual conceptualisations of polysemous adjectives in English, such as awesome, gay, wicked. It considers the extent to which individual conceptualisations are non-random and can be related to the socio-demographic characteristics of the speaker. The experimental survey data collected from 72 speakers is analysed via hierarchical agglomerative clustering, decision tree analysis, and logistic regression analysis. The results reveal that not only individual adjectives, as indicated in Robinson (2010a), but whole groups of polysemous adjectives currently undergoing semantic change form usage patterns that can be explained by a very similar sociolinguistic distribution. This study demonstrates that employing a socio-cognitive perspective when researching polysemy is hugely advantageous. Keywords: adjectives, decision tree analyses, hierarchical agglomerative clustering, logistic regression, semantic variation, semantic change

1. Polysemy Polysemy, which is usually defined as one form that has several related1 yet distinct2 meanings, has been widely explored in various areas of linguistics (for an overview, 1. Polysemous meanings are related historically (as opposed to homonymous meanings which are not). From the methodological point of view there are different approaches as to whether a particular sense is a valid reading of a polysemous category. While certain studies include historically-related polysemous meanings in their dataset (e.g. Sweetser 1990), other studies consider only senses that are conceptually related in a given point in time (e.g. Beretta et al. 2005; Klein and Murphy 2002). Some discussion of diachronically-related senses that can be perceived as unrelated is available in Geeraerts (1997) and Blank (2003). 2. Challenges and potential solutions for determining the number and boundaries between polysemous readings are discussed in Dunbar (2001), Geeraerts (1993), Gries (2006), Hanks

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see Allan and Robinson 2012; Cuyckens and Zawada 2001; Geeraerts and Cuyckens 2007; Lewandowska-Tomaszczyk 2007; Nerlich et al. 2003; Rakova et al. 2007; Ravin and Leacock 2000; Vanhove 2008). Although polysemy was traditionally associated with the lexicon, much of the research has shown that polysemy also emerges when syntactic, morphological, and phonological usage is considered (see e.g. Brugman 1981; Taylor 1995:â•›142). It has become apparent that polysemy is not just a feature of certain words, but that it is a form of categorisation (see e.g. Taylor 1995:â•›99; Lakoff 1987:â•›12). Therefore, much of the research on polysemy has since focused on learning more about patterns of human categorisation. Some of the key observations of polysemous usage indicate that knowledge is categorised in terms of family resemblance models with less central meanings clustered around a prototype (see e.g. Geeraerts 1989, 1993; Janda 1990; Lakoff 1987:â•›379). Since the majority of these observations are drawn from the analysis of intralinguistic data only, there is little known about the extent to which the categorisation of specific linguistic events varies between speakers in the same community. For instance, can we assume that the prototypical centre of a polysemous category will be the same for each speaker in a given community? Much research on language variation indicates that linguistic usage does indeed differ between speakers in a community (Chambers et al. 2002; Coulmas 1997; Fought 2004; Labov 2001). These studies demonstrate that the way people speak may be predicted, for example, from their profession, the area in which they live, their social networks (Milroy 1980, 1987), practices they engage in (Eckert 2000) or identities they construct and adopt (Bucholtz 2011). Theoretically, Cognitive Linguistics agrees with the social grounding of linguistic variation by arguing for the experiential and perspectival nature of meaning (Geeraerts 1993:â•›60). However, little research has been done to relate linguistic usage patterns directly to extralinguistic categories and to account for the socio-cultural grounding of categorisation. Notable exceptions are represented in the literature by Geeraerts et al. (1994), Geeraerts et al. (2010), Kristiansen and Dirven (2008), Pütz et al. (2012a), Pütz et al. (2012b), Pütz et al. (2014), Reif et al. (2013), Robinson (2012a), and Robinson (2012b).

2. Scope of the study The current chapter contributes to the discussion of the extralinguistic grounding of individual conceptualisations of polysemous categories. It considers the extent to which individual conceptualisations are non-random and can be related to the socio-demographic characteristics of the speaker. The current chapter also demonstrates (2000), Kilgariff (1997), Krishnamurthy and Nicholls (2000), Lehrer (1990), and summarised in Lewandowska-Tomaszczyk (2007), and Ravin and Leacock (2000).



Quantifying polysemy in Cognitive Sociolinguistics

how various statistical techniques (i.e. hierarchical agglomerative clustering, logistic regression, and decision tree analyses) may be employed in order to enhance the way investigations of polysemy are carried out. The current chapter elaborates on my earlier study (Robinson 2010a) that demonstrated the benefits of implementing a sociolinguistic perspective in cognitive research on polysemy. In that study, I found out that the usage of innovative or conservative senses of the adjective awesome can be predicted from the socio-demographic characteristics of a speaker. For example, the use of awesome ‘terrible’ can be predicted from the speech of people of 60 years or older. Not only do these findings support cognitive linguistic understanding of polysemy but they also indicate that significant differences exist in the extent to which the different meanings of the same semantic category are salient for different speakers. Although these findings provide compelling evidence for the existence of socio-semantic usage patterns, the conclusions regarding systematic, socially-grounded usage can be only generalised as far as the adjective awesome is concerned. What remains to be verified is whether speakers’ usage of other similar words (e.g. other adjectives currently undergoing change) is structured in a similar way. The current chapter addresses this issue by investigating the usage of eight polysemous adjectives that are presently undergoing change.3 Firstly, I establish whether any meaningful patterns can be detected when the usage of several polysemous adjectives is considered simultaneously. Provided that meaningful usage patterns emerge, I then determine whether these are non-randomly related to the socio-demographic characteristics of the speakers who use these categories. In order to achieve the aims of the research, various exploratory and confirmatory statistical techniques are implemented. Thus, after introducing the data (Section 3), I summarise the aims of the hierarchical agglomerative cluster analysis (Section 4) and apply this exploratory method to analyse the dataset (Section 5). This analysis is supplemented with confirmatory analyses involving logistic regression (Section 6) and a decision tree analysis (Section 7) before the conclusions are drawn (Section 8).

3. This chapter is based on my doctoral research (Robinson 2010b). I would like to thank the University of Sheffield for funding this research project and Joan Beal, Ewa Dąbrowska, Philip Durkin, and Susan Fitzmaurice for generous advice and guidance on many aspects of this research. I would also like to thank Christopher S. Butler, Dagmar Divjak, and anonymous reviewers for comments on the earlier version of the current chapter. All other shortcomings are mine.

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3. Data and method Initial steps in the research follow those presented in Robinson (2010a). Eight polysemous adjectives currently undergoing change (Table 1) and five controlling adjectives have been chosen for the study. Available corpora (the British National Corpus (henceforth, BNC) and the Oxford English Corpus (henceforth, OEC)) and dictionaries (the Oxford English Dictionary (henceforth, OED)) indicate that the investigated adjectives have recently developed a distinctive meaning in British English. For a few of them, a potentially disappearing meaning has also been identified (see Table 1). In order to determine the usage patterns of these adjectives in a speech community, I carried out interviews with 72 speakers from South Yorkshire, UK. The speaker sample was equally representative of both men and women, different age groups (11–94 years old), and socio-economic backgrounds. Each of the speakers was asked a series of questions aimed at eliciting the most salient usage of polysemous adjectives. These questions followed a schema of asking for a referent that could be best described with an adjective in question, as shown in the following example: (1) Interviewer: Who or what is wicked? Participant: My mum. (referent) Interviewer: Why is your mum wicked? Participant: Because she lets me play my music as loudly as I want to. (justification for use) Each participant provided, on average, three instances of use of the investigated adjectives, which yielded more than seventeen hundred cases for analysis (excluding counts of those for controlling adjectives). The information obtained on both the referents and justification for the use of each adjective allowed me to put individual responses into groups of similar usage. Each of these usage groups was then given a sense label. This sense label was mainly Table 1.╇ The summary of potentially disappearing and emerging senses of the investigated adjectives Adjective

Incoming meaning

Potentially disappearing meaning

awesome chilled cool fit gay wicked solid skinny

great good good/trendy attractive lame good hard, tough ‘latte’/low fat

terrible

happy

mean



Quantifying polysemy in Cognitive Sociolinguistics

Table 2.╇ Example of the database structure Participant

wicked ‘good’

wicked ‘evil’

awesome ‘great’

awesome ‘terrible’

Speaker A Speaker B Speaker C Speaker D

2 3 0 0

1 0 2 3

3 2 0 1

0 0 2 3

derived on the basis of the match between the usage and the citation of senses used in the dictionaries. For instance, Example (1) above would be generalised with the meaning wicked ‘good’. Another sense group that emerged for the adjective wicked was wicked ‘evil’. Occasionally, speakers indicated that they were aware of a certain use of an adjective but they clearly distanced themselves from using this sense. In such cases, a category of a ‘reported’ sense was introduced.4 A category labelled ‘N/A’ was introduced in order to account for overlapping senses that could not be reliably assigned to any of the above groups or for other problematic answers.5 The raw frequency of use of each sense for each participant was recorded in the database. The next step in the analysis was to verify if any common usage patterns emerge across all senses used by participants. Usage patterns can be determined by identifying clusters in which two or more senses are used similarly (frequently or infrequently) by a number of speakers. Let us examine Table 2 to illustrate this. Table 2 presents a mini database that is structured in a similar way to the one used in the current study. One can observe that speakers A and B use awesome ‘great’ and wicked ‘good’ more frequently than other senses and that speakers C and D use awesome ‘impressive’ and wicked ‘evil’ more frequently than other senses of the adjectives. Thus, one may conclude that two distinct usage patterns emerge for two different groups of speakers: one for speakers A and B and another one for speakers C and D. In order to establish usage patterns in a large database, like the one used in the current study, I used the exploratory technique of hierarchical agglomerative cluster analysis (hereafter, HAC). Once semantic usage patterns are established, I consider the question of why these senses cluster together.6 Two variants are considered. Since the adjectives used 4. This separation of ‘reported’ senses from ‘non-reported’ senses is performed for practical reasons of potentially showing where in a community constraints on usage emerge. This is not to suggest that these are two different senses. 5. For instance, when the adjective gay used as a female name Gay. 6. Before one starts to analyse the visual output of a cluster analysis, it must be stressed that every HAC will always cluster elements together even if the clustering makes no sense. In other words, HAC will impose a structure on any data even if such a structure does not exist (also see Divjak and Fieller, this volume).

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in this study are undergoing change, one option is to assess whether senses that cluster together are similar in terms of the historical information we have about them. Do recently developed senses group separately from historically older senses? Another possibility is to consider whether speakers who share the same socio-demographic characteristics (in terms of age, gender, education, etc.) use the same combinations or clusters of senses. The findings of this analysis help to answer the question of whether there are any systematic semantic usage patterns and whether these are socially grounded. In order to find out more information about the users of the senses, I employed two confirmatory techniques: logistic regression and answer tree analysis.

4. Hierarchical agglomerative clustering There are a number of exploratory techniques used by social scientists that can help to find groups in data, such as principal component analysis, factor analysis, and different types of cluster analysis. These techniques differ in respect to their aims. Principal component analysis and factor analysis are methods for reducing the dimensionality of data (summarising the information in a complete set of variables using fewer variables), whereas cluster analysis aims to organise observations in meaningful structures. I use the exploratory technique of HAC in the current study because I am not interested in data reduction (as the dataset contains a comparatively small number of dimensions) and I intend to investigate groups in the data which are non-randomly similar. HAC belongs to a family of multivariate exploratory statistical methods (i.e. non-hypothesis-testing) for finding groups in data based on measured characteristics. HAC starts with each case in a separate cluster and then combines the clusters sequentially, reducing the number of clusters in each step until only one cluster is left. This hierarchical clustering process can be represented as a dendrogram, where each step in the clustering process is illustrated by a fork in the tree diagram. A detailed discussion of HAC as well as other types of cluster analysis is presented in Divjak and Fieller (this volume). The dendrogram in Figure 1 is an example of how senses from Table 1 cluster7 when their usage evidence for awesome ‘great’ (meaning 1), awesome ‘terrible’ (meaning 2), wicked ‘good’ (meaning 3), and wicked ‘evil’ (meaning 4) is inputted into the cluster analysis. The numbers visible on the junctions of the dendrogram represent the measurement of the distance at which clusters fuse together in the hierarchical cluster analysis. This example illustrates meanings 1 and 3 being combined at a fusion value of 2, whereas meanings 2 and 4 are combined at a fusion value of 1. The elements that are clustered earlier (represented by lower fusion values) are more closely related than 7. Distance measure used: phi-square; amalgamation strategy used: Ward.



Quantifying polysemy in Cognitive Sociolinguistics

Awesome ‘great’

2

Wicked ‘good’ Awesome ‘terrible’ 1 Wicked ‘evil’

Figure 1.╇ HAC of senses of presented in Table 1

elements that are clustered later (represented by higher fusion values). The cluster analysis groups senses that are used in a similar way by different people. This dendrogram indicates that different people in the research sample are mostly using the same combination of senses 1 and 3 (1+3) and 2 and 4 (2+4), rather than other combinations such as (1+4), (2+3), or (1+2+3).

5. Hierarchical agglomerative cluster analysis of collected data Having briefly outlined what constitutes HAC, I move on to discuss details of the computational steps of performing HAC on the current dataset. The analysis was performed using software called ClustanGraphics 7.05 (hereafter, Clustan).

5.1

Selection of polysemous adjectives

Table 3 presents the eight adjectives that are included in the HAC together with relevant meanings (a total of thirty-five meanings). Milligan and Cooper (1986, cited in Everitt et al. 2001:â•›179) suggest that only variables that are expected to be forming clusters should be included in the analysis. Irrelevant or masking variables should be excluded, if possible. Therefore, controlling adjectives and meanings grouped in the category ‘N/A’ are excluded from the HAC. The raw frequencies of the use of different senses are recorded in an SPSS database (following the format of the example of Table 2). Certain types of variables need transforming or standardising before the HAC is run (e.g. standardizing to z-scores). However, there is no need to standardise the variables in the current study as their scales do not differ. For more information on standardising variables for cluster analysis, see Divjak and Fieller (this volume).

5.2

Dissimilarity matrix

The next step involves generating a dissimilarity matrix which shows the distances between items. This procedure calculates either the similarities or dissimilarities (also

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Table 3.╇ Adjectives and their meanings explored in the HAC Adjective Meanings awesome chilled cool fit gay skinny solid wicked

great relaxed

terrible cold

impressive calm, collected cold

reported relaxed good, calm, reported trendy collected good, trendy attractive athletic healthy suitable reported attractive lame unmanly homosexual happy reported reported reported lame homosexual happy latte/ thin showing mean tight fitting low fat skin hard of one hard dependable (person) substance (object) good evil reported good

referred to as distances or proximities), either between pairs of variables or between pairs of cases. Between-variable dissimilarities are generated using SPSS 18 and they are copied into Clustan. Distances can be measured by using different metrics according to different data types (see Divjak and Fieller, this volume). For instance, proximities in count data in the current dataset are measured with phi-square.

5.3

Amalgamation strategy

Once distances between items are calculated, an amalgamation strategy is applied. This procedure involves using one of a few available algorithms (for a summary, see Divjak and Fieller, this volume) that define how separate elements are to be clustered. In the current dataset, the algorithm Increase in Sum of Squares (sometimes called Ward)8 is chosen. This method merges the two elements whose merging least increases their sum of squared deviations from their mean. The Ward algorithm is considered to be a robust method for data classification, which is sensitive to outliers (Gries

8. Other algorithms have also been considered (single linkage, complete linkage, and average linkage). The basic operation of such methods is similar as they fuse individuals or groups of individuals who are closest or most similar. Differences arise because various methods define the distance between individuals or groups of individuals in different ways (see Everitt et al. 2001:â•›Chapter 3). Scholars agree that there is no single best amalgamation method (Everitt et al. 2001:â•›Chapter 8; Moisl 2009; and Tan et al. 2006:â•›639–642).



Quantifying polysemy in Cognitive Sociolinguistics

2007). This method also appears to have affinity with other linguistic research, e.g. Beitel et al. (2001), Divjak and Gries (2006), Gries and Stefanowitsch (2006). There is one more step to complete before we can start analysing the dendrogram. The order of the original data can also influence the amalgamation of values. In order to obtain the optimal ordering of the cases, I follow the ‘serialize procedure’. This procedure yields the best order of variables that can be obtained from the current proximity matrix.

5.4

Dendrogram

An HAC of the meanings of the adjectives resulted in the dendrogram presented in Figure 2. The vertical layout of the dendrogram in Figure 2 means that we analyse it from left to right. The HAC of the current dataset clustered senses that are used in similar ways by the same people. For example, the fact that wicked ‘good’ and awesome ‘great’ clustered together means that a number of people who used wicked ‘good’ in the interview were also likely to use awesome ‘great’. Skinny ‘thin’ and awesome ‘great’ are fused later and belong to different clusters. It does not mean that no participant exhibited the use of these two senses. Instead, it just means that people using skinny ‘thin’ were less likely to also use awesome ‘great’ in the same interview.

5.5

Best-cut

After generating a dendrogram, one needs to decide which subclusters are meaningful and therefore should be highlighted for analysis. There are many “rules of thumb” as far as the analysis of cluster levels is concerned, but I will briefly talk about two approaches to this process. First of all, one may delimit borders of individual clusters based on the structure of the dendrogram and perceived (dis)similarities between variables. This procedure involves considering whether various subclusters make sense from the point of the intuitive (dis)similarities between data and the scope of the investigation. Another possibility is to employ statistical measures to determine the best number and size of clusters in the dendrogram (also called best cut). Ideally, conclusions from introspection and statistical analysis should overlap (although this is not always the case). The last scenario is that none of the possible divisions of the dendrogram make sense in the context of a given research question (statistically and through introspection). This is always a possibility since “cluster analysis can create as well as reveal structure” (Breckenridge 2000:â•›261) (cf. Divjak and Fieller, this volume). Initial inspection of the dendrogram in Figure 2 indicates that three large clusters could be delimited (see highlighted clusters in Figure 3), the top one being more independent from the remaining two. This three-cluster solution seems sensible in the

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96 Justyna A. Robinson TokensGayLame TokensWickedGood TokensAwesomeGreat TokensCoolGoodTrendy TokensChilledRelaxed TokensFitAttractive TokensGayReportedLame TokensSolidHardPerson TokensFitReportedAttractive TokensSolidOfOneSubstance TokensAwesomeImpressive TokensGayUnmanly TokensSkinnyShowingSkin TokensSkinnyTightFitting TokensFitAthletic TokensSkinnyThin TokensGayHomosexual TokensSolidHardObject TokensWickedEvil TokensGayReportedHappy TokensChilledCalmCollected TokensWickedReportedGood TokensCoolReported TokensSolidDependable TokensSkinnyLatte TokensFitSuitable TokensCoolCold TokensGayHappy TokensCoolCalmCollected TokensFitHealthy TokensGayReportedHomosexual TokensSkinnyMean TokensAwesomeTerrible TokensChilledCold TokensChilledReportedRelaxed

Figure 2.╇ Dendrogram of clustered senses

ClustanTM



Quantifying polysemy in Cognitive Sociolinguistics

TokensGayLame TokensWickedGood TokensAwesomeGreat TokensCoolGoodTrendy TokensChilledRelaxed TokensFitAttractive TokensGayReportedLame TokensSolidHardPerson TokensFitReportedAttractive TokensSolidOfOneSubtance TokensAwesomeImpressive TokensGayUnmanly TokensSkinnyShowingSkin TokensSkinnyTightFitting TokensFitAthletic TokensSkinnyThin TokensGayHomosexual TokensSolidHardObject TokensWickedEvil TokensGayReportedHappy TokensChilledCalmCollected TokensWickedReportedGood TokensCoolReported TokensSolidDependable TokensSkinnyLatte TokensFitSuitable TokensCoolCold TokensGayHappy TokensCoolCalmCollected TokensFitHealthy TokensGayReportedHomosexual TokensSkinnyMean TokensAwesomeTerrible TokensChilledCold TokensChilledReportedRelaxed

Figure 3.╇ Dendrogram with three and seven-cluster division

ClustanTM

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light of the current research project. Taking into consideration diachronic information on the usage of individual meanings (cf. Table 1), one can notice that each of the three clusters groups senses that are of different historical depth. Thus, the top cluster includes novel senses, the bottom cluster largely includes senses that are considered to be disappearing, and the middle cluster mostly represents diachronically ‘middle’ senses (neither recent innovations, nor necessarily disappearing senses). Moreover, the most recent and the oldest senses are grouped into two clusters positioned at the extreme ends of the dendrogram. These visual characteristics indicate that these two clusters are substantially different from each other in terms of usage/people who use them. The statistical delineation of clusters was carried out by following the best-cut procedure. Best cut in the data was established by using a significance test (upper tail rule, cf. Mojena 1977) on the fusion values at every stage in which the clusters join together in the dendrogram. Best cut indicates the level at which the change in fusion values is significant for most groups. This is then displayed by highlighting partitions on the dendrogram (these clusters are delimited with squares on Figure 3). The partition corresponds to the largest number of clusters, which is significant at the level of 5%. The best-cut procedure indicates that the seven-cluster solution turns out to be statistically significant. The seven-cluster solution breaks Cluster 2 down into two further clusters and Cluster 3 into four further clusters, whereas Cluster 1 remains unchanged. At first sight, it is less apparent why these sub-clusters would be separated. One potential explanation could involve historical information on the usage of some of these subclusters. Therefore, one could suggest that the cluster (skinny ‘mean’ and awesome ‘terrible’) contains disappearing senses. At this point, a decision needs to be made as to the level (seven or three clusters) at which to carry out further analysis. This initial exploratory analysis shows that the three-cluster solution already seems to exhibit interesting sense groupings. Going deeper into subclusters (seven clusters) might yield more detailed, but not necessarily as relevant, information (from the point of view of the current research project) on groups of variables. Besides, one rule of thumb says that one should distinguish as few clusters as possible. In the current chapter, I present the analysis at the level of three clusters only.9

9. The analysis of clusters at the level that a researcher intuitively considers appropriate (three clusters) may lead to ignoring interesting nuances in use that can be revealed at a more detailed ‘best-cut’ level of seven clusters. Therefore, the analysis of the seven-cluster solution of the current data is presented in Robinson (2010b).



5.6

Quantifying polysemy in Cognitive Sociolinguistics

Validation of clusters

The validation of a given clustering involves a series of procedures that determine the robustness of a present solution for making predictions. Different studies suggest various ways of assessing the validity of a given clustering (see Duda et al. 2001:â•›557–559; Everitt et al. 2001: Chapter 8; Moisl and Jones 2005; and Tan et al. 2006:â•›532–555). In the current study, I examine both the internal stability and the external validity of the present cluster solution following suggestions presented by Clatworthy et al. (2005).

5.6.1 Confirmatory analysis: Internal stability This first step in the validation procedure aims at answering the question of whether a given cluster solution can be replicated on new data. In order to validate the clustering in Figure 2, I run a tree validation procedure (also called bootstrap validation), which involves a series of random trials on randomised proximities. Each trial generates a different dendrogram for the given data and the series of trials provide a mean dendrogram and confidence intervals. The validation is achieved by comparing the initial clustering with the clustering in the randomised dendrogram. The validation procedure confirms that the obtained dendrogram and the best-cut division of the dendrogram can be replicated even on randomised data. 5.6.2 Confirmatory analysis: External validity (sociolinguistic analysis) As Clatworthy et al. (2005:â•›333) point out, the internal stability of clusters is not sufficient evidence to determine the value of a cluster solution. External validity procedures are employed to determine whether a set of external predictors (i.e. variables which were not included in the clustering process) can be associated with the obtained cluster solution and whether the same cluster solution can be replicated from a new independent sample. This approach is considered to be one of the better ways to validate cluster solutions (Aldenderfer and Blashfield 1984:â•›66). In Sections 6 and 7, the external validity of the cluster solution is examined. I verify whether any information about the speakers (their age, gender, etc.) who provided the usage data for this study could explain the way in which the senses in Figure 2 are grouped. This practically means employing other statistical measures to validate the use of clusters (linguistic variables) against external variables (socio-demographic variables). In order to perform external validation, multivariate techniques (logistic regression modelling and decision tree analysis) are employed. From a statistical point of view, verifying the external stability is a necessary element of cluster analysis. From the viewpoint of the current study, this procedure can be considered as a way of testing whether any meaningful semantic usage patterns emerge from analysing sociolinguistic variation. This naturally leads to gaining more insights as to whether conceptualisations of polysemous categories are non-randomly grounded in socio-cognitive contexts.

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5.6.3 Summary of cluster-variables Each of the three main clusters represents a usage pattern which is treated as a linguistic variable. In order to carry out statistical calculations, each of these conceptual patterns-variables needs to be presented as a binary variable to suit further statistical analyses. In order to do this, counts of senses belonging to a given cluster are added up. Following this, by the means of a visual bander10 (SPSS 18), a new variable is created that reflects the characteristics of a whole cluster. This is done through collapsing a large number of ordinal categories into a smaller set of categories, representing low and high usage of a given cluster of senses. Table 4 presents the summary of the dependent variables used, along with associated coding and category information. Table 4.╇ Linguistic variables (dependent variables) used to investigate their association with socio-demographic variables (independent variables) Dependent variables

Coded as

Categories

Cluster 1 Cluster 2 Cluster 3

1, 0 1, 0 1, 0

High use High use High use

Low use Low use Low use

The following independent variables are considered in the analyses: age group, gender, education, National Statistics Socio-Economic Classification score for a participant’s profession11 (hereafter, NSEC), and a postcode or a neighbourhood variable, Table 5.╇ Socio-demographic variables (independent variables) used to investigate their association with the use of different clusters of senses (dependent variables) Independent Coded as variables

Categories

Age group Gender NSEC Education

(1, 2, 3, 4) (1, 2) (1, 2, 3) (1, 2, 3, 4, 5)

Postcode

(1, 2, 3)

Up to 18 Male Higher Schooling prior the age of 16 Lower property prices

19–30 Female Medium Secondary school Middle property prices

31–60

Over 60

Lower College

University

Current student

Higher property prices

10. A visual bander is an SPSS tool to recode values of a variable into groups. Data frequently need to be manipulated before analyses are conducted. Data may need to be recoded, computations may need to be made, new variables may need to be created, or certain records may need to be selected (for more information, see Einspruch 2005). 11. See Office for National Statistics: Standard Occupational Classification (2000) for details.



Quantifying polysemy in Cognitive Sociolinguistics 101

which is based on property values in areas defined by the postcode of a participant’s residence. For a summary of the coding of the independent variables, see Table 5.

6. Logistic regression Having explored the data via HAC, confirmatory statistical analyses are carried out in order to validate emergent groups in the data. More specifically, I aim to assess the overall effect of socio-demographic categories on the use of particular clusters of meanings, hypothesising that the clustering solution can be explained by the categories of age, gender, NSEC, education and/or postcode value. In order to address the above-mentioned aim, a multifactor statistical model is employed, i.e., a model that considers several external factors simultaneously and measures their effect on the use of each cluster. In addition, the appropriate statistical approach needs to allow us to check for confounding variables. Socio-demographic factors may constitute such cases, i.e., education and occupation may be confounded, as people who are more educated are likely to have better jobs. Logistic regression analysis fulfils these requirements. Logistic regression can be used to test hypotheses about the relationship of several independent variables to a dichotomous dependent variable (see Hosmer and Lemeshow 1989; Kleinbaum 1994; Speelman (this volume); Tabachnick and Fidell 2001 for introductions to logistic regression). Logistic regression is increasingly being used in linguistic studies (e.g. Benki 1998; Bresnan et al. 2007; Kallel 2007; Levshina et al. (this volume); Tummers et al. 2004). The logistic regression model also allows for estimating odds ratios for each of the independent variables in the model. For instance, one may establish how many times a given meaning is more likely to be used by age group than by age group <19–30>. Logistic regression also provides information on variance (the percentage to which an independent variable is explained by the dependent ones) and is used to determine the importance of independent variables. In the current study, logistic regression is performed using SPSS 18 to assess the overall effect of socio-demographic factors (independent variables) on the use of clusters. All responses (including missing values) for seventy-two participants are included in the analysis. All sociolinguistic factors are entered into the model, and then the factors are examined to verify whether they meet removal criteria using a forward stepwise method. The final model is established once no further variables are eligible for removal. The final model is then reported. The resultant fitted model informs us about significant changes in regression coefficients (expressed as B) between predictors. In cases where a stable regressive model could not be established and a final solution could not be found (even by modifying model criteria, such as increasing the

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number of iterations: i.e. the series of approximations used by the logistic regression), I obtain insights into investigated variation by using multivariate statistical modelling based on decision trees (for more details, see Section 7).

6.1

Logistic regression of Cluster 1

Logistic regression analysis is performed to verify the hypothesis that the likelihood of high use of Cluster 1 can be modelled from speakers’ age, gender, NSEC, education and/or postcode (neighbourhood). Logistic regression analysis on Cluster 1 yields an unstable solution, so one cannot make predictions regarding the use of this cluster. Nevertheless, interesting findings can be obtained from examining decision trees (see Section 7.1).

6.2 Logistic regression of Cluster 2 Logistic regression analysis is performed to verify the hypothesis that the likelihood of high use of Cluster 2 can be predicted from speakers’ age, gender, NSEC, education and/or postcode (neighbourhood) value. The summary of the logistic regression analysis of the use of Cluster 2 is presented in Table 6. The final model reported includes variables that best account for the observed variation. Insignificant variables are excluded from the model. Table 6 shows the coefficients of regression Beta (hereafter, B), their standard errors, the Wald chi-square statistics, associated p-values, and odds ratios.12 The resultant fitted model indicates which independent variables are included in the final logistic model. It also informs us about significant changes in regression coefficients (B) between predictors. B determines the direction of the relationship between a given predictor and the dependent variable (the use of Cluster 2). If B is positive, the odds for the use of Cluster 2 are increased; when B is negative, then the odds are decreased; B equalling 0 leaves the odds unchanged. Explanations of the indicator variables can be found directly under each regression table. Model summary. According to the model, a high use of Cluster 2 can be modelled from speakers’ age (p = .005) and NSEC (p = .005). Age. The most significant differences of use exist between age groups <19–30> and (p = .001, B = –5.752), and also between age groups and <31–60> (p = .009, B = 3.407). This means that ‘middle’ age groups speak more similarly to each other. The analysis of probability measures (hereafter, P) presented in

12. For further discussion of stepwise regression, regression coefficient, iterations and the output of the logistic regression analysis in SPSS, see Brace et al. (2006) and Norušis (1999).

Quantifying polysemy in Cognitive Sociolinguistics 103



Table 6.╇ Summary of the logistic regression analysis of Cluster 2 Variables AgeGroup AgeGroup(1)a AgeGroup(2)b AgeGroup(3)c NSEC NSEC(1)d NSEC(2)e Constant a:

B

S.E.

–5.752 â•⁄–.313 â•⁄3.407

1.709 â•⁄.841 1.301

â•⁄3.905 â•⁄1.010 â•⁄–.056

1.467 â•⁄.929 â•⁄.380

Wald

df

p

Odds ratio

12.907 11.333 â•⁄â•⁄.138 â•⁄6.855 10.564 â•⁄7.085 â•⁄1.180 â•⁄â•⁄.021

3 1 1 1 2 1 1 1

.005 .001 .710 .009 .005 .008 .277 .883

â•⁄â•⁄.003 â•⁄â•⁄.732 30.179 49.672 â•⁄2.745 â•⁄â•⁄.946

change between the age group <19–30> in relation to the age group

b:

change between the age group <31–60> in relation to the age group <19–30>

c:

change between the age group in relation to the age group <31–60>

d:

change between the NSEC group in relation to the NSEC group <Medium>

e:

change between the NSEC group <Medium> in relation to the NSEC group

Table 7.╇ Probability values used for logit of Cluster 2 Age group

Age group probability

NSEC group

NSEC probability

Up to 18 19–30 31–60 Over 60

â•⁄2.5% 88.9% 91.6% 26.6%

NSEC 1 NSEC 2 NSEC 3

94.7% 26.5% 11.6%

Table 7 indicates that speakers of age groups <19–30> and <31–60> are most likely to be high users of Cluster 2 (P = 88.9% and 91.6% respectively). NSEC. The significant ‘jump’ in B-coefficients exists between NSEC2 and NSEC1 (p = .008, B = 3.905). Speakers who occupy higher occupations (NSEC1) are most likely to exhibit higher use of Cluster 2 (P = 94.7%), in comparison to speakers of middle and lower occupations (P (NSEC2) = 26.5%, P (NSEC3) = 11.6%). These findings are graphically presented in the form of logistic function estimate values (logit) in Figures 4 and 5. The bars with positive values (above 0) represent categories of independent variables (age group and NSEC, respectively), the occurrence of which correspond to a probability of the use of Cluster 2. In the figures, the taller the bar above 0, the higher the probability of high use of Cluster 2. The bars with negative values (below 0) represent categories of independent variables, the occurrence of which correspond to a probability of the use of Cluster 2. The lower the bar, the higher the probability of ‘not high’ use of Cluster 2. In the logistic regression analysis, the predictive and explanatory power of the fitted model needs to be assessed. In order to validate predicted probabilities, the

104 Justyna A. Robinson

3 2 1 0 –1 –2 –3 –4

upto 18

19–30

31–60

over 60

Figure 4.╇ Logistic function estimate values for age group in Cluster 2

4 3 2 1 0 –1 –2 –3

NSEC1

NSEC2

NSEC3

Figure 5.╇ Logistic function estimate values for NSEC in Cluster 2

c-statistic is used (see Peng et al. 2002:â•›6). The c-statistic analyses the proportion of observed to initially-predicted probabilities of occurrences of Cluster 2. In the case of Cluster 2, the fitted model (one that includes socio-demographic variables) achieves a success rate of 80.6%, which is an improvement over the intercept model (51.4%), i.e., a model that does not include any of the socio-demographic variables to account for the observed variation, but includes a constant term only and the model that does not take into consideration NSEC (73.6%). The explanatory power of the calculated model refers to how effectively it fits the actual data for estimating the outcome variable (Moss et al. 2003:â•›925). This could be assessed by a number of ‘goodness-of-fit’ measures. –2 Log Likelihood (hereafter, –2LL) indicates the overall fit of the model. It reflects the significance of the unexplained variance in the model. Its lowering values indicate improvement of a model fit (increasing the likelihood of the observed results). R-square measurements (Cox and Snell, Nagelkerke tests) indicate how much variation the model actually explains. Sometimes these measures may yield different results (for further discussion, see

Quantifying polysemy in Cognitive Sociolinguistics 105



Field 2005:â•›239–240). The Hosmer and Lemeshow test is another measure that is considered by some researchers to be a more accurate measure for assessing the goodness-of-fit of the model (Peng et al. 2002:â•›6). It tells you how closely the observed and predicted probabilities match and insignificant results in the Hosmer and Lemeshow test signify a model that fits the data well. In the case of Cluster 2, –2LL (53.740) and an insignificant Hosmer–Lemeshow test indicate that the model fits the data well and is more adequate for explaining variation than models that do not consider socio-demographic factors. R-square measurements (Cox and Snell = .472, Nagelkerke = .630) indicate that the variation in the outcome variable is explained moderately well by the logistic regression model. Logistic regression analysis evidences that the use of Cluster 2 can be satisfactorily modelled from the age and NSEC of speakers, although age group has a more significant overall effect on the use of the given variable than NSEC. Logistic regression analysis confirms our hypothesis and validates the external stability of Cluster 2.

6.3

Logistic regression analysis of Cluster 3

Logistic regression analysis is performed to verify the hypothesis that the likelihood of high use of Cluster 3 is modelled from speakers’ age, gender, NSEC, education and/or postcode (neighbourhood). Logistic regression on this cluster yields an unstable solution, so predictions regarding the use of this cluster cannot be made. Nevertheless, interesting findings can be observed from examining decision trees (see Section 7.3).

7. Decision tree analysis In cases where the logistic regression model cannot be established, I use the results of another multivariate technique. A decision tree analysis is a technique based on separating cases into segments that are as different from each other as possible. For instance, with a decision tree analysis one can easily detect segments and patterns such as ‘female bridge players with at least 5 years’ experience are likely to win a game’, or ‘students who miss more than 40 days of school a year are twice as likely to drop out’. This procedure uses appropriate algorithms that predict the class (belonging) of a dependent variable from the values of predictor variables. The choice of algorithms largely depends on the type of data. The most appropriate algorithm chosen for our analysis is Chi-square Automatic Interaction Detection (hereafter, CHAID).13 This is

13. Other algorithms have also been considered: CandRT, QUEST (for a summary, see SPSS White Paper, Answer Tree Algorithm Summary, 2005). All p-values in the CHAID algorithm

106 Justyna A. Robinson

a non-parametric stepwise regression procedure that produces splits until it gets a significant p-value for each split. The CHAID algorithm (available via Answer Tree 3.0) is used to examine factors predicting the use of senses in a cluster. It supplements logistic regression analysis, especially in cases where a logistic regression model cannot be determined. However, it does not mean that both techniques are different ways of answering the same questions. The CHAID algorithm identifies groups of speakers that use similar meanings in a similar way. Logistic regression estimates an overall effect of an independent variable (i.e. age, gender, or social class of speakers) on the use of a particular meaning cluster. Therefore, the two methods are two different ways of looking at the same data. Decision trees have been widely used in database marketing research (Chaturvedi and Green 1995:â•›245; Magidson 1994; and Rao and Steckel 1995) and in clinical science (Barrio et al. 2006:â•›595; Boscarino et al. 2003:â•›303; and Saltini et al. 2004:â•›737) for performing classification or segmentation. However, the use of decision trees in linguistics is rare (but cf. Heylen 2005; Robinson 2012a; Schmid 2010).

7.1

Decision tree of Cluster 1

I run the decision tree analysis in order to verify the importance of socio-demographic factors (summarised in Table 5) in predicting high use of Cluster 1. More specifically, this analysis shows whether there are any significant socio-demographic groups (e.g. age) or subgroups (age by gender) that use the senses in Cluster 1. The output of the analysis is presented in the form of a decision tree. The decision tree presenting a multivariate analysis of Cluster 1 is presented in Figure 6. The output presents several levels of significant splits (here two levels). Each split is based on the rule of the lowest p-value. In other words, if two splits are significant, the actual split in the decision tree follows the split according to the independent variable for which the p-value is the lowest. In the case of a tie, the rule with the higher chi-square value is listed first. In the case of another tie, the rule with lower degrees of freedom (hereafter, df) is listed first. Both chi-square and df values are displayed in the tree for each split. In the decision tree in Figure 6, the square at the top (Node 0) represents the characteristics of a variable to be analysed. There are two categories in this variable: low uses of Cluster 1 and high uses of Cluster 1. There are 39 cases of the former and 33 cases of the latter, accounting for, respectively, 54.17% and 45.83 % of the variable. These frequencies are visually presented in the form of bars at the bottom of each square (node). Low use of the cluster is represented by a darker shade of grey, whereas a high use of the cluster is represented by a lighter shade of grey. analysis were adjusted for multiple comparisons using the Bonferroni method (SPSS Answer Tree 3.0).

Quantifying polysemy in Cognitive Sociolinguistics 107



WARDCluster1 (Binned) Node 0 Category % low 54.17 high 45.83 Total (100.00)

n 39 33 72

AGEGROUP Adj. P-value=0.000, Chi-square=45.9182, df=3 upto 18 Node 1 Category % low 5.56 high 94.44 Total (25.00)

19–30 n 1 17 18

Node 2 Category % low 38.89 high 61.11 Total (25.00)

31–60

over 60

Node 3 Category % low 72.22 high 27.78 Total (25.00)

n 7 11 18

Node 4 Category % low 100.00 high 0.00 Total (25.00)

n 13 5 18

n 18 0 18

NSEC Adj. P-value=0.0412, Chi-square=6.0710, df=1 3;2 Node 5 Category % low 54.55 high 45.45 Total (15.28)

1 n 6 5 11

Node 5 Category % low 100.00 high 0.00 Total (9.72)

n 7 0 7

Figure 6.╇ Decision tree of Cluster 1

The first significant split takes into consideration the age group to which speakers belong. The statistics for the significance of this spilt are described just above the split. The statistics summary indicates that age group is the most significant predictor of using Cluster 1 (p < .001, χ2 = 45.91, df = 3). Speakers who use this cluster most frequently belong to the two youngest generations; age group exhibits high use in 94.44% of cases and age group <19–30> does so in 61.11% of cases. The results are also presented graphically: light grey bars at the bottom of Nodes 1 and 2 (squares in Figure 6 representing age groups and <19–30>, respectively) indicate the large frequency of the category representing high usage of Cluster 1. Nodes 3 and 4 (representing age groups <31–60> and , respectively) indicate the high proportion of speakers who exhibit a low usage of the senses grouped in Cluster 1. This is represented graphically by the light grey bars at the bottom of nodes 3 and 4 (Figure 6). The second significant split is based on the NSEC of speakers (p < .0412, χ2 = 6.07, df = 1). The multivariate analysis combined together NSEC2 and NSEC3 (medium

108 Justyna A. Robinson

and lower occupations) and separated them from NSEC1 (higher occupations). All speakers who are <31–60> years old and occupy higher professional positions indicate low usage of Cluster 1 (100% of low usage responses). The risk estimate for this decision tree is 0.18, which indicates that if I use the decision rule based on the current decision tree I correctly classify 82% (100% minus 18%) of cases (the calculations of risk are not presented on the decision tree). The multivariate analysis via Answer Tree 3.0 externally validates the use of Cluster 1, showing that the age of participants and, in the case of middle age speakers, their occupation, predicts high use of the senses grouped in Cluster 1.

7.2

Decision tree analysis of Cluster 2

The overall effect of socio-demographic factors in modelling high use of Cluster 2 is established using logistic regression analysis. Decision tree analysis is run in order to verify whether I could obtain any further insights into the use of Cluster 2 in relation to socio-demographic dimensions, especially in the context of determining significant subgroups of use. Figure 7 illustrates the relative importance of socio-demographic factors in predicting the use of Cluster 2 meanings. The most important factor in predicting usage is the age of participants (p = .0002, χ2 = 20.8, df = 2). Speakers of age <19–60> are grouped together as the highest users of Cluster 2. Moreover, multivariate analysis shows that in every age group, speakers living in the most affluent neighbourhoods (Postcode 3, i.e. above £142,795) or holding professional positions (NSEC1) most frequently exhibit high use of the meanings in the cluster (p < .05). Additionally, there is a distinction at the level of gender (p = .01) in the youngest age group of speakers living in the most affluent areas. In this group males are all ‘high users’ of Cluster 2 whereas females are all ‘low users’ of that cluster. Risk estimate indicates that 85% of variation can be correctly classified when applying the decision rule based on the current decision tree. To conclude, decision tree analysis validates the findings of logistic regression and provides additional evidence for the external stability of Cluster 2.

7.3

Decision tree of Cluster 3

Decision tree analysis is run in order to assess the relative importance of socio-demographic factors in predicting high use of Cluster 3 (see Figure 8). The multivariate statistical analysis shows that age group is the most significant predictor of using Cluster 3 (p < .001, χ2 = 44.43, df = 2). Speakers who use this cluster most frequently belong to the two oldest generations. All of the speakers are high users of the cluster. Speakers of age group <31–60> use this cluster in 77.78% of

Quantifying polysemy in Cognitive Sociolinguistics 109 WARDCluster2 (Binned) Node 0 Category % low user 54.17 high user 45.83 Total (100.00)

n 39 33 72

AGEGROUP Adj. P-value=0.002, Chi-square=20.6041, df=2 upto 18

19–30; 31–60

Node 1 Category % n low user 88.89 16 high user 11.11 2 Total (25.00) 18

POSTCODE Adj. P-value=0.0466, Chi-square=5.8557, df=1 <£117,543–£142,795>;below £117,543 Node 4 Category % n low user 100.00 13 high user 0.00 0 Total (18.06) 13

3:2 Node 6 Category % low user 38.46 high user 61.54 Total (36.11)

n 3 2 5

GENDER Adj. P-value=0.0105, Chi-square=6.5399, df=1 male

female n 0 2 2

Figure 7. Decision tree of Cluster 2

Node 3 Category % n low user 61.11 11 high user 38.89 7 Total (25.00) 18

NSEC Adj. P-value=0.0153, Chi-square=7.8391, df=1

above £142,795 Node 5 Category % low user 60.00 high user 40.00 Total (6.94)

Node 10 Category % low user 0.00 high user 100.00 Total (2.78)

over 60

Node 2 Category % n low user 27.78 10 high user 72.22 26 Total (50.00) 36

Node 11 Category % n low user 100.00 3 high user 0.00 0 Total (4.17) 3

1 n 10 16 26

Node 7 Category % n low user 0.00 0 high user 100.00 10 Total (13.89) 10

NSEC Adj. P-value=0.0020, Chi-square=11.6157, df=1 3:2 Node 8 Category % n low user 90.91 10 high user 9.09 1 Total (15.28) 11

1 Node 9 Category % n low user 14.29 1 high user 85.71 6 Total (9.72) 7

110 Justyna A. Robinson

WARDCluster3 (Binned) Node 0 Category % low 45.83 high 54.17 Total (100.00)

n 33 39 72

AGEGROUP Adj. P-value=0.0000, Chi-square=44.4320, df=2 31–60

upto 18;19–30 Node 1 Category % low 80.56 high 19.44 Total (50.00)

over 60

Node 2 Category % low 22.22 high 77.78 Total (25.00)

n 29 7 36

n 4 14 18

Node 3 Category % n low 0.00 0 high 100.00 18 Total (25.00) 18

POSTCODE Adj. P-value=0.0200, Chi-square=7.3649, df=1 below £117,543;above £142,795

<£117,543–£142,795>

Node 4 Category % n low 7.14 1 high 92.86 13 Total (19.44) 14

Node 5 Category % n low 75.00 3 high 25.00 1 Total (5.56) 4

Figure 8.╇ Decision tree of Cluster 3

cases (especially when they live in the highest and lowest postcodes (p = .02, χ2 = 7.36, df = 1)). Risk estimate indicates that 87.5% of variation can be correctly classified when applying the decision rule based on the current decision tree. Decision tree analysis confirms the hypothesis and provides evidence for the external stability of Cluster 3. Overall, the external validity of the cluster solution has been confirmed. The use of each of the three clusters can be predicted from the language of speakers who differ in socio-demographic terms.

8. Summary and discussion of results Having carried out HAC on the usage data, it has become apparent that each of the main three clusters can be most satisfactorily predicted from the speech of different generations (see summary in Table 8). The use of Cluster 1 (innovative speech) is best predicted from the speech of the youngest speakers, the use of Cluster 3 (historically older senses) is best predicted from the speech of older speakers, and the use of



Quantifying polysemy in Cognitive Sociolinguistics

Table 8.╇ Summary of the exploratory and confirmatory analyses of the use of polysemous adjectives Cluster 1 Cluster 2 Cluster 3

Exploratory analysis

Confirmatory analysis

More recent senses Middle senses Oldest senses

Younger generations Middle generations especially NSEC1 Older generations

Cluster 2 (historically neither old nor recent senses) from the speech of middle age groups. Additionally, the results of the statistical analysis of Cluster 2 show that speakers in professional occupations are mostly ‘high users’ of the senses grouped here. The HAC reveals that sociolinguistically meaningful semantic usage patterns emerge when usage evidence from several polysemous words is considered. It becomes apparent that the use of a selected group of senses can be most typical for a socio-demographically defined group of speakers. In other words, there are speakers for whom the same senses (e.g. fit ‘attractive’, gay ‘lame’, and wicked ‘good’) are the most salient readings of polysemous categories (fit, gay, and wicked). This finding suggests that not only individual words, such as awesome, but whole groups of polyÂ� semous adjectives currently undergoing semantic change form usage patterns that can be explained by a very similar sociolinguistic distribution. This study validates Robinson (2010a) by providing further evidence for the social grounding of polysemous conceptualisations and suggests that employing a socio-cognitive perspective in linguistic research is clearly advantageous. This study also showcases the benefits of engaging various statistical techniques to explore lexical meaning.14

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Geeraerts, D. (1989). Prospects and problems of prototype theory. Linguistics, 27(4), 587–612. DOI: 10.1515/ling.1989.27.4.587 Geeraerts, D. (1993). Vagueness’s puzzles, polysemy’s vagaries. Cognitive Linguistics, 4(3), 223– 272. DOI: 10.1515/cogl.1993.4.3.223 Geeraerts, D. (1997). Diachronic prototype semantics: A contribution to historical-lexicology. Oxford: Clarendon Press. Geeraerts, D., Grondelaers, S., & Bakema, P. (1994). The structure of lexical variation. Meaning, naming, and context. Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110873061 Geeraerts, D., & Cuyckens, H. (Eds.). (2007). Oxford handbook of Cognitive Linguistics. Oxford: Oxford University Press. Geeraerts, D., Kristiansen, G., & Piersman, Y. (Eds.). (2010). Advances in Cognitive Sociolinguistics. Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110226461 Gries, St. Th. (2006). Corpus-based methods and Cognitive Semantics: The many meanings of to run. In St. Th. Gries, & A. Stefanowitsch (Eds.), Corpora in Cognitive Linguistics: Corpus-based approaches to syntax and lexis (pp. 57–99). Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110197709 Gries, St. Th. (2007). Cluster analysis: A practical introduction with R (for Windows). Paper presented at Departmental Research Seminar, University of Sheffield. Gries, St. Th., & Stefanowitsch, A. (2006). Cluster analysis and the identification of collexeme classes. In S. Rice, & J. Newman (Eds.), Empirical and experimental methods in cognitive/ functional research. Stanford: CSLI. Hanks, P. (2000). Do word meanings exist? Computers and the Humanities, 34(1–2), 205–215. DOI: 10.1023/A:1002471322828 Heylen, K. (2005). A quantitative corpus study of German word order variation. In S. Kepser, & M. Reis (Eds.), Linguistic evidence: Empirical, theoretical and computational perspectives (pp. 241–264). Berlin: Mouton de Gruyter. DOI: 10.1515/9783110197549.241 Hosmer, D. W., & Lemeshow, S. (1989). Applied logistic regression. New York: Wiley. Janda, L. (1990). The radial network of a grammatical category – its genesis and dynamic structure. Cognitive Linguistics, 1(3), 269–288. DOI: 10.1515/cogl.1990.1.3.269 Kallel, A. (2007). The loss of negative concord in Standard English: Internal factors. Language Variation and Change, 19(1), 27–49. DOI: 10.1017/S0954394507070019 Kilgariff, A. (1997). I don’t believe in word senses. Computers and the Humanities, 31(2), 91– 113. DOI: 10.1023/A:1000583911091 Klein, D., & Murphy, G. L. (2002). Paper has been my ruin: Conceptual relations of polysemous senses. Journal of Memory and Language, 47(4), 548–570. DOI: 10.1016/S0749-596X (02)00020-7 Kleinbaum, D. G. (1994). Logistic regression: A self-learning text. New York: Springer-Verlag. DOI: 10.1007/978-1-4757-4108-7 Krishnamurthy, R., & Nicholls, D. (2000). Peeling an onion: A lexicographer’s experience of manual sense-tagging. Computers and the Humanities, 34(1–2), 85–97. DOI: 10.1023/A:1002407003264 Kristiansen, G., & Dirven, R. (Eds.). (2008). Cognitive Sociolinguistics: Language variation, cultural models, social systems. Berlin: Mouton de Gruyter. DOI: 10.1515/9783110199154 Labov, W. (2001). Principles of linguistic change: Social factors. Oxford: Blackwell. Lakoff, G. (1987). Women, fire, and dangerous things: What categories reveal about the mind. Chicago: Chicago University Press. DOI: 10.7208/chicago/9780226471013.001.0001

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Lehrer, A. (1990). Polysemy, conventionality, and the structure of the lexicon. Cognitive Linguistics, 1(2), 207–246. DOI: 10.1515/cogl.1990.1.2.207 Lewandowska-Tomaszczyk, B. (2007). Polysemy, prototypes and radial categories. In D. Geeraerts, & H. Cuyckens (Eds.), Oxford handbook of Cognitive Linguistics (pp. 139– 169). Oxford: Oxford University Press. Magidson, J. (1994). The CHAID approach to segmentation modelling. In R. P. Bagozzi (Ed.), Advanced methods of marketing research (pp. 118–159). Cambridge, MA.: Blackwell. Milligan, G. W., & Cooper, M. C. (1986). A study of comparability of external criteria for hierarchical cluster analysis. Multivariate Behavioural Research, 21(4), 41–58. DOI: 10.1207/s15327906mbr2104_5 Milroy, L. (1980). Language and social networks. Oxford: Blackwell. Milroy, L. (1987). Observing and analysing natural language: A critical account of sociolinguistic method. Oxford & New York: Blackwell. Moisl, H. L. (2009). Exploratory multivariate analysis. In A. Lüdeling, & M. Kytö (Eds.), Corpus linguistics: An international handbook (pp. 874–898). Berlin: Mouton de Gruyter. DOI: 10.1515/9783110213881.2.874 Moisl, H. L., & Jones, V. (2005). Cluster analysis of the Newcastle Electronic Corpus of Tyneside English: A comparison of methods. Literary and Linguistic Computing, 20(1), 125–146. DOI: 10.1093/llc/fqi026 Mojena, R. (1977). Hierarchical grouping methods and stopping rules: An evaluation. Computer Journal, 20(4), 359–363. DOI: 10.1093/comjnl/20.4.359 Moss, M., Wellman, D. A., & Cotsonis, G. A. (2003). An appraisal of multivariable logistic models in the pulmonary and critical care literature. Chest, 123(3), 923–928. DOI: 10.1378/chest.123.3.923 Nerlich, B., Todd, Z., & Clarke, D. D. (2003). The acquisition of get between four and ten years. In B. Nerlich, Z. Todd, V. Herman, & D. Clarke (Eds.), Polysemy: Flexible patterns of meaning in mind and language (pp. 333–357). Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110895698 Nerlich, B., Todd Z., Herman, V., & Clarke, D. D. (2003). Polysemy: Flexible patterns of meaning in mind and language. Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110895698 Norušis, M. J. (1999). SPSS regression models 10.0. Chicago: SPSS Inc. Office for National Statistics.(2000). Standard Occupational Classification. Volume 2. Coding Index. London: The Stationery Office. The Oxford English Corpus. Accessed via http://www.sketchengine.co.uk [March 2008]. Oxford English Dictionary Online. Oxford University Press. Accessed via http://www.oed.com [March 2008]. Peng, C.-Y. J., Lee, K. L., & Ingersoll, G. M. (2002). An introduction to logistic regression analysis and reporting. Journal of Educational Research, 96(1), 3–14. DOI: 10.1080/00220670209598786 Pütz, M., Robinson, J. A., & Reif, M. (Eds.). (2012a). Cognitive Sociolinguistics: Variation in cognition and language use. Special issue of Review of Cognitive Linguistics, 10(2). DOI: 10.1075/rcl.10.2.01int Pütz, M, Robinson, J. A., & Reif, M. (2012b). The emergence of Cognitive Sociolinguistics: An introduction. Annual Review of Cognitive Linguistics, 10(2), 241–263. DOI: 10.1075/rcl.10.2.01int



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Pütz, M., Robinson, J. A., & Reif, M. (Eds.). (2014). Cognitive Sociolinguistics. Social and cultural variation in cognition and language use. Benjamins Current Topics, 59. Amsterdam/ Philadelphia: John Benjamins. Rakova, M., PethÅ‚, G., & Rákosi, C. (Eds.). (2007). The cognitive basis of polysemy: New sources of evidence for theories of word meaning. Frankfurt/Main: Peter Lang. Rao, V. R., & Steckel, J. H. (1995). Selecting, evaluating, and updating prospects in direct mail marketing. Journal of Direct Marketing, 9(20), 20–31. DOI: 10.1002/dir.4000090205 Ravin, Y., & Leacock, C. (Eds.). (2000). Polysemy: Theoretical and computational approaches. Oxford: Oxford University Press. Reif, M., Robinson, J. A., & Pütz, M. (Eds.). (2013). Variation in language and language use: Sociolinguistic, socio-cultural and cognitive perspectives. Frankfurt/Main: Peter Lang. Robinson, J. A. (2010a). Awesome insights into semantic variation. In D. Geeraerts, G. Kristiansen, & Y. Piersman (Eds.), Advances in Cognitive Sociolinguistics (pp. 85–109). Berlin & New York: Mouton de Gruyter. Robinson, J. A. (2010b). Semantic variation and change in present-day English. Unpublished PhD dissertation, University of Sheffield. Available via http://etheses.whiterose.ac.uk/2232/ Robinson, J. A. (2012a). A sociolinguistic perspective on semantic change. In K. Allan, & J. A. Robinson (Eds.), Current methods in historical semantics (pp. 191–231). Berlin & Boston: Mouton de Gruyter. Robinson, J. A. (2012b). A gay paper: Why should sociolinguistics bother with semantics? English Today, 28(4), 38–54. DOI: 10.1017/S0266078412000399 Saltini, A., Mazzi, M. A., Del Piccolo, L., & Zimmermann, C. (2004). Decisional strategies for the attribution of emotional distress in primary care. Psychological Medicine, 34(4), 729– 739. DOI: 10.1017/S0033291703001260 Schmid, H. J. (2010). Decision trees. In A. Clark, C. Fox, & S. Lappin (Eds.), The handbook of computational linguistics and natural language processing (pp. 180–196). Oxford: Blackwell. DOI: 10.1002/9781444324044.ch7 SPSS (2005). Answer tree algorithm summary; SPSS white paper series. Sweetser, E. (1990). From etymology to pragmatics: Metaphorical and cultural aspects of semantic structure. Cambridge: Cambridge University Press. DOI: 10.1017/CBO9780511620904 Tabachnick, B. G., & Fidell, L. S. (2001). Using multivariate statistics. Boston: Allyn and Bacon. Tan, P.-N., Steinbach, M., & Kumar, V. (2006). Introduction to data mining. Boston: Pearson Addison-Wesley. Taylor, J. R. (1995). Linguistic categorization: Prototypes in linguistic theory. Oxford: Oxford University Press. Tummers, J., Speelman, D., & Geeraerts, D. (2004). Quantifying semantic effects: The impact of lexical collocations on the inflectional variation of Dutch attributive adjectives. In G. Purnelle, C. Fairon, & A. Dister (Eds.), Le poids des Mots: Actes des 7emes journées internationales d’analyse statistique des données textuelles (pp. 1079–1088). Louvain-la-Neuve: Presses Universitaires de Louvain. Vanhove, M. (Ed.). (2008). From polysemy to semantic change: Towards a typology of lexical semantic associations. Amsterdam: John Benjamins. DOI: 10.1075/slcs.106

The many uses of run Corpus methods and Socio-Cognitive Semantics Dylan Glynn

University of Paris VIII

Multifactorial usage-feature analysis (profile-based approach) has been successfully applied to polysemy research (Gries 2006; Glynn 2009, 2010). This chapter represents a repeat analysis of Gries (2006). The study has three aims: (i) to verify the results of the previous study; (ii) to identify limitations in the application of the statistical technique employed (hierarchical cluster analysis) in the previous study; and (iii) to demonstrate the need to account for sociolinguistic dimensions in polysemy research. The study is based on a sample of 500 occurrences of the lexeme to run, extracted in even proportions from British English and American English and from online personal journals (blogs) and conversations (American National Corpus and British National Corpus). Keywords: cluster analysis, Cognitive Semantics, corpus linguistics, polysemy, multifactorial usage-feature analysis, sociolinguistics

1. Introduction Gries’ (2006) study ‘Corpus-based methods and cognitive semantics: The many senses of to run’ counts amongst the most influential contributions to the description of polysemy in Cognitive Linguistics. It is important not because its methodology is original, nor because it is complete or extensive, nor even because of the theoretical claims it makes, but because it simply and overtly shows how corpus-driven methods can be applied to the study of polysemy. Its contribution is the combination of theory and method: two pieces of a puzzle that establish the foundations of a theoretically and empirically coherent approach to the description of semasiological structure. The current study does not challenge the theory, the method, or the results of Gries (2006), but seeks to refine each. The chapter divides into two parts. The first part considers three theoretical issues. Firstly, how can current corpus-driven methods of semantic analysis inform the description of prototype effects on conceptual

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structure? Secondly, how is the notion of lexical sense operationalised in multifactorial usage-feature analysis? Thirdly, it is argued that the study of prototype structured lexical senses must also integrate the social dimensions of language for descriptive adequacy. The second part of the chapter takes the form of a case study that repeats the semasiological analysis of run presented in Gries (2006). This case study treats three issues. Firstly, Gries’ results are largely confirmed, but it is shown that cluster analysis, the statistical method employed, produces unstable representations. It is argued that its use needs further research before it can be considered reliable. Secondly, correspondence analysis, an alternative statistical technique, is introduced. By adding a sociolinguistic dimension to the analysis, it is shown that this statistical technique is capable of representing a more complex semasiological structure. Thirdly, with the use of confirmatory statistical modelling, it is demonstrated that in order to obtain descriptive adequacy, semasiological analysis must account for sociolinguistic structure.

2. Usage-based Cognitive Semantics 2.1

Corpus-driven radial network analysis

How can quantitative corpus-driven analysis inform our understanding of polysemy and prototype structures in lexical semantics? In order to answer this question, we need to identify the aims of the endeavour. Lakoff (1990) presented the commitment to empiricism and inductive research as the gold standard of Cognitive Semantics. Radial network analysis (Lakoff 1987) and Frame Semantics (Fillmore 1985) are analytical models designed to offer an empirical means for describing meaning structure, assuming both prototype effects and encyclopaedic semantics.1 The research of the era demonstrated that: i. linguistic semantics, in the strict sense, cannot adequately account for meaning structure in language – instead, it demonstrated the need for ‘encyclopaedic semantics’; ii. necessary and sufficient conditions cannot adequately determine socio-conceptual categories – instead, it demonstrated the need for ‘prototype effects’. Although prototype category theory and the radial network analysis that employs it (Lakoff 1987) represented a necessary and substantial step toward an empirical 1. Lakoff (1987) was an early protagonist of both the theory of prototype categorization and the model of radial network analysis. Prototype theory was developed and refined by Geeraerts (1989, 1993, 1997, 2000), Taylor (1989), and Kleiber (1990). Radial network analysis was developed and formalised by, especially, Rudzka-Ostyn (1989), Cuyckens (1993), and Janda (1993).



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Cognitive Semantics, it did not quite attain that goal. Theoretically and empirically, the shortcomings are well established (Geeraerts 1993; Sandra and Rice 1995). Methodologically, radial network analysis often continued the Structuralist and Generativist tradition: i. analytically, radial network analysis assumed this structure to take the form of discrete senses or ‘nodes’; ii. empirically, radial network analysis employed introspection to determine semasiological structure. Seen from this perspective, the Cognitive Semantics era of radial network analysis made the first important steps towards empiricism, but ultimately fell short of the mark. We will now briefly consider the shortcomings of radial network analysis and then move on to consider how corpus-driven methods, especially usage-feature analysis (profile-based) corpus methods (Geeraerts et al. 1994; Gries 2003), resolve these shortcomings. There is no need to re-cover well-trodden ground. Let us assume the theoretical models of encyclopaedic semantics (Fillmore 1985; Lakoff 1987) and prototype categorisation (Rosch 1975; Lakoff 1987). The first replaces truth-conditional semantics with world knowledge. The second replaces necessary and sufficient conditions with prototype structure. These two criteria for semasiological structure accepted, we can focus on the two problems: (i) the analytical assumption of discrete senses and (ii) the methodological technique of introspection. Firstly, the assumption of discrete senses is something that is intuitively attractive. Indeed, like it is obvious that the world is flat, it would seem obvious that words have meanings and that we choose between those meanings in communication. Understood in these terms, senses are reified as discrete units. This naïve operationalisation may aid in language learning, dictionary writing and, typically, only comes amiss in inter-personal disputes. However, the evidence for discrete lexical senses is as naïvely sound as the horizon is evidence for the flatness of the world. At a broader conceptual level, Fuzzy Set Theory, a distinct yet related part of Prototype Set Theory, disposes of the notion of discrete conceptual categories. If we do not suppose that the concept associated with a lexeme is discrete, why then do we continue to assume that the sub-categories of lexical senses are discrete? Lakoff ’s (1987) study of over identifies a list of usage-features in terms of minimal perceptual distinctions expressed as image schemata. Yet rather than seeing meaning construction as the relative correlation of schema features, Lakoff continues to hunt for ‘senses’ as reified configurations of those schema features. Indeed, there appears no reason to assume the existence of discrete lexical senses and there is a growing body of research that refutes them (Geeraerts 1993; Kilgarriff 1997; Zlatev 2003; Glynn 2010 inter alia). Let us assume, therefore, that discrete senses are a useful heuristic in discussing

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semasiological structure in lexicography, but let us not assume that reified senses actually exist. Secondly, radial network analysis employed introspective methodology. Although introspection has an essential and inarguable role in language research, both for proposing hypotheses and performing analyses, with no truth-conditional tests to help determine conceptual structure, it will only ever be one part of an empirical science. Tyler and Evans (2001) have attempted to develop a ‘principled approach’ to identifying semasiological structure. This goes a long way towards minimising the risk of ad hoc categorisation using introspection. It does not, however, offer the possibility of result falsification. It is this second point that is essential. According to their own models of language, Generativists and Structuralists both had means for falsification using introspection. First, a proposed structure could be falsified by the intuition of a native speaker, whose linguistic knowledge was thought to exactly represent the grammar of a language. Second, truth-conditional semantic tests could be ‘failed’, thus establishing the lack of membership of a discrete category. However, if we assume a usage-based model of language, then neither of these possibilities is open to us, making introspection severely limited in terms of its ability to test hypotheses or falsify results. Accusing the tradition of radial network analysis of relying solely on introspection and of assuming the existence of discrete senses is, perhaps, unfair. Lakoff (1987) is careful in his wording to avoid the issue and Geeraerts (1989, 1995) explicitly develops a representational format that permits the description of polysemy without employing ‘nodes’. Moreover, there exist both corpus-driven and experimental studies in the tradition (cf. Glynn, this volume 7–38). Indeed, the corpus-driven usage-feature approach propounded by Gries (2006) goes back to the very origins of Cognitive Semantics (Dirven et al. 1982), just as elicitation-driven usage-feature analysis (Lehrer 1982) also finds itself at the origins of the theoretical paradigm. Moreover, as early as Geeraerts (1993), Geeraerts et al. (1994), and Lehrer and Lehrer (1994), in both theoretical and empirical terms, the argument for a non-reified approach to lexical senses was put forward. Therefore, even if it did not represent the main drive of research, Cognitive Semantics can be argued to have been slowly moving towards empirical methods and some in the field have long held that meanings cannot be understood as reified objects. Seen in this light, Gries (2006) is but one empirical Cognitive Semantic study in a long history. Its step was to explicitly apply corpus-driven usage-feature and multivariate statistics to the question of prototype-structured polysemy. This step, interpreting multivariate results in terms of prototype effects, is important. Empirical methods and non-reified senses may be theoretically sound, but with no way of modelling non-discrete results or coherently representing the structuring of language, the application of the method will struggle to gain ground. Therefore, a corpus-driven usage-feature methodology will build on the radial network tradition by fulfilling four aims:

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a. b. c. d.

2.2

identifying encyclopaedic semantic structure; identifying prototype effects in that conceptual structure; positing non-discrete lexical sense; positing results that can be empirically falsified.

Operationalising prototype structured non-discrete lexical senses

It is one thing to demonstrate that lexical senses are not discrete in nature, it is another question altogether to develop a rigorous means for identifying and describing non-discrete semasiological structures. Multifactorial usage-feature analysis achieves this while simultaneously and empirically accounting for prototype effects in the structure. This section explains how the method represents non-discrete senses but also how it offers corpus evidence for the prototype structuring of those senses. Is it possible to make claims about the prototypicality of conceptual structure with corpus data? Prototype structure is an analytical model; it is not an object of study. It can be used to explain different structures in language, depending on how it is operationalised. Gries (2006:â•›75) offers a “non-exhaustive” list of different operationalisations of the notion of prototype structured polysemy: intuition determined judgements of similarity and ‘goodness’; elicitation ease; diachronic evidence; centrality/predominance in a radial network, and so forth. Geeraerts (1987:â•›288) argues that there are two basic operationalisations of prototypicality. He terms these the analytic and introspective criteria. Although his debate was with the proponents of truth-conditional semantics, we can rephrase this, mutatis mutandis, as frequency-based versus salience-based prototypicality. There are many different approaches to prototype structure, but it is likely that they will all be based on one of these two operationalisations: perceptual – conceptual ‘prominence’ versus relative frequency ‘commonness’. For the semasiological variation of a term such as run, we can suppose there would be little debate that ‘fast pedestrian motion’ is the prototypical ‘sense’. From synchronic frequency of use, diachronic evidence of earliest uses, and intuition-based conceptual salience, to widely accepted theories of embodiment and primacy of perception, all evidence points unanimously to ‘fast pedestrian motion’ as the ‘central’ meaning. However, as Geeraerts (1987) shows, theoretically, there is no reason a priori to assume that prototype models using one or the other operationalisation would offer the same results. Of course, this is not to say they will not. For an example as conceptually basic as run, it is likely they will and this is why, in Gries’ (2006:â•›76) comparison of different methods, each method indicates the same prototype structure. However, if we are developing a methodology for identifying semantic structure, it is important we do not make the assumption that these different methods should necessarily offer convergent results.

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Schmid (2000) and Gries (2003) have both made claims about the relationship between frequency and conceptual structure. These claims have yet to be confirmed empirically and the authors appear to have distanced themselves from their earlier position (Schmid 2010; Gries p.c). Although frequency of occurrence surely has an important role in determining conceptual structuring, conceptual and perceptual salience are also likely to have an impact. It is, therefore, unlikely that there is a oneto-one index where more frequent equates more central. Arppe and Järvikivi (2007), Arppe et al. (2009), Tribushinina (2009) and Gilquin (2010) are recent examples of research seeking to understand how these two fundamentally different operationalisations of prototypicality interact. Eventually, we may understand how their interaction impacts upon language structure and learning, but for the moment, this has not been determined. Having established the fact that we are restricting the notion of prototypicality to one based on frequency, let us turn to the non-discrete senses that we attempt to structure in these prototype terms. It is important to understand that the two senses that Gries identifies as the most frequent, and therefore (proto)typical, were predicted by a set of usage-features (Gries 2006:â•›85). They were not identified in the data as senses per se. For this reason, it is not, in fact, these two senses, but two ‘configurations of features’, to use the terminology of Geeraerts et al. (1994), or the ‘behaviour profiles of ID tags’ to use Gries’ terminology, that are the (proto)typical structures. This is why we should not speak of the many ‘senses’ of run but of the many ‘uses’ of run, where ‘use’ is understood as a re-occurring configuration of features (or ID-tags). This does not contradict Gries’ results. On the contrary, it further emphasises their theoretical and methodological implications. Given the context of tense (past), transitivity (transitive), complement syntax (to + infinitive), and agent type (Human), Gries is able to predict, with 100% accuracy, occurrences of the lexeme that would be traditionally defined as the ‘fast pedestrian motion’ sense of run. However, what Gries has identified as a ‘sense’ is merely a tendency for this configuration of features to occur together. In a given example, one or two of these features may not be applicable, but, relatively, it would still be an example of this usage/sense (as opposed to discrete lexical sense). What this gives us is a non-discrete operationalisation of ‘lexical sense’. It is important to understand that this is independent from prototypicality. The fact that this configuration of features is so stable and predictive only means that this particular sense is relatively discrete. In other words, it has a clear behavioural profile and its usage pattern can be accurately identified. This is independent from the relative frequency of this configuration, which determines its (proto)typicality. In terms of frequency, the features of ‘past tense’, ‘transitive’, ‘finite to infinitive syntax’, and ‘human agent’ were also the most frequent. Therefore, we have a non-discrete definition of a sense of run, but also a quantification of its typicality, or frequency-based prototypicality.



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This discussion has sought to show how lexical senses can be operationalised through usage-feature analysis and how this brings in, seamlessly, the notion of frequency-based prototypicality. Yet the implications go further than providing an operational definition of prototypicality and lexical sense. These configurations of usage-features are, in fact, usage-contexts. This brings us to the question of the sociolinguistic dimension of meaning.

2.3

Multidimensional prototype effects: Form, meaning and context

Having established that corpus-driven usage-feature analysis can attain the goals set out in the era of radial network analysis, we now turn to what is argued to be an essential element of the object of study that is often side-lined. If we accept the usage-based model of language and the two operationalisations above ((i) sense – the configuration of features and (ii) prototypicality – the frequency of those configurations), the description of semasiological structure must integrate the social dimensions of language into its analysis. To appreciate why this is the case and why it is important, we must return to the question of prototype structuring. The operationalisation of semasiological structure in terms of frequency has an inherent limitation. Frequency, as a tool for determining linguistic structure, must necessarily be treated relatively. It is precisely this mistake Chomsky makes with the infamous argument that I live in New York is more common than I live in Dayton, Ohio tells us nothing of language structure. Chomsky (1964:â•›215) holds that frequency is external to language structure and will give us information about the world, or the context, instead of language itself. Although it is possible to argue that language is a mirror of the world and therefore, at some level, I live in New York is, in fact, more important in language than I live in Dayton, it would be difficult to demonstrate this to be the case for the identification of semasiological prototypicality. Instead, we can simply examine frequency relative to context. To understand how this notion applies to the polysemy, let us consider the example of Gries’ two frequency-based (proto)typical senses ‘fast pedestrian motion’ and ‘manage’. If the corpus had been children’s literature or sports magazines, ‘fast pedestrian motion’ would likely be frequent and ‘manage’ infrequent. By contrast, in the context of economic news press the ‘fast pedestrian motion’ is likely to be extremely infrequent, especially compared to the ‘manage’ sense. It should be obvious how essential the notion of context is to frequency-based studies of meaning. Are we trying to determine a typical meaning that is true for all language in all contexts? If this were possible (especially for a language as diverse as English), it is surely not possible with any corpus currently available or that will be available in the foreseeable future. Even taking a single context distinction, spoken versus written, the largest and most ‘balanced’ corpus in existence is non-representative to an unimaginable degree. The is because, in reality, the amount of spoken language greatly

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outweighs the quantity of written langauge, where the reverse is currently true of electronic corpora. In brief, the study of frequency-based prototype effects must be relative to context. We, therefore, must posit (proto)typicality structures, not for an entire language but for a language context, a specific place and time. We must avoid employing usage-based methods to describe the reductionist notion of the langue of Structuralism or the ideal speaker competence of Generativism. Our object of study is synchronically and diachronically varied – our models of conceptual structure must be sensitive to this.

3. Case study: run in America and Britain in diaries and conversation 3.1

Two corpus-based studies on ‘run’

Our current study imitates Gries (2006) in the set of usage-features (ID tags) analysed as closely as possible. The aim is not to test the results or to improve upon them through more advanced statistical analysis or a larger, more diverse sample. The aim is merely to show that even for a lexeme as culturally ‘simple’ and as socially ‘neutral’ as run, one must account for the social dimension of language in semantic analysis.2 In doing so, we will see why the statistical method he employs faces issues of reliability and we will introduce a different statistical technique. We begin with a summary of Gries’ (2006) study. Gries’ analysis is based on 815 occurrences of the lemma to run, extracted from the British component of the International Corpus of English and the Brown Corpus of American English. Approximately 400 occurrences were taken from each. These occurrences were manually analysed and categorised (using intuition) as belonging to one of 48 senses. These senses were taken from the Collins Cobuild E-Dictionary, the Merriam Webster’s American online dictionary, and the WordNet project. This categorisation in terms of dictionary senses is the first factor of the analysis. Although it is normally the goal of usage-feature analysis to determine different ‘senses’ through the identification of ‘feature configurations’ (Geeraerts et al. 1994) or ‘behavioural profiles’ (in Gries’ terminology), being able to match such configurations against

2. Kudrnáčová (2010) has also followed up Gries’ (2006) study with a more fine-grained corpus-based semantic analysis. Her study is not quantitative, but her corpus-illustrated insights will inform future research. In descriptive terms, the next step is to apply a more detailed usage-feature analysis and begin, not with dictionary senses, but a range of subtle semantic features. The senses should then be clusterings of those semantic features rather than simply matches between dictionary entries and observed occurrences.



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dictionary definitions is a useful heuristic. In Gries (2006), it is used to show how a frequency-based study can inform an understanding of prototype structure in polysemy. The 815 occurrences in Gries’ data set are analysed for a range of factors, or usage dimensions. These factors consist of the usage-features typical in this kind of methodology – formal and semantic features ranging from syntax and collocation, tense and aspect, to the semantics of the argument structure and participants. In this study, the formal factors include tense, aspect, voice, transitivity, mood, and clause type. The semantic factors include subject type, object type, and complement type. These ‘type’ features are categories such as human, concrete countable object, concrete mass noun, machines, abstract entities, organisations, locations, quantities, events, processes, etc. The dictionary senses found are exemplified and enumerated. The most frequent dictionary senses identified are that of ‘fast pedestrian motion’ (203 occurrences  / 25%, exemplified on p. 63) and ‘manage’ (101 occurrences / 12% exemplified on p. 71). The analysis and subsequent categorisation of the occurrences as dictionary senses is systematically explained by example. It is this systematic explanation that is used in the current study to repeat the analysis and to categorise the occurrences as dictionary definitions. The current study is based on 500 occurrences of run, 250 each of British and American English, subdivided again into 125 examples each from conversation and online personal diaries. The sample was restricted to this relatively small number due to practical reasons – usage-feature analysis is laborious and resource consuming. The point of the study being to investigate the need to include sociolinguistic parameters in polysemy research, the improved descriptive accuracy afforded by increasing this number would not substantially improve the ability to demonstrate the point. Also, the methods under investigation must be shown to produce coherent results with small numbers, since, for the same practical reasons, the usage-feature (or profile-based) method tends to deal with small samples. The British and American diary examples were taken from the LiveJournal corpus, developed by Dirk Speelman, at the University of Leuven, and the conversation examples were taken from the British National Corpus and the American National Corpus. The usage-feature analysis is replicated using the same dictionary senses employed by Gries and the same range of formal and semantic usage-features. An aside should be made here. Despite the fact that Gries more than adequately demonstrates the principle of the method, descriptively, the study is preliminary (Gries 2006:â•›81). The obvious question of why one would focus on dictionary senses (instead of solely usage-features, or ID-tags, to use Gries’ terminology) can be answered by the fact that the study’s aim is to show how prototype structure can be handled with the method. Nevertheless, in terms of descriptive adequacy, this option is far from ideal. Moreover, as the author stresses himself, the size of the sample is too small to properly apply multivariate statistical analysis. It is not that the sample is small in itself, but the type-token (or perhaps ‘sense-token’) ratio is not acceptable

126 Dylan Glynn

for multifactorial analysis. Gries repeatedly stresses this point, but it should be added that this problem is compounded by the fact that the study is not restricted to run, but includes all the verb particle constructions based on run. Arguably, this makes the study partially one of near-synonymy instead of polysemy. Many of the senses identified are determined formally by the combination of the verb and the particle. Verb particle constructions in Germanic, just like the prefixed verb constructions in Slavic (see Fabiszak et al., this volume 223–252), challenge the distinction between synonymy and polysemy. In any case, many of the senses in question are both formally and semantically distinct. A true test of the usage-feature method for the study of semasiological variation is when that variation is not linked to any overt, or obvious, formal distinction. By excluding the verb particle construction, Gries’ study would have included less semantic variation but also less formal variation for ‘automatically’ determining it. This does not detract from the goal or the results of Gries’ study, but future work should take such questions into account. Note that the current study also uses dictionary senses as one of its analytical factors and includes the particle constructions. This is done solely to permit a comparison with Gries. Table 1 lists the most common senses in the current study, compared with the figures from Gries (2006). The list of senses applied in this study was determined by the senses submitted to the hierarchical cluster analysis in Gries (2006:â•›82). For some of these senses, the number of occurrences (supplied in the preceding section, Gries 2006:â•›63–73) are not known. Although the reasoning behind the categorisation of the examples as dictionary definitions is reasonably clear, taxonomical issues of hyperonymy in the discussion occasionally mean that the number of occurrences for a given sense is not stated. This is the case for ‘function’ vs. ‘execute’ and ‘manage’ and for ‘free motion’ versus ‘motion’ and ‘fast motion’. The application of Gries’ dictionary senses to our data was reasonably straightforward, using the examples and explanations included in the study. There were, of course, some classification issues. For example, what constitutes ‘fast’ in ‘fast motion’? Table 1.╇ Most frequent dictionary senses Dictionary sense

Current study

Gries (2006)

‘fast pedestrian motion’ ‘escape’ ‘motion’ ‘fast motion’ ‘free motion’ ‘execute’ ‘in charge of ’ ‘manage’ ‘function’ ‘become used up’

160 (32%) â•⁄ 57 (11.5%) â•⁄ 23 (4.5%) â•⁄ 17 (3.5%) â•⁄ 17 (3.5%) â•⁄ 18 (3.5%) â•⁄ 16 (3%) â•⁄ 25 (5%) â•⁄ 17 (3.5%) â•⁄ 26 (5%)

203 (25%) â•⁄ 32 (4%) â•⁄ 24 (3%) â•⁄â•⁄4 (0.5%) â•⁄â•›– â•⁄ 28 (3.5%) â•⁄ 24 (3%) 101 (12%) â•⁄â•›– â•⁄ 14 (2%)



The many uses of run 127

The large difference in the number of occurrences on this point suggests that there may have been a difference in coding for this sense. Nevertheless, assuming there is bound to be some analytical variation, the results are reasonably comparable. This is especially true given the small size of the samples and the differences between the corpora. The principal differences are ‘become used up’ and ‘escape’, which are more frequent in this study, and ‘manage’, which is substantially more frequent in Gries’ study. For this final difference, even if we allow for some confusion over the semantically similar categories of ‘execute’, ‘in charge of ’, ‘function’, and ‘manage’, the difference is marked. We can suppose that such differences are a result of register. Indeed, this is precisely the problem with frequency-based studies addressing (proto)typicality. Thematic variation, or variation in ‘topic of discourse’, can have a substantial effect, even upon coarse-grained analysis of semasiological structure. There is no need to examine such differences and similarities further. Both samples are small, with a high type-token ratio, which means statistical significance would tell us little. Remembering that the ultimate point is to show that frequency-based prototype structures are context dependent, it is sufficient to show that the overall study is comparable to that of Gries’. Below is an exemplified list of the most common senses. The examples are all extracted from the LiveJournal Corpus sample under investigation. For further exemplification and discussion, see Gries (2006:â•›63–73). (1) ‘fast pedestrian motion’ I want to like run into a bathroom at school and cry my eyes out whenever i see him. (2) ‘escape’ does anyone have about $400 laying around, i think i want to run away to Las Vegas for a few days, lol. (3) ‘motion’ Action Cat is really starting to like the new kitty, who I call Buddy cause he has yet to receive a formal name. They run around and play all the time now and it’s really cute. (4) ‘fast motion’ Hang on, till I get the brake on, or you’ll run into the river. (5) ‘free motion’ we’ve made three different trips … the group of friends that i run around with. (6) ‘execute’ you know like it’s easier for you to go and run a program you know through the disk.

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(7) ‘in charge of ’ there’s er it was for the er cat scanner and it was run by the Co-Op it was, it was just oh I saw that sign outside. (8) ‘manage’ I am now the new landlord of the rose and crown pub which mama used to run. (9) ‘function’ they said that uh cars would cost two dollars and they would run forever. (10) ‘become used up’ Well, it doesn’t do so bad. It’s usually cigs we run out of not petrol.

3.2

Semasiological clustering without social dimensions

Gries (2006:â•›81–82) submits all the senses (minus ‘idiomatic’ ones) to an agglomerative hierarchical cluster analysis (see Divjak 2010; Divjak and Fieller, this volume, 405–442, for an explanation of the technique). The senses are clustered using the full range of features (Gries 2006:â•›fn. 19, p. 94). The results of the cluster analysis are reasonably coherent, especially given the number of senses versus the number of examples and the number of usage-features. There is some degree of intuitively sound clustering, which could be re-interpreted as prototype structuring. Nevertheless, there is also a large amount of clustering that does not appear semantically motivated. Gries (2006:â•›81, 83) accepts this and suggests that the data sparseness is, at least partially, to blame. Replicating the procedure gives similar results – a reasonable degree of intuitively sound clustering but also a reasonable amount of ‘noise’ in the dendrogram where clusters make little or no sense. For the sake of brevity, we will not present the dendrogram, but instead present the cluster results obtained by simplifying the data and limiting the usage-features used to cluster them. In order to obtain a more coherent clustering of senses, rare senses were omitted. Also, the two most frequent senses, ‘fast pedestrian motion’ and ‘escape’, were omitted. These two senses were found to systematically dominate the clustering, rendering the relations between the other senses difficult to discern. We can suppose that these two senses were so distinct in usage that the clustering could not model their relationship and more subtle relations of the other senses simultaneously. This effect was found, regardless of the distance measure used. A combination of three factors is used to cluster the dictionary senses. Following Gries’ study, these factors consist of Transitivity, Subject ‘Type’ Semantics and Object ‘Type’ Semantics. Figure 1 presents the results using the simplified range of senses and these three factors. It is produced using the Euclidean distance measure (the simplest

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free motion

motion

fast motion

in charge of

manage

execute

become used up

meet free motion metaphoric

increase

motion metaphoric

check/rehearse

motion into difficulty

broadcast

campaign

caused motion

be

copy

extend temporarily

flow

exist in abundance

function

diffuse

10 0

5

Height

15

20

Cluster dendrogram

hclust (*, "average")

Figure 1.╇ Hierarchical cluster analysis of dictionary senses. Distance matrix – Euclidean; agglomeration method – ‘average’

distance measure) and ‘average’ as the agglomeration method (a common agglomeration method). We must interpret such plots with caution. Even having removed the rarely occurring senses, some of the remaining senses are still infrequent, for example – ‘caused motion’, ‘motion into difficulty’ and ‘campaign’. Nevertheless, the overall picture seems reasonably coherent. Examining the dendrogram, two broad sense clusters emerge, clustered by the right and the left branches. The left branch includes most of the abstract senses, with perhaps the exception of ‘function’, which is less abstract. Note, however, that the analysis has ‘function’ and ‘diffuse’ as quite distinct from this abstract cluster. It appears that the analysis has trouble incorporating these senses. The intuitive adequacy of the model is left up to the reader, but it is worth pointing out that the literal motion senses are coherently grouped together as well as the control senses (‘manage’, ‘in charge of ’, ‘execute’). However, the place of ‘become used up’ with these two groupings of senses is not clear, nor is the relationship between the ‘control’ senses and the literal motion senses. There does exist an internal logic to the cluster of abstract senses. The metaphoric motion senses are grouped together, just as are the ‘spread’ senses of ‘flow’, ‘exist in abundance’, and ‘extend temporarily’. The other groupings are not illogical, but apart from representing abstract or metaphoric meanings of run, they share little semantically.

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Gries (2006:â•›fn. 19, pp. 93–94) found that changing the distance matrix and/or the agglomerating method did not alter the results. This was not the case with the current data set. Experimenting with different agglomeration methods greatly improved or worsened the interpretability of the dendrogram and, occasionally, the actual results of the cluster analysis. Likewise, different distance measures also produced different results. This could, perhaps, be a sign of the instability of the analysis – attempting to cluster 23 senses based on a sample of 500 is far from an ideal condition in multivariate statistics. Figure 2 presents the results of the Canberra distance matrix. It is clustered with the Ward agglomeration method. The different agglomeration methods did not change the results for the Canberra matrix, only legibility. The Ward method gave the clearest dendrogram. In Figure 2, again we see two main branches. At first, the overall branching and clustering of the senses appears more coherent than those produced using the Euclidean distance measure. However, if we inspect the clustering more closely, intuitive semantic coherence is not wholly systematic. At the coarse-grained level, we have lost the clear distinction between relatively concrete uses such as ‘manage’ and ‘literal motion’ versus ‘metaphoric motion’ as well as the extending and disseminating senses. For the four sub-clusters, there is a little more semantic coherence. The first sub-cluster of ‘execute’ and ‘manage’ is intuitively sound. The second is also coherent,

execute manage free motion motion motion metaphoric fast motion in charge of difficulty campaign meet exist in abundance extend temporarily be copy flow rehearse caused motion free motion metaphoric diffuse function become used up broadcast increase

10 0

5

Height

15

20

25

Cluster dendrogram

dist_mat hclust (*, "ward")

Figure 2.╇ Hierarchical cluster analysis of dictionary senses. Distance matrix – Canberra; agglomeration method – ‘Ward’

The many uses of run 131



save for the sense ‘in charge of ’. This is semantically related to ‘execute’ and ‘manage’ and, therefore, given the small sample, is more or less in the ‘correct’ branch. The next sub-cluster of ‘difficulty’ (run into difficulty), ‘campaign’ (run for election), and ‘meet’ (run into a friend) is semantically coherent, given a broad interpretation of ‘campaign’ that includes meeting people and difficulties. This is not as unlikely an interpretation as one might first suppose. Recall that the different semantic types of objects and subjects determine these sense clusters. Moving to the right across the clusters, the next sub-cluster of ‘exist in abundance’ and ‘extend temporarily’ is intuitively coherent. However, the rest of the group appears semantically heterogeneous. The last cluster on the right, although distinct with a long branch stemming from the rest of the dendrogram, also lacks obvious semantic coherence. Although one is able interpret semantic structure here, it is not self-evident why ‘diffuse’ and ‘function’ or ‘broadcast’ and ‘increase’ should group together. The point of both this small study and Gries’ is merely to consider two methodological possibilities. In light of this, the fact that the two distance matrices produced different clusterings raises important methodological questions. Standards and checks for appropriateness need to be developed before the use of cluster analysis can be relied upon to determine frequency-based semasiological structure.3

3.3

Semasiological clustering with social dimensions

Before we consider the effects of social variation on semantic structure, it must be stressed that one would not expect to find substantial variation with these data and for this lexeme. Therefore, even a small degree of variation is a sign of the extent of the issue. There are four reasons for this: 1. In terms of cultural variation, run is a ‘simple’ lexeme. It is the kind of lexeme where one would not expect variation across dialects. 2. In terms of register, run is a ‘neutral’ lexeme, not belonging to either formal or informal registers. It is the kind of lexeme where one would expect relatively little variation across text types. One exception to this might be the two central senses of ‘fast pedestrian motion’ versus ‘manage’, where text type would be expected to show variation in use.

3. Divjak and Gries (2006:â•›37) state that the Canberra distance matrix is best suited to small cell counts, such as we have here. Gries (2009:â•›317) says the choice is subjective. Gries and Stefanowitsch (2010:â•›79) employ the Manhattan distance matrix, citing Levy et al. (1999) as justification. Levy et al.’s study compares five distance matrices but not Canberra. It seems that the question of how the choice of distance matrix affects the results needs to be investigated systematically. Divjak and Fieller (this volume, 405–442) also discuss the range of methods.

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3. Although the differences between American and British English are substantial, the dialects remain mutually intelligible for most speakers of both varieties, especially in written language and educated speech. In other words, the difference between American and British English is not that great, making dialect a good test case. 4. Although there are certainly differences between the registers of spoken conversation and online personal diaries, the style of the latter is also extremely informal and is also dialogic. Unlike traditional diaries, authors here engage in discourse with readers and the style of the genre is conversational and casual. Therefore, just as for dialect variation, one would not expect substantial differences in the text type variation. We could repeat the clustering presented in the previous section for the two dialects and the two registers and compare the clustering. However, the cluster analyses on the full data set are obviously unstable and halving the data would make any multivariate analysis impossible. Let us begin, rather, with a Chi-squared test of independence that identifies statistically significant differences along the lines of register and dialect. A Pearson’s Chi-squared test of independence for dialect identifies significant differences between the British and American data for the dictionary senses (p = 0.001263). The residuals show that ‘become used up’ but also ‘escape’ and ‘fast motion’ are more typical of the British use, and ‘meet’, ‘increase’ but also ‘execute’ and ‘diffuse’ of the American use. Register also reveals a significant difference (p = 6.376e-05) with the residuals showing that ‘escape’, ‘fast pedestrian motion’, ‘metaphoric motion’ are associated with the diaries, and ‘caused motion’, ‘diffuse’, ‘execute’, ‘function’, and ‘increase’ with the conversation data. Having established that there is significant variation, let us move to trying to capture how that variation interacts with the semasiological structure. Although cluster analysis is a powerful tool for identifying how the different senses are related, it cannot show how register and dialect affect those relations. Ideally, given enough data, we could label the occurrences of the different senses for dialect and register and even both simultaneously. The cluster analysis would then show the relations between the different senses relative to the social factors, clustering, for instance, ‘fast pedestrian motion BrEng’ and ‘fast pedestrian motion AmEng’ etc. Although a straightforward procedure, for the number of senses involved, this would require a much larger data set. Another statistical technique, explained in Glynn (this volume, 443–485), is correspondence analysis. A multivariate and exploratory technique similar in many ways to cluster analysis, it visualises relations between all the factors considered rather than just one factor. Figure 3 presents the results of a binary correspondence analysis, which examines the interaction of dialect, register, and dictionary sense.

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Cause Motion Flow Extend Time

0.5

Use up

BrE.Conv

Function Motion Manage

Escape

Rehearse Fast Ped. Motion

Increase

AmE.Conv Diffuse Execute Difficulty

AmE.Blog Met. Motion

–0.5

0.0

Fast Motion BrE.Blog Free Motion Become Broadcast

Meet

Campaign

Extend Space

–1.0

Copy

–0.5

0.0

0.5

1.0

1.5

Figure 3.╇ Binary correspondence analysis of register, dialect, and dictionary sense

The first two dimensions of the analysis explain 87% of the variation (inertia), which is a relatively stable analysis. Immediately, it is visible that American Conversation (AmE.Conv) is distinct in use relative to the dictionary senses, dominating the right two quadrants of the plot on the central axis line. The senses ‘increase’, ‘diffuse’, and ‘motion into difficulty’ (Difficulty) are distinctly and highly associated with the American conversation data point on the right of the plot. In the bottom half of the plot, we find a range of senses distinctly associated with the American diary genre (AmE.Blog). The senses ‘campaign’, ‘copy’, and perhaps ‘metaphoric motion’ (Met. Motion) are highly and distinctly associated with American diary use. ‘Meet’ and ‘extend space’ are likely to be associated with American English but are not distinct to either register, lying between the two data points for American Diary and American Conversation. Moving to the British uses, the plot becomes more difficult to interpret. The analysis suggests that there is less register variation in the British sample, the two data points British Conversation (BrE.Conv) and British Diary (BrE.Blog) both lying in the same top left quadrant. Nevertheless, the dialect variation is clear – the senses ‘flow’ and ‘extend time’ are highly and distinctly associated with the British use. Other senses, such as ‘use up’, ‘cause motion’ and ‘escape’, are also relatively associated with British use, but this association is not distinctive.

134 Dylan Glynn

0.5

S.Cause Motion

S.Flow S.Use up

S.Function

0.0

S.Increase

S.Diffuse

S.Execute

Reg.Conversation Lang.BrEng S.Manage S.Free Motion S.Motion S.Broadcast S.Become S.Fast Motion

S.Extend Time

S.Fast Ped. Motion

S.Difficulty

S.Escape S.Rehearse

Lang.AmEng

Reg.Blog

S.Meet

–0.5

S.Extend Space

S.Metaphoric Motion S.Campaign

S.Copy

-1.0

-0.5

0.0

0.5

1.0

Figure 4.╇ Multiple correspondence analysis. Burt matrix, method ‘adjusted’

In order to obtain a clearer picture of the interactions at hand, let us submit the same data to a multiple correspondence analysis. The binary analysis, in Figure 3, gives us a reliable and stable representation of the associations, but it cannot capture interactions between dialect and register. This is because these two factors were concatenated in order to produce a two-dimensional contingency table for the analysis. We can expand that table into a three-dimensional table and apply multiple correspondence analysis. The results are more difficult to interpret and can be less stable (less accurately capturing and representing associations in the data). However, the plot in Figure 4 was produced using the recently developed ‘adjusted’ method which addresses both issues of stability and clarity. Fortunately, the results are clear and the explained inertia is 86.7% (Dim. 1: 61.2%, Dim. 2: 25.5%), which for a adjusted multiple correspondence analysis, using Burt matrices, is a stable result (Greenacre 2007). Further details on and an explanation of the technique of correspondence analysis, and its limitations and strengths, can be found in Glynn (this volume, 443–485). The results presented in Figure 4 largely reflect the binary correspondence analysis, but by treating the factors of dialect and register independently, the analysis affords us a clearer depiction of their interaction. Each of the four quadrants is characterised by one of the four sociolinguistic features: the top right – British dialect (Lang. BrEng); the bottom right – diary register (Reg.Blog); the bottom left – American dialect (Lang.AmEng); and the top left – conversation register (Reg.Conversation).



The many uses of run 135

We see that senses, such as ‘execute’ and ‘diffuse’ between the American data point and the Conversation data point, are common to these two usage dimensions. The senses ‘campaign’ and ‘metaphoric motion’, lying between the American data point and the register of diary (Reg.Blog), are common to these dimensions. The senses ‘beyond’ the American data point, relative to the British dialect data point in the top right-hand quadrant, are neutral with regard to register, but are distinctly American in contrast to British. These senses include ‘extend in space’, ‘copy’, and ‘meet’. Repeating the interpretation, beginning from the top right-hand quadrant and the British data point, we see that ‘use up’ is distinctly typical of British conversation and that ‘fast motion’ is typical of British diaries. The senses ‘flow’ and ‘extend time’ are less associated with a given register, but are distinctly British, relative to the American data. Again we see that register variation for the British use is less important. Finally, note the position of ‘manage’ and ‘fast pedestrian motion’. These data points, along with some other senses, are in the centre of the plot. The senses located in the centre are the senses that are not affected by either of the two sociolinguistic usage factors. These senses are central, but not just in the way that Gries (2006) argued. Although still understood in terms of frequency, we now also have two usage dimensions, dialect and register. Not only are these senses among the most frequent, they are among the senses least affected by context. This is a crucial refinement to the frequency operationalisation of (proto)typicality – uses that that are common (frequent) across all contexts are more central to the meaning of a lexeme. This finding is equally as important as discerning which senses are typical of specific contexts. Gries (2006) stresses that the small sample means that the study can only be seen as a methodological test, rather than a fully descriptive analysis. For these reasons, the statistical techniques employed are only exploratory. He suggests the use of configural frequency analysis to identify statistical significance in the results, allowing one to determine which correlations are not chance, and which may be simply a result of the small sample. Although configural frequency analysis would be an excellent choice for this, it requires more data than is available in either study. It also follows that, with more data, log-linear analysis or multinomial logistic regression would be even better, giving not only statistical significance but also predictive strength to the model. Such analyses are now within the capabilities of corpus-driven research, but require a larger scale analysis. Moreover, before such an analysis is undertaken, the identification of senses must be better operationalised. The analysis of the usage-features must be found to cluster into senses and then these multivariate senses must be shown to be statistically significant. With senses based on clusters of usage-features (ID Profiles), rather than revealed by matching occurrences with dictionary entries, we can then return to the clustering. This step in corpus-driven polysemy research has begun (Glynn 2009, 2010, in press), but remains at the initial stages. Once we are armed with the analytical tools to identify multivariate senses (rather than dictionary senses), then we

136 Dylan Glynn

need to progress to modelling the semasiological structure and the prototype effects, using more advanced statistical procedures such as configural frequency analysis and log-linear analysis. The present purposes are to demonstrate that sociolinguistic effects must be integrated into the study of prototype structuring. To these ends, let us submit the data to binary logistic regression. Explained in Speelman (this volume, 487–533), logistic regression is a confirmatory multivariate technique that allows us not only to determine which of the usage features and/or dictionary senses are significantly associated with either of the sociolinguistic factors, but it also enables us to determine how important that association is.

Logistic Regression – Dialect

Let us begin with dialect. Three logistic regression models are reported: a multiple model based on usage-features excluding dictionary senses (Model 1); a second multiple model that includes dictionary senses (Model 2); and a simple model with the dictionary senses as a sole predictor variable (Model 3). The models are all checked for multicollinearity, and factors producing a variance inflation of more than 2.5 are removed.4 Moreover, the models are checked for singularity with a Kappa calculated condition number – any model with a value higher than 6 is rejected.5 The strict check on variance inflation and singularity assure an orthogonal model. The models are also checked for influential observations as well as overfitting, neither of which is a problem. Outliers are not removed. In a backward elimination of factors, model selection was based on significance values and the Akaike’s information criterion (AIC), not on predictive strength.6 For readers unfamiliar with logistic regression, the testing of the model and criteria for acceptability were extremely strict, making the results as conservative as possible. For the sake of brevity, some non-significant levels are omitted, indicated by ‘…’. Positive coefficients predict British English and negative coefficients (“–”) predict American English. Since we are comparing models, only the coefficients and some

4. Some authorities indicate a variance inflation factor of 10 to be acceptable (DeMaris 2003:â•›517; Dodge 2008:â•›96; Chatterjee and Hadi 2006:â•›238; Marques de Sá 2007:â•›307; Speelman p.c.), other authorities are non-committal (Faraway 2002:â•›117–120; Maindonald and Braun 2003:â•›201–203). Glynn (2010) and Speelman (this volume, 487–533) opt for a maximum inflation value of 4. Szmrecsanyi (2006:â•›215) notes that even values as low as 2.5 can be a cause for concern. Multicollinearity is a serious issue in regression and can lead to Type I errors. Since we do not necessarily understand the relationship between many of the factors in our model, a maximum VIF of 2.5 is used to determine which factors can be combined in the model. 5. Baayen (2008:â•›182) states that a condition number between 0 and 6 indicates no multicollinearity and 15 indicates a medium degree. 6. The AIC score helps compare the parsimony of different models. The scores are relative and a lower number indicates a more parsimonious model.

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Table 2.╇ Logistic regression models for dialect Coefficients

Model Statistics

Transitivity – Transitive Tense – Past Tense – Present Aspect – Progressive Aspect – Simple Mood – Imperative Mood – Interrogative Clause Type – SubPronoun Clause Type – SubNP Clause Type … Subject – Human Subject – Locations Subject – Machine Subject … Sense – Use Up Sense – Diffuse Sense – Execute Sense – Campaign Sense – Fast Motion Sense – Flow Sense – Increase Sense – Meet Sense … d.f. G2 C Nagelkerke R2 Bootstrapped R2

Model 1

Model 2

Model 3

â•⁄0.596619* â•⁄0.658282* â•⁄0.387003 â•⁄– â•⁄– â•⁄0.533600 â•⁄1.048808* –1.807732º –0.490190 â•⁄… –1.446052º –0.289667 –1.564679* â•⁄… â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– 20 41.39** â•⁄0.668 â•⁄0.112 â•⁄0.0138

â•⁄0.487405º â•⁄– â•⁄– â•⁄0.178450 â•⁄0.542254º â•⁄0.392821 â•⁄1.094234* –2.225015 –2.225015º â•⁄… â•⁄– â•⁄– â•⁄– â•⁄– â•⁄0.955200º –1.364175º –1.196454* –1.289732 â•⁄0.792536 â•⁄1.405831 –2.287706* –1.566828* â•⁄… 27 70.71*** â•⁄0.716 â•⁄0.186 â•⁄0.0435

â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄0.94852* –1.65945* –1.14862* –1.65945 â•⁄0.82546 â•⁄1.55943 –2.12945* –1.59046* â•⁄… 20 60.16*** â•⁄0.671 â•⁄0.156 â•⁄0.057

essential model statistics are reported.7 In Table 2, the coefficients for each of the levels (usage-features) are listed with the alpha levels (º p < 0.1, * p < 0.05, ** p < 0.01, *** p < 0.001).8 The degrees of freedom (d.f.), Log Likelihood chi-squared or deviance measure (G2), the C index or coefficient of concordance statistic (C), the Nagelkerke 7. The R output includes the estimated standard errors and the Wald Chi square, or z-test (z) obtained by dividing the coefficient by its error. See Speelman (this volume, 487–533) for a detailed explanation. The output for a logistic regression analysis, using rms in R, is explained in Baayen (2008:â•›2004) and Gries (2009:â•›297). See also Chatterjee and Hadi (2006). 8. Significance levels are primarily used for model selection. Caution should be taken in interpreting them relatively (Faraway 2002:â•›126).

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pseudo R2 (N. R2), and a bootstrapped estimation of the pseudo R2 (Boot. R2) are included as model statistics. Models 1 and 2 are the result of a backward elimination of a full model without and with dictionary senses, respectively. Object and complement usage-features were, interestingly, found to be not at all significant. This could be due to the large amount of features (levels) belonging to these factors. A much larger data set is needed to handle such complexity. For these same reasons, it was not possible to examine interactions. Moreover, in order to improve the model, some small cells were removed for the variable of dictionary sense. This weakens predictive strength, but improves overall parsimony of the model. In model 2, entering subject semantics and dictionary senses simultaneously shows signs of multicollinearity. The subject is, thus, omitted. Although models 1 and 2 show some significant features, we are not interested in finding differences between the two dialects, but in finding differences in the semasiological structuring of the two dialects. Since we do not know how the different formal usage-features interact in terms of semasiological structure, it is difficult to interpret models 1 and 2 in these terms. It is clear, however, that these usage-features do not offer a predictive model, which reassures us that there are no ‘obvious’ differences that would superficially distinguish one dialect from the other in a trivial manner. Model 3, on the other hand, is simple to interpret. If we recall the residuals of the Chi-squared test shown above, we see confirmation of those results, but this time with statistical significance as well as a score indicating effect size. For the American data, the sense ‘increase’ is by far the most distinctive feature, followed by ‘execute’, ‘meet’ and then ‘diffuse’. ‘Campaign’ is not statistically significant (p-0.1338), but it would almost surely become significant with more data. We saw in the correspondence analysis that ‘campaign’ is highly associated with American usage and it is known that this sense is effectively unique to the American dialect. In British English, the verb stand for an elected post is more typical than run for an elected post. The sense ‘motion into difficulty’ behaved similarly to ‘campaign’, but was removed due to its small count. With the current data set, five of the senses are statistically significant. This confirms what we saw in the Chi-squared test and correspondence analysis. In the logistic regression, the coefficients give us a rank of influence similar to the Pearson’s residuals obtained from the Chi-squared tests. This kind of ranking is exactly the type of information needed for understanding the effects of such dialect variation on prototype structuring. However, none of the five senses in question is a particularly strong predictor, though the sense ‘increase’, associated with American usage with a coefficient of 2.1, is quite strong. At the other end of the spectrum, ‘become used up’ predicting British English is a relatively weak predictor. Ranked in order of influence, we now know that ‘increase’, ‘diffuse’, ‘meet’ and then ‘execute’ are distinctly American in use, where only ‘become used up’ is a significant predictor for British usage.



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The statistics presented beneath the table of coefficients show that the model is not predictively strong. A fourth model, without the infrequent senses of ‘campaign’ and ‘motion to difficulty’, produces comparable statistics (G2: 57.18, d.f. 18, R2: 0.151, C: 0.667). The poor predictive strength of the model, of course, is to be expected. If the differences between the dictionary senses in themselves were so great that one could predict one dialect over the other with this information alone, we would have such obvious semasiological variation that this study would not be needed. What the logistic regression gives us is a clear and specific picture that, although all the senses are possible in both dialects (‘campaign’ aside), the differences in frequency of occurrence are great enough that even with a small data set, significant differences can be identified.

Register effects

Just as for the dialect effects, we will consider three models: a single regression analysis of the dictionary senses and two multiple logistic regressions. Table 3 summarises the models. Model selection followed the same criteria as for the previous logistic regression. Positive coefficients predict conversation register and negative coefficients predict diary register. Just as for the regression analyses above, none of the models are predicatively strong. This means that, for the features analysed, we cannot predict whether an example will be one dialect or the other or one register or the other. This does not mean, however, that we cannot interpret the table of coefficients to see where significant differences do exist. In model 1, we have an interesting selection of significant Subject Semantic and Object Semantic categories. The interaction of such features is likely to represent the usage-configurations of profiles that could be understood as non-reified senses. Evidence for this can be found in the high collinearity that is produced when these variables entered into the regression with dictionary senses. Of course, further research is needed to ascertain what these configurations would consist of. Many individual (as opposed to configurations of) Subject and Object Semantic categories could be seen as operationalisations of different dictionary senses in their own right. For example, the Object Semantic feature of ‘machine’ would be a reasonable operationalisation of the sense ‘operate’ (or ‘execute’), just as the Subject Semantic category of ‘machine’ would indicate ‘function’. We see here highly significant and important predictors of the register conversation. This is the kind of extra-linguistic effect on frequency-based prototype structure we referred to in section 1, when we compared run ‘manage’ and run ‘fast pedestrian motion’. Rather than dictionary senses, we see how different semantic features are interacting with other dimensions of use. Although not predicatively strong, model 1 offers interesting insights into the kind of semantic variation we have between the two registers.

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Table 3.╇ Logistic regression models for register Usage – feature (levels)

Model 1

Model 2

Model 3

Tense – Past Tense – Present Clause Type – Subj. NSub Clause Type – Subj. Pronoun Clause Type – Subj. NP Subject Sem. – Human Subject Sem. – Location Subject Sem. – Machine Subject Sem. – Quality Subject Sem. … Object Sem. – Animate Object Sem. – Concrete Count Noun Object Sem. – Concrete Mass Noun Object Sem. – Events Object Sem. – Human Object Sem. – Location Object Sem. – Machine Object Sem. – Organisation Object Sem. – Quantity Object Sem. – NA Object Sem. … Sense – Become Used Up Sense – Diffuse Sense – Escape Sense – Execute Sense – Function Sense – In Charge of Sense – Increase Sense – Manage Sense – Meet Sense – Motion to Difficulty d.f. G2 C Nagelkerke R2 Bootstrapped Nagelkerke R2

–0.57321º â•⁄0.0518 â•⁄– â•⁄– â•⁄– â•⁄1.21485º â•⁄2.30656* â•⁄2.53738** â•⁄2.56357* â•⁄… â•⁄ 2.61971 + â•⁄1.92852** â•⁄2.12490** â•⁄ 2.09651 ** â•⁄1.60972* â•⁄1.68428** â•⁄2.26511** â•⁄2.30594 â•⁄1.65779º â•⁄1.17705º â•⁄… â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– 25 67.45*** â•⁄0.697 â•⁄0.176 â•⁄0.064

â•⁄– â•⁄– –1.12794* –0.46960 –0.67469* â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄1.12163* â•⁄2.09507** –0.60738º â•⁄1.43060* â•⁄1.92870** â•⁄1.36388* â•⁄2.77507* â•⁄0.82270º â•⁄0.73929º â•⁄1.88122* 26 82.31*** â•⁄0.721 â•⁄0.211 â•⁄0.077

â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄– â•⁄0.9639* â•⁄1.9373* –0.4453 â•⁄1.4265** â•⁄1.8684** â•⁄ 1.1164 * â•⁄2.4073* â•⁄0.5691 â•⁄0.4457 â•⁄1.8320* 19 63.95*** â•⁄0.69 â•⁄0.167 â•⁄0.063



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Models 2 and 3 differ little. The addition of other factors in the multiple regression of model 2 merely identifies some syntactic variation. The dictionary senses again confirm what we saw in the Chi-squared test, although we now see that none of the senses are significantly associated with the diary register. We see also that the senses ‘increase’, ‘motion to difficulty’ and ‘diffuse’ are the senses most highly associated with conversation.

4. Summary This study examined the semasiological variation of run, replicating the study of Gries (2006), but adding two sociolinguistic contexts. The aim was to add two usage dimensions to the polysemy ‘map’ in order to more accurately represent usage-structure. The descriptive findings of Gries are largely confirmed. One further sense, ‘escape’, was found to be relatively important. More importantly, the study added to Gries’ results by identifying which senses are neutral with regard to the two contexts considered. That certain senses are not affected by sociolinguistic variation, yet others are, adds considerable weight to the argument that they represent the prototype senses. The theoretical and methodological goal of this study was straightforward – to demonstrate that, although at times subtle, sociolinguistic factors have a significant impact upon semasiological structure. Cognitive Linguistics has propounded a usage-based model of language since its beginning, but its approach to semantic structure remained largely Structuralist and Generativist in its assumptions and methodologies. The increased use of observational techniques as well as multivariate statistics improves our understanding of the complexity of polysemy structures, but also brings out the need to treat semantic structure in a radically new way. Our very own model of language states that language structure is varied and emergent, and that categorisation is rarely discrete. We must accept the ramifications of this in our research and resist the temptation to assume that discrete reified lexical senses exist or that those senses exist in some abstract system, independent from the variation of societies and cultures that use them. Since meaning is emergent, multidimensional, and ultimately non-reifiable, a description of polysemy that is both cognitively and communicatively realistic will depend upon developing empirical methodology that can adequately describe the complexity of this object of study.

References Arppe, A., & Järvikivi, J. (2007). Every method counts: Combining corpus-based and experimental evidence in the study of synonymy. Corpus Linguistics and Linguistic Theory, 3, 131–159.

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Arppe, A., Gilquin, G., Glynn, D., Hilpert, M., & Zeschel, A. (2010). Cognitive corpus linguistics: Five points of debate on current theory and methodology. Corpora, 5, 1–27. DOI: 10.3366/cor.2010.0001 Baayen, R. H. (2008). Analyzing linguistic data: A practical introduction to statistics using R. Cambridge: Cambridge University Press. DOI: 10.1017/CBO9780511801686 Chatterjee, S., & Hadi, A. (2006). Regression analysis by example. Chichester & New Jersey: Wiley. DOI: 10.1002/0470055464 Chomsky, N. (1964). A transformational approach to syntax. In J. A. Fodor, & J. Katz (Eds.), The structure of language (pp. 211–241). Englewood Cliffs: Prentice-Hall. Cuyckens, H. (1993). The Dutch spatial preposition “in”: A cognitive-semantic analysis. In C. Zelinsky-Wibbelt (Ed.), The semantics of prepositions: From mental processing to natural language processing (pp. 27–72). Berlin & New York: Mouton de Gruyter. DeMaris, A. (2003). Regression with social data: Modeling continuous and limited response variables. Chichester & New Jersey: Wiley. Dirven, R., Goossens, L., Putseys, Y., & Vorlat, E. (1982). The scene of linguistic action and its perspectivization by SPEAK, TALK, SAY, and TELL. Amsterdam & Philadelphia: John Benjamins. DOI: 10.1075/pb.iii.6 Divjak, D. (2010). Structuring the lexicon: A clustered model for near-synonymy. Berlin & New York: Mouton de Gruyter. Divjak, D., & Gries, St. Th. (2006). Ways of trying in Russian: Clustering behavioral profiles. Corpus Linguistics and Linguistic Theory, 2, 23–60. DOI: 10.1515/CLLT.2006.002 Dodge, Y. (2008). The concise encyclopedia of statistics. Heidelberg & New York: Springer. Faraway, J. (2002). Extending the linear model with R: Generalized linear, mixed effects and nonparametric regression models. London: Chapman and Hall. Fillmore, C. (1985). Frames and the semantics of understanding. Quaderni di Semantica, 6, 222–254. Geeraerts, D. (1987). On necessary and sufficient conditions. Journal of Semantics, 5, 275–291. DOI: 10.1093/jos/5.4.275 Geeraerts, D. (1989). Prospects and problems of prototype theory. Linguistics, 27, 587– 612. DOI: 10.1515/ling.1989.27.4.587 Geeraerts, D. (1993). Vagueness’s puzzles, polysemy’s vagaries. Cognitive Linguistics, 4, 223– 272. DOI: 10.1515/cogl.1993.4.3.223 Geeraerts, D. (1995). Representational formats in Cognitive Semantics. Folia Linguistica, 39, 21–41. Geeraerts, D. (1997). Diachronic prototype semantics: A contribution to historical lexicology. Oxford: Clarendon Press. Geeraerts, D. (2000). Salience phenomena in the lexicon: A typology. In L. Albertazzi (Ed.), Meaning and Cognition (pp. 125–136). Amsterdam & Philadelphia: John Benjamins. Geeraerts, D., Grondelaers, S., & Bakema, P. (1994). The structure of lexical variation: Meaning, naming, and context. Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110873061 Gilquin, G. (2010). Corpus, cognition and causative constructions. Amsterdam & Philadelphia: John Benjamins. DOI: 10.1075/scl.39 Glynn, D. (2009). Polysemy, syntax, and variation: A usage-based method for Cognitive Semantics. In V. Evans, & S. Pourcel (Eds.), New directions in Cognitive Linguistics (pp. 77– 106). Amsterdam & Philadelphia: John Benjamins.



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Glynn, D. (2010). Testing the hypothesis: Objectivity and verification in usage-based Cognitive Semantics. In D. Glynn, & K. Fischer (Eds.), Quantitative Cognitive Semantics: Corpus-driven approaches (pp. 239–270). Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110226423 Glynn, D. (In press). Cognitive socio-semantics: The theoretical and analytical role of context in meaning. Review of Cognitive Linguistics. Gries, St. Th. (2003). Multifactorial analysis in corpus linguistics: A study of particle placement. London & New York: Continuum Press. Gries, St. Th. (2006). Corpus-based methods and Cognitive Semantics: The many senses of to run. In St. Th. Gries & A. Stefanowitsch (Eds.), Corpora in Cognitive Linguistics: Corpus-based approaches to syntax and lexis (pp. 57–99). Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110197709 Gries, St. Th. (2009). Statistics for Linguistics with R: A practical introduction. Berlin: Mouton de Gruyter. DOI: 10.1515/9783110216042 Gries, St. Th., & Stefanowitsch, A. (2010). Cluster analysis and the identification of collexeme classes. In S. Rice, & J. Newman (Eds.), Empirical and experimental methods in cognitive/ functional research (pp. 73–90). CSLI: Stanford. Janda, L. (1993). A geography of case semantics: The Czech dative and the Russian instrumental. Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110867930 Kilgarriff, A. (1997). I don’t believe in word senses. Computers and the Humanities, 31, 91–113. DOI: 10.1023/A:1000583911091 Kleiber, G. (1990). Sémantique du prototype : catégorie et sens lexical. Paris: Presses Universitaires de France. Kudrnáčová, N. (2010). On pragmatic and cognitive processes in meaning variation. Linguistica Silesiana, 31, 55–67. Lakoff, G. (1987). Women, fire, and dangerous things: What categories reveal about the mind. Chicago & London: University of Chicago Press. DOI: 10.7208/chicago/9780226471013.001.0001 Lakoff, G. (1990). The invariance hypothesis. Cognitive Linguistics, 1, 39–74. DOI: 10.1515/cogl.1990.1.1.39 Lehrer, A. (1982). Wine and conversation. Bloomington: Indiana University Press. Lehrer, K., & Lehrer, A. (1994). Fields, networks, and vectors. In F. Palmer (Ed.), Grammar and meaning: A festschrift for John Lyons (pp. 26–47). Cambridge: Cambridge University Press. Levy, J., Bullinaria, J., & Patel, M. (1999). Explorations in the derivation of cooccurrence statistics. South Pacific Journal of Psychology, 10, 99–111. Maindonald, J., & Braun, J. (2003). Data analysis and graphics using R: An example-based approach. Cambridge: Cambridge University Press. Marques de Sá, J. (2007). Applied statistics using SPSS, STATISTICA, MATLAB and R. Heidelberg & New York: Springer. DOI: 10.1007/978-3-540-71972-4 Rosch, E. (1975). Cognitive representations of semantic categories. Journal of Experimental Psychology, 104, 192–233. DOI: 10.1037/0096-3445.104.3.192 Rudzka-Ostyn, B. (1989). Prototypes, schemas, and cross-category correspondences: The case of ask. In D. Geeraerts (Ed.), Prospects and problems of prototype theory (Special edition of Linguistics 27) (pp. 613–661). Berlin & New York: Mouton de Gruyter. Sandra, D., & Rice, S. (1995). Network analysis of prepositional meaning: Mirroring whose mind – the linguist’s or the language user’s? Cognitive Linguistics, 6, 89–130. DOI: 10.1515/cogl.1995.6.1.89

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Schmid, H.-J. (2000). English abstract nouns as conceptual shells: From corpus to cognition. Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110808704 Schmid, H.-J. (2010). Does frequency in text instantiate entrenchment. In D. Glynn, & K. Fischer (Eds.), Quantitative Cognitive Semantics: Corpus-driven approaches (pp. 101– 135). Berlin & New York: Mouton de Gruyter. Szmrecsanyi, B. (2006). Morphosyntactic persistence in spoken English: A corpus study at the intersection of variationist sociolinguistics, psycholinguistics, and discourse analysis. Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110197808 Taylor, J. (1989). Linguistic categorization: Prototypes in linguistic theory. Oxford: Clarendon Press. Tribushinina, E. (2009). On prototypicality of dimensional adjectives. In J. Zlatev, M. Andrén, M. Johansson Falck, & C. Lundmark (Eds.), Studies in language and cognition (pp. 111– 128). Newcastle: Cambridge Scholars. Tyler, A., & Evans, V. (2001). Reconsidering prepositional polysemy networks: The case of over. Language, 77, 724–65. DOI: 10.1353/lan.2001.0250 Zlatev, J. (2003). Polysemy or generality? Mu. In H. Cuyckens, R. Dirven, & J. Taylor (Eds.), Cognitive approaches to lexical semantics (pp. 447–494). Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110219074.447

Visualizing distances in a set of near-synonyms Rather, quite, fairly, and pretty Guillaume Desagulier

Université Paris 8, Université Paris Ouest / Nanterre La Défense, UMR 7114 MoDyCo

I aim to uncover revealing aspects of the conceptual structure of four English moderators (rather, quite, fairly, and pretty) and shed new light on previous studies on degree modifiers. I develop an original methodology for handling and visualizing measures of significant attraction between lexical items. This methodology combines univariate and multivariate statistics. Collexeme analysis is used as input for hierarchical agglomerative cluster analysis, and multiple distinctive collexeme analysis is used as input for correspondence analysis. Visualizing collexemes with exploratory tools does more than depict proximities and distances between individuals and variables. It is also an accurate means to (a) unveil fine semantic differences in a set of near-synonymous constructions, (b) determine entrenchment continua, and (c) represent a significant part of the complex inventory of intensifying constructions. Keywords: Cognitive Construction Grammar, collostructional analysis, correspondence analysis, degree modifiers, hierarchical cluster analysis, near-synonymy

1. Introduction It is a well-known fact that natural languages avoid true synonymy: “languages abhor absolute synonyms just as nature abhors a vacuum” (Cruse 1986:â•›270). This is why absolute synonyms are rare whereas near-synonyms are extremely frequent. In Cognitive-Grammar terms (Langacker 1987; 1991), synonymous expressions have identical conceptual content and impose the same construal upon that conceptual content, while near-synonyms share the same conceptual content but differ in terms of

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construal.1 If we could measure conceptual content similarities and construal differences, and then represent them graphically, we could unveil fine semantic differences in sets of near-synonyms. Bearing in mind that “a word is known by the company it keeps” (Firth 1957), I explore the collocation preferences of four English degree modifiers: rather, quite, pretty, and fairly. Because these adverbs are near-synonyms, we may expect them to share identical conceptual content but differ in how this conceptual content is construed. Although these adverbs can grade other adverbs (pretty badly, fairly easily) or noun phrases (quite a shock, rather a surprise), I restrict my investigation to the prototypical contexts where they are used as degree modifiers of adjectives, as examples (1) to (4) illustrate: (1) I heard a rather odd conversation.  (Corpus of Contemporary American English) (2) These two teams are quite similar in some ways. 

(ibid.)

(3) I think it’s fairly easy for anyone to get anything they want (…). 

(ibid.)

(4) He seemed in pretty good form. 

(ibid.)

In the above sentences, rather, quite, pretty, and fairly index the properties of the adjectives they modify as ‘not fully X’. They function as ‘word modifiers’, not as ‘phrasal modifiers’ (Stoffel 1901). They are constituents of adjective phrases and they scale inherent qualities or properties of the heads.2 This paper addresses three challenges. The first challenge is to determine the conceptual content that rather, quite, pretty, and fairly presumably share. The second challenge is to spot the distinctive construals that these adverbs impose on the conceptual content of the adjectives they modify. The third challenge is to identify how adjectives modify the conceptual content of moderators. The working hypothesis is that overlap in collocation preferences will reveal that rather, quite, fairly, and pretty have similar conceptual content, whereas subtle differences will indicate that these four degree modifiers impose different modes of construal. In the pages that follow, moderators are contrasted in their collocation preferences in the 415M-word Corpus of Contemporary American English (Davies 1990-present). The proposed method requires extracting all tokens of the <moderator  + 1. For example, the distributive quantifiers each and every both particularize a referent by referring to its discreteness in a group. But they impose different ways of construing this conceptual content: each profiles a discrete entity within a group, whereas every profiles a group of discrete entities. 2. Moderators, and degree modifiers in general, should not be mixed up with scalar focus modifiers (even, rarely, barely). While the former are inherently scalar, focus modifiers are not: they merely evoke a scale (Traugott 2008).



Visualizing distances in a set of near-synonyms 147

adjective> construction and implementing two techniques from a family of methods known as collostructional analysis. First, a collexeme analysis (Stefanowitsch & Gries 2003) determines which adjectives are most strongly attracted to each moderator. Overlap in collocation preferences will be an indication that moderators have similar conceptual content. Then, a multiple distinctive collexeme analysis (Gries & Stefanowitsch 2004) determines those adjectives that are distinctively associated with each moderator. If, despite overlap, the moderators attract distinct adjective classes, then: (a) moderators form a functionally coherent paradigm; (b) this paradigm has a complex internal structure. When one investigates semantic similarities and differences between related lexemes or constructions, one can choose among many association measures, such as mutual information (pointwise MI, MI2, MI3), the t-score, the Fisher-Yates exact test, the binomial test, the χ2 test, etc. Not all of them are equally satisfactory though (Evert 2004; Wiechmann 2008). For example, pointwise mutual information (Church & Hanks 1990) tends to overestimate rare words and is sensitive to data sparseness (Manning and Schütze 1999:â•›180–181; Kilgarriff 2001). The χ2 test presupposes that the linguistic phenomenon under investigation is distributed randomly across a corpus, but as Kilgarriff (2005) puts it, “language is never, ever, ever, random”. Collostructional analysis is a good place to start because it is a “safe” option that is based on association measures that (a) do not overestimate effect for low-frequency pairs and (b) do not violate distributional assumptions. However, one of the collostructional analysis methods, namely multiple distinctive collexeme analysis, should be used cautiously. Multiple distinctive collexeme analysis is best used to investigate collocation preferences within a predefined closed set of functionally similar constructions (i.e. alternations). Therefore, one needs to make sure that the paradigm under investigation is structured coherently before running such an analysis. As far as moderators are concerned, this is no easy task because they can scale upwards or downwards depending on the adjectives they modify (Paradis 1997:â•›87). Additionally, past research has shown that context dependency between adverbs and adjectives is not always decisive (Allerton 1987; Paradis 1997; Athanasiadou 2007). It is often impossible to decide whether quite is a maximizer or a moderator. A second difficulty is to generalize the output of collostructional analyses. Collexeme and (multiple) distinctive collexeme analyses output large tables containing as many rows as there are collexemes for each variable. The linguist uses these tables to find out whether collexemes fall into distinct semantic classes, but such classes are generally scattered across many rows, and are invisible to the naked eye. Finally, in order to fully determine the semantic profile of the <moderator + adjective> construction, one needs to capture not only the semantic relations between each moderator and its distinctive adjectives (which collostructional analysis does), but also the semantic relations between moderators and between adjectives. A multifactorial analysis can handle all three types of semantic relations.

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To solve each of these issues, the output of collexeme and multiple distinctive analyses serves as input for two multifactorial methods: hierarchical cluster analysis (Divjak & Fieller, this volume 405–442) and correspondence analysis (Benzécri 1973; Benzécri 1984; Greenacre 2007). Both are unsupervised, exploratory clustering techniques. They help find structure in multivariate data thanks to observation groupings. In both cases, the linguist makes no assumption as to what groupings should be there. Hierarchical cluster analysis uses distance matrices to cluster data in a tree-like format – more specifically a dendrogram. This method is used to determine the preferred collexemes of 23 degree modifiers in English and to cluster the results to see if the classes that one obtains are consistent with the traditional functional classes that degree modifiers fall into: maximizers, boosters, moderators, approximators and diminishers (Allerton 1987; Paradis 1997; Quirk et al. 1985). If moderators form a coherent functional category, it is relevant to perform a multiple distinctive collexeme analysis. If this category proves coherent, it will come precisely from the kind of collocates that moderators attract. To account for the semantic correspondences between moderators and adjectives, I focus on the distinctive lexical preferences of the four moderators rather, quite, fairly, and pretty. More specifically, I submit the output of multiple distinctive collexeme analysis to correspondence analysis, a multifactorial approach that provides a low-dimensional map of the data by calculating matrices between the rows and the columns of a contingency table. The larger the distance is between two rows or columns, the further apart the row or column coordinates will be on the map. Correspondence analysis has two advantages. First, it captures semantic relations between (a) moderators, (b) adjectives, and (c) moderators and adjectives. Second, it offers an elegant and efficient way of visualizing distances between lexical variables and collexemes, even when these are computed from large tables. The paper is organized as follows. Section 2 reviews previous qualitative and quantitative research on degree modifiers of adjectives. Section 3 presents the corpus and the methods used. Section 4 summarizes the results. In Section 5, I discuss the results and explain why an original combination of univariate and multivariate statistical methods can only improve our understanding of near-synonymy.

2. Previous research 2.1

Typologies of degree modifiers

Degree modifiers – also known as intensifiers – are a subclass of degree words (Bolinger 1972). They give specifications of degree concerning the adjectives they modify. Adverbs such as very, extremely, absolutely scale adjectival properties “upwards”, whereas other adverbs, such as slightly, a little, somewhat scale adjectival



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properties “downwards”. Rather, quite, fairly, and pretty set the qualities that gradable adjectives denote to a moderate level. Along with moderately and relatively, these degree modifiers are known as ‘moderators’ (Paradis 1997). Like most degree modifiers, rather, quite, fairly, and pretty are typologically unstable because they do not always neatly fit in the functional categories that linguists have assigned them. For example, quite is likely to be interpreted as a maximizer when it modifies an extreme/absolutive adjective (this novel is quite excellent) or a telic/limit/liminal adjective (quite sufficient), but it is likely to be a moderator when it modifies a scalar adjective (quite big) (Paradis 1997:â•›87). Past research has shown that context dependency between adverbs and adjectives is not always decisive. It is often impossible to decide whether quite is a maximizer or a moderator. For example, quite is ambiguous when it modifies the adjective different (Allerton 1987:â•›25). Recent claims that quite has undergone grammaticalization have lead linguists to think that this adverb is ambiguous with absolutive and scalar adjectives alike (the village is quite beautiful, the play is quite good). Similarly, rather, pretty and fairly can scale upwards or downwards due to increasing subjectification (Nevalainen & Rissanen 2002; Athanasiadou 2007). Given that context dependency is the only way to determine whether a given degree modifier such as quite is a maximizer or a moderator, conducting a quantitative study of collocational preferences between adverbs and adjectives across corpora is a methodologically sound approach. It is also a popular approach, as evidenced by the number of corpus-based studies of degree modifiers from the early 1990s onwards (Altenberg 1991; Lorenz 2002; Kennedy 2003; Simon-Vandenbergen 2008). Most of these quantitative approaches are intuitively attractive, but they are problematic for two reasons. First, some of them do not rely on corpora that are sufficient in size and thus fail to provide a detailed picture of the collocational preferences of degree modifiers. By way of illustration, the London Lund Corpus, which Altenberg (1991) and Paradis (1997) exploit, contains 0.5M-words. Some linguists could object that it is presumably too small to reveal relatively rare, but not necessarily statistically insignificant, patterns of attraction between intensifiers and adjectives. Second, linguists tend to use measures that are inadequate to reveal two-way interactions between collocants. Raw frequencies and coarse-grained relative frequencies such as percentages and counts per n-thousand words (Altenberg 1991; Paradis 1997) underestimate significant collocations because they do not filter away lexemes that are highly frequent regardless of the specific contexts where they occur. Likewise, the choice of pointwise mutual information (Kennedy 2003) is not particularly helpful for the reasons outlined in Section 1.3

3. This can be confirmed easily on COCA, whose search interface allows end users to compute MI scores: (corpus.byu.edu/mutualinformation.asp).

150 Guillaume Desagulier

In the wake of Stoffel (1901), typologies of degree modifiers have proliferated (Quirk et al. 1985; Allerton 1987; Paradis 1997), a sign that these adverbs do not all lend themselves easily to a classificatory exercise. One recurring issue is the lack of a fully satisfactory organizing principle. Quirk et al. (1985) posit a coarse-grained distinction between ‘amplifiers’, which “scale upward from an assumed norm”, and ‘downtoners’, which “scale downwards”.4 Amplifiers further subdivide into ‘maximizers’ and ‘boosters’, and downtoners into ‘approximators’, ‘compromisers’, ‘diminishers’, and ‘minimizers’. However, Quirk et al.’s classification is problematic in at least two respects. Firstly, its internal structure is unjustified and inconsistent. In this regard, Allerton (1987:â•›18–19) and Paradis (1997:â•›24) observe that the distribution of degree modifiers across the aforementioned categories is inaccurate. Secondly, Quirk et al. disregard the fact that the semantic influence between an intensifier and the head it modifies is bidirectional. Allerton observes that some approximators do not occur with all adjectives (e.g. virtually unique vs. ?virtually large). He proposes a four-entry classification of degree modifiers of adjectives (scalar modifiers, telic modifiers, absolutive modifiers, differential modifiers). This classification takes into account the collocational restrictions of the <degree modifier + adjective> sequence (1987:â•›19–21). However, Allerton gives no corpus evidence to support his claims and, although convincing, his model is not empirically grounded. Paradis’s taxonomy is finer-grained. Like Quirk et al., Paradis (1997:â•›27–28) proposes a general bipartition between modifiers that scale upwards (‘reinforcers’) and modifiers that scale downwards (‘attenuators’). She postulates the existence of a cline between these two poles. She unifies each set on the cline by means of the principle of cognitive synonymy (Cruse 1986). She further subdivides ‘reinforcers’ and ‘attenuators’ into ‘totality modifiers’ and ‘scalar modifiers’. Unlike Quirk et al., but like Allerton, Paradis is well aware that some degree modifiers are polysemous, semantically fuzzy, and therefore paradigmatically unstable. Unlike Allerton’s, Paradis’s typology is empirically founded. She devotes a chapter of her monograph to the distribution of degree modifiers of adjectives across the London-Lund Corpus of spoken English (1997:â•›Chapter 2). Her goal is both to examine the distribution of degree modifiers of adjectives across modes (spoken vs. written) and to inspect the detail of collocational preferences in the hope of establishing a subtle classification. She concludes that intonation is the key to understanding the meaning and the grading force of degree modifiers (1997:â•›Chapter 4). Previous corpus-based approaches to degree modifiers make extensive use of raw counts, or relative frequencies that do not filter away overrepresented adjectives. Other 4. Strictly speaking, Quirk et al.’s two-branch model is restricted to degree modifiers used as subjuncts, but as Paradis (1997:â•›23–24) observes, this model applies equally well to degree modifiers of adjectives.



Visualizing distances in a set of near-synonyms 151

approaches may also suffer from the kind of corpus that they use, the lack of statistical methods, or the selection of inadequate statistics. If one uses a corpus that is relatively small, statistical methods that are invalid for low counts, such as (pointwise) mutual information or χ2, are inappropriate, and one ends up being trapped in a vicious circle. This is a problem if one wants to investigate collocations, some of which might be relatively rare but by no means insignificant, both statistically and semantically.

2.2

Corpus-based Cognitive Linguistics

Cognitive Linguistics is a usage-based approach to language that makes no principled distinction between language use and language structure. A linguistic unit is entrenched and stored in grammar when a usage pattern generalizes across recurring instances of language use. The more frequently speakers encounter a linguistic unit, the more the linguistic unit is entrenched, i.e. established as a cognitive routine. In Cognitive Linguistics, entrenched patterns of usage provide privileged access to speakers’ knowledge of their language. The meaning of a linguistic unit “involves both conceptual content and the construal of that content” (Langacker 2008:â•›44). Conceptual content is referred to as a domain: a consistent knowledge representation that serves as a basis for the construal of other conceptual units. For instance, adjectives such as damp, dampish, moist or dry relate to conceptual units to be construed with respect to the domain of wetness. The content that the domain designates can further be construed with respect to the more basic domain of property. Construal is the way a speaker presents a conceptual representation through the choice of a linguistic expression. While lexemes and constructions bring with them a conventional meaning, this coded meaning is modified by the context in which linguistic units occur. Far from being a fixed, pre-assigned feature, meaning is negotiated locally and socially. By adopting a specific focal adjustment, the speaker linguistically organizes a scene and influences the way the conceptual representation that the expression evokes will be received by the hearer. This is consistent with the theoretical framework of Cognitive Construction Grammar (CCxG), as laid out in Langacker (1987), Goldberg (1995), and further refined in Goldberg (2003, 2006, 2009) and Langacker (2008, 2009). One of the tenets of CCxG concerns the link between constructions and construal.5 Most Construction Grammar supporters recognize that a given construction is both a product and a vector of conceptualization (see Note 1). Goldberg (2003:â•›219) notes that a linguistic pattern counts as a construction “as long as some aspect of its form or function is not strictly predictable from its component parts or from other constructions recognized to exist”. Productive or semi-productive constructions such as day after day, twistin’ 5. The fact that the noun construction has two corresponding verbs, construct and construe, is not innocent.

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the night away, or boy, was she in trouble! are idiosyncratic and non-compositional. They must be learned on the basis of the input. Likewise, it may well be the case that entrenched types of the <moderator + adjective> construction provide access to conceptual structures in ways that are not necessarily compositional. Competence-based versions of Construction Grammar might deny the <moderator + adjective> pattern the constructional status or at least warn that we should not treat de facto all collocation patterns as constructions. In Fillmorean Construction Grammar, for example, only collocation patterns that are truly productive count as constructions, other kinds of collocation patterns being consigned the ‘meta-grammar’ together with other ‘patterns of coining’ (Kay 2013). In contrast, usage-based models of Construction Grammar such as CCxG have a broader understanding of the notion of a construction. In a neo-Saussurean fashion, they consider that all form-meaning pairings count as constructions: “it’s constructions all the way down” (Goldberg 2003). To put it plainly, according to competence-based models of Construction Grammar, the linguist has no a priori reason to think that a unit counts as a construction, whereas according to usage-based models, linguists have no a priori reason to believe that a unit is not a construction. In this paper we adopt a usage-based perspective because it leaves it to empirical analysis to decide whether a unit counts as a construction or not. Our choice is reinforced by the fact that the quantitative apparatus designed for constructions can also handle regular collocation patterns (i.e. patterns that competence-based models consider as not necessarily constructional). The entrenchment of some instances of the <moderator + adjective> construction explains why moderators scale in different ways depending on the adjective they modify. For example, the scaling force of pretty depends on the adjective it modifies. As Athanasiadou points out, “pretty small is not very small, but pretty straight is very/ quite straight” (Athanasiadou 2007:â•›557). More recently, Goldberg (2006:â•›45) allowed that “individual patterns that are fully compositional are recorded alongside more traditional linguistic generalizations”. This means that all types of the <moderators + adjective> construction, i.e. entrenched as well as non-entrenched types, are worth investigating because each is the trace and the vector of construal mechanisms in the domain of degree modification. Since corpus-based linguistics provides a comprehensive array of methods to capture context and knowledge, it is not surprising that it has become central in the investigation of cognitive patterns of usage in Cognitive Linguistics (Gries & Stefanowitsch 2006). Paradis (1997:â•›62) claims that the semantic relation between degree modifiers and adjectives is bidirectional. More precisely, the adjective selects a degree modifier, which in turn restricts the interpretation of the adjective. This means two things. First, we should not examine probabilistic co-occurrences of words regardless of their morphosyntactic environment. Instead, we should inspect co-occurrences of moderators and adjectives within constructional patterns because both moderators and adjectives contribute to the meaning of the <moderator + adjective>

Visualizing distances in a set of near-synonyms 153



construction. Second, the semantic interaction between a moderator and an adjective is not necessarily compositional.

2.3

Cognitive synonyms or near-synonyms?

According to Paradis (1994:â•›160; 1997:â•›71), moderators are ‘cognitive synonyms’ because substituting one for the other does not change the truth-value of the proposition (Cruse 1986:â•›270ff.).6 Cognitive synonyms share identical conceptual content and differ only in style (die vs. pass away), register (drunk vs. pissed), and connotation (firm vs. stubborn). In other words, cognitive synonymy is a matter of both sameness and difference. Near-synonyms are sometimes referred to as ‘plesionyms’ (Hirst 1995; Edmonds & Hirst 2002; Storjohann 2009). Plesionyms differ from cognitive synonyms because the former involve a slight change in denotational reference, be it in terms of degree (drunk vs. hammered), fuzzy boundary (forest vs. woods), viewpoint (slim vs. skinny), intensity (break vs. destroy), etc. Substituting near-synonyms alters truth conditions but the sentences where they appear remain semantically similar. Cognitive synonymy and near-synonymy are often hard to tell apart, and an opposition between these two concepts is somehow unhelpful. According to Edmonds and Hirst, near-synonyms bring with them a finer-grained representation than cognitive synonyms. Their conclusion is that “it should not be necessary to make a formal distinction between cognitive synonyms and plesionyms” (Edmonds & Hirst 2002). The conceptual content that moderators share is essentially functional: rather, quite, fairly, and pretty moderate the qualities denoted by the adjectives they modify. But moderators are not completely interchangeable in all contexts. Two reasons have been put forth. First, moderators do not express the same degree of moderation. Second, they involve distinct modes of construal (Paradis 2000, 2008). I will put forth another reason: moderators do not always operate within the same conceptual domains.

3. Method I combine two broad types of statistics: analytical statistics and multifactorial methods. Analytical statistics uses measures such as frequencies in the domain of hypothesis testing. Rather than formulate and test hypotheses, multifactorial methods aim to formulate a statistical model, i.e. the statistical description of variation and complex relations in a multi-variable dataset.

6. Cruse’s definition of cognitive synonymy echoes Quine’s (1951).

154 Guillaume Desagulier

To describe and interpret the distribution of the four moderators, we shall start with a study of collocation patterns. The information concerning the distribution of moderators will serve as input for two methods of multifactorial analysis. The paragraphs that follow will justify the choice of the Corpus of Contemporary American English, explain how the data was extracted, and present the measures of lexico-grammatical co-occurrence that are used, namely collexeme analysis, and multiple distinctive collexeme analysis. Finally, two multifactorial analyses will be introduced: hierarchical cluster analysis and correspondence analysis. Their input will be provided by the results of the collexeme and multiple distinctive collexeme analyses.

3.1

The corpus

At the time of writing, the Corpus of Contemporary American English (Davies, 1990-present), henceforth COCA, consists of 414,771,808 words of spoken and written American English divided among 169,140 texts. The spoken part contains approximately 85 million words and consists of transcripts of conversation from TV and radio programs. The written part is divided evenly between four genres: fiction (80 million words), popular magazines (86 million words), newspapers (82 million words), and academic journals (82 million words). The whole corpus spreads across the period from 1990 to 2010, and 20 million words are added each year. One advantage of COCA is that it is probably the largest publicly and freely available annotated corpus of English. Its size and sampling scheme increase the reliability and validity of observations of relatively rare linguistic phenomena. However, one major disadvantage with COCA is that the texts themselves are not available for download for copyright reasons. The only way to run queries is via the native search interface.7 Nevertheless, it is simple to copy and export query results into a text editor or a spreadsheet, clean up the data, cross-tabulate, and run statistical tests. Davies claims that COCA is balanced. To some extent this is true because words are evenly distributed across genres. Yet, as is the case with all major corpora, balance is more an ideal than a reality. COCA also suffers from the fact that speaker-related metadata are not computed relative to the overall size of the corpus, making them very difficult to measure statistically. For example, COCA indicates the identity of the speakers, but gender is left implicit. However, for the current purposes, the fact that speaker-related information is hard to obtain is of little importance since the main

7. This could be a major issue in light of Leech’s “standards of good practice” for corpus users and corpus compilers (Leech 1997:â•›6). At the top of Leech’s list is the following recommendation: “[t]he raw corpus should be recoverable.” Even if the whole texts are unavailable to the COCA end-users, it is nevertheless possible to “dispense with the annotations, and to revert to the raw corpus” (ibid.), although partially.

Visualizing distances in a set of near-synonyms 155



focus of the present study is on function-related distributions and collocation patterns, regardless of dialectal issues. Last but not least, queries on the COCA yield duplicates. This is largely due to automatic text collection, a small price to pay for a corpus of this size. I have not removed duplicates for two reasons. First, duplicates that result from a genuine verbatim quotation are very hard to distinguish from duplicates that result from an error in automatic text compilation. Second, the number of duplicates does not affect the statistics in any significant way. All corpora come with restrictions, and it is important to bear these in mind when interpreting results. All things considered, the advantages of COCA outnumber its disadvantages.

3.2

From collocates to collexemes

A common assumption in corpus linguistics is that the context of a variable (lexical or phrasal) reveals important aspects of its syntactic and semantic properties (Sinclair 1991; Biber et al. 1998). The easiest way to analyze the context of a variable is to extract its collocates and determine those that most typically combine with the variable. According to Sinclair (1991:â•›170), collocation is “the occurrence of two or more words within a short space of each other in a text”. Traditionally, the conventional size of what Sinclair calls ‘a short space’ varies from 1 to 5 words on both sides of the variable, depending on the case study. Syntactic studies tend to examine wider spans, while lexical studies (e.g. those that focus on idiomatic compounds such as bread and butter) examine shorter spans. Some authors also assume that statistical methods can easily filter out the noise generated by a wide concordance span, but once again the wider the span, the weaker the syntactic claims the linguist can make. In the literature on intensifiers, little is said as to the optimal span to investigate. In his study on amplifiers, Kennedy inspects “a window of two words” on each side so as to “retrieve collocations that may have been separated by intervening words” (2003:â•›472–473). Amplifiers can modify elements that precede or follow. This fact alone justifies a two-way search. Amplifier collocates can be adjectives, other adverbs, or verbs, and given their multifunctionality, “intervening words” are frequent. Moderators are slightly different. Insofar as they are ‘word modifiers’ (Stoffel 1901), there is no need to inspect too wide a range of words, and since these adverbs are premodifiers it is useless to inspect the left context.8 Bearing these specificities in mind, I extracted 8. In many collocation-based studies, node words or phrases are often clustered on the basis of their collocates within a relatively large span. One big problem with this method is that the semantic relation between many of these collocates and the node(s) is loose, which brings about noise. By adopting a constructional approach, and therefore treating the sequence <moderator + adjective> as a construction, I restrict the semantic investigation to the syntactic frame of the construction and inevitably minimize the risk of obtaining noise in the data points.

156 Guillaume Desagulier

all adjectives that occur in the first two slots to the right of rather, quite, fairly, and pretty. I also adopted the “paradigmatic reduction” outlined in Lorenz (2002:â•›144) and considered only moderators of adjectives so as to focus on subtle semantic relations. Collocation extraction is a preliminary step to determining sequences of moderators and adjectives that co-occur more frequently than would be expected by chance. Determining collocation strength is a particularly helpful way of spotting differences between semantically similar expressions. Even though we assume that rather, quite, pretty and fairly are near-synonyms, and therefore map onto similar content domains in a quality-related conceptual space, we may expect significantly distinct collocation patterns for each moderator. A related assumption is that distinct collocation patterns reflect subtle differences in schematic-domain profiling. As mentioned earlier, the semantic relation between degree modifiers and adjectives has been described as bidirectional. While this is a convincing assumption, a simple collocate-based inquiry based on raw counts and/or basic relative frequencies is unsatisfactory because it fails to distinguish those adjectives that are significantly attracted to a degree modifier from those that are frequent in the corpus regardless of the context where they appear.9 In this study of the <moderator + adjective> construction, we shall turn to collexeme analysis (Stefanowitsch & Gries 2003), a method that can both handle two-way semantic influences and filter out adjectives that have a high overall token frequency in the corpus. Collexeme analysis is part of a family of methods known as collostructional analysis (Hilpert, this volume, 391–404).10 It investigates which lexemes typically occur in a given slot in a single grammatical construction (e.g. the X-er, the better). It takes as input the frequency of a lexeme in a given construction, the frequency of the same lexeme in all other constructions, the frequency of the construction with other lexemes, and the frequency of all other constructions with other lexemes (Stefanowitsch & Gries 2003:â•›218). The data is tabulated and the 2x2 table is submitted to the Fisher-Yates Exact test (Pedersen 1996). Unlike χ2-statistics, the Fisher-Yates Exact test does not presuppose or violate any distributional assumptions (Kilgarriff 2005). Unlike χ2-statistics and Mutual Information, the Fisher-Yates Exact test is not invalid when counts are low. This means that rare collocations in COCA (such as quite medical or pretty social) can nevertheless be included in the overall calculation of collostruction strength. The p-value that one obtains through the Fisher-Yates Exact test is an indication of the association strength between the lexeme and the construction: 9. Raw counts provide the simplest association measure for pair types. When the construction under investigation displays low token frequency, raw counts are often the only option. However, they should be regarded as a last resort. 10. Each of these methods measures the degree of attraction or repulsion between lexical items and constructions. In collostructional analysis, a construction is defined as a conventional pairing of form and meaning, in light of Goldberg (1995).



Visualizing distances in a set of near-synonyms 157

the smaller the p-value, the stronger the association between a lexeme and a construction. In recent versions of collexeme analysis, the p-value is transformed in an inverse logarithmic function so as to make the distinction between very small p-values easier to identify. In the present study, this operation will be repeated for all adjective types that co-occur with each moderator. Collexeme analysis will first help determine which adjectives are most strongly attracted to the construction <moderator + adjective> by quantifying the bidirectional attraction between a moderator and the adjective it modifies. Second, it will help confirm that rather, quite, pretty, and fairly are functional synonyms by revealing significant overlap in the selection of adjectives. The more significant the overlap, the more these four moderators map onto similar content domains, and the stronger the claim that moderators are cognitive synonyms. Cognitive synonyms also display differences. To make these differences apparent, one can look for the distinctive collexemes of each construction. This is where a second method of collostructional analysis is needed: distinctive collexeme analysis (Gries & Stefanowitsch 2004). Insofar as we want to compare four near-synonymous constructions, , , <pretty + adjective>, and , and contrast them in their respective collexeme preferences, we should implement multiple distinctive collexeme analysis (Hilpert 2006; Gilquin 2007). This method differs from simple collexeme analysis because it filters away overlapping collocates and retains only those adjectives that are specific to each moderator. The output makes it possible to classify the distinctive adjectives according to their function and meaning, and to get a better grasp of the individual functional specificities of rather, quite, pretty, and fairly.

3.3

Collexemes as input for multivariate statistics

Moderator collexemes can serve as input for two usage-based techniques whose aim is to capture semantic relations between near-synonyms on the basis of multiple factors: hierarchical cluster analysis and correspondence analysis. Both methods are exploratory. Instead of testing a hypothesis in relation to pre-assigned categorical clusters, multifactorial analyses follow a bottom-up approach. Indeed, clusters are determined by the similarity of the members of the same groupings and their dissimilarity to the members of other groupings. In theory, these methods dispense with the linguist’s preconception of how the data is categorized. But in practice the clustering results in large part from the criteria that the linguist adopts to combine points into clusters. Recent research on lexical near-synonymy in Cognitive Linguistics has made extensive use of cluster analysis (Divjak 2006, 2010; Divjak & Fieller this volume, 405–441; Divjak & Gries 2008). Hierarchical cluster analysis is the generic name of a family of statistical techniques for clustering data (i.e. for structuring observed data into groups) and representing them graphically in a tree-like format. Among these clustering techniques, I use hierarchical agglomerative clustering, whereby individual

158 Guillaume Desagulier

data points are successively agglomerated into similar clusters, and similar clusters are merged iteratively into bigger clusters until one last cluster is obtained.11 Results appear in the form of a dendrogram, which facilitates an objective and accurate identification of semantic classes and subclasses for a given lexical set. Hierarchical agglomerative cluster analysis will be used to justify the existence of the paradigm of moderators within the broader paradigm of degree modifiers of adjectives. The collostruction strength of the collexemes of 23 English degree modifiers of adjectives will serve as input to compute the distance matrix. Correspondence analysis is another distance-based clustering technique that represents the structure of cross-tabulations graphically on a multi-dimensional plane (Benzécri 1973; Benzécri 1984; Greenacre 2007; Glynn, this volume, 443–486). In lexical semantics, correspondence analysis offers a convenient way of mapping correlations between lexical items graphically. Like hierarchical cluster analysis, correspondence analysis has become a popular method in Cognitive Semantics (Glynn 2010a). Interpreting a correspondence map is relatively simple: the closer the data points on the map, the stronger the correlation between these data points. However, interpreting a map can also be tricky, since it flattens multi-dimensional distances onto a two-dimensional plane. Nevertheless, correspondence analysis yields promising results in areas such as exemplar-based semantics or cognitive sociolinguistics (Glynn 2010b). Cognitive linguists like the fact that a correspondence map may provide access to the complex conceptual maps that structure language knowledge and language use. Correspondence analysis is used to show how moderators imply a specific construal depending on the adjectives they correlate with. Input is provided by the cross-tabulation of the frequencies of 25 distinctive collexemes for each moderator. The list of 25 distinctive collexemes will be obtained via the multiple distinctive collexeme analysis outlined above. This paper attempts to show that near-synonymy is a complex phenomenon whose study can only benefit from a combination of different statistical methods. These methods range from frequencies and collocations – including (multiple distinctive) collexeme analysis – to exploratory multifactorial techniques – namely cluster analysis and correspondence analysis. If cognitive synonymy is indeed a matter of sameness and difference, only a combination of statistical techniques can provide a sound-enough basis for a complete picture of semantic relations to emerge regarding moderators.

11. Hierarchical divisive clustering proceeds in reverse order: it starts at the root and successively splits the clusters.

Visualizing distances in a set of near-synonyms 159



4. Results 4.1

Collexeme analysis

Because rather, quite, pretty, and fairly are alternate ways of expressing moderation, we should expect them to display similarities and differences. Each feature will be illustrated in turn, starting with similarities, which will be captured by means of a collexeme analysis. Collexeme analysis generates a ranked list of attracted lexemes (i.e. ‘collexemes’) and rejected lexemes. This list can be used to determine what meanings are congruent with the semantics of the construction and what meanings are incongruent. For our current purpose, we shall focus on congruent meanings.

Table 1.╇ Top 10 adjectival collocates of rather, quite, fairly, and pretty in COCA rather

quite

adjective

frequency in corpus

frequency in construction

adjective

frequency in corpus

frequency in construction

large different small difficult unusual simple limited good high strange

119,992 â•⁄17,021 165,348 â•⁄â•⁄6,672 â•⁄17,736 â•⁄48,134 â•⁄â•⁄3,533 378,826 191,591 â•⁄23,457

260 231 189 129 116 â•⁄96 â•⁄95 â•⁄89 â•⁄85 â•⁄80

different sure clear good right possible similar ready common simple

â•⁄17,021 137,372 â•⁄81,553 378,826 â•⁄â•⁄4,558 â•⁄88,919 â•⁄60,967 â•⁄55,338 â•⁄63,239 â•⁄48,134

2,247 1,347 â•⁄â•‹805 â•‹â•⁄ 578 â•‹â•⁄ 548 â•‹â•⁄ 458 â•‹â•⁄ 328 â•‹â•⁄ 300 â•‹â•⁄ 278 â•‹â•⁄ 271

fairly

pretty

adjective

frequency in corpus

frequency in construction

adjective

frequency in corpus

frequency in construction

good easy large common high simple new certain small typical

378,826 â•⁄59,914 119,992 â•⁄63,239 191,591 â•⁄48,134 â•⁄64,824 â•⁄71,149 165,348 â•⁄20,483

346 337 281 278 247 243 202 201 190 154

good sure bad clear big tough cool close hard strong

378,826 137,372 â•⁄90,297 â•⁄81,553 187,641 â•⁄33,746 â•⁄â•⁄3,235 â•⁄94,845 123,894 â•⁄69,137

7,492 1,241 â•‹â•⁄ 743 â•‹â•⁄ 729 â•‹â•⁄ 583 â•‹â•⁄ 486 â•‹â•⁄ 481 â•‹â•⁄ 471 â•‹â•⁄ 436 â•‹â•⁄ 383

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Let us postulate that each moderator of adjectives forms a construction that attracts certain adjectival collexemes and rejects others. To calculate the collostruction strength of a given adjective A for a given <moderator + adjective> construction C, collexeme analysis needs four frequencies: the raw frequency of A in C, the raw frequency of A in all other constructions (i.e. ¬C), the frequency of C with adjectives other than A (i.e. ¬A), and the frequency of ¬C with that of ¬A (Stefanowitsch & Gries 2003:â•›218, Hilpert this volume). To generate a ranked list of attracted adjectives based on collostruction strength, this operation is repeated for each adjective that co-occurs with each moderator in the corpus. Table 1, above, summarizes the frequencies of the 10 most frequent adjectives in the four <moderator + adjective> constructions in COCA, i.e. , , and <pretty + adjective>. Each of the four subcomponents of the table are submitted to a collexeme analysis, along with the following information: corpus size: 415M words frequency of : 12,574 frequency of : 29,735 frequency of : 10,834 frequency of <pretty + adj.>: 35,949 Table 2 presents the ten most strongly attracted adjectives of the four moderators based on collostruction strength.12 Table 2.╇ Top 10 collexemes of rather, quite, fairly, and pretty rather

quite

adjective

coll. adjective strength

large different unusual small difficult odd remarkable limited vague strange

1025.19 â•⁄709.26 â•⁄705.49 â•⁄521.34 â•⁄480.6 â•⁄436.5 â•⁄415.88 â•⁄413.37 â•⁄400.68 â•⁄384.69

different sure clear possible similar good ready simple remarkable common

fairly coll. adjective strength 15082.43 â•⁄8231.32 â•⁄4923.96 â•⁄2216.18 â•⁄1614.27 â•⁄1482.02 â•⁄1480.81 â•⁄1357.46 â•⁄1297.76 â•⁄1259.48

easy common simple large good straight-forward certain typical high consistent

pretty coll. adjective coll. strength strength 2686.55 2078.88 1883.49 1751.18 1523.3 1433.43 1326.03 1315.09 1250.31 1112.44

good sure clear bad tough cool amazing big close strong

12. It was performed thanks to the script Coll.analysis 3.2 for R (Gries 2007).

61820.34 â•⁄8148.39 â•⁄4764.46 â•⁄4734.36 â•⁄3635.13 â•⁄3628.34 â•⁄2848.64 â•⁄2604.22 â•⁄2531.19 â•⁄2139.59



Visualizing distances in a set of near-synonyms 161

One might object that there is little difference between the ranked list based on raw frequencies (Table 1) and the ranked list based on collostruction strength (Table 2). However, the latter is more reliable since collostruction strength is the product of an association measure – here Dunning’s log-likelihood ratio – which uses absolute and collocate frequencies to determine which lexemes co-occur more frequently than expected in a given construction. All the above collexemes are attracted to each construction at the very significant level of p < 0.001 since coll.strength > 3.13 Upon inspection, collexeme analysis informs a semantic analysis of moderator constructions. The collexemes of rather split into sets of adjectives that denote spatial dimension (large, small, limited), atypicality (unusual, odd, vague, strange, remarkable), difference, and difficulty. The collexemes of quite split into the following classes: difference/similarity (different, similar), epistemic modality (sure, possible), dynamic modality (ready), positive value (good, clear), (a)typicality (common vs. remarkable), and simplicity. As regards fairly, collexemes divide up into adjectives that denote simplicity (easy, simple, straightforward), typicality (common, typical, consistent), spatial dimension or position (large, high), positive value (good), and epistemic modality (certain). The collexemes of pretty fall into the following sets: positive/negative values (good vs. bad, cool, clear, strong), difficulty (tough), nonstandard identification (amazing), spatial dimension or position (big, close), and epistemic modality (sure). As expected, collexeme analysis reveals that the behavioral profiles of moderators are both similar and different. Similarity is evidenced by the significant degree of overlap in the selection of collexemes. Many adjectives co-occur with more than one moderator (certain, clear, common, different, difficult, good, large, remarkable, simple, sure). Some semantic classes are shared among moderators. For example, both rather and quite are compatible with the expression of (a)typicality. Moderating qualities that belong to the class of spatial extension can be done by means of fairly or rather. The expression of epistemic modality is a feature common to quite, pretty, and fairly. This confirms that moderators are synonyms to some extent. However, at a finer-grained level of analysis, semantic correspondences between moderators are not that straightforward. Even though the expression of atypicality is observed with quite, it is in fact a distinctive feature of rather because adjectives denoting that semantic class are more varied with rather. Even though the expression of epistemic modality is common to the three moderators, it is actually characteristic of quite. The adjective different co-occurs with both rather and quite. However, a quick look at the collostruction strength shows that different is far more distinctive of quite (coll. strength = 15082.43) than it is of rather (coll. strength = 709.26). Good is attracted to pretty, fairly, and quite, but it is definitely more distinctive of pretty

13. As a rule, if collostruction strength is based on p-values, the following equivalences hold true: coll.strength > 3 = p < 0.001; coll.strength > 2 = p < 0.01; coll.strength > 1.3 = p < 0.05.

162 Guillaume Desagulier

(coll. strength = 61820.34) than it is of fairly (coll. strength = 1523.3), and quite (coll. strength = 1482.02).14 Collexeme analysis is not the easiest way of spotting differences in collocational preferences because it does not filter away overlapping adjectives and it requires a tedious comparison of collostruction strengths to determine relevant thresholds of attraction. This can be done by means of a multiple distinctive collexeme analysis (MDCA), which contrasts constructions in their distinctive collocational preferences by getting rid of overlapping collexemes. As explained above, this method is best suited for comparing related constructions, preferably alternations. Whether rather, quite, pretty, and fairly are alternative ways of expressing moderation is undeniable. However, the internal structure of the paradigm that these four adverbs belong to is problematic because some of these adverbs (e.g. quite) can be used as maximizers. To make sure the paradigm of moderators is internally coherent and thus to maximize the interpretation of MDCA, one interesting option is to conduct a hierarchical cluster analysis over a pool of 23 degree modifiers in English and see if the four adverbs cluster together on the basis of their preferred collexemes.

4.2

Collexeme analysis as input for hierarchical cluster analysis

Hierarchical cluster analysis describes a range of multifactorial methods for investigating structure in data, with the goal of identifying subgroups of similar objects. Following Gries & Stefanowitsch (2010), I use hierarchical agglomerative clustering (Everitt et al. 2011:â•›Section 4.2) to see how English degree modifiers cluster on the basis of their preferred collexemes. The 23 degree modifiers, which include the four moderators under investigation, are: a bit, a little, absolutely, almost, awfully, completely, entirely, extremely, fairly, frightfully, highly, jolly, most, perfectly, pretty, quite, rather, slightly, somewhat, terribly, totally, utterly, very. Originally, Paradis selected them because they epitomize the degree modifier paradigm in most lexicographic works (1997:â•›15–17). If rather, quite, pretty, and fairly cluster together, then these four adverbs form a homogeneous paradigm despite their multifunctional behavior. For each of the 23 adverb types listed above, I first extracted all adjectival collocates in COCA, amounting to 432 adjective types and 316,159 co-occurrence tokens. Then, I conducted a collexeme analysis for each of the 23 degree modifiers. To reduce the data set to manageable proportions, the 35 most attracted adjectives were selected on the basis of their collostruction strength. For these 23 adverb types and their 432 adjective types, a 23-by-432 co-occurrence table containing the frequency of each adverb-adjective pair type was submitted to a hierarchical agglomerative cluster analysis, which requires a distance object as input. The distance object is a dissimilarity matrix

14. It is also a collexeme of rather, although to a much lesser extent (coll. strength = 34.34).

Visualizing distances in a set of near-synonyms 163

au bp edge #

88 3 20

JOLLY

ALMOST

FRIGHTFULLY

86 11 72 26 89 44 17 15 14 85 68 6 TERRIBLY

HIGHLY

VERY

MOST

EXTREMELY

QUITE

FAIRLY

83 24 12 88 59 4 91 73 2 PRETTY

A_BIT

SOMEWHAT

A_LITTLE

UTTERLY

SLIGHTLY

ENTIRELY

PERFECTLY

90 64 9 86 43 7 88 73 3

92 12 18

75 36 16 73 48 82 84 10 5

TOTALLY

96 100 1

ABSOLUTELY

88 16 13 81 29 1162 36 8

RATHER

79 7 19

AWFULLY

84 7 21

COMPLETELY

Height

200 250 300 350 400 450 500 550 600



Figure 1.╇ Cluster dendrogram of 23 degree modifiers of adjectives in English, clustered according to their adjectival collexemes (distance: Canberra; cluster method: Ward)

that one obtains by converting tabulated frequencies into distances with a user-defined distance measure. When variables are ratio-scaled, the linguist can choose from several distance measures (Euclidean, City-Block, correlation, Pearson, Canberra, etc.).15 For our purpose, the measure of dissimilarity of the adverb types in the columns was computed using the Canberra distance metric, because it handles the relatively large number of empty occurrences best (see Divjak & Gries [2006:â•›37] for further methodological details). Finally, one needs to apply an amalgamation rule that specifies how the elements in the distance matrix get assembled into clusters. Here, clusters were amalgamated using Ward’s method (Ward 1963), which evaluates the distances between clusters using an analysis of variance. This method has the advantage of generating clusters of moderate size.16 Figure 1 shows the resulting dendrogram. The plot should be read from bottom to top. There are three numbers around each node. The number below each node specifies the rank of the cluster (here, from 1 to 21, i.e. from the 1st generated cluster to the 21st). The two numbers above each node

15. For reasons of space, I cannot discuss the reasons why one should prefer a distance measure over another. A description of some distance measures can be found in Gries (2010:â•›313–316). 16. All computations were performed with R 2.13 (R Development Core Team 2011) and the package pvclust (version 1.2-2, www.is.titech.ac.jp/~shimo/prog/pvclust/). This package allows the user to include confidence estimates through multiscale bootstrap resampling, a possibility missing in other packages, such as hclust.

164 Guillaume Desagulier

indicate two types of p-values,17 which are calculated via two different bootstrapping algorithms: AU and BP. The number to the left indicates an ‘approximately unbiased’ p-value (AU) and is computed by multiscale bootstrap resampling. The number to the right indicates a ‘bootstrap probability’ p-value (BP) and is computed by normal bootstrap resampling. The number to the left is a much better assessment of how strongly the cluster is supported by the data. In both cases, the closer the number is to 100, the stronger the cluster. AU p-values suggest the clusters we obtain represent the data accurately. Indeed, the plot shows the standard values of most clusters are significantly high, with AU p-values ranging from 79 to 96. An AU p-value of 96 implies that the hypothesis that the cluster is invalid is rejected with a significance level of 0.04. The dendrogram displays several homogeneous clusters:18 a. cluster 19 groups together maximizers; it breaks down into cluster 1 (completely, totally) and cluster 13 (perfectly, absolutely, entirely, utterly); b. cluster 9 groups together diminishers (slightly, a little, a bit, somewhat); c. cluster 12 groups together moderators (rather, pretty, fairly, quite); d. cluster 18 groups together boosters and breaks down into cluster 16 (most, very, extremely, highly), cluster 6 (awfully, terribly), and cluster 14 (frightfully, jolly); the presence of an approximator (almost) within the cluster of boosters (cluster 15) is surprising but may be due to its intensive use as a sentential adverb, more than a modifier of adjectives.19 The cluster analysis based on collexemes yields functionally and semantically motivated groups. As Paradis (1997:â•›27) observed, rather, quite, pretty, and fairly do cluster together under the moderator paradigm (cluster 12) despite their multifunctionality. However, the internal structure of this cluster still needs explaining. It is not clear why fairly and quite cluster together (cluster 2), and why rather is not part of cluster 4, which groups together pretty and cluster 2. Furthermore, the stratification of cluster 12 does not follow their conventional distribution in terms of grading force (rather> quite> pretty> fairly), as found in Paradis (1997:â•›148–155). For now, suffice it is to say that moderators form a functionally coherent class. Performing MDCA to explore internal distinctions is therefore relevant.

17. The term “p-value” is the one that the authors of the pvclust package have adopted. Actually, it seems that these p-values are confidence estimates. 18. In the classification of degree modifiers that follows, I adopt Paradis’s terminology. 19. See Paradis (1997:â•›37) for confirmation.

Visualizing distances in a set of near-synonyms 165



4.3

Multiple distinctive collexeme analysis

We saw above that rather, quite, pretty, and fairly display similarities and differences. One way to amplify these differences is to conduct a multiple distinctive collexeme analysis. Instead of computing the degree of attraction between a lexical item and a construction, distinctive collexeme analysis contrasts constructions in their respective collocational preferences (Gries & Stefanowitsch 2004). This method has proved useful when it comes to distinguishing minimal semantic and functional differences between near-synonymous constructions (e.g. the ditransitive vs prepositional dative alternation). The input is slightly different from what we have in collexeme analysis. This time, one needs to tabulate the type frequency of the collexeme in the first construction, the type frequency of the same collexeme in the second construction, and the frequencies of the two constructions with words other than the collexeme under investigation (Gries & Stefanowitsch 2004:╛102). Again, 2x2 tables are submitted to the Fisher-Yates Exact test for each relevant lexeme. However, when one wants to compare more than two constructions and input more complex tables, such as Table 3 below, the Fisher-Yates Exact test cannot be used. Instead, one needs to carry out a one-tailed exact binomial test, and the method goes under the name of multiple distinctive collexeme analysis.20 The same script as the one used for collexeme analysis was used. Below, Tables 4 to 7 list, for each moderator, the ten most distinctive adjectives. MDCA compares the observed frequency of each adjective with its expected frequency. If adjectives were distributed at random over the different moderator constructions, we would not find any significant deviation between observed and expected frequencies because the distribution of each adjective would follow the frequencies of the moderators. For each construction token, the script performs a binomial test Table 3.╇ Input for a multiple distinctive collexeme analysis of an adjective in four moderator constructions Construction

Adjective A

Other adjectives

Row totals

rather + adj quite + adj pretty + adj fairly + adj column totals

a c e g a+c+e+g

b d f h b+d+f+h

a+b c+d e+f g+h a+b+c+d+e+f+g+h

20. Gilquin (2007) illustrates how multiple distinctive collexeme analysis determines the verbs that are distinctively associated with the non-finite verb slot of English periphrastic causative constructions.

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Table 4.╇ The 10 most distinctive adjectives of rather rather + adj

observed frequency

expected frequency

pbin rather

SumAbsDev

odd unusual strange vague difficult simplistic lengthy peculiar bizarre curious formal

â•⁄74 116 â•⁄80 â•⁄56 129 â•⁄28 â•⁄36 â•⁄31 â•⁄51 â•⁄29 â•⁄29

14.51 37.58 25.70 12.71 65.35 â•⁄4.70 â•⁄9.26 â•⁄5.94 14.09 â•⁄5.94 â•⁄5.94

38.99 30.40 21.54 24.75 13.89 18.31 13.81 17.21 17.46 14.91 14.91

56.75 46.39 38.70 35.86 35.86 28.42 27.53 27.08 25.83 25.09 23.49

Table 5.╇ The 10 most distinctive adjectives of quite quite + adj

obs freq

exp freq

pbin quite

SumAbsDev

different right possible ready true likely similar capable willing correct

2247 â•⁄548 â•⁄458 â•⁄300 â•⁄235 â•⁄206 â•⁄328 â•⁄152 â•⁄142 â•⁄106

825.30 184.75 150.95 104.02 â•⁄91.23 â•⁄76.46 148.32 â•⁄51.19 â•⁄49.55 â•⁄36.10

Inf 238.72 216.96 120.33 â•⁄70.29 â•⁄69.12 â•⁄66.10 â•⁄66.87 â•⁄56.31 â•⁄45.22

Inf 410.01 374.49 206.00 120.24 118.13 116.57 114.97 â•⁄96.25 â•⁄78.33

Table 6.╇ The 10 most distinctive adjectives of fairly fairly + adj

obs freq

exp freq

pbin fairly

SumAbsDev

common easy new constant recent certain typical consistent straightforward regular

278 337 202 117 122 201 154 130 123 â•⁄70

â•⁄83.86 108.56 â•⁄43.38 â•⁄16.63 â•⁄20.36 â•⁄66.03 â•⁄35.55 â•⁄33.26 â•⁄30.73 â•⁄12.05

76.85 83.94 88.58 84.16 72.50 49.00 61.99 45.98 44.94 40.51

145.26 130.39 123.43 123.41 109.92 â•⁄98.80 â•⁄89.24 â•⁄68.47 â•⁄65.25 â•⁄59.78

Visualizing distances in a set of near-synonyms 167



Table 7.╇ The 10 most distinctive adjectives of pretty pretty + adj

obs freq

exp freq

pbin pretty

SumAbsDev

good bad cool tough big hard scary smart amazing close

7731 â•⁄758 â•⁄488 â•⁄489 â•⁄591 â•⁄447 â•⁄212 â•⁄196 â•⁄347 â•⁄498

3613.04 â•⁄343.37 â•⁄214.45 â•⁄226.02 â•⁄295.44 â•⁄225.61 â•⁄â•⁄98.34 â•⁄â•⁄91.32 â•⁄195.03 â•⁄314.03

Inf 201.75 144.61 122.02 113.65 â•⁄83.52 â•⁄52.78 â•⁄48.17 â•⁄44.89 â•⁄40.52

Inf 349.84 252.23 213.70 204.40 143.97 â•⁄93.43 â•⁄83.66 â•⁄82.05 â•⁄77.60

to determine the probability of a particular observed frequency given the expected frequency.21 This probability is then log-transformed. The resulting value (pbin) captures distinctiveness.22 It is used to determine whether a given adjective is distinctive for a particular construction or not, and whether the co-occurrence between the adjective and the moderator construction is statistically significant or not. The co-occurrence is statistically significant if the absolute distinctiveness value is higher than 1.3, p < 0.05. Finally, SumAbsDev gives the sum of all absolute pbin values for a particular adjective. The higher the figure, the more the adjective deviates from its expected distribution. MDCA makes patterns of attraction more visible. It confirms that rather attracts adjectives that denote atypicality/deviation from a norm (odd, unusual, strange, vague, peculiar, bizarre, curious). Additionally, rather attracts adjectives that denote difficulty/simplicity. By far, the most distinctive collexeme of quite is different (pbin and SumAbsDev = infinite). Its antonym (similar) is also among the 10 most distinctive collexemes. Modal meanings are well represented: possible and likely denote epistemic meaning, and ready, capable, and willing denote dynamic meaning. Also distinctive of quite are adjectives that denote factuality (right, true, correct). Fairly attracts some sets that are semantically close, such as typicality (common, typical), similarity/stability (constant, consistent, regular), and epistemicity (certain). Other sets include easiness (easy, straightforward), and time location (new, recent). Lastly, the most distinctive collexeme of pretty is good (pbin and SumAbsDev = infinite). Good belongs to the 21. For instance, the probability to find 74 occurrences of odd in when you would have expected it 14.51 times. 22. It receives a positive sign when the verb occurs more frequently than expected in the construction and a negative sign when the verb occurs less frequently than expected. In short, positive values indicate attracted collexemes whereas negative values indicate repelled collexemes. For reasons of space, I have selected positive values only.

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category of positive values, along with cool and smart. Pretty also attracts an antonym such as bad, which denotes a negative value. Other distinctive semantic sets include difficulty (tough, hard), spatial dimension or location (big, close), deviation from a norm (amazing), and psychological stimulus (scary). Since MDCA excludes overlap (i.e. those adjectives which collexeme analysis revealed as common to at least two moderators), it makes some tendencies that collexeme analysis revealed more apparent: a. atypicality as well as difficulty/simplicity are the most distinctive features of rather; b. difference/similarity and modal meanings are the most distinctive features of quite; c. typicality is a distinctive feature of fairly, along with similarity/stability; d. whatever their polarity, value judgments are the most distinctive features of pretty, along with difficulty and dimension/position. But MDCA also reveals tendencies that were harder to grasp with collexeme analysis. Indeed, moderators follow a division of labor in the expression of some functions. Atypicality is a distinctive feature of rather, whereas typicality is a distinctive feature of fairly. Easiness is a distinctive feature of fairly, whereas the expression of difficulty is distinctive of both rather and pretty. There is a difference in register though: it seems that pretty is less formal than rather (rather difficult vs. pretty tough, pretty hard). All in all, MDCA shows that even though moderators are functionally close, they do not profile the same conceptual domains. Even though collexeme analysis and MDCA reveal tendencies that were much harder to capture with only raw frequencies, the above observations are partial because of the limited number of selected collexemes. For a deeper assessment of the synonymy of moderators and the division of labor that they follow, we should increase the level of granularity of our analysis. One obvious solution is to investigate more collexemes, but the more data we have, the more difficult it is to make generalizations. Rather than inspect and compare collostruction-based frequency tables manually, we should also be able to compute and visualize the relative attraction between (a) moderators, (b) adjectives, (c) moderators and adjectives. With this goal in mind, we can use the output of MDCA as input for correspondence analysis.

4.4 Multiple distinctive collexeme analysis as input for correspondence analysis Correspondence analysis (henceforth CA) is an exploratory statistical technique that takes the frequencies of multiway tables as input, then summarizes and visualizes distances between the variables. It determines the probability of global association

Visualizing distances in a set of near-synonyms 169



Table 8.╇ Input for correspondence analysis (sampled) Adjective (distinctive collexeme)

fairly

pretty

quite

rather

able abstract accurate amazing aware awful awkward bad beautiful big …

â•⁄3 14 83 â•⁄6 â•⁄1 â•⁄0 â•⁄0 19 â•⁄1 56 …

â•⁄â•⁄4 â•⁄â•⁄7 â•⁄66 347 â•⁄11 100 â•⁄12 758 â•⁄â•⁄2 591 â•⁄…

â•⁄67 â•⁄â•⁄5 109 â•⁄97 109 â•⁄12 â•⁄â•⁄7 â•⁄32 129 â•⁄45 â•⁄…

â•⁄0 22 â•⁄4 22 â•⁄0 â•⁄6 27 22 21 23 …

between rows and columns, and tests this association using the χ2 test.23 Two rows/ columns will be close to each other if they associate with the columns/rows in the same way. Table 8 shows a sample of the input used for CA. It brings together the 25 most distinctive collexemes of each moderator and the raw frequency of each collocation type. The whole table contains 400 cells. CA uses these frequencies to compare (a) line profiles, i.e. adjectives, (b) column profiles, i.e. moderators, (c) line profiles and column profiles, i.e. moderators and adjectives. This method reintroduces overlap because the table contains raw frequencies of adjectives that co-occur with at least two moderators. As we saw above, overlap is a characteristic of the paradigm of moderators. Taking overlap into account is therefore a way of mapping co-occurrence patterns more realistically than if we simply ignored it. CA transposes the multidimensional distances to a two-dimensional plane that maps the correlations between the variables. More precisely, it transforms the input table (i.e. a table of numerical information) into a graphic display in which each row and each column is represented as a point in a Euclidean space. Figure 2, below, is the graphic output of CA.24

23. Since CA is an exploratory technique, one does not need to check whether the conditions of use of χ2-statistics are met. For our current purpose, the hypothesis of independence can be rejected because χ2 = 33623.82, df = 297, and p-value < 2.2e-16. 24. To conduct CA and output the graph, I used R with the packages FactoMineR (http:// cran.r-project.org/web/packages/FactoMineR/index.html) and dynGraph (http://cran.rproject.org/web/packages/dynGraph/index.html).

170 Guillaume Desagulier

Correspondence analysis graph 2,0

Dimension2 (28.14%)

1,5

1,0

0,5

0,0

–0,5

–1.5

–0.75

0

0.75

1.5

Dimension1 (52.77%)

Figure 2.╇ CA biplot of the <moderator + adjective> construction in COCA

The plot is built along two axes, which are the principal axes of inertia.25 Their intersection defines the average profile of all the points in the cloud. CA decomposes the overall inertia by identifying a small number of representative dimensions. Each axis corresponds to a dimension. The plot displays only two dimensions, which are selected according to their eigenvalues. The eigenvalue of a dimension measures how much information is present along the axis of that dimension. The first axis (dimension 1, eigenvalue = 0.533) represents 52.77% of the inertia, whereas the second axis (dimension 2, eigenvalue = 0.284) represents 28.14% of the inertia. There is a third dimension, whose eigenvalue is 0.193. Even though dimension 3 accounts for 19.08% of the inertia, it is not taken into account in the plot. This is not a problem because the first two dimensions already explain 80.91% of the information contained in the input table, and the results can be interpreted with enough accuracy without dimension 3. Because the plot contains a lot of data, we should examine each dimension in turn. On the horizontal axis, dimension 1 contrasts pretty and quite. Each of them attracts 25. In CA, “inertia” is very similar to the “moment of inertia” in applied mathematics. It measures the total variance of the data table.

Visualizing distances in a set of near-synonyms 171



Correspondence analysis graph

1,5

Dimension2 (27.06%)

1,0

0,5

0,0

–0,5

–0.5

0

0.5

0.75

1.5

Dimension1 (57.51%)

Figure 3.╇ CA biplot of the <moderator + adjective> construction in COCA (with semantic annotation)

its own cloud of adjectives, and each cloud is clearly delimited. On the vertical axis, dimension 2 opposes fairly and rather (at the top of the cloud) to pretty and quite (at the bottom of the cloud). This goes against the implicit assumption that moderators split up between rather and quite on the one hand, and pretty and fairly on the other hand (see, for example, Downing & Locke 2006). The proximity between fairly and rather is evidenced by the continuum formed by their distinctive collexemes (both horizontally and vertically). Comparatively, only two adjectives (surprising and difficult) stand halfway between rather and quite. In all likelihood, the boundary between fairly and rather can be drawn above a cluster of adjectives with negative connotations (obscure, crude, mundane, lengthy, simplistic), which are distinctive of rather. At this stage, it is still difficult to spot any division of labor among moderators because of the granularity of the plot. Figure 3, above, presents the graphic output of CA once all adjectives have been semantically annotated. The relative position of moderators in the cloud is very similar to the configuration displayed in Figure 2.

172 Guillaume Desagulier

Annotating adjectives makes it considerably easier to identify the functional specificities of each moderator as well as the division of labor among them. The specificities of each moderator are listed below: rather: dimension or position in space (ex. long, high), atypicality/oddity (ex. odd, bizarre), negative attitudes (ex. ironic), unclearness (ex. vague, obscure); quite: epistemic, dynamic, and factual meanings (ex. likely, able, true), difference (ex. different, separate), psychological states (ex. surprised, concerned, content); fairly: location in time (ex. recent, new), typicality (ex. typical, common, standard); pretty: appreciative and unappreciative values (ex. good, great vs. bad, awful), cleverness and stupidity (ex. smart vs. stupid, dumb), difficulty (ex. difficult, tough, hard), psychological stimuli (ex. scary, funny). The above list shows that moderators follow a division of labor in the intensification of some complementary meanings: – rather modifies spatial location and atypicality whereas fairly modifies time location and typicality; – rather modifies the expression of negative attitude whereas quite modifies the expression of positive attitude; – pretty modifies the expression of difficulty whereas fairly and rather modify the expression of simplicity; – pretty modifies the expression of psychological stimuli whereas quite modifies the expression of psychological states; – quite modifies the expression of difference whereas fairly and rather modify the expression of similarity/stability. Lastly, some meanings are not distinctive of any moderator in particular: – modifying the degree of surprise/salience and atypicality/extraordinariness is common to pretty, rather, and quite; – modifying the degree of simplicity and similarity/stability is common to both fairly and rather. To summarize, we have three major configurations: – first configuration: moderators operate within one conceptual content; – second configuration: two complementary aspects of a conceptual domain are intensified by two distinct moderators; – third configuration: one conceptual content can be intensified indiscriminately by different moderators.



Visualizing distances in a set of near-synonyms 173

5. Discussion and conclusion In this paper, we have proposed and combined several statistical methods to provide a bidirectional semantic modeling of the <moderator + adjective> construction. We have made three points. Firstly, we have reasserted the need for better statistics in the collocation-based study of degree modifiers. Collostructional analysis is superior to most techniques based on raw counts and/or percentages because it filters away co-occurring pairs that are unrealistically too frequent or too rare, regardless of the size of the corpus. Secondly, we have shown that combining univariate and multivariate statistics can help map usage patterns and conceptual structure in a set of near-synonyms. The relationship between moderators and adjectives is indeed bidirectional, and it can be represented spatially. Thirdly, my results partly support Paradis (1997) regarding the cognitive synonymy of moderators, which are both similar and different. Moderators are similar because they have a functional basis in common, namely modifying the degree of a property denoted by an adjective. Moderators are also different because they do not modify the same classes of adjectives. In Cognitive Grammar terms, moderators do not always operate within the same conceptual domains. If they do, they follow a division of labor. These findings are of great significance to the study of constructions since two items that co-occur significantly are likely to be entrenched as a constructional unit.26 Figure 2 shows that some pairs are more entrenched than others. For example, quite surprised is more entrenched than quite surprising; pretty crazy is more entrenched than pretty silly; rather vague is more entrenched than rather abstract; and fairly straightforward is more entrenched than fairly easy. Once a pairing of lexemes is sufficiently entrenched, it is likely to acquire a meaning/function of its own. Figure 3 shows that the division of labor of moderators is not limited to the expression of intensification. It includes the expression of various meanings, such as the expression of modality, value judgments, dimension, position in time or in space, etc. Cognitive Construction Grammar takes an inventory approach to the mental representation of grammar. Such an approach assumes that grammar predominantly stores language structure in a complex constructional network instead of building structure “on demand”. In a section on partial productivity, Goldberg postulates that the candidates for the verb slot in the ditransitive construction are stored in speakers’ memories as similarity clusters on the basis of their type frequencies (1995:â•›133–136). The higher the type frequency, the bigger the cluster, and the more productive the 26. However we should be wary of not establishing too strong a correspondence between high frequencies and entrenchment (Geeraerts 2000). Studies in cognitive semantics have shown that what determines the entrenchment of a linguistic unit is not so much its high frequency as its absolute frequency as its frequency of occurrence relative to the frequency of similar units in similar contexts (Geeraerts, Grondelaers & Bakema 1994). Also, some linguistic units are entrenched not because they occur frequently, but because they are salient (Schmid 2007, 2010).

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verb class is. In an effort to map usage patterns, Goldberg provides a two-dimensional representation where verbs cluster spatially according to similarity (1995:â•›135). Accordingly, give, pass, bequeath or grant are good candidates for the verb slot in the ditransitive construction, whereas envy or forgive are poor (but by no means impossible) candidates. Goldberg’s map is a theoretical abstraction because it is not based on actual corpus data or similarity metric, as opposed to Figure 2 and Figure 3 in Section 4. Although the latter bear on a different case study, they can be considered as corpus-driven and statistically grounded extensions of Goldberg’s graphic intuition. Figure 2 is flexible enough to represent both entrenched collocations (e.g. rather vague, quite different, fairly new, pretty good) and collocations that are improbable, yet possible (e.g. rather neat, quite cool, fairly stupid, pretty right). It reflects the fact that speakers tend to use certain adjectives with certain degree-modifiers, but can also extend moderators idiosyncratically to other classes of adjectives. The existence of dense, neat clusters of adjectives around pretty and quite suggests that speakers are more conservative in their use of adjectives with these two moderators. Figure 3 confirms that adjectives cluster around moderators on the basis of semantic similarity. In sum, I have presented evidence that shows that types of the <moderator + adjective> construction form a network structured by similarity clusters. Recent studies on near-synonymy in the Cognitive Linguistic framework have concluded that multifactorial techniques can help map usage patterns (Glynn 2010b) and spot “clusters in the mind” (Divjak & Gries 2008; Divjak 2010). Given how representative the corpus I have used is, the same kind of conclusions can be drawn regarding the <moderator + adjective> construction, pending experimental verification. Perhaps in comparison to other less macroscopic approaches, the results presented in this paper seem conditional. Nevertheless, these results take usage-based representations of linguistic units seriously and are verifiable. One can test these findings with a different corpus and compare the results. Confirmatory statistics such as logistic or log-linear regression will have to corroborate the claim that these findings are not due to chance and provide a faithful representation of the reality of the data. For reasons of space, I have deliberately left aside three aspects of the <moderator + adjective> construction, some of which have received much attention in the past, such as syntactic idiosyncrasies (Allerton 1987; Gilbert 1989), grading force (Paradis 1997), and subjectivity (Nevalainen & Rissanen 2002; Athanasiadou 2007). However, I believe that the methodology presented in this paper can shed new light on each of these aspects. Regarding syntactic idiosyncrasies, distinctive collexemes can be used as input for correspondence analysis to obtain a clearer picture of alternations such as vs. , vs. , or vs. . Regarding grading force, adjectives can be annotated according to gradability in correspondence analysis following the categories proposed in Paradis (1997:â•›49), namely non-gradable, scalar, extreme, limit. Regarding subjectivity, the methodology I have proposed can be applied to a diachronic corpus (see



Visualizing distances in a set of near-synonyms 175

also Hilpert 2006), so as to conduct a quantitative assessment of subjectification over the long-term history of rather, quite, fairly, and pretty. I have made use of multifactorial methods to visualize data that is not properly speaking multifactorial. Instead of clustering lexical co-occurrence data alone, it will be in the interest of future research to expand what I have presented in Figure 3 and integrate more strata of richly annotated data within the same plot (e.g. information concerning grading force, boundedness, and semantic classes of adjectives). The resulting two-dimensional map will provide a finer-grained representation of the scale of synonymy of moderators. It will also help explain why collostructions featuring the same adjective do not have the same connotation depending on which moderator is used.27 To summarize, using multiple distinctive collexemes as input for correspondence analysis has three assets. First, it enables the linguist to ignore collocates that would be frequent or infrequent whatever the context (because they have a high overall frequency throughout the corpus) and focus on relevant pairs. Once distinctive collexemes have been identified, their raw frequencies can be used safely in a multi-way table to map correlations between moderators and adjectives by means of a multivariate statistical technique. Second, one graphic output is enough to synthesize similarities and differences in a set of near-synonyms. Similarities between moderators (e.g. rather and fairly) are evidenced by their relative proximity on the map. Differences (e.g. pretty vs. quite) are made apparent by the relative distance between items. This is also true of adjectives, which tend to cluster according to meaning. Third, visualizing distinctive collexemes in a correspondence analysis plot can do more than depict proximities and distances within separate paradigms. It is also a potentially accurate means of determining entrenchment continua along the two dimensions that structure the Euclidean space. Hopefully, the methodology I have proposed can be used to represent the complex inventory of constructions that shapes speakers’ grammars.

References Allerton, D. J. (1987). English intensifiers and their idiosyncrasies. In R. Steele & T. Threadgold (Eds.), Language topics: Essays in honour of Michael Halliday (pp. 15–31). Amsterdam & Philadelphia: John Benjamins.

27. For example, even though good is a distinctive collexeme of pretty, raw frequencies show that it also co-occurs with fairly and quite. Presumably, it does not have the same meaning in each construction. It will be in the interest of future research to include context-based variables to clarify these variations in meaning.

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Altenberg, B. (1991). Amplifier collocations in spoken English. In S. Johansson & A. Stenström (Eds.), English computer corpora: Selected papers and research guide (pp. 127–149). Berlin & New York: Mouton de Gruyter. Athanasiadou, A. (2007). On the subjectivity of intensifiers. Language Sciences, 29, 554–565. DOI: 10.1016/j.langsci.2007.01.009 Benzécri, J-P. (1973). L’analyse des données, 2. L’analyse des correspondances. Paris: Dunod. Benzécri, J.-P. (1984). Analyse des correspondances, exposé élémentaire (2nd ed.). Paris: Dunod. Biber, D., Conrad, S., & Reppen, R. (1998). Corpus linguistics – Investigating language structure and use. Cambridge: Cambridge University Press. DOI: 10.1017/CBO9780511804489 Bolinger, D. L. M. (1972). Degree words. The Hague: Mouton. DOI: 10.1515/9783110877786 Church, K. W., & Hanks, P. (1990). Word association norms, mutual information, and lexicography. Computational Linguistics, 16, 22–29. Cruse, D. A. (1986). Lexical semantics. Cambridge: Cambridge University Press. Davies, M. (1990–present). The Corpus of Contemporary American English (COCA): 410 + million words. http://corpus.byu.edu/coca Divjak, D. (2006). Ways of intending: Delineating and structuring near-synonyms. In St. Th. Gries & A. Stefanowitsch (Eds.), Corpora in Cognitive Linguistics: Corpus-based approaches to syntax and lexis (pp. 19–56). Berlin & New York: Mouton de Gruyter. Divjak, D. (2010). Structuring the lexicon: A clustered model for near-synonymy. Berlin & New York: Mouton de Gruyter. Divjak, D., & Gries, St. Th. (2006). Ways of trying in Russian: Clustering behavioral profiles. Corpus Linguistics and Linguistic Theory, 2, 23–60. DOI: 10.1515/CLLT.2006.002 Divjak, D., & Gries, St. Th. (2008). Clusters in the mind? Converging evidence from near synonymy in Russian. The Mental Lexicon, 3, 188–213. DOI: 10.1075/ml.3.2.03div Downing, A., & Locke, P. (2006). English grammar: A university course (2nd ed.). London: Routledge. Edmonds, P., & Hirst, G. (2002). Near-synonymy and lexical choice. Computational Linguistics, 28, 105–144. DOI: 10.1162/089120102760173625 Everitt, B. S, Landau, S., Leese, M., & Stahl, D. (2011). Cluster Analysis (5th ed.). Oxford: Wiley-Blackwell. DOI: 10.1002/9780470977811 Evert, S. (2004). The statistics of word cooccurrences: Word pairs and collocations. Unpublished doctoral dissertation. Institut für maschinelle Sprachverarbeitung. University of Stuttgart. Firth, J., R. (1957). A synopsis of linguistic theory, 1930–1955. In J. R. Firth (Ed.), Studies in linguistic analysis. Special volume of the Philological Society (pp. 1–32). Oxford: Blackwell. Geeraerts, D. (2000). Salience phenomena in the lexicon: A typology. In L. Albertazzi (Ed.), Meaning and Cognition (pp. 79–101). Amsterdam & Philadelphia: John Benjamins. Geeraerts, D., Grondelaers, S., & Bakema, P. (1994). The structure of lexical variation: Meaning, naming, and context. Berlin, New York: Mouton de Gruyter. Gilbert, E. (1989). Quite, rather. Cahiers de recherche en grammaire anglaise, 4, 4–61. Gilquin, G. (2007). The verb slot in causative constructions. Finding the best fit. Constructions, SV1-3/2006. www.elanguage.net/journals/index.php/constructions/article/view/18/23 Glynn, D. (2010a). Corpus-driven Cognitive Semantics. An introduction to the field. In D. Glynn & K. Fischer (Eds.), Corpus-driven Cognitive Semantics: Quantitative approaches (pp. 1–42). Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110226423.1 Glynn, D. (2010b). Synonymy, lexical fields, and grammatical constructions. A study in usage-based Cognitive Semantics. In H. Schmid & S. Handl (Eds.), Cognitive foundations of linguistic usage-patterns: Empirical studies (pp. 89–118). Berlin & New York: Mouton de Gruyter.



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Goldberg, A. E. (1995). Constructions: A construction grammar approach to argument structure. Chicago: University of Chicago Press. Goldberg, A. E. (2003). Constructions: A new theoretical approach to language. Trends in Cognitive Sciences, 7, 219–224. DOI: 10.1016/S1364-6613(03)00080-9 Goldberg, A. E. (2006). Constructions at work: The nature of generalization in language. Oxford: Oxford University Press. Goldberg, A. E. (2009). The nature of generalization in language. Cognitive Linguistics, 20, 201– 224. DOI: 10.1515/COGL.2009.013 Greenacre, M. J. (2007). Correspondence analysis in practice (2nd ed.). Boca Raton: Chapman & Hall/CRC. DOI: 10.1201/9781420011234 Gries, St. Th. (2007). Coll.analysis 3.2. A program for R for Windows 2.x. Gries, St. Th. (2010). Statistics for linguistics with R: A practical introduction. Berlin & New York: Mouton de Gruyter. Gries, St. Th., & Stefanowitsch, A. (2004). Extending collostructional analysis: A corpus-based perspective on ‘alternations’. International Journal of Corpus Linguistics, 9, 97–129. DOI: 10.1075/ijcl.9.1.06gri Gries, St. Th. & Stefanowitsch, A. (2010). Cluster analysis and the identification of collexeme classes. In J. Newman, & S. Rice (Eds.), Empirical and experimental methods in cognitive/ functional research (pp. 73–90). Stanford, CA: CSLI. Gries, St. Th. & Stefanowitsch, A. (2006). Corpora in Cognitive Linguistics: Corpus-based approaches to syntax and lexis. Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110197709 Hilpert, M. (2006). Distinctive collexeme analysis and diachrony. Corpus Linguistics and Linguistic Theory, 2, 243–256. DOI: 10.1515/CLLT.2006.012 Hirst, G. (1995). Near-synonymy and the structure of lexical knowledge. In J. Klavans (Ed.), AAAI Symposium on Representation and Acquisition of Lexical Knowledge: Polysemy, Ambiguity, and Generativity (pp. 51–56). Cambridge (Mass.): AAAI Press. Kay, P. (2013). The limits of (Construction) Grammar. In T. Hoffmann & G. Trousdale (Eds.), The Oxford Handbook of Construction Grammar (pp. 32–48). Oxford: Oxford University Press. Kennedy, G. (2003). Amplifier collocations in the British National Corpus: Implications for English language teaching. TESOL Quarterly, 37, 467–487. DOI: 10.2307/3588400 Kilgarriff, A. (2001). Comparing corpora. International Journal of Corpus Linguistics, 6, 97–133. Kilgarriff, A. (2005). Language is never, ever, ever, random. Corpus Linguistics and Linguistic Theory, 1, 263–276. Langacker, R. W. (1987). Foundations of Cognitive Grammar. Vol. 1. Theoretical prerequisites. Stanford: Stanford University Press. Langacker, R. W. (1991). Foundations of Cognitive Grammar. Vol. 2. Descriptive application. Stanford: Stanford University Press. Langacker, R. W. (2008). Cognitive Grammar: A basic introduction. Oxford: Oxford University Press. Langacker, R. W. (2009). Cognitive (construction) grammar. Cognitive Linguistics, 20, 167–176. Leech, G. (1997). Introducing corpus annotation. In R. Garside, G. Leech, & T. McEnery (Eds.), Corpus annotation: Linguistic information from computer text corpora (pp. 1–18). London: Longman.

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Lorenz, G. (2002). Really worthwhile or not really significant? A corpus-based approach to the delexicalization and grammaticalization of intensifiers in Modern English. In I. Wischer, & G. Diewald (Eds.), Speech, place, and action: Studies in deixis and related topics (pp. 143–161). New York: Wiley. Manning, C. D., & Schütze, H. (1999). Foundations of statistical natural language processing. Cambridge, MA: MIT Press. Nevalainen, T., & Rissanen, M. (2002). Fairly pretty or pretty fair? On the development and grammaticalization of English downtoners. Language Sciences, 24, 359–380. Paradis, C. (1994). Compromisers – a notional paradigm. Hermes, 13, 157–167. Paradis, C. (1997). Degree modifiers of adjectives in spoken British English. Lund: Lund University Press. Paradis, C. (2000). It’s well weird: Degree modifiers of adjectives revisited: The nineties. In J. M. Kirk (Ed.), Corpora galore: Analyses and techniques in describing English (pp. 147–160). Amsterdam & Atlanta: Rodopi. Paradis, C. (2008). Configurations, construals and change: Expressions of degree. English Language and Linguistics, 12, 317–343. Pedersen, T. (1996). Fishing for exactness. In Proceedings of the South-Central SAS Users Group Conference (pp. 188–200). Austin, TX. Quine, W. V. O. (1951). Main trends in recent philosophy: Two dogmas of empiricism. The Philosophical Review, 60, 20–43. Quirk, R., Greenbaum, S., Leech, G., & Svartvik, J. (1985). A comprehensive grammar of the English language. London & New York: Longman. R Development Core Team. (2011). R: A language and environment for statistical computing. Vienna: Austria: R Foundation for Statistical Computing. Schmid, H.-J. (2007). Entrenchment, salience, and basic levels. In D. Geeraerts & H. Cuyckens (Eds.), The Oxford handbook of Cognitive Linguistics (pp. 117–138). Oxford: Oxford University Press. Schmid, H.-J. (2010). Does frequency in text instantiate entrenchment in the cognitive system? In D. Glynn & K. Fischer (Eds.), Quantitative methods in cognitive semantics: Corpus-Â� driven approaches (pp. 101–133). Berlin, New York: Mouton De Gruyter. Simon-Vandenbergen, A.-M. (2008). Almost certainly and most definitely: Degree modifiers and epistemic stance. Journal of Pragmatics, 40, 1521–1542. Sinclair, J. (1991). Corpus, concordance, collocation. Oxford: Oxford University Press. Stefanowitsch, A., & Gries, St. Th. (2003). Collostructions: Investigating the interaction of words and constructions. International Journal of Corpus Linguistics, 8, 209–243. Stoffel, C. (1901). Intensives and downtoners: A study in English adverbs. Heidelberg: Carl Winter. Storjohann, P. (2009). Plesionymy: A case of synonymy or contrast? Journal of Pragmatics, 41, 2140–2158. Traugott, E. C. (2008). The semantic development of scalar focus modifiers. In A. van Kemenade & B. Los (Eds.), The handbook of the history of English (pp. 335–359). Oxford: Blackwell. Ward, J. H. (1963). Hierarchical grouping to optimize an objective function. Journal of the American Statistical Association, 58, 236–244. Wiechmann, D. (2008). On the computation of collostruction strength: Testing measures of association as expressions of lexical bias. Corpus Linguistics and Linguistic Theory, 4, 253–290.

A case for the multifactorial assessment of learner language The uses of may and can in French-English interlanguage Sandra C. Deshors and Stefan Th. Gries

New Mexico State University / University of California, Santa Barbara

In this study, we apply Gries and Divjak’s Behavioral Profile approach to compare native English can and may, learner English can and may, and French pouvoir. We annotated over 3,700 examples across three corpora according to more than 20 morphosyntactic and semantic features and we analysed the features’ distribution with a hierarchical cluster analysis and a logistic regression. The cluster analysis shows that French English learners build up fairly coherent categories that group the English modals together followed by pouvoir, but that they also consider pouvoir to be semantically more similar to can than to may. The regression strongly supports learners’ coherent categories; however, a variety of interactions shows where learners’ modal use still deviates from that of native speakers. Keywords: Behavioral Profiles, hierarchical cluster analysis, logistic regression, modal verbs

1. Introduction and overview Acquiring a foreign language is one of the most cognitively challenging tasks, given how languages differ in every level of linguistic analysis. From a cognitively and psycholinguistically-oriented perspective, learning a language requires identifying a very large amount of co-occurrence data – tense t and number n require subject-verb agreement with morpheme m, idiom i consists of word w and word x, communicative function f is communicated with intonation curve c, etc. – as well as storing and retrieving them. Crucially, these types of co-occurrences are typically probabilistic only rather than absolute/deterministic and, thus, hard to discern and learn: usually, learners need to cope with many-to-many mappings between forms and functions,

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and often it is only the confluence of differently predictive information on several levels of linguistic analysis that narrows down the search for a particular meaning (in comprehension) or a particular form (in production). In the Competition Model by Bates and MacWhinney (1982, 1989), for example, this situation is modeled on the assumption that forms and functions are cues to functions and forms, respectively, and many different cues of different strengths, validities, and reliabilities must be integrated to, say in production, arrive at natural-sounding choices. Semantics is a particularly tricky linguistic domain in this regard, in native language, but even much more so in foreign language learning. Not only do languages often carve up semantic space very differently (so that the categories of the language acquired first will influence category formation in the following), but semantic differences are also often much less explicitly noticeable (than, say, the presence or absence of a plural morpheme), which makes the identification of probabilistic co-occurrence patterns all the more difficult. In order to allow for a precise description of semantic, or more generally functional, characteristics of synonyms, antonyms, and senses of polysemous words, Gries and Divjak developed the so-called Behavioral Profile (BP) approach (cf. Gries and Divjak 2009). This approach, to be discussed in more detail below, is highly compatible with a psycholinguistic perspective of the type outlined above and involves a very fine-grained annotation of corpus data as well as their statistical analysis. The method of behavioral profiles has been successfully employed in a variety of contexts – synonyms, antonyms, and word senses of polysemous words have been studied both within one L1 or across two different L1s – as well as having received first experimental support, but so far there have been no studies that test the BP approach’s applicability to L1 and L2 data, which is what we will undertake here. The semantic domain we will explore is one that has proven particularly elusive, namely, modality. While many semantic phenomena can be clearly delineated and, to some degree, explained by the linguistic analyst, modality has been much more problematic; in fact, even the scope of the notion of modality has not really been agreed upon yet. In this chapter, we specifically focus on the semantic domain of possibility as reflected in: – the choices of can vs. may in essays written by native speakers of English; – the choices of can vs. may in essays written by French learners of English;1 – the use of pouvoir in essays written by native speakers of French. In Section 2, we discuss in what sense these modals pose a particular challenge to the analyst as well as present previous corpus-based work on can and may and highlight 1. Following Bartning (2009), the term “advanced learner” is henceforth assumed to refer to “a person whose second language is close to that of a native speaker, but whose non-native usage is perceivable in normal oral or written interaction” (Hyltenstam et al. 2005:â•›7, cited in Bartning 2009:â•›12).

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some of the shortcomings of such work. In Section 3, we discuss the BP approach in general as well as our own data and methods in particular. Section 4 presents the results of our exploration, and Section 5 concludes the chapter.

2. Setting the stage 2.1

What is problematic about the modals?

As near synonyms in the domain of modality, may and can have fueled much theoretical debate with regard to their semantic relations. As a pair, both forms have overlapping semantics which cover simultaneously the meanings of possibility, permission and ability (cf. Collins 2009). This means that both forms can be used to express epistemic, deontic and dynamic types of possibility. It follows that the semantic investigation of may and can triggers two problematic questions: first, to what extent the various senses of each form can be distinguished, and second, to what degree both forms are semantically equivalent? With regard to the first question, studies such as Leech (1969) and Coates (1983) have illustrated the difficulty in distinguishing between the senses of may and can. Leech (1969:â•›76), for instance, notes that “[t]he permission and possibility meanings of may are close enough for the distinction to be blurred in some cases”. Similarly, Coates (1983:â•›14) identifies a “continuum of meaning” – i.e. gradience – in which possible modal uses shade into each other. In the case of the meanings of can, for instance, Coates notes that while permission and ability correspond to the core of two largely intersecting fuzzy semantic sets, possibility, on the other hand, is found “in the overlapping peripheral area” (p. 86). With regard to the issue of the semantic equivalence of may and can, the literature reveals similarly debated standpoints. While some studies recognize the similarities of the two forms, others do not. In the former case, for instance, Collins (2009:â•›91) states that “[t]he two modals of possibility may and can, share a high level of semantic overlap” (despite their differing frequency of occurrence and different degrees of formality), and Leech (1969:â•›75) notes that “[i]n asking and giving permission, can and may are almost interchangeable”. Conversely, studies such as Coates (1983) have clearly distinguished the two forms. For instance, while Coates (1983) does recognize that the English modals share certain meanings and can be organized into semantic clusters, she generally denies the synonymy of may and can by classifying the two forms into two distinct semantic groups. Although she accepts that the two forms may have overlapping meanings in some cases, she claims that even then, the two forms do not occur in free variation. The occurrence of one form over the other has been shown to be influenced, to some extent, by its linguistic context. It has indeed been illustrated that particular

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co-occurring grammatical categories interfere with the interpretation of the modals. Leech (2004:â•›77), for instance, notes that certain uses of may are only to be found in particular grammatical contexts: “only the permission sense, for instance, is found in questions (…) and the negation of the possibility sense is different in kind from the negation of the permission sense”. Generally, several grammatical categories have been recognized as interacting with the uses of may and can. While negation is one category that has commonly been identified (cf. Hermerén 1978; Palmer 1979; Coates 1980, 1983; De Haan 1997; Huddleston 2002; Radden 2007; Byloo 2009), voice and sentence types have also been shown to have similar influences on the forms. Overall, the above-mentioned studies all provide clear illustrations of the complexity of the semantic relations between may and can on the basis of empirically gathered evidence. However, they all tend to be based on generalized observations of idiosyncratic behavioral tendencies. In that respect, they all raise the issue of how to provide a more systematic account of the modals’ semantic characteristics and how to integrate qualitative findings into a quantitative and empirically-grounded approach.

2.2

Previous corpus-based work on the modals

2.2.1 Native English As already mentioned above, Hermerén (1978) has shown that the semantics of the modals in native English are morphosyntactically motivated to a considerable degree such that linguistic categories such as voice, grammatical person, type of main verb (action, state, etc.), aspect and sentence type influence the interpretation of the modals: “if these categories can be shown to modify the meaning of the modal […] it is important that this should be accounted for in the description of the semantics of the modals” (p. 74). While this claim calls for empirical validation, one implication of Hermerén’s (1978) argument is that the quantitative study of modal forms will require a powerful and versatile methodological approach. In a very similar fashion, Klinge and Müller (2005:â•›1) argue that, to capture the essence of modal meaning, “it seems necessary to cut across the boundaries of morphology, syntax, semantics and pragmatics and all dimensions from cognition to communication are involved”. A second corpus-based study of the modals in native English is Gabrielatos and Sarmento (2006). This study illustrates an attempt to account for syntactic contextual information while using a quantitative corpus-based approach to investigate core English modals (i.e. can, could, may, might, must, shall, should, will and would). Although their study does not involve the comparison of English varieties, it presents, however, a comparative analysis of the frequencies of uses of the modals in an aviation corpus and a representative corpus of American English. Generally, it raises the following questions:



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– To what degree do syntactic structures and modal forms interact contextually? – To what degree does such interaction affect investigated modal forms semantically? – How can such interaction be quantitatively investigated in a corpus including cross-linguistic and interlanguage data? The authors acknowledge that the modals’ distribution varies as a function of their syntactic contexts and they show that frequencies of occurrence of core English modals reflect the type of syntactic environment in which they feature: “there is a great deal of variation in the use of modal verbs and the structures they occur in, depending on the context of use” (p. 234). However, their lack of a suitable cognitively-motivated theoretical framework prevents them from providing a meaningful interpretation of the data and to further explore their findings. To this date, Collins (2009:â•›1) presents: the largest and most comprehensive [study] yet attempted in this area [modality] based on an analysis of every token of the modals and quasi-modals (a total of 46,121) across the spoken and written data.

Collins (2009) investigates the meanings of the modals in three parallel corpora of contemporary British English, American English and Australian English. Despite the author’s recognition that a corpus quantitative approach “typically combined with a commitment to the notion of ‘total accountability’ may influence hypotheses applied to the data, or formulated on the basis of it” (p. 5) and despite the large size of his data set, his analysis is of limited informative value due to: – a theoretical framework that does not allow for the full exploitation of the linguistic context of the modals, and; – a statistical approach that inhibits rather than unveils linguistic patterns at play in the data. With regard to the first point, Collins (2009) restricts his approach to the identification of the forms’ lexical meanings. His theoretical framework consists of a traditional tripartite taxonomy including epistemic, deontic and dynamic senses. Regrettably, while he recognizes that some uses of the modals can yield preferences for particular syntactic environments, his analysis does not address that fact in a systematic quantitative fashion. As for the second point, while, statistically, Collins (2009) limits his investigation to providing frequency tables of modal forms, his overall approach is problematic because it is based on the erroneous assumption that the frequent occurrence of a modal form warrants its linguistic relevance. In the case of may and can, for instance, Collins uses raw frequencies to show that deontic may is the “least common” sense of the three as it is chosen 7% of the time over epistemic may (79%) and dynamic may (8.1%). However, he does not show whether the (low) frequency of deontic may is significantly different from the also low frequency of dynamic may, and our

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analysis of his data shows that, excluding the indeterminate cases, the distribution of may’s senses across the American, Australian, and British data is highly significant (χ2 = 42.68; df = 4; p < 0.001). This, in turn, raises the questions of: – To what extent are Collins’ (2009) frequencies of the occurrences of modal forms in each corpus comparable? – Since the observed frequency discrepancies are not a matter of chance, then what motivates, linguistically, the different uses of each form in each independent corpus? So in sum, while studies such as Gabrielatos and Sarmento (2006) and Collins (2009) provide many descriptive results, they are often merely or largely form-based alone and are lacking in terms of determining which of the many frequencies are statistically and/or linguistically relevant. As a result, such studies do not come close to allow us to develop a characterization of modals that essentially allows us to classify/predict modal use.

2.2.2 Learner English and contrastive approaches From a cross-linguistic and an interlanguage perspective, investigating the modals raises two related issues, namely (i) the possibility of a lack of (direct) semantic equivalence between the modal forms in the learner’s native language (L1) and his/her target language (L2), and (ii), the fact that such cross-linguistic semantic dissimilarity will affect the uses of the forms in L2. The modals may and can and native French pouvoir illustrate the case in point. Despite the fact that all three forms contribute to the expression of the semantic notion of possibility, pouvoir synchronically covers the whole range of the modal uses of may and can. One corpus-based study of learners’ use of modals is Aijmer (2002), which is based on a corpus of Swedish L2 English writers. She compares (i) the frequencies of key modal words in native English and advanced Swedish-English interlanguage, as well as (ii) frequencies encountered in Swedish learner English with those from comparable French and German L2 English. Aijmer’s study indicates “a generalized overuse of all the formal categories of modality” and she further points out that “it is only at a functional level that any underuse was detected, with the learner writers failing to use may at all in its root meaning” (p. 72). Similarly, Neff et al. (2003) investigate the uses of modal verbs (can, could, may, might and could) by writers from several L1 backgrounds. Neff et al. (2003) use a learner corpus including Dutch-, French-, German-, Italian-, and Spanish-English interlanguage, which they contrast with a reference corpus of American university English. Neff et al. (2003:â•›215) identify the case of can as potentially interesting “since it is overused by all non-native writers”. They further report that the frequency of may by French native speakers stands out in comparison to the frequencies by all other non-native speakers included in the study, but since their study does basically nothing



A case for the multifactorial assessment of learner language 185

but compare raw frequencies of occurrence regardless of any contextual features , it is not particularly illuminating. Generally, and similar to Gabrielatos and Sarmento (2006) and Collins (2009), both Aijmer (2002) and Neff et al. (2003) made the disadvantageous methodological decision to conveniently, but ultimately problematically, rely on information that is retrievable without human effort. In addition, even the studies that address learner use do not relate their findings to the wider context of (second) language acquisition. In a corpus-based contrastive study, Salkie (2004) investigates the nature of the semantic relations between the three forms in native English and native French. He uses a subpart of the parallel corpus INTERSECT (cf. Salkie 2000), and focuses on three working hypotheses, namely that: – “pouvoir corresponds more closely to one of the English modals rather than the other” (p. 169); – “pouvoir is less specific than the English modals” (p. 170); – “pouvoir has a sense which is different from both the English modals but is not just a general sense of possibility” (p. 170). While Salkie (2004) concludes in favour of the third hypothesis, it is worth pointing out, however, that his results were based on only 100 randomly extracted occurrences of each English modal form (i.e. may and can) and their respective French translations. By way of a more general summary, it is probably fair to say that corpus-based approaches to modality in L1 and L2s leave things to be desired. Some studies point to the immense complexity of the subject but do not choose multifactorial or multivariate methods that are capable of addressing this degree of complexity. In addition, some studies are based on large numbers of modals but, frankly, do not do very much with the vast amount of data other than present arrays of statistically under-analyzed frequency tables. On the other hand, the analytically much more interesting studies of the kind of Salkie (2004) are based on very small samples. Finally, many studies are largely if not exclusively form-based and focus only on learners’ over-/underuse of modals in particular examples or kinds of contexts.

2.3

Characteristics of the present study

2.3.1 Methodological considerations The above discussion fairly clearly indicates what kinds of steps would be desirable, an approach that: – can integrate linguistic information and patterning from many different levels of linguistic analysis in a way alluded to by Hermerén (1978), as well as Klinge and Müller (2005);

186 Sandra C. Deshors and Stefan Th. Gries

– involves not only a sample that is studied with regard to more linguistic parameters, but at the same time also larger than the previous studies that aimed at more than description; – explores similarities and differences of L1 uses of can and may, but also explores the way these English modals are used in L2 language (here from French learners) as well as how the same concept is used by the learners in their L1 (here pouvoir). Given these demands, we decided to use the so-called Behavioral Profile approach, which fits the above wish list very well. It combines the statistical methods of contemporary quantitative corpus linguistics with a cognitive-linguistic and psycholinguistic perspective or orientation (cf. Divjak and Gries 2006, 2008, 2009; Gries 2006, 2010b; Gries and Divjak 2009, 2010; and others). As such, it diverges radically from the above-mentioned more traditional corpus-based approaches to modality in both L1 and L2. Methodologically, it involves four steps: – the retrieval of all instances of a word’s lemma from a corpus in their context; – a manual annotation of a number of features characteristic of the use of the word forms in the data; these features are referred to as ID tags and typically involve morphosyntactic and semantic features in particular. Each ID tag contributes to the profiling of the investigated lexical item(s); – the generation of a table of co-occurrence percentages, which specify, for example, which words (from a set of near-synonymous words) or senses (of a polysemous word) co-occur with which morphosyntactic and/or semantic ID tags; it is these vectors of percentages that are called profiles; – the evaluation of that table by means of statistical techniques. Given how this approach is completely based on various kinds of co-occurrence information, it comes as no surprise that, just like much other work in corpus linguistics, the BP approach assumes that “the distributional characteristics of the use of an item reveals many of its semantic and functional properties and purposes” (Gries and Otani 2010:â•›3). While these previous studies have investigated a variety of different lexical relations (near synonymy, polysemy, antonymy) both within languages (English, Finnish, Russian) and across languages (English and Russian), the present study will add to the domains in which Behavioral Profiles have been used in two ways: (i) so far, no non-native language data have been studied, and (ii) we will add French to the list of languages studied. As the first BP study focusing on learner data, and only the second BP study that compares data from different languages, this paper is still largely exploratory. We will mainly be concerned with the following two issues: – To what degree can the Behavioral Profiling handle the kind of learner data that are inherently more messy and volatile than native data and provide a quantitatively adequate and fine-grained characterization of the use of can and may by



A case for the multifactorial assessment of learner language 187

native speakers and learners, and how does that use compare to the use of French speakers’ use of pouvoir? – As a follow-up, and if meaningful groups of uses emerge, to what degree do the distributional characteristics that BP studies typically include allow us to predict native speakers’ and learners’ choices of modal verbs, and how do these speaker groups differ? The former question will be explored with the kind of cluster-analytic approach usually employed in BP studies; for the latter question, we will turn to a logistic regression (cf. Arppe 2008 for another BP approach using (multinomial) regression).

2.3.2 Theoretical orientation In previous studies, the BP approach was used for more than just the quantitative description of the data. Rather, it is firmly grounded in, and attempts to relate the results of the statistical exploration of the data to usage-based/exemplar-based approaches within Cognitive Linguistics and psycholinguistics. While this orientation is also compatible with our current goals, there is one particular earlier model in L2/ FLA research that is especially well-suited to, or compatible with, our current objectives, namely the Competition Model (CM) by Bates and MacWhinney (cf. Bates and MacWhinney 1982, 1989). This model is “a probabilistic theory of grammatical processing which developed out of a large body of crosslinguistic work in adult and child language, as well as in aphasia” (Kilborn and Ito 1989:â•›261). MacWhinney (2004:â•›3) himself characterized it as a “unified model [of language acquisition] in which the mechanisms of L1 learning are seen as a subset of the mechanisms of L2 learning”. The CM is characterized by the two following assumptions: – Linguistic signs map forms and functions onto each other (probabilistically) such that forms and functions are cues to functions and forms respectively. – In language production, forms compete to express underlying intentions or functions, and in language comprehension, the input contains many different cues of different strengths, validities, and reliabilities, which must be integrated: native speakers “depend on a particular set of probabilistic cues to assign formal surface devices in their language to a specific set of underlying functions” (Bates and MacWhinney 1989:â•›257). As a usage-based and probabilistic model, the CM assumes that both frequency and function determine the choice of grammatical forms in language production; as with most usage-based and/or corpus-linguistic approaches, we too consider frequency in a corpus as a proxy for frequency of exposure (in both comprehension and production). Cross-linguistically, this is an important assumption because across languages cues are instantiated in different ways and speakers assign them varying degrees of strength. It is therefore important to describe and explain L1 statistical regularities as

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“[t]hey are part of the native speaker’s knowledge of his/her language, and they are an important source of information for the language learner” (Bates and MacWhinney 1989:â•›15). Overall, Kilborn and Ito (1989: 289) conclude that existing psycholinguistic studies have successfully demonstrated that the CM is appropriate for the characterization of learner language through cue distributions and they report “extensive evidence for the invasion of L1 strategies into L2 processing”. In addition, it is also obvious how much the CM is compatible with a BP approach. The main notions that drive the Competition Model are cue strengths, validities, and reliabilities, and all of these are essentially conditional probabilities, i.e. percentages. While the BP approach as such does not cover the full complexity of how conditional cue strengths, validities, and reliabilities can interact, it is a useful and experimentally validated (cf. Divjak and Gries 2008) approach employing a similar logic. A theory of language transfer requires that we have some ability to predict where the phenomena in question will and will not occur. In this regard contrastive (Gass 1996:â•›324) analysis alone falls short; it is simply not predictive.

3. Data and methods 3.1

Retrieval and annotation

The data are from three untagged corpora: the French subsection of the International Corpus of Learner English (henceforth ICLE-FR), the Louvain Corpus of Native English Essays (LOCNESS), and the Corpus de Dissertations Françaises (CODIF). All corpora included in the present work were collected by the Centre for English Corpus Linguistics (CECL) at the Université Catholique de Louvain (UCL) and made available to us by the Director of the Centre, Professor Sylviane Granger. ICLE-FR has a total of 228,081 words, including 177,963 words of argumentative texts and 50,118 words of literary texts. LOCNESS is a 324,304-word corpus that includes three sub-data sets: a 60,209-word-sub-corpus of British A-Level essays, a 95,695-word sub-corpus of British university essays and a sub-corpus of American university essays that has 168,400 words. The CODIF is a corpus of essays written by French-speaking undergraduate students in Romance languages at the Université Catholique de Louvain (UCL). CODIF also includes argumentative and literary texts and has a total of 100,000 words.2

2. Information on the total number of words featuring in each individual text type (i.e. argumentative, literary) is not available.

A case for the multifactorial assessment of learner language 189



Table 1.╇ Excerpt of an annotation table including selected variables Case Match Corpus ClType 5 133 1760 1886 2876 3540 3645

may may may can cannot peut peuvent

native native native il il fr fr

coordinate main main coordinate subordinate main subordinate

Use

VerbSemantics

Neg

RefAnim

process state process process state process process

ment/cog/emotional copula ment/cog/emotional ment/cog/emotional abstract ment/cog/emotional abstract

affirmative affirmative negative affirmative negative negative negative

animate inanimate animate animate inanimate animate inanimate

Given the corpora’s compositions, the three corpora included in our study are highly comparable. They all consist of written data produced by university students (ICLE, CODIF, the LOCNESS British and American university sections) or by students approaching university entrance (i.e. the LOCNESS British A-Level section).3 All participants’ contributions are in the form of an essay of approximately 500 words long. In terms of content, all essays deal with similar topics such as: crime, education, the Gulf War, Europe, or university degrees. The data we subjected to the BP approach consist of instances of may and can in native English and French-English interlanguage as well as pouvoir in native French from the above corpora. Using scripts written in R (cf. R Development Core Team 2010), we retrieved 3,710 occurrences of the investigated modal forms from all sub-corpora, which were imported into a spreadsheet software and annotated for 22 morphosyntactic and semantic variables.4 Table 1 exemplifies this database with a very small excerpt of these data, and Table 2 presents the total range of variables included in the study and their respective levels. For each variable, an encoding taxonomy was designed prior to annotation. Due to the large number of variables included in this study and the absence of a number of them from previous studies on the English modals, not all encoding taxonomies were theoretically motivated. In cases where the annotation is not based on accounts from the existing literature, a bottom-up approach was adopted for the identification of recurrent features in the data. This procedure, for instance, was carried out in the case of the variable VerbSemantics where, prior to annotation, recurrent semantic features were identified as characteristic of the lexical verbs used alongside the modals.

3. The inclusion of the LOCNESS British A-Level section alongside sub-corpora solely including university participants is not judged problematic as LOCNESS only involves English native speakers whose level of English is not expected to develop any further. 4. Although the annotation process included a variable encoding the semantic role of the subject referent of the modals, this study does not account for that variable due to its high correlation with VOICE.

190 Sandra C. Deshors and Stefan Th. Gries

Table 2.╇ Overview of the variables used in the study and their respective levels Type

Variable

Levels

data

Corpus GramAcc (acceptability) Neg (negation) SentType (sentence type) ClType (clause type) Form SubjMorph: subject morphology SubjPerson: subject person SubjNumber: subject number Voice Aspect Mood SubjRefNumber: subject referent number Senses SpeakPresence Use

native, interlanguage, French yes, no affirmative, negated declarative, interrogative main, coordinate, subordinate can, may, pouvoir (and negated forms) adj., adv., common noun, proper noun, relative pronoun, date, noun phrase, etc. 1, 2, 3 singular, plural active, passive perfect, perfective, progressive indicative, subjunctive singular, plural

syntactic

morphological

semantic

VerbSemantics

RefAnim: subject referent animacy AnimType: subject referent animacy type

epistemic, deontic, dynamic weak, medium, strong accomplishment, achievement, process, state abstract, general action, action incurring transformation, action incurring movement, perception, etc. animate, inanimate animate, floral, object, place/time, mental/ emotional, etc.

Because of space restrictions, we are not able to provide a more comprehensive account of the annotation process (but cf. Deshors 2010 for details). However, three variables – Senses, VerbType, and VerbSemantics – require some brief explanatory comments.

3.1.1 The variable Senses As for Senses, the semantic category of modality includes a wide range of heterogeneous meanings that many scholars have attempted to unite under a variety of categorization systems (cf. Palmer 1979; Coates 1983; Bybee and Fleischman 1995; Huddleston 2002; Nuyts 2006; Byloo 2009). While Depraetere and Reed (2006:â•›277) note that “in classifying modal meanings, it is possible to use various parameters as criterial to their classification”, this study assumes a coding taxonomy based on a traditional tripartite distinction between epistemic, deontic and dynamic meanings.



A case for the multifactorial assessment of learner language 191

Following Nuyts (2006:â•›6), epistemic senses concern “an indication of the epistemic estimation, typically, but not necessarily, by the speaker, of the chances that the state of affairs expressed in the clause applies in the world”. Consider (1) as an illustration of epistemic may: (1) indeed, Europe 92 may lead to the disappearance of cultural differences Following Palmer (1979:â•›58), deontic modality refers to cases where “[b]y uttering a modal, a speaker may actually give permission (may, can)”. (2) illustrates deontic can: (2) if all public schools started to say you can only come here if you are Hispanic or if you are Polish, our schooling system would be in great chaos Finally, dynamic meanings denote “an ascription of a capacity to the subject-participant of the clause (the subject is able to perform the action expressed by the main verb in the clause)” (Nuyts 2006:â•›3). Generally, dynamic modality expresses the potentiality of an event occurring. Nuyt’s type of dynamic modality includes ability/ capability cases where the possibility of event occurrence stems from the ability of the (grammatical) subject to carry out the event. In that regard, the term ability is not restricted to a ‘physical’ interpretation and equally applies to mental and technical types of ability. Example (3) illustrates dynamic can: (3) Mrs Ramsay is the central character because she can see the whole personality of the other ones Generally, our frequencies of use of may and can in their different senses match those previously encountered in existing studies solely concerned with the native use of the modals, such as Coates (1980) and Collins (2009). While Coates (1980:â•›218), for instance, reports that “by far the most common usage of may is to express epistemic possibility”, she stresses the distinctive nature of the uses of may and can: The patterns resulting from my analysis of the data (…) leads me to conclude that in normal everyday usage may and can express distinct meanings: may is primarily used to express epistemic possibility, while can primarily expresses root possibility.5

3.1.2 The variable VerbType The variable VerbType targets the lexical verbs with which the forms are used and characterizes their telicity. Conceptually, the variable VerbType follows Vendler (1967) in its recognition that the notion of time is crucially related to the use of a

5. Coates (1980, 1983) categorizes modal meaning according to a two-way distinction that includes epistemic and non-epistemic modality. She refers to the latter type as “root” modality.

192 Sandra C. Deshors and Stefan Th. Gries

verb and is “at least important enough to warrant separate treatment” (p. 143). This variable assesses: – whether may and can have preferences for lexical verbs denoting a state, a process, an accomplishment or an achievement,6 and if so, – it identifies in which type of corpus preferential patterns occur.

3.1.3 The variable VerbSemantics Similarly to the variable VerbType, VerbSemantics identifies the type of semantic information conveyed by the lexical verbs used with the modals. The internal organization of this variable results from a bottom-up approach and does not follow any particular theoretical framework. This variable consists of the levels denoting abstract process, physical actions, actions incurring movement, actions incurring some physical transformation, communicative processes, mental/cognitive/emotional processes, perception processes and verbal statement involving a copula verb. Example (4) illustrates a case where the lexical verb expresses a mental/cognitive/emotional process: (4) Her search for the final touch can be seen as a search for harmony Once all matches were annotated, the resulting data table was evaluated statistically.

3.2

The BP approach in this study: Statistical analysis

As mentioned above, the data were evaluated in two different ways.7 The first of these involved the type of cluster analysis that is characteristic of much work using the BP methodology. In this first part, we used Gries ’s (2010a) R script Behavioral Profiles 1.01 and computed five behavioral profiles, one for each modal form as occurring in each language variety, i.e. native can, native may, interlanguage (IL) can, IL may, and native pouvoir (FR). Such profiles consist of vectors of co-occurrence percentages of a single modal form with each level of all independent variables and provide form-specific summaries of their semantic and morphosyntactic behavior in each sub-corpus. In a second step, the profiles were assessed statistically with a hierarchical cluster analysis to explore the similarity and differences between the modal forms, and in keeping with previous studies (cf. Divjak and Gries 2006), we chose the Canberra metric as a measure of (dis)similarity and Ward’s rule as an amalgamation strategy. 6. Accomplishment verbs encode verbal statements that imply a unique and definite time period; achievement verbs encode verbal statements that imply a unique and definite time instant; process verbs identify statements that reflect non-unique and indefinite time periods; state verbs identify statements that reflect non-unique and indefinite time instants. 7. All statistical computations and plots were performed with R (for Linux), version 2.11.0 (see R Development Core Team 2010).

A case for the multifactorial assessment of learner language 193



Following Gries and Otani (2010), we computed different cluster analyses, one involving all variables that the uses of the modals were annotated for, one for only the syntactic variables, and one for only the semantic variables. The second analytical step involved a binary logistic regression including the following variables and predictors: – Form as the dependent variable with only two levels here: can vs. may; – GramAcc, Neg, SentType, ClType, SubjMorph, SubjPerson, SubjNumber, Voice, Aspect, Mood, SubjRefNumber, Senses, SpeakPresence, Use, VerbSemantics, RefAnim, AnimType as independent variables in the form of main effects; – all these variables’ interactions with Corpus as additional predictors (to see which variables’ influence on modal use differs the most between L1 English and L2 English). The logistic regression was then performed with the model selection process during which insignificant predictors were discarded from the model: first insignificant interactions, then individual variables that were not significant and did not participate in a significant interaction.

4. Results and discussion 4.1

Cluster analysis

Our first cluster analysis yielded the results shown in Figure 1. The left plot is a dendrogram of the five modal forms that were clustered; the right plot represents average silhouette widths for assuming two, three, and four clusters. The average silhouette widths point to a two-cluster solution, maybe a three-cluster solution, but the difference is minor since the former would result in a French-vs.-English clustering, and the latter in a French-vs.-can-vs.-may clustering. This is compatible with Salkie’s analysis, who argued that pouvoir is very different from both can and may, and intuitively, both these solutions “make sense”, which provides first evidence in favor of the approach. To anticipate the potential objection that this may seem trivial, let us mention that it is in fact not. The data in Figure 1 show that the BP vectors are good and robust descriptors of how the modals behave because many other theoretically possible cluster solutions, such as the ones listed in (5), would not have made linguistic sense at all. (5) a. {{{canil maynative pouvoir} cannative} mayil} b. {{{cannative mayil pouvoir} canil} maynative} c. {{canil maynative} {pouvoir mayil} cannative}

1.0

0.03

0.4

0.6

0.8

0.07

0.2

(Average) silhouette widths

0.1

0.0

MAY.native

MAY.il

CAN.native

CAN.il

POUVOIR.fr

Height

700 750 800 850 900 950

194 Sandra C. Deshors and Stefan Th. Gries

0 1 2 3 4 Number of clusters in the solution

18 16 14

CAN.native

CAN.il

MAY.native

MAY.il

POUVOIR.fr

12 6

CAN.native

CAN.il

8

10

MAY.il

MAY.native

POUVOIR.fr

Height

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

Figure 1.╇ Dendrogram for all independent variables (il = interlanguage)

Figure 2.╇ Dendrograms for all morphosyntactic variables (left panel) and all semantic variables (right)

However, in what follows we show that a fine-grained comparative description of cross-linguistic language varieties can be obtained by focusing on differences between the independent variables used for clustering. Consider Figure 2, which shows the dendrograms for all morphosyntactic variables and all the semantic variables in the left and right panel, respectively. Interestingly, the results show that the intuitively very reasonable dendrogram in Figure 1 is not replicated by looking at morphosyntax or semantics alone, which to some extent at least contrasts with Gries and Otani’s results, where the results did not differ very much between the three clusterings. The reasonable similarities of Figure 1 emerge only when all variables are combined. In particular, in both panels of Figure 2 canil and cannative are grouped together, but then the remaining forms are grouped differently. In the morphosyntactic dendrogram, the two kinds of may are successively amalgamated and the French pouvoir is only added after all English forms have been

A case for the multifactorial assessment of learner language 195

affirmative

er en ce s di ff o rn yo in lt se ve ra

negated

subord clauses

main clauses

0.4 0.2 0.0 –0.2 –0.4

Syntactic differences mat interlang - may native



Figure 3.╇ Snakeplot for most extreme differences between syntactic ID tags of may

clustered. In other words, morphosyntactically, we find a clear English-French divide, but interlanguage may is too different from native may to be grouped together. To identify the source of this difference, we used what in BP approaches has been called a snakeplot, namely a plot of the pairwise differences between the percentages for, in this case, mayil and maynative (cf. Divjak and Gries 2009 or Gries and Otani 2010 for more examples). As indicated in Figure 3, the main morphosyntactic ways in which learners deviate from native speakers are that learners underuse may in subordinate clauses and in negated clauses. This is in fact an interesting finding because it means that learners disprefer the rarer of the two modals – may – in those contexts which are already morphosyntactically more challenging, as if using can is the default they resort to when they are already under a higher processing load (cf. the so-called complexity principle). In the semantic dendrogram, by contrast, we find a different patterning. Semantically, canil and cannative are again very similar and grouped together early, but then the next clustering step groups the two forms of may together. However, interestingly, it is not the English forms that are then all grouped together – rather, contrary to Salkie’s earlier analysis, pouvoir is semantically more similar to can than may is.

4.2

Logistic regression

The model selection process involved thirteen steps during which insignificant predictors were discarded. The final and minimally adequate model includes 16 significant variables and 6 significant interactions and returned a highly significant correlation: loglikelihood chi-square = 3296.47; df = 60; p < 0.001; the correlation between the

196 Sandra C. Deshors and Stefan Th. Gries

Table 3.╇ Overview of the results of the final GLM model Predictor

Chi-square (df)

Predictor

Chi-square (df)

Corpus GramAcc Use Elliptic ClType VerbType VerbSemantics SubjPerson SubjNumber SubjMorph RefAnim

â•⁄ 24.9 (1) *** â•⁄ 13.8 (1) *** â•⁄ 67.9 (1) *** 100.0 (2) *** â•⁄ 10.9 (1) *** â•⁄ 97.4 (2) *** 384.9 (6) *** â•⁄ 26.6 (2) *** â•⁄â•⁄ 1.3 (1) ns â•⁄ 49.1 (4) *** â•⁄ 59.2 (1) ***

AnimType Voice SentType Negation SpeakPresence Corpus:ClType Corpus:VerbSemantics Corpus:SubjNumber Corpus:RefAnim Corpus:AnimType Corpus:Negation

â•⁄â•⁄â•⁄98.2 (11) *** â•⁄â•⁄â•⁄55.0 (1) *** â•⁄â•⁄â•⁄47.2 (1) *** â•⁄â•⁄â•⁄87.2 (1) *** 29905.9 (2) *** â•⁄â•⁄â•⁄60.0 (2) *** â•⁄â•⁄â•⁄32.2 (6) *** â•⁄â•⁄â•⁄37.4 (1) *** â•⁄â•⁄ 122.2 (1) *** â•⁄â•⁄ 118.2 (11) *** â•⁄â•⁄â•⁄12.0 (1) ***

observed forms – may vs. can – and predicted probabilities is very high: R2 = 0.955. Correspondingly, the model’s classificatory power was found to be very powerful with a classification accuracy of 99%. Table 3 summarizes all the significant variables and interactions yielded in the final model. Overall, the final model includes one significant interaction involving a morphological variable (out of seven morphological variables), two significant interactions involving syntactic variables (out of three syntactic variables) and three significant interactions involving semantic variables (out of eight semantic variables). But what do the interactions reflect? Let us begin with Corpus:ClType, as represented in Figure 4. The frequencies of may and can differ with regard to the type of clauses in which they occur in native and learner English. The (weak!) effect is that, in interlanguage

may

may

can

can

can

may

may

can

can

can

0.4 0.2

Coordinate

Main Subordinate

0.0

0.4 0.2 0.0

may

0.6

0.8

may

0.6

0.8

1.0

Native

1.0

Interlanguage

Coordinate

Figure 4.╇ Bar plots of relative frequencies of Corpus:ClType

Main Subordinate

A case for the multifactorial assessment of learner language 197



0.8

may

0.4

0.6

may

can

can

0.2 Affirmative

Negative

0.0

0.4

can can

0.2 0.0

Native 1.0

may may

0.6

0.8

1.0

Interlanguage

Affirmative

Negative

Figure 5.╇ Bar plots of relative frequencies of Corpus:Neg

English, can is more strongly preferred over may in main clauses than it is in native English. While, as previously noted, existing literature concerned with the native use of the modals commonly recognizes negation as “an important aspect of modal meaning” (Hermerén 1978), our study not only confirms the need to include negation in an investigation of the uses of the modals but further recognizes its significance as a morphological criteria to assess interlanguage (dis)similarity. Consider Figure 5 for the interaction Corpus:Neg. Figure 5 shows that, while all speakers prefer to use can in negated clauses, the interlanguage speakers do so more strongly. This result does not come as a surprise: On the one hand, this is also compatible with the complexity principle – negated clauses are more complex and preferred with the more frequent modal. On the other hand, where epistemic may not would be used in English, French speakers would tend to use a lexical verb along with the adverb peut-être to indicate the speaker’s uncertainty, as illustrated in (6): (6) a. This may not be the case b. Ce n’est peut-être pas le cas Consider Figure 6 for the interaction Corpus:SubjNumber. While native speakers use can more often with singular subjects than with plural subjects, it is the other way round with the learners, again a result compatible with the complexity principle. While the native speakers’ choices of may and can do not vary much between animate and inanimate subjects, the learners’ choices do: with animate subjects, they prefer can much more strongly. Figure 7 represents the interaction Corpus:RefAnim.

198 Sandra C. Deshors and Stefan Th. Gries

may

can

can

pl

sg

may

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can

0.2 0.0

0.0

0.2

0.4

0.6

0.8

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0.8

1.0

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1.0

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pl

sg

Figure 6.╇ Bar plots of relative frequencies of Corpus:SubjNumber

1.0

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can

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Figure 7.╇ Bar plots of relative frequencies of Corpus:RefAnim

Consider Figure 8 for the interaction Corpus:VerbSemantics; the upper panel represents the interlanguage data, the lower panel represents the native speaker data, and the bars are sorted from large absolute pairwise differences (left) to small absolute pairwise differences (right). The learners and the native speakers differ most strongly with semantically more abstract verbs and time/place verbs, as in He thinks that if he can achieve one impossible act, then this will change everything. The learners prefer can with abstract verbs more strongly than the native speakers, but they prefer may more strongly with time/place verbs. However, there are also (less pronounced) differences for verbs that would typically have a human agent.

A case for the multifactorial assessment of learner language 199



may

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Figure 8.╇ Bar plots of relative frequencies of Corpus:VerbSemantics

For instance, the learners prefer may with communication verbs and can with action-transformation verbs. Virtually no difference at all is found with copulas. As for the final interaction, Corpus:AnimType, we do not represent it here graphically. While it is significant, the large number of categories plus the fact that the most pronounced differences occur with a small number of very infrequent categories does not yield much in terms of interesting findings. As for the main effects, we will not discuss them here in detail. This is because these main effects by definition do not tell us anything about the can and may variables across languages (since these variables do not interact with Corpus). However, since they do tell us something about which modal verb is preferred by both native speakers and learners, we summarize them here visually in Figure 9. The x-axis lists the main effects, on the y-axis we show the percentage of can obtained for levels of these main effects, and then the levels are plotted at their observed percentage of can; the dashed line represents the overall percentage of can in the data.

weak

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200 Sandra C. Deshors and Stefan Th. Gries

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Figure 9.╇ Main effects of the logistic regression

Finally, a brief look at the regression’s misclassifications seems to indicate that they did not occur randomly. While all 34 misclassifications occurred in the interlanguage data, 29 of them occurred with may in a form characteristic only of the French-English learner language. In the large majority of those misclassifications, may is found to express a possibility that results from some sort of theoretical demonstration. Consider the examples in (7) and (8). While the ones in (7) illustrate our current point, (8) provides an additional example of an atypical occurrence of learner may, which clearly denotes a strong sense of possibility and whose interpretation is heavily reminiscent of that of can. (7) a. So we may say that … b. To conclude, we may say that … c. As a conclusion, we may say that … d. This is why we may now speak of the stupefying effect e. This is the reason why we may say that … (8) “Dresden is an old town”, we may read of its history

5. Concluding remarks By way of a summary, the BP approach and the subsequent logistic regression allows us to recognize how can and may (in native and learner English), as well as pouvoir, relate to each other as well as what helps determine native speakers’ and learners’ choices. On the whole, distributionally we do find the expected groupings: the cans, then the mays, and only then pouvoir. However, it is interesting that, semantically,



A case for the multifactorial assessment of learner language 201

English can is more similar to French pouvoir than to English may, and the subsequent regression results provided some initial information on why that is so. More specifically, the way learners choose one of the two verbs is often compatible with a processing-based account in terms of the complexity principle – they choose the more basic and frequent can over may when the environment is complex – but is also strongly influenced by the animacy of the subject and the semantics of the verb: can is overpreferred by learners with animate subjects and with abstract verbs, and underpreferred with time/place verb semantics. With regard to the modals per se, our results confirm previous studies’ recognition of the influential role of the linguistic context in the uses of may and can. Indeed, while the main effects included in our final logistic regression model support studies that have identified morphosyntactic components such as Voice and SentType as particularly influential categories (Leech 1969, 2004; Huddleston 2002; Collins 2009), our results reveal the necessity to also take the semantic context of modals more seriously, as reflected by the strong effects of VerbType and VerbSemantics. More generally speaking and in the parlance of the Competition Model, the cluster analysis and the high classification accuracy of the regression suggest that, on the whole, the learners have built up mental categories for can and may that are internally rather coherent. However, the interactions in the regression show that these cues are weighted incorrectly and sometimes trigger a verb choice that is not in line with native speaker choices, but that even this kind of incorrect choice is largely predictable (because the regression can still make the correct classifications (cf. Deshors 2010 for more detailed discussion as well as a distinctive collexeme analysis revealing additional verb-specific preferences). In other words, even though this is the first study involving learner data (and only the second involving different languages), the BP approach and especially the follow-up in terms of the logistic regression are therefore an interesting diagnostic: (i) the overall results can testify to the strength of the categories that are being studied, and (ii) the regression with its inclusion of the interactions of all variables with “native speaker vs. learner” exactly pinpoints where interactions become significant, i.e. where the categories of the learner are still substantially different from the native speaker. For further applications and extensions, see Gries and Wulff (2013) for a similar application to the choice of (of- and s-) genitives by native speakers and learners, and Gries and Deshors (to appear) for an even more advanced approach to precisely pinpoint where non-native speakers’ choices deviate from those of native speakers and how much so. Needless to say, more and more rigorous testing is necessary, but to our knowledge this is the first study proposing this kind of approach more generally and the use of a regression with a native-learner variable as a measure of L2 “proficiency”; the results illustrate that learners’ “non-nativeness” manifests itself at all linguistic levels simultaneously.

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References Aijmer, K. (2002). Modality in advanced Swedish learners’ written interlanguage. In S. Granger, J. Hung, & S. Petch-Tyson (Eds.), Computer learner corpora, second language acquisition and foreign language teaching (pp. 55–76). Amsterdam: John Benjamins. Arppe, A. (2008). Univariate, bivariate and multivariate methods in corpus-based lexicography: A study of synonymy. Unpublished PhD dissertation, University of Helsinki. Available at: . Bartning, I. (2009). The advanced learner variety: 10 years later. In E. Labeau, & F. Myles (Eds.), The advanced learner variety: The case of French (pp. 11–40). Frankfurt/Main: Peter Lang. Bates, E., & MacWhinney, B. (1982). Functionalist approaches to grammar. In E. Wanner, & L. R. Gleitman (Eds.), Language acquisition: The state of the art (pp. 173–218). Cambridge: Cambridge University Press. Bates, E., & MacWhinney, B. (1989). Functionalism and the competition model. In B. MacÂ� Whinney, & E. Bates (Eds.), The cross-linguistic study of sentence processing (pp. 3–73). Cambridge: Cambridge University Press. Bybee, J., & Fleischman, S. (1995). Modality in language and discourse. Amsterdam: John Benjamins. DOI: 10.1075/tsl.32 Byloo, P. (2009). Modality and negation: A corpus-based study. Unpublished PhD dissertation, University of Antwerp. Coates, J. (1980). On the non-equivalence of may and can. Lingua, 50(3), 209–220. DOI: 10.1016/0024-3841(80)90026-1 Coates, J. (1983). The semantics of the modal auxiliaries. London: Croom Helm. Collins, P. (2009). Modals and quasi modals in English. Amsterdam: Rodopi. De Haan, F. (1997). The interaction of modality and negation: A typological study. New York: Garland. Depraetere, I., & Reed, S. (2006). Mood and modality in English. In B. Aarts, & A. MacMahon (Eds.), The handbook of English linguistics (pp. 268–287). London: Blackwell. Deshors, S. C. (2010). A multifactorial study of the uses of may and can in French-English interlanguage. Unpublished PhD dissertation, University of Sussex. Divjak, D. S., & Gries, St. Th. (2006). Ways of trying in Russian: Clustering behavioral profiles. Corpus Linguistics and Linguistic Theory, 2(1), 23–60. DOI: 10.1515/CLLT.2006.002 Divjak, D. S., & Gries, St. Th. (2008). Clusters in the mind? Converging evidence from near synonymy in Russian. The Mental Lexicon, 3(2), 188–213. DOI: 10.1075/ml.3.2.03div Divjak, D. S., & Gries, St. Th. (2009). Corpus-based cognitive semantics: A contrastive study of phasal verbs in English and Russian. In K. Dziwirek, & B. Lewandowska-Tomaszczyk (Eds.), Studies in cognitive corpus linguistics (pp. 273–296). Frankfurt/Main: Peter Lang. Gabrielatos, C., & Sarmento, S. (2006). Central modals in an aviation corpus: Frequency and distribution. Letras de Hoje, 41(2), 215–240. Gass, S. (1996). Second language acquisition and linguistic theory: The role of language transfer. In W. C. Ritchie, & T. K. Bhatia (Eds.), Handbook of second language acquisition (pp. 317–340). San Diego: Academic Press. Gries, St. Th. (2006). Corpus-based methods and cognitive semantics: The many meanings of to run. In St. Th. Gries, & A. Stefanowitsch (Eds.), Corpora in cognitive linguistics: Corpus-based approaches to syntax and lexis (pp. 57–99). Berlin: Mouton de Gruyter. DOI: 10.1515/9783110197709



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Gries, St. Th. (2010a). Behavioural Profiles 1.01: A program for R 2.7.1 and higher. Gries, St. Th. (2010b). Behavioral profiles: A fine-grained and quantitative approach in corpus-based lexical semantics. The Mental Lexicon, 5(3), 323–346. Gries, St. Th., & Deshors, S. C. (To appear). Using regressions to explore deviations between corpus data and a standard/target: two suggestions. Corpora. Gries, St. Th., & Divjak, D. S. (2009). Behavioral profiles: A corpus-based approach to cognitive semantic analysis. In V. Evans, & S. Pourcel (Eds.), New directions in cognitive linguistics (pp. 57–75). Amsterdam: John Benjamins. Gries, St. Th., & Divjak, D. S. (2010). Quantitative approaches in usage-based cognitive semantics: Myths, erroneous assumptions, and a proposal. In D. Glynn, & K. Fischer (Eds.), Quantitative cognitive semantics: Corpus-driven approaches (pp. 333–354). Berlin: Mouton de Gruyter. Gries, St. Th., & Otani, N. (2010). Behavioral profiles: A corpus-based perspective on synonymy and antonymy. ICAME Journal, 34, 121–150. Gries, St. Th., &Wulff, S. (2013). The genitive alternation in Chinese and German ESL learners: Towards a multifactorial notion of context in learner corpus research. International Journal of Corpus Linguistics, 18(3), 327–356. Hermerén, L. (1978). On Modality in English: A study of the semantics of the modals. Lund: LiberLäromedel/Gleerups. Huddleston, R. D. (2002). The Cambridge grammar of the English language. Cambridge: Cambridge University Press. Hyltenstam, K., Bartning I., & Fant L. (2005). High Level Proficiency in Second Language Use. Research program for Riksbanken Jubileumsfond. (Stockholm university) http://www. biling.su.se/~AAA. Kilborn, K., & Ito, T. (1989). Sentence processing strategies in adult bilinguals. In B. MacÂ� Whinney, & E. Bates (Eds.), The cross-linguistic study of sentence processing (pp. 257–291). Cambridge: Cambridge University Press. Klinge, A., & Müller, H. H. (2005). Modality: Intrigue and inspiration. In A. Klinge, & H. H. Müller (Eds.), Modality studies in form and function (pp. 1–4). London: Equinox. Leech, G. (1969). Towards a semantic description of English. Bloomington, IN: Indiana University Press. Leech, G. (2004). Meaning and the English verb. London & New York: Longman. MacWhinney, B. (2004). A unified model of language acquisition. Retrieved from [Accessed 18 June 2010]. Neff, J., Dafouz, E., Herrera H., Martínez, F., & Rica, J. P. (2003). Contrasting the use of learner corpora: The use of modal and reporting verbs in the expression of writer stance. In S.  Granger, & S. Petch-Tyson (Eds.), Extending the scope of corpus-based research: New applications, new challenges (pp. 211–230). Amsterdam: Rodopi. Nuyts, J. (2006). Modality: Overview and linguistic issues. In W. Frawley (Ed.), The expression of modality (pp. 1–26). Berlin: Mouton de Gruyter. Palmer, F. (1979). Modality and the English modals. London & New York: Longman. Radden, G. (2007). Interaction of modality and negation. In W. Chłopicki, A. Pawelec, & A. Pokojska (Eds.), Cognition in language: Volume in Honour of Professor Elżbieta TabaÂ� kowska (pp. 224–254). Kraków: Tertium. R Development Core Team (2010). R: A language and environment for statistical computing. Foundation for statistical computing. Vienna, Austria. .

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Salkie, R. (2000). Corpus linguistics: A brief guide to research in French language and linguistics. AFLS Cahiers, 6, 44–52. Salkie, R. (2004). Towards a non-unitary analysis of modality. In L. Gournay, & J.-M. Merle (Eds.), Contrastes: mélanges offerts à Jacqueline Guillemin-Flescher (pp. 169–182). Paris: Ophrys. Vendler, Z. (1967). Verbs and times. In Z. Vendler (Ed.), Linguistics in philosophy (pp. 97–121). New York: Cornell University Press.

Dutch causative constructions Quantification of meaning and meaning of quantification Natalia Levshina, Dirk Geeraerts, and Dirk Speelman

F.R.S. – FNRS, Université catholique de Louvain / University of Leuven

This chapter is a multivariate corpus-based study of two near-synonymous periphrastic causatives with doen and laten in Dutch. Using multiple logistic regression and classification trees, the study explores the conceptual differences between the constructions. The results support the existing definition of doen as the direct causation auxiliary, and interpretation of laten as the indirect causative (e.g. Verhagen and Kemmer 1997). However, the analyses also reveal more specific patterns: the most distinctive semantic pattern of doen is affective causation, whereas the contexts with the highest probability of laten refer to inducive causation. These differences remain valid when we control for geographic and thematic variation, as well as for the individual Effected Predicates treated as random effects in a mixed model. Keywords: classification trees, logistic regression, mixed model, periphrastic causatives

1. Introduction This chapter is a contribution to empirical Cognitive Semantics (e.g. Glynn and Fischer 2010).1 It is a corpus-based multivariate onomasiological study (cf. Tummers et al. 2005), which uses quantitative corpus evidence to describe, explain and predict the choices that speakers make between semantically related constructions when they categorize their experience. To do so, the linguist needs to identify the relevant semantic, pragmatic, social and other features that influence this choice. This kind of 1. This research was supported with a grant from the Flemish Research Fund – FWO (G033008). The authors would also like to thank Kris Heylen for his help in collecting the corpus data. The usual disclaimers apply.

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study requires advanced statistical multivariate techniques, such as logistic regression, which allow the researcher to model the impact of each factor, while controlling for the others. The approach is relatively new, but a number of studies have been implemented already. It is interesting to note that a substantial share of these studies focus on constructions that differ from each other with respect to information structure and processing. Examples are the dative alternation in English (e.g. Bresnan et al. 2007), presence or absence of the presentative er-construction in Dutch (Grondelaers et al. 2007), particle placement in English (Gries 2003), word order variation in Dutch final verbal clusters (de Sutter 2009) and in the German ‘middle field’ (Heylen 2005). It seems that these alternations, a challenge for traditional linguistic descriptions, have benefited the most from the multifactorial probabilistic methods due to a variety of ways in which the underlying information-processing factors can be captured. However, more “semantic” constructional variation, like the one discussed here, can benefit from these methods too because highly abstract grammatical meaning can be captured in a corpus by a multitude of indirect indicators used as circumstantial evidence. The current chapter, which is an elaboration of the pilot study carried out by Speelman and Geeraerts (2009), focuses on the near-synonymous Dutch causative constructions with doen and laten. Our study incorporates several linguistic, thematic and geographical factors in a multivariate statistical model, which allows us to test the existing semantic hypotheses about doen and laten, keeping the conceptual factors apart from the other sources of variation. We argue that the distinctive conceptual features that emerge in the quantitative model constitute the distinctive prototypes of the constructions – the semantic configurations with the highest intercategorial cue validity. Although the Prototype Theory of categorization (Rosch 1975; Rosch and Mervis 1975) has been dominant in Cognitive Linguistics, many psychological and, more recently, linguistic studies (e.g. Medin and Schaffer 1978; Bybee and Eddington 2006) have demonstrated the crucial role of specific exemplars (or low-level schemata) in category organization and development. This is why we also test whether the abstract semantic differences between the constructions still hold if we take into account the lexemes that fill in the effected predicate slot, many of which display strong preference for doen or laten. The method applied for this purpose is mixed-effect modelling with the general semantic and other factors as fixed effects and the specific effected predicates as random effects. The chapter has the following structure. First, we give a brief introduction of the Dutch causative constructions. In Section 3, the data and the potentially relevant variables are presented. Section 4 reports the results of the multiple logistic regression analysis and additional tests, which are interpreted linguistically and cognitively in Section 5. The chapter ends with a summary of our findings.

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2. Dutch causative constructions Modern standard Dutch has two periphrastic causatives with the infinitive: the constructions with doen ‘do’ and laten ‘let’. They share the same schematic pattern: an initiator causes another entity to acquire a state or perform an action. Consider example (1): (1) De politie deed/liet de auto stoppen. the police did/let the car stop ‘The police stopped the car’. Using the terminology from Kemmer and Verhagen (1994), de politie ‘the police’, is the causer of the event; de auto ‘the car’ is the causee that performs the action specified by the effected predicate stoppen ‘stop’. The forms deed and liet are the past forms of the causative auxiliaries doen and laten, respectively. The most striking feature of the Dutch causatives is that laten as a causative auxiliary can refer both to the enabling and coercive types of causation (see Verhagen and Kemmer 1997:â•›69). Compare the situations in (2a), (2b) and (2c): (2) a. De trainer liet de spelers loopoefeningen doen.  [coercive] the coach let the players running-exercises do ‘The coach made the players do running exercises’. [ambiguous] b. Hij liet iedereen zijn roman lezen.  He let everyone his novel read ‘He made/had/let everyone read his novel’. c. De politie liet de dader ontsnappen.[enabling] the police let the criminal escape ‘The police let the criminal escape’. There have been a number of usage-based studies that have tried to establish the differences between the constructions (Kemmer and Verhagen 1994; Verhagen and Kemmer 1997; Degand 2001; Stukker 2005; Speelman and Geeraerts 2009). Verhagen and Kemmer (1997) write about the semantic difference between doen and laten in terms of the speaker’s conceptualization of the situation as direct or indirect causation, respectively. Direct causation means that “there is no intervening energy source ‘downstream’ from the initiator: if the energy is put in, the effect is the inevitable result” (Verhagen and Kemmer 1997:â•›70). Indirect causation, which also includes the situations of enablement and permission, emerges when the situation “can be conceptualized in such a way that it is recognized that some other force besides the initiator is the most immediate source of energy in the effected event” (Ibid.:â•›67). Speelman and Geeraerts (2009) showed, in their multivariate analysis of the Corpus of Spoken Dutch, that there is also a substantial amount of geographic and register variation in the use of the constructions. From the conceptual point of view, it

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was suggested that doen is an obsolescent form with a tendency towards semantic and lexical specialization, most probably in direct physical causation (Speelman and Geeraerts 2009:â•›200), although this hypothesis was not tested. The highly abstract conceptual patterns, such as direct and indirect causation, cannot be directly observed in a corpus-based study. Our aim is to explore a set of independent contextual factors (“diagnostic features”, according to Speelman and Geeraerts 2009) that can serve as indirect, or circumstantial, evidence of semantic differences between the constructions. These contextual factors, operationalized as independent variables in the logistic regression model, are listed in Section 3, as well as the extralinguistic (geographic and thematic) variables that are explored in this study.

3. Data and variables 3.1

Data

The study is based on an 8 million token corpus of Netherlandic and Belgian Dutch, compiled from the TwNC and LeNC newspaper corpora (2001–2002). The corpus was balanced with regard to four subject domains of the articles: politics, economy, football and music. We used a syntactically parsed version of the data, which was obtained with the help of the Alpino parser of Dutch (Bouma et al. 2001). This allowed us to extract the contexts with constructions automatically. The contexts were then checked manually to avoid spurious hits and formally similar but functionally different constructions, such as the adhortative laten in Laten we gaan ‘Let’s go’. We also excluded idiomatic expressions with effected predicates that do not occur independently, e.g. begaan, which only occurs in the set expression laten begaan ‘release, give freedom’. After the manual cleaning, we were left with 6,808 observations, which were then coded for seven semantic, syntactic, geographical and thematic variables presented in the next section.

3.2

The response variable

The speaker’s choice for doen or laten in the given context was used as the binary response variable. The distribution of the constructions in the data set was skewed towards laten, which occurred 5,636 times, while doen was used only in 1,172 contexts, which is approximately 5 times less.

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3.3

The linguistic predictors

The variable CrSem refers to the semantic class of the causer: animate (humans and animals) or inanimate (material and abstract entities). All previous studies reported the more frequent use of animate causers with laten and inanimate ones with doen. Verhagen and Kemmer (1997) and Stukker (2005) studied the causer’s semantics only in combination with the semantic class of the causee. They found, however, that inanimate causers in combination with both animate or inanimate causees tend to be used more frequently with doen because these configurations correspond to physical and affective causation types, respectively, which imply direct causation. The most typical configuration for laten, which normally represents inducive causation, consists of animate causers and causees. This type of causation is indirect because humans cannot influence other humans’ minds directly, telepathy disregarded (Verhagen and Kemmer 1997:â•›71). The remaining possibility, the combination of animate causers with inanimate causees, allows both for direct and indirect interference of the causer. CeSem stands for the semantic class of the causee, which can also be animate or inanimate. If the causer is not the main source of energy in indirect causation, then it should most probably be the causee (cf. Stukker 2005). Thus, one could expect a higher degree of animacy of the causee in the laten-construction in comparison with doen. This variable has not been examined separately in any of the previous studies, although from Verhagen and Kemmer’s (1997) description of causation types it follows that the chances for inanimate causees to be used with doen are somewhat higher than for animate ones. Both explicit and implicit causees (see below) were classified, depending on the context and the semantics of the effected predicate. Nevertheless, we were unable to classify 13 cases with implicit causees, so we left those contexts out. CdEventSem describes the semantic class of the caused event. It can be mental or non-mental (physical or social). In case of metaphorical meaning, we assigned the semantic class that corresponded to the target domain. For example, in (3) the caused event was coded as mental: (3) Het doet het belletje rinkelen. it makes the bell_DIM ring ‘It rings a bell’. This variable was included to test whether doen is associated with the physical causation, as Speelman and Geeraerts (2009) suggested. EPTrans refers to the transitivity (including ditransitivity) or intransitivity of the effected predicate. The previous studies showed that laten is more favoured by transitive verbs, which was regarded as evidence for the indirectness of the causative situations indicated by this construction because it involved a longer causation chain with more participants.

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The variable CeSynt was inspired by Kemmer and Verhagen’s (1994) observations about the laten-construction. In some contexts, the causee in Dutch allows not only for zero-marking as in (4a), but also for the prepositions aan and door, the dative and instrumental/agentive markers in Dutch, respectively, as in (4b) and (4c):2 (4) a. Hij liet zijn vrouw zijn nieuwe gedicht lezen. ‘He made/let his wife read his new poem’. b. Hij liet zijn nieuwe gedicht aan zijn vrouw lezen. ‘He let his wife read his new poem.’ c. Hij liet zijn nieuwe gedicht door zijn vrouw lezen. ‘He had his new poem read by his wife’. d. Hij liet zijn nieuwe gedicht lezen. ‘He had his new poem read’. Kemmer and Verhagen (1994) argue on the basis of cross-linguistic evidence that propositional or indirect-object marking of the causee implies a smaller degree of integration of the causee into the causative event and its lower affectedness in comparison with the default zero-marking (or, for personal pronouns, marking with the case of the direct object). This smaller integration and affectedness is typical of indirect causation. Therefore, we should expect prepositional marking to boost laten. On the other hand, Kemmer and Verhagen also suggested that implicitness of the causee, like in (4d), means even larger peripherality and non-affectedness of the causee (Kemmer and Verhagen 1994:â•›139). However, a more recent research study by Loewenthal (2003) has shown that implicit causees in the laten-construction have a moderate degree of affectedness, although the peripherality claim may still hold. Considering all this, and also the low frequencies of the prepositional marking, we distinguished two levels of the predictor: “Central” (the causee is explicit and unmarked) and “Peripheral” (the causee is implicit or marked with a preposition).

4. Statistical analysis Multiple logistic regression allows us to model the speaker’s behaviour by taking into account several factors that influence the speaker’s choice simultaneously. The analyses were carried out with the help of R statistical software (R Development Core Team 2010). The first step of multivariate analysis is the selection of variables that have an impact on the speaker’s choice. To select the relevant variables, we used the forward and backward stepwise selection procedures based on Akaike’s Information 2. Note that all three marking options are available only for one effected predicate, lezen ‘read’. The aan-marking is typical for verbs of perception and, consequently, mental causees, whereas the preposition door normally marks agentive causees.

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Table 1.╇ Results of multiple regression (simple main effect model) Predictor

Estimate (log odds ratio)

(Intercept) CrSem = Inanimate EPTrans = Intransitive Country = BE CdEventSem = Mental CeSynt = Peripheral SubjectDomain = Football SubjectDomain = Music SubjectDomain = Politics

–4.38 (p < 0.001) â•⁄ 3.44 (p < 0.001) â•⁄ 1.48 (p < 0.001) â•⁄ 0.68 (p < 0.001) â•⁄ 0.79 (p < 0.001) –0.90 (p < 0.001) â•⁄ 0.12 (p = 0.38) â•⁄ 0.45 (p < 0.001) â•⁄ 0.35 (p = 0.009)

Criterion (AIC). This criterion helps strike a balance between the predictive power of a model and its parsimony. All predictors, except CeSem, entered the final model (see Table 1).3 The order of the variables in the table reflects their importance in predicting the speaker’s behaviour, as selected by the forward stepwise algorithm. The most important predictor is CrSem, and the least influential one is SubjectDomain. The column with the estimates provides the log odds ratios of the doen-construction for the given value of the predictor in comparison with the reference level (the values of the variables not mentioned in the table: the animate causer, the transitive effected predicate, the Netherlands, the explicit zero-marked causee, the non-mental effected predicate, and Economy as the article’s subject domain). If the log odds ratio is equal to 0, doen and laten have equal chances to occur, which means that the predictor is not informative. A positive value means that the chances of doen are higher for the given value in comparison with the reference level of the same predictor. A negative log odds ratio, conversely, stands for relatively higher chances of laten. For example, the inanimate causer increases the log odds ratio of doen in comparison with the reference level, the animate causer, by 3.40, which corresponds to the simple odds ratio of 29.96 (i.e. the chances for inanimate causers to occur in the doen-construction are almost 30 times as high as those of the animate causers). The p-values next to the estimate demonstrate how confident one can be that the estimate is not equal to 0: the lower the p-value, the more certain one can be. Conventionally, a value of α = 0.05 is used as a cut-off point for significant effects. The overall quality of the model is satisfactory, as the measurements in the lefthand column in Table 3 suggest. The most intuitive measure is the proportion of correct predictions of doen and laten by the model. We can correctly predict 90.1% of

3. Not all statisticians agree on the value of stepwise selection (e.g. Harrell 2001). However, analysis of the full model and single term deletion tests yield the same model structure.

212 Natalia Levshina, Dirk Geeraerts, and Dirk Speelman

the speakers’ choices (the cut-off probability is set to 0.5). However, this is not the most informative measure because laten is so frequent that if we simply predicted laten for all contexts, we would be correct in 82.8% of the cases, which serves as the baseline. There are special measures that neutralize the skewness, for example, the index of concordance C, also called the area under the ROC curve (see Hosmer and Lemeshow 2000:â•›160), which is 0.893 in our case. This number means that for all pairs of contexts with doen and laten, the model assigns a higher probability to the auxiliary actually observed in the context in almost 90% of the cases. C is equal to 0.5 if the predictions are random, and is equal to 1 if they are perfect. The related measures are Somers’ Dxy = 0.787 (rank correlation between the predicted probabilities and observed responses ranging from 0 to 1) and Goodman-Kruskal’s Gamma = 0.795 (with the range from –1 to 1). R2 is Nagelkerke’s generalized R2 index for logistic regression models, which is analogous to the measure of explained variation in linear models. It stands for a proportional reduction in the absolute value of the log-likelihood measure in comparison with the intercept-only model (see e.g. Menard 2001:â•›24–27 for more details). It ranges from 0 (no predictive power) to 1 (a perfect fit of the data). For this model, R2 = 0.523. All these values demonstrate that the model has a substantial predictive power. However, one more thing should be taken into account. The effect of some of the predictors on the response variable may be non-additive, i.e. it cannot be explained by the summary effect of the predictors taken separately. An example of such an interaction from health care is a situation when one and the same medical treatment produces different effects on patients depending on their sex or age. In this study, we focused on the interactions between the intralinguistic variables (semantic and syntactic ones). We selected a model with interaction terms on the basis of AIC. The procedure was performed in such a way that all five semantic and syntactic variables in all possible combinations had a chance to occur in the model. One three-way interaction CrSem:EPTrans:CeSynt turned out to be significant. Table 2 displays the model with the interaction (it also lists the relevant lower-order interaction terms). In a model with interaction terms, interpretation of the coefficients is less straightforward because we can no longer estimate an independent impact of a predictor that participates in an interaction without taking into account different levels of the other variables with which it interacts. For example, the estimate for CrSem = Inanimate in Table 2 should be interpreted as the combination of CrSem = Inanimate AND EPTrans = Transitive AND CeSynt = (the two latter terms are the reference levels of the corresponding variables). Table 3 lists the summary statistics for the two models. One can see that the predictive power of the model with interactions is slightly better in comparison with the main-effect only model, although not dramatically. This shows that our main-effect only model was informative, but too coarse to deal with some combinations of the predictor values.

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Table 2.╇ Model with main effects and three-way interactions Predictor

Estimate (log odds ratio)

(Intercept) CrSem = Inanimate (for EPTrans = Transitive and CeSynt = Central) EPTrans = Intransitive (for CrSem = Animate and CeSynt = Central) Country = BE CdEventSem = Mental CeSynt = Peripheral (for EPTrans = Transitive and CrSem = Animate) SubjectDomain = Football SubjectDomain = Music SubjectDomain = Politics EPTrans = Intransitive: CeSynt = Peripheral (for CrSem = Animate) CrSem = Inanimate: CeSynt = Peripheral (for EPTrans = Transitive) CrSem = Inanimate: EPTrans = Intransitive (for CeSynt = Central) CrSem = Inanimate: EPTrans = Intransitive: CeSynt = Peripheral

–3.59 (p < 0.001) â•⁄ 3.67 (p < 0.001) â•⁄ 0.41 (p = 0.051) â•⁄ 0.68 (p < 0.001) â•⁄ 0.78 (p < 0.001) –1.93 (p < 0.001) â•⁄ 0.16 (p = 0.27) â•⁄ 0.49 (p < 0.001) â•⁄ 0.34 (p = 0.014) â•⁄ 3.48 (p < 0.001) –0.31 (p = 0.437) â•⁄ 0.26 (p = 0.459) –2.60 (p < 0.001)

Table 3.╇ Summary statistics for two models Statistic

Model without interactions

Number of observations Proportion of correct predictions (baseline = 82.8%) C Dxy Gamma Generalized R2 AIC

6795 (doen: 1170, laten: 5625) 90.1% 90.3% 0.893 0.787 0.795 0.523 3695.8

Model with interactions

0.91 0.821 0.829 0.553 3525.2

Three-way interactions are hard to grasp intuitively, so we used another technique, named CART (Classification And Regression Trees), to visualize the interactions in a convenient way. The algorithm splits up the observations according to the values of each predictor, trying to separate the observations with doen from those with laten in the best possible way. It begins with the split that allows the cleanest separation, and then proceeds with the resulting subsets, choosing the next best split.

214 Natalia Levshina, Dirk Geeraerts, and Dirk Speelman CrSem=Anim

EPTrans=Tr

Laten 5111/318 CeSynt=Periph Laten 307/122

Doen 20/61

Doen 187/669

Figure 1.╇ Classification tree for semantic and syntactic variables

The procedure then cross-validates the resulting tree against different subsets of data, selecting the most parsimonious model with the purest “leaves”. Figure 1 shows the classification tree for our dataset (only the semantic and syntactic variables took part in the classification). It was implemented with the help of the rpart package in R.4 The minimum number of observations allowed in a split was 20; the algorithm performed 10 cross-validations. Under these conditions, only three of the five linguistic features take part in splits: CrSem, EPTrans and CeSynt. Recall that they are also the ones that interact significantly in the regression model. Each split is labeled with a decision rule, e.g. “CrSem=Anim”. If the condition is met, i.e. for all animate causers, one should follow the left branch; otherwise, the right branch should be explored. The names of the leaves display the predominant construction in the group; the numbers below stand for the number of laten- and doen-observations. The error rate of the classification was low: 9.5%, in comparison with 17.2% if we simply always predicted laten as the default auxiliary (cf. the baseline in Table 4). The first observation one can make is that doen needs more conditions to be met (inanimate causer AND intransitive effected predicate, or, in very few cases, inanimate causer AND transitive effected predicate AND explicit unmarked causee), whereas the animate causer is perfectly sufficient to obtain a leaf with a sufficient probability of laten, which also contains the largest number of observations. In addition, laten 4. An alternative solution is to use conditional inference trees. Their main advantage is that they neutralize the bias towards covariates with many possible splits (see Hothorn et al. 2006). However, all linguistic variables in the present analysis are binary, so this factor should not cause problems.



Dutch causative constructions 215

emerges in more specific situations with the inanimate causer, transitive effected predicate and peripheral causee. The classification also tells us that the features EPTrans and CeSynt are relevant for the classification only in the case of the inanimate causer. For animate causers, these features are not powerful enough to influence the outcome. In a similar way, the syntactic expression of the causee has a decisive effect only in the case of an inanimate causer and a transitive effected predicate.

5. Linguistic interpretation of the statistical models Some of our expectations based on the (in)direct causation hypothesis were confirmed by the marginal effects of the variables in the simple main effect model: inanimate causers, intransitive effected predicates and syntactically central causees do favour doen. However, we found no indication that the semantic class of the causee is significant, although one might expect that an animate causee is a better candidate for an indirect causation event because it is the main source of energy in the causation process. This lack of evidence creates a dilemma that is common in empirical studies (Geeraerts 1999). On the one hand, it may cast doubt on the indirect-direct causation hypothesis in the way it was formulated above. Alternatively, one could question our operationalization of the causee’s role in terms of animacy or inanimacy. The latter scenario seems to be more reasonable. The fact that doen is preferred by mental caused events suggests that the causation categorized with doen frequently involves animate causees as experiencers. In contrast, the laten-construction, preferred by more dynamic non-mental caused events, contains animate causees, who can play a more active, agentive role. Therefore, other, more sophisticated ways of determining the causee’s role could be helpful. The observed preference of doen by mental caused events is unexpected. In combination with inanimate causers, it seems that doen is highly associated with affective causation, which involves a stimulus (causer) that triggers a mental reaction of an experiencer (causee). This behaviourist-like causation type is very direct. However, Verhagen and Kemmer’s (1997) theory did not predict the predominance of affective causation within the semantics of doen; Speelman and Geeraerts (2009) even spoke about direct physical causation as doen’s specialization. Next, we calculated the probabilities of doen and laten for every configuration of the linguistic features, as predicted by the model with interactions. To do so, we first calculated the sum of the relevant estimates provided in Table 2, including the intercept value, and then transformed the resulting log odds ratios into probabilities.5 The

5. According to the formula P = exp(x)/(1+exp(x)), where x is the sum of the log odds ratios (coefficients) for all variables (the relevant values) and the intercept.

216 Natalia Levshina, Dirk Geeraerts, and Dirk Speelman

configurations with the highest probabilities of doen and laten can be illustrated by contexts (5) and (6), respectively. (5) Het artikel (…) deed mij terugdenken aan mijn ontmoeting met de Algerijnse ambassadeur in Brussel, voorjaar 1972 op een receptie in Den Haag. ‘The article (…) made me think back to my meeting with the Algerian ambassador in Brussels in the spring of 1972 at a reception in The Hague’. (6) Prinses Juliana zou in de jaren 60 liefdesbrieven aan haar dochters hebben laten analyseren door een grafoloog. ‘They say that in the 1960s Princess Juliana had love letters to her daughters studied by a graphologist’. Context (5), where the probability of doen is 89.7%, contains an inanimate causer, an intransitive effected predicate, an explicit unmarked causee and a mental caused event. This is a typical example of affective causation. Context (6) illustrates the configuration with the highest probability (99.2%) of laten, combining an animate causer, a transitive effected predicate, a peripheral causee and a non-mental caused event. The example evokes the service frame, when the causer uses the causee’s professional services to have some work done. Note that both examples contain animate causees, who play different semantic roles (an experiencer and agent, respectively). In his linear discriminant analysis of verb particle placement, Gries (2003) interprets the clusters of attributes with a highest distinctive load (highest discriminant scores of the sentences) as prototypes of each of the two constructions that he contrasts. Can we follow this approach and claim that contexts like (5) and (6) exemplify the prototypes of the constructions with doen and laten, respectively? Indeed, it was shown by Rosch and Mervis (1975) that the features that help maximally distinguish the given category from the others are also the features that are maximally shared between the members of the same category. The presence of these features, operationalized as a family resemblance score of a category member, also correlated positively with the member’s prototypicality in the category based on typicality ratings. This could lead us to the conclusion that the doen- and laten-observations such as (5) and (6), with the most distinctive features, should also be the best representatives of the categories from the intracategorial perspective. However, the more recent studies of natural language categories (e.g. Ceulemans and Storms 2010) show that these kinds of salience do not always correlate. The results of additional experiments (Levshina 2011) show that significant positive correlations between the intra- and intercategorial types of salience operationalized in several different ways are observed only in the case of doen, and not in the case of laten. A possible explanation is that laten, which is used much more frequently than doen, is also a more heterogeneous category. In a polysemous category, the sense that is the most semantically distant from a contrasting category may not be central intracategorially. In addition, one can imagine that the distinctive features of laten with regard to

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another construction may be different from those with regard to doen. All this means that we should be very specific about the perspective and operationalization when using the term ‘prototype’. The configurations of the distinctive features exemplified by the sentences (5) and (6) are thus distinctive corpus-based ‘prototypes’ with regard to the choice between doen and laten modelled with the help of logistic regression. In addition, the analyses reveal that doen is indeed quantitatively and semantically restricted, as Speelman and Geeraerts (2009) wrote. This can be illustrated by the classification tree in Figure 1, which shows clearly that a larger number of semantic and syntactic conditions should be satisfied for doen to have more chances to occur in a context than laten. Therefore, doen seems to have more Gestalt-like semantics than laten, which has a looser set of semantic features. This conclusion can be supported by the fact that laten is a highly schematic auxiliary with a semantic range from permission to coercion. So far, we have not discussed the behaviour of the Subject Domain variable. The effect of the topic on the distribution of doen and laten was not predicted by any of the previous hypotheses. It would be natural to assume that different topics differ with regard to lexicon. This is why we looked at the top five most popular effected predicates in the four subject domains, which are shown in Table 4 with their relative frequencies. One can see that the four topics are dominated by the same highly frequent verbs: zien ‘see’, weten ‘know’, horen ‘hear’, denken ‘think’, liggen ‘lie’, vallen ‘fall’, gaan ‘go’ with different relative frequencies. This might not be a serious problem if these highly frequent verbs did not demonstrate an outspoken preference either for laten or doen. For instance, weten is a typical laten-verb, with 450 occurrences in our data, all of them with laten. Some previous research, e.g. Levshina et al. (2009), which was based on collostructional analysis (Stefanowitsch and Gries 2003), also showed that attraction between the effected predicates and the constructions (auxiliaries) is indeed very strong. This is why the differences in the relative frequencies of these influential predicates may have an effect on the distribution of doen and laten in the subject domains. One of the ways to capture this idiomatic difference is to incorporate the lexical “noise” in the model as random effects. This method, called mixed-effect modelling, has proved to be a powerful tool in linguistic research, especially in Table 4.╇ Top five most frequent effected predicates in the four subject domains Economy

Football

Music

Politics

zien ‘see’ 13% weten ‘know’ 11% liggen ‘lie’ 5% vallen ‘fall’ 3% stijgen ‘go up’ 3%

liggen ‘lie’ 9% zien ‘see’ 8% weten ‘know’ 5% vallen ‘fall’ 4% spelen ‘play’ 2%

horen ‘hear’ 11% denken ‘think’ 8% zien ‘see’ 4% klinken ‘sound’ 3% weten ‘know’ 2%

weten ‘know’ 10% zien ‘see’ 6% vallen ‘fall’ 4% gaan ‘go’ 2% denken ‘think’ 2%

218 Natalia Levshina, Dirk Geeraerts, and Dirk Speelman

psycholinguistic experiments with individual subject- and item-related noise (see a variety of case studies in Baayen 2008). It is also helpful in corpus-based studies when idiosyncrasies of individual words cannot be handled with the help of coarse-grained semantic classifications. Using the lmer package in R , we fit a mixed-effect with the effected predicates (1,165 types represented by 6,795 tokens) as random effects. By doing so, we “tell” the model that some effected predicates may inherently prefer doen, and that some verbs may prefer laten. The algorithm slightly lowers or increases the value of the intercept for each verb depending on its preferences in the data. It also takes into account the frequency of the verb in the data set. Ideally, we would have to do the same for the constructional slots of the causer and the causee. However, application of this method is less evident for nominal slots because of pronominal reference and lower type-token ratios. There is also evidence that the ties between nouns and constructions in which they appear are weaker than those between constructions and verbs (cf. Tomasello et al. 1997). Fitting a mixed-effect model (with main effects only) yields the results shown in Table 5. The factors and the tendencies that we had in the corresponding model without random effects remain very similar, with the exception of the subject domain, which ceases to contribute substantially to the model’s performance (according to AIC). Therefore, we can conclude that the difference in probabilities of doen and laten across different topics is due to the lexical effects. Also, most of the absolute values of the coefficients in the mixed model are slightly higher than those in the fixed-effect only model (see Table 1) because we have filtered out some part of the lexical “noise”, which caused overfitting in the initial model. The model demonstrates that the abstract features related to direct or indirect causation are still significant when conditioned on the lexical effects (cf. Bresnan et al. 2007:â•›87). At the same time, additional tests show that the random-effect model alone would allow the prediction of the choice of doen and laten correctly in a vast majority of cases (78% for the Netherlandic subcorpus and 74% for the Belgian data). This can be seen as evidence of strong exemplar effects at the level of the effected predicates. Table 5.╇ Logistic regression model with effected predicates as random effects Predictor

Estimate (log odds ratio)

(Intercept) CrSem = Inanimate EPTrans = Intransitive Country = BE CdEventSem = Mental CeSynt = Peripheral SubjectDomain = Football SubjectDomain = Music SubjectDomain = Politics

–5.95 (p < 0.001) â•⁄ 4.22 (p < 0.001) â•⁄ 2.25 (p < 0.001) â•⁄ 0.76 (p < 0.001) â•⁄ 1.11 (p < 0.001) –0.83 (p = 0.003) Not Available



Dutch causative constructions 219

However, the best-performing model is the one with both the abstract and the lexical features. This finding is perfectly in line with the non-reductionist constructionist approach to language, which assumes that high-level generalizations coexist with low-level schemata in the speaker’s knowledge about constructions (Langacker 1987; Goldberg 1995, 2006).

6. Conclusion In this multivariate corpus-based onomasiological probabilistic study, we used logistic regression to find the factors that influence the choice between the causative constructions with doen and laten by speakers of Dutch. The analyses showed that the highest probability of doen is observed in the contexts of affective causation: an inanimate stimulus causing a conceptually and syntactically central cognizer to experience some mental state (an intransitive event). Conversely, the laten-construction has the highest chances of being observed when the causer is animate, the effected predicate is transitive, the causee is implicit or marked with a preposition (syntactically and conceptually peripheral), and the caused event is non-mental. This configuration can be exemplified by the service frame. The combinations of these features, which have the highest cue validity with regard to the choice between the categories, can be regarded as the distinctive prototypes of the constructions. Their relations with the other salience phenomena, such as family resemblance, goodness of membership, entrenchment, etc., are to be explored empirically, although there are indications that the inter- and intracategorial typicality measures tend to correlate for compact categories without rich polysemy (in our case, doen). We also found evidence of exemplar effects in categorization at the level of the lexemes that fill in the effected predicate slot, which can serve as powerful predictors of the speaker’s choice on their own. However, the best prediction is achieved when the model combines both the above-mentioned semantic generalizations and the lexemes. This supports the constructionist hypothesis that the mind stores linguistic knowledge at different levels of generalization. In addition, the results show that the doen-construction has more chances of being chosen by a Flemish speaker than by a Dutch one, which supports the previous findings by Speelman and Geeraerts (2009) for spoken data and can be explained historically (the Flemish variety is believed to retain more archaic features). The constructions also display different behaviour across the four subject domains, which, as the mixed-effect model demonstrates, can be explained by the domain-specific differences in the distribution of the effected predicates.

220 Natalia Levshina, Dirk Geeraerts, and Dirk Speelman

References Baayen, R. H. (2008). Analysing linguistic data: A practical introduction to statistics using R. Cambridge: Cambridge University Press. DOI: 10.1017/CBO9780511801686 Bresnan, J., Cueni, A., Nikitina, T., & Baayen, R. H. (2007). Predicting the dative alternation. In G. Boume, I. Kraemer, & J. Zwarts (Eds.), Cognitive foundations of interpretation (pp. 69– 94). Amsterdam: Royal Netherlands Academy of Science. Bouma, G., van Noord, G., & Malouf, R. (2001). Alpino: Wide-coverage computational analysis of Dutch. In W. Dalemans, K. Sima’an, J. Veenstra, & J. Zavrel (Eds.), Computational linguistics in the Netherlands 2000: Selected papers from the Eleventh CLIN meeting (pp. 45– 59). Amsterdam: Rodopi. Bybee, J. (2010). Language, usage and cognition. Cambridge: Cambridge University Press. DOI: 10.1017/CBO9780511750526 Bybee, J., & Eddington, D. (2006). A usage-based approach to Spanish verbs of ‘becoming’. Language, 82(2), 323–355. DOI: 10.1353/lan.2006.0081 Ceulemans, E., & Storms, G. (2010). Detecting intra and inter categorical structure in semantic concepts using HICLAS. Acta Psychologica,133 (3), 296–304. DOI: 10.1016/j.actpsy. 2009.11.011 De Sutter, G. (2009). Towards a multivariate model of grammar: The case of word order variation in Dutch clause final verb clusters. In A. Dufter, J. Fleischer, & G. Seiler (Eds.), Describing and modeling variation in grammar (pp. 225–254). Berlin & New York: Mouton de Gruyter. Degand, L. (2001). Form and function of causation. A theoretical and empirical investigation of causal constructions in Dutch. Leuven: Peeters. Geeraerts, D. (1999). Idealist and empiricist tendencies in cognitive semantics. In T. Janssen, & G. Redeker (Eds.), Cognitive linguistics: Foundations, scope and methodology (pp. 163– 194). Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110803464.163 Geeraerts, D. (2006). Salience phenomena in the lexicon: A typology. In D. Geeraerts (Ed.), Words and other wonders: Papers on lexical and semantic topics (pp. 74–97). Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110219128.1.74 Glynn, D., & Fischer, K. (2010). Quantitative methods in Cognitive Semantics: Corpus-driven approaches. Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110226423 Goldberg, A. E. (1995). Constructions: A construction grammar approach to argument structure. Chicago: University of Chicago Press. Goldberg, A. E. (2006). Constructions at work: The nature of generalizations in language. Oxford: Oxford University Press. Gries, St. Th. (2003). Multifactorial analysis in corpus linguistics: A study of particle placement. New York: Continuum. Grondelaers, S., Geeraerts, D., & Speelman, D. (2007). A case for a cognitive corpus linguistics. In M. Gonzalez-Marquez, I. Mittleberg, S. Coulson, & M. Spivey (Eds.), Methods in cognitive linguistics (pp. 149–169). Amsterdam & Philadelphia: John Benjamins. Harrell, F. E. (2001). Regression modelling strategies with applications to linear models, logistic regression, and survival analysis. Heidelberg & New York: Springer. Heylen, K. (2005). A quantitative corpus study of German word order variation. In S. Kepser, & M. Reis (Eds.), Linguistic evidence: Empirical, theoretical and computational perspectives (pp. 241–264). Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110197549.241



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Hosmer, D. W. & Lemeshow, S. (2000). Applied logistic regression. New York: Wiley. DOI: 10.1002/0471722146 Hothorn, T., Hornik, K., & Zeileis, A. (2006). Unbiased recursive partitioning: A conditional inference framework. Journal of Computational and Graphical Statistics, 15(3), 651–674. DOI: 10.1198/106186006X133933 Kemmer, S., & Verhagen, A. (1994). The grammar of causatives and the conceptual structure of events. Cognitive Linguistics, 5(2), 115–156. DOI: 10.1515/cogl.1994.5.2.115 Langacker, R. W. (1987). Foundations of cognitive grammar: Volume I: Theoretical prerequisites. Stanford: Stanford University Press. Levshina, N. (2011). Doe wat je niet laten kan: A usage-based analysis of Dutch causative constructions [Do what you cannot let: A usage-based analysis of Dutch causative constructions]. Unpublished doctoral dissertation, University of Leuven. Levshina, N., Geeraerts, D., & Speelman, D. (2009). Collostructional analysis of Dutch causative constructions. Paper presented at the Third International AFLiCo Conference, 28 May, Paris. Loewenthal, J. (2003). Meaning and use of causeeless causative constructions with laten in Dutch. In A. Verhagen, & J. van de Weijer (Eds.), Usage-based approaches to Dutch (pp. 97– 130). Utrecht: LOT. Medin, D. L., & Schaffer, M. M. (1978). Context theory of classification learning. Psychological Review, 85(3), 207–238. DOI: 10.1037/0033-295X.85.3.207 Menard, S. (2001). Applied logistic regression analysis. Thousand Oaks: Sage. R Development Core Team (2010). R: A language and environment for statistical computing. Foundation for statistical computing. Vienna, Austria. . Rosch, E. (1975). Cognitive representation of semantic categories. Journal of Experimental Psychology, 104(3), 192–233. DOI: 10.1037/0096-3445.104.3.192 Rosch, E., & Mervis, C. B. (1975). Family resemblances: Studies in the internal structure of categories. Cognitive Psychology, 7(4), 573–605. DOI: 10.1016/0010-0285(75)90024-9 Speelman, D., & Geeraerts, D. (2009). Causes for causatives: The case of Dutch doen and laten. In T. Sanders, & E. Sweetser (Eds.), Causal categories in discourse and cognition (pp. 173– 204). Berlin & New York: Mouton de Gruyter. Stefanowitsch, A., & Gries, St. Th. (2003). Collostructions: Investigating the interaction between words and constructions. International Journal of Corpus Linguistics, 8(2), 209–243. DOI: 10.1075/ijcl.8.2.03ste Stukker, N. (2005). Causality marking across levels of language structure. Unpublished PhD dissertation, University of Utrecht. Tomasello, M., Akhtar, N., Dodson, K., & Rekau, L. (1997). Differential productivity in young children’s use of nouns and verbs. Journal of Child Language, 24(2), 373–87. DOI: 10.1017/S0305000997003085 Tummers, J., Heylen, K., & Geeraerts, D. (2005). Usage-based approaches in cognitive linguistics: A technical state of the art. Corpus Linguistics and Linguistic Theory, 1(2), 225–261. DOI: 10.1515/cllt.2005.1.2.225 Verhagen, A., & Kemmer, S. (1997). Interaction and causation: Causative constructions in modern standard Dutch. Journal of Pragmatics, 27(1), 61–82. DOI: 10.1016/S0378-2166 (96)00003-3

The semasiological structure of Polish myśleć ‘to think’ A study in verb-prefix semantics Małgorzata Fabiszak, Anna Hebda, Iwona Kokorniak, and Karolina Krawczak Adam Mickiewicz University, Poznań

The aim of the present chapter is to investigate the semasiological structure of the Polish verb myśleć ‘to think’ relative to the construal imposed by its prefixes. It juxtaposes the results of cognitive linguistic corpus-based introspective analysis with the results of a series of statistical tests of almost 4,000 manually coded example sentences. Multiple correspondence analysis employs the techniques presented in Glynn (this volume), hierarchical cluster analysis follows Divjak and Fieller (this volume) and logistic regression is based on Speelman (this volume). The study shows that the do- prefix has a strong preference for clausal, processual complements, while the wy- prefix opts for nominal complements, suggesting objectifiable results of the thinking process. Keywords: hierarchical cluster analysis, logistic regression, multiple correspondence analysis, Polish verbal prefixes, Polish verb myśleć ‘to think’

1. Introduction Given that it is a universal human capacity to think and to verbalize one’s thoughts in an intersubjective context, it is a reasonable assumption that a lexeme designating such a cognitive activity and state would be present in every language (Fortescue 2001:â•›15). However, despite its universality, an accurate explanation of the meaning and use of a cognition verb, such as myśleć in Polish or think in English, is a particularly challenging task. The difficulty in representing the semantic structure of such predicates stems from their conceptual schematicity. This schematicity is elaborated by instantiation in context to produce any one of the verb’s multiple senses. Along lexical and discursive lines, it encodes various loads of intentionality, modality, subjectivity, and in some of its uses, it is highly grammaticalized. Through detailed corpus-driven

224 Małgorzata Fabiszak et al.

conceptual analysis, our project takes up the challenge of systematically describing the semantic structure of prefixed think verbs in Polish.1 Specifically, the analysis examines the contribution of six prefixes to the semantics of the mental predicate relative to its object. The first stage of the study employs introspective analysis in order to establish a set of testifiable hypotheses about the semantic contribution of these highly schematic prefixes. The second stage turns to a quantitative analysis of a large number of occurrences, annotated manually for an array of grammatical and semantic features. The ‘behavioural profiles’ of the verbs that result from this analysis are identified through subsequent multivariate statistical modeling (Geeraerts et al. 1994; Gries 2006; Glynn 2010b). Thinking, in most general terms, can be perceived as “internalized (and abbreviated) speech”, which is thus tantamount to “self-awareness” (Fortescue 2001:â•›17f.). This “private, internal activity” can be further specified into at least three kinds of processes, which consist of “evaluating” someone or something, “believing in the truth of a proposition” or “‘mulling over’ some mental content” (Fortescue 2001:â•›30). On a metalinguistic plane, ‘think’ can be regarded as a language-independent semantic universal (Wierzbicka 1992, 1996, 1997, 1999), which has recently been corroborated in several cross-linguistic studies, e.g. by Amberber (2003) on Amharic or by Junker (2003) on East Cree, an Algonquian language. The question remains, however, as to which senses of ‘think’ should be universally constitutive of the core of human thought (Fortescue 2001:â•›32). It is, after all, indisputable that language-specific exponents of think are characterized by polysemy and that they enter onomasiological relations by way of “lexical elaboration” (Goddard 2003). Attempts have also been made to reduce such presumably irreducible concepts. Jackendoff (1983:â•›234ff., as cited in Fortescue 2001:â•›32) factorized such mental predicates to the formula [be [rep[x]][in y’s mind]]. This formula is similar to the metaphorical representation of the thought process, as analysed within Conceptual Metaphor Theory, where the mind is understood as a container for thoughts-objects (Lakoff and Johnson 1980; Szwedek 2007). Perhaps a good solution would be to view the mental verb ‘think’ as belonging to “a network of experiential categories” or as a “radial” or “polycentric” category, whose most focal sense should be “the lowest common denominator” shared by all senses of ‘think’ (Fortescue 2001:â•›32–35).

1. The EmBeR project focuses on the conceptualization of abstract categories, such as Em(otion), Be(lief), and R(eason) in Polish and English. It uses corpus-driven techniques and multivariate statistics in an effort to capture the complex semantic structure of the three categories. Team members include Małgorzata Fabiszak, Anna Hebda, Iwona Kokorniak, Karolina Krawczak, and Barbara Konat at Adam Mickiewicz University, Poznań, Poland. We are greatly indebted to Dylan Glynn for introducing us to the methods of multivariate statistics. Our thanks also extend to three anonymous reviewers and the editors of this volume for their constructive comments. Any remaining shortcomings remain our own.



The semasiological structure of Polish myśleć ‘to think’ 225

Linguistically speaking, ‘think’ is indeed characterized by semantic generality and impoverishment (Danielewiczowa 2002:â•›131), but its conceptual schematic structure is contextually expanded (Kustova 2000:â•›250). It is therefore of utmost importance to examine the structural and semantic characteristics of this mental verb, bearing in mind that even seemingly negligible differences in verb valency may be significant (Danielewiczowa 2000:â•›231). There is at least a twofold distinction to be drawn in the semasiological structure of ‘think’ between states and activities, which is formally realized in English in the use of aspects, where the progressive can only be applied to non-stative mental events (e.g. Vendler 1967:â•›110f.; D’Andrade 1987, 1995). This bipartite division leads to the treatment of the mind as a “processor” or “container” (D’Andrade 1987, as cited in Palmer 2003:â•›270). Goddard (2003:â•›112) goes beyond Vendler’s (1967) bifurcation into think about and think that, and specifies the semantic prime think into four subgroups, depending on their conceptual syntactic features, whereby: a. b. c. d.

X thinks about Y [topic of thought] X thinks something (good/bad) about Y [complement] X thinks like this: ——— [quasi-quotational complement] X thinks that [——— ]S [propositional complement]. (Goddard 2003:â•›112)

Danielewiczowa (2000) proposes a further distinction, showing that thinking can also be dynamic, intentional, knowledge-driven, factual or hypothetical. It can be conscious or overwhelmingly intensive and subconscious, it can induce change in the subject, be a point-of-time or period-of time event, refer to an object or be self-oriented. The object of thinking can be abstract or concrete, factual or hypothetical, verifiable or non-verifiable (Danielewiczowa 2002:â•›132f.). It can vary considerably in terms of content, length, cohesion, origin, and structure (Pawłowska 1981). Object semantics will also be affected by how the object is introduced. For example, the complementizer że [that] is likely to specify the object more than pronouns such as co [what], gdzie [where], dlaczego [why], which only hint at what the object relates to (Pawłowska 1981). Insofar as the grammatical form of mental verbs influences their “semantic potential” and “pragmatic effects” (Danielewiczowa 2000:â•›265), their aspect, object form and object semantics will naturally entail changes in the function and profiling of such predicates. It is the aim of the present study to identify the semasiological organization of and onomasiological relations between the instantiations of think relative to the construal imposed by prefixes. Obviously, the schematic semantics of the unprefixed predicate contributes to the content of each of the prefixed forms. It constitutes the superordinate meaning component, the “semantic primitive” or “building block” of the subordinate expressions (Wierzbicka 1992:â•›9). Their semantico-pragmatic load is specified and disambiguated by their prefixal modification. It is, therefore, expected

226 Małgorzata Fabiszak et al.

that the internal structure of such prefixed ‘think’ forms and the near-synonymous relations holding between them will be particularly distinct. Myśleć ‘think’, when unaccompanied by any prefix, is an imperfective verb. Its aspect may change into the perfective one by means of adding a prefix, such as do(domyślić się ‘guess sth’), po- (pomyśleć ‘think sth’), prze- (przemyśleć ‘think over’), roz- (rozmyślić się ‘change one’s mind’), wy- (wymyślić ‘come up with’), za- (zamyślić się ‘fall into deep thought’), and others. However, the ‘perfectivized’ verb form can be further ‘imperfectivized’ through suffixation (cf. Comrie 1976), e.g. domyślać się ‘guess’, rozmyślać ‘ponder’, wymyślać ‘invent’. In the present contribution, the semantics of the aforementioned prefixes relative to their perfective and imperfective aspects will be considered in quantitative terms in relation to their combination with objects. The procedure adopted here is in line with the tradition of corpus-driven Cognitive Linguistics, as practised by Dirven et al. (1982), Geeraerts et al. (1994), Gries (2003, 2006), Divjak (2006, 2010), and Glynn (2009, forthc.), to mention but a few. In accordance with this tradition, introspective conceptual analysis, if crucial and necessary, is viewed as insufficient, as it cannot produce falsifiable answers to research questions. It is, therefore, essential for a large number of examples of the object of study to be subjected to detailed manual conceptual analysis of their syntactic and semantic characteristics. Once this stage is completed, the annotated data can be submitted to exploratory and, subsequently, confirmatory multivariate statistical modelling. The purpose of this procedure is to find and verify “patterns of usage features” (Glynn 2009, 2010b), also known in the field as “feature configurations” (Geeraerts et al. 1994) or “behavioural profiles” (Gries 2006; Divjak and Gries 2006). Summing up, thinking in its simplicity and universality is a multidimensional mental event of states and processes, which can be dynamic, factual, hypothetical, consciously entertained by the subject, or unconscious, based on and expressing knowledge, or unfounded, oriented toward an object or objectless, intentional or unintentional. All these features contribute to the holistic semasiological structure of ‘think’, rather than portioning it indefinitely. In this article we seek to account for some of the active semantic components in Polish prefixed myśleć, mapping its meaning from usage events. Section 2 presents a conceptual linguistic analysis of the Prefix, Aspect and Object Form relations, illustrated with examples from the PWN Corpus of the Polish Language. Section 3 describes the corpus, Section 4 outlines the coding procedure, and Section 5 presents the multivariate analysis. The results of the usage-feature analysis are submitted to the exploratory statistical techniques: multiple correspondence analysis and hierarchical cluster analysis. Where applicable, the results are further supported by the confirmatory method of logistic regression analysis. The selection of these three statistical techniques is motivated by the different affordances they offer to researchers. Correspondence analysis has been developed for nominal categorical data and allows the visualisation of the correspondences between multiple factors – linguistic features. The most promising tendencies observed in the



The semasiological structure of Polish myśleć ‘to think’ 227

correspondence analysis maps are then further tested with the confirmatory statistical method – logistic regression, which goes beyond the identification of correspondences and gives probability scores indicating which of the correspondences are significant and what is the contribution of the individual features to the overall pattern. Finally, cluster analysis offers a representation which can be best compared with the result of the introspective conceptual analysis offered in Section 2.

2. Introspective conceptual analysis of the prefixed forms of myśleć ‘to think’ in Polish At first sight, the grammatical constructions that the verb myśleć ‘think’ and its prefixed forms go into may appear to be arbitrary and unpredictable. However, as Langacker (1991:â•›294) points out, the unpredictability of grammar arises from the objectivist approach to semantics. By contrast, the Cognitive Grammar approach finds: semantic value in every one of its uses. Moreover, it is precisely because of their conceptual import – the contrasting images they impose – that alternate grammatical devices are commonly available to code the same situation.  (Langacker 1991:â•›295)

Thus, a fine-grained analysis should elucidate the complex nature of grammatical structures (Langacker 1991:â•›294). Myśleć ‘think’ can be considered as an imperfective verb. Its aspect may change into the perfective one by means of adding a prefix, such as do- (domyślić się), po- (pomyśleć), prze- (przemyśleć), roz- (rozmyślić się), wy- (wymyślić), za- (zamyślić się), and others. However, these ‘perfectivized’ forms may undergo suffixal imperfectivization, resulting in the imperfective form, e.g. domyślać się, rozmyślać, wymyślać. The semantics of the aforementioned prefixes will be considered below and their combination with objects will be accounted for. The prefix do- may combine with verbs to indicate an approximation to a goal or result (Śmiech 1986:â•›90–91). In cognitive terms, it represents the path image schema in which the goal or final point of the path along which a movement takes place is in focus. Reaching the goal may involve encountering certain difficulties along the way, where the trajector (TR) makes every effort to achieve the goal regardless of any obstacles. The intensity of the effort is observed by Dickey (2009), who calls do- verbs “intensive-resultative”. In domyśla/ić się the TR corresponds with the subject of the main clause. What constitutes the landmark (LM) here is the metonymic gathering of information in the course of the thinking activity. Whether the activity is complete or not is indicated, in the case of domyśla/ić się, by the suffix, where -ać, as in (1a–b), construes an uncompleted process, and -ić , as in (2a–b), a completed process. The gathered information

228 Małgorzata Fabiszak et al.

in the LM position is usually rendered explicitly in sentences, i.e. either with a nominal phrase, as in (1a) and (2a), or with a clausal complement, as in (1b) and (2b). (1) a. Nie domyślał się przyczyny [Not DO-thought-masc.3.sg.impf refl cause-sg.gen sporu. [argument-sg.gen] ‘He did not guess what the reason for the argument was.’ b. Nie domyślał się, że ktoś jest w [Not DO-thought-masc.3.sg.impf refl that someone-nom is in] pokoju. [room-sg.loc]2 ‘He did not guess that someone was in the room.’ (2) a. Nietrudno było domyślić się przeznaczenia tego [easily was DO-think-inf refl purpose-gen this-gen] miejsca. [place-gen] ‘One could easily guess what the purpose of this place was.’ b. Zaskoczony, zupełnie nie kontrolowałem wtedy [Surprised totally not controlled-masc.3sg.impf then] twarzy i mogę się domyślić, co [face-gen and can-1sg.pres refl DO-think-inf what wyczytała z niej ta biedna out-read-fem.3sg.perf from it-fem.gen this poor-fem-3sg] brzydula [ugly girl-nom] ‘Surprised, I did not control my facial expression and I can guess what she read in it, this poor ugly girl.’ The nominal phrase that domyśla/ić się can be combined with takes the genitive case, which in one of its uses may conceptualize a goal that is being aimed at (Rudzka-Â� Ostyn 2000:â•›201). It is not due to chance, then, that do-predicates are called ‘attainment verbs’, as both their nominal complement and the prefix construe the attainment of a desired result (e.g. Dickey unpubl. manusc.:â•›15). Additionally, the reflexive pronoun in domyśla/ić się indicates that the experiencer of the process taking the subject position is both the instigator and the passive experiencer affected by the result of the process (Dąbrowska 1997:â•›93). The ‘beneficial’ or ‘favourable’ effect of the process on the subject has been observed by Przybylska

2. In the word-for-word gloss the prefixes are rendered with capital letters in their Polish form. We follow here Tabakowska (2003a).



The semasiological structure of Polish myśleć ‘to think’ 229

(2006:â•›60–61), as well as by Tabakowska (2003b:â•›15), who considers it rather natural that “one does not, under normal circumstances, want to cause damage to oneself ”. Another prefix, po-, may form delimitative verbs to indicate (i) a short duration of an action; (ii) a limited nature of an action; or (iii) when combined with the dative reflexive pronoun sobie, an ‘affective’ state of the subject (Piernikarski 1975:â•›33). In combination with myśleć, po- tends to indicate sense (ii). It may change the verb into a perfective one, which according to Dickey’s (2000) ‘east-west aspect theory’ has the meaning of temporal definiteness, where a temporally definite event “is unique in the temporal fact structure of a discourse, i.e. (…) it is viewed as both (a) a complete whole and (b) qualitatively different from preceding and subsequent states of affairs” (Dickey and Hutcheson 2003:â•›27–28).3 When it comes to complementation, pomyśleć may take a clausal complement, as in (3a), or a prepositional phrase with o ‘about’, and a nominal phrase in the locative (LOC) case. It may refer to “dispersed motion in any direction relative to a landmark” in the abstract temporal domain (Radden and Dirven 2007:â•›321), thus indicating that the object of thinking is not directly focused on, as in (3b). In less frequent cases, the object of thinking is profiled by means of nad ‘over’ with the nominal in the instrumental (INSTR) case, where the preposition, in one of its spatial senses, construes a multiplex path with “a single point-like TR moving in a variety of directions (…) to trace a multiplex collection of paths, which in turn can be construed as a mass” (Dewell 1994:â•›375). Metaphorically, in relation to pomyśleć, this schema can be understood as considering alternative ways to follow before reaching a final solution, where only the solution is mentioned explicitly, as in (3c): (3) a. Z radością pomyślałaś, że [With joy-instr PO-thought-fem.2sg.perf that] spotkałaś mężczyznę, który lubi [met-em.2sg.perf man-gen who like-3sg.pres] cię taką, jaka jesteś. [you-acc such like be-2sg.pres] ‘You have thought with joy that you met a man who likes you the way you are.’ b. Gdyby miał normalne warunki do pracy, [if had-masc.3sg normal conditions-acc to work-gen] nawet nie pomyślałby o wyjeździe. [even not PO-thought-masc.3sg.cond about departure-loc] ‘If he had normal working conditions, he wouldn’t even think about going abroad.’ 3. However, Śmiech (1986:â•›18–19) adds that a verb with the po- prefix, although taking a perfective form, may behave like an imperfective one. In the case of pomyśleć, the process seems to be completed and the verb form is perfective.

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c. Gdyby chociaż można było gdzieś tam [if at least can-3sg.pres was-3sg somewhere there] dostać pracę to może pomyślałbym [get-inf job-acc then perhaps PO-thought-masc.3sg.cond] nad powrotem [over comeback-instr] ‘If it were possible to get a job somewhere there, I would think about coming back.’ Prze-, yet another prefix, in the spatial domain may depict a three-dimensional and bounded LM, such as a tunnel in which the TR moves from one end to the other, where the TR “gradually fills the whole volume of the landmark” (Pasich-Piasecka 1993:â•›19). When extended metaphorically, prze- may carry the meaning of ‘entirely through’, as observed by Pasich-Piasecka (1993:â•›18). In przemyśleć, the prefix not only implies the in-depth nature of the mental activity, but also points to its completeness. The TR does not move in the physical, but in the temporal space here, covering a certain period of time to perform the activity. The entity depicted is in the accusative case, as in (4), constitutes the LM which is directly affected by the experiencer of the process: (4) Wszystko przemyślał, wszystko [all-acc PRZE-thought-masc.3sg.perf all-acc rozważył considered-masc.3sg.perf] ‘He thought everything over, he considered everything.’ As Janda (1993:â•›143–145) points out, the accusative is the case marker which shows the dynamicity of the process and perfectly reflects the fact that the entity taking it is directly influenced by the TR and, as a result, may undergo certain changes. The prefix in the verb przemyśleć points to the completeness of the temporally extended process, which quite often may be complemented by other elements in the sentence, such as cały ‘whole’, wszystko ‘all’, etc. Due to its extended and complete sense, przemyśleć belongs to the perdurative group of verbs (Grochowska 1979:â•›70; Przybylska 2006:â•›160; Dickey 2009, unpubl. manusc.). Roz-, in its basic image schema, represents the TR and LM constituting one entity before a change, which takes different forms afterwards. Thus, the comparison of the two states of the entity before and after the change profiles different senses of roz-, which are to a great extent determined by the verb they go with (Przybylska 2006:â•›201). When in combination with roz-, myśleć may take either an imperfective or a perfective form. In the former case, the observed change is in the intensity of the mental activity. As Przybylska (2002:â•›271) notes, the activity is represented in both the basic and the prefixed form of the verb; the difference may lie in the duration and intensity of the activity. The same observation is made by Dickey (unpubl. manusc.:â•›14),



The semasiological structure of Polish myśleć ‘to think’ 231

who calls this type of verbs ‘procedural’ as they “do not alter the basic lexical meaning of the source verb” and modify only the aforementioned aspects. Compare the following sentences (invented examples): (5) a. Piotr myślał o Marysi. [Peter-masc.nom.sg was thinking-3sg.impf about Mary-fem.loc.sg] ‘Peter was thinking about Mary.’ b. Piotr rozmyślał o [Peter-masc.nom.sg through-was thinking-3sg.impf about Marysi. Mary-fem.loc.sg] ‘Peter mused/was musing about Mary.’ In both (5a) and (5b), the verbs take the imperfective form; in the latter case, however, the prefix emphasizes the extendedness of the process. The dispersed nature of the mental activity is additionally highlighted by the preposition which rozmyślać may go with. Just like pomyśleć, it may be combined with o ‘about’ and the nominal phrase in LOC, as in (5b), or with nad ‘over’ and the substantive in INSTR, as in (5c). The prepositions and the case markers show that the objects are not directly affected by the process. The prepositions, whose senses discussed earlier for pomyśleć are also relevant for rozmyślać, profile either proximity or a variety of directions to follow, respectively. The cases, on the other hand, indicate just the area, but not the direct focus, of attention. (5) c. Otarł je szybko i, zacisnąwszy [Wiped-masc.3sg.perf them fast and clenching] szczęki, rozmyślał gorączkowo nad [jaws-acc was ROZ-thought-masc.3sg.impf frantically over sposobami ratunku ways-INSTR help-gen] ‘He wiped them fast and, clenching his jaws, he frantically pondered over the ways to help.’ d. Zrób sobie kawę i przestań bezproduktywnie [Make-imp self-dat coffee-acc and stop-imp unproductively rozmyślać! ROZ-think-inf] ‘Make yourself a coffee and stop pondering unproductively.’ As can be observed, the sense of roz- is strongly related to the prepositional senses it goes with. However, rozmyślać does not have to take any object and it still implicitly shows that the TR’s (subject’s) thoughts go in more than one direction, as in (5d). Roz- can also take a perfective form with myśleć, resulting in a reflexive verb rozmyślić się ‘change one’s mind’. The observed change in the subject’s mental state is

232 Małgorzata Fabiszak et al.

between the ‘normal’ process of the mental activity represented by the unprefixed form into the ‘changed’ mental state represented by the prefixed form. The reflexive pronoun emphasizes the internal mental change of the subject, which may also bring about a change in the subject’s behaviour, frequently conceived of by observers as a negative change (Przybylska 2002:â•›279–280). The behavioural change may be considered to be the oblique result of the mental activity (Dickey unpubl. manusc.:â•›15). Consider (6), where Salisz’s change of mind may result in his change of behaviour and his calling another person back, reflected in (6) by zawoła go z powrotem ‘call him back’: (6) Pędził co sił w obawie, że Salisz [Rushed-masc.3sg.impf what strength-pl.gen in fear-loc that Salisz się rozmyśli, że zawoła go z refl] [ROZ-think-3sg.fut that call-3sg.fut him-acc with powrotem. return-instr] ‘He ran with all his might for fear that Salisz would change his mind and call him back.’ The prefix wy- in the spatial domain construes the TR’s emergence from the LM, or its coming into existence by leaving the bounded region of the LM, thus evoking the container image schema. Some correspondences can be found between wy- and English out of, which in its prototypical image schema depicts “removal or departure of one concrete object from within another object or place” (Lindner 1983:â•›81). In combination with myśleć, wy- metaphorically refers to a mental state as a result of which one, as in (7a), or more ideas, as in (7b), emerge from one’s mind: (7) a. Sama wymyśliłam przepis na moje [alone-fem WY-thought-fem.3sg.perf recipe-acc on my najukochańsze ciasto. lovliest-acc cake-acc] ‘I came up with the recipe for my favourite cake myself.’ b. Co pewien czas panny wymyślały takie [What some maidens-nom WY-thought-fem.3pl.impf such time wieloznaczne słowa. ambiguous-acc] [words-acc] ‘Every now and again girls came up with such ambiguous words.’ In the perfective form of the verb (7a), one focuses on the effect of the process of thinking, indicating also its thorough nature. The result is reflected in the direct object position, representing the LM, which takes the accusative marking, usually in the singular form, to profile a single completed event. In the imperfective form of the verb (7b), however, the distributive nature of wy- is more conspicuous (Śmiech 1986). As Dickey (unpubl. manusc.) observes, in

The semasiological structure of Polish myśleć ‘to think’ 233



this case “closure is either not reached or not salient in the conceptualization, e.g. for states, events in process, [or] habitually repeated events”. Whether the mental activity is in constant process, producing regular results, or whether it can be considered as a habitually repeated event should not really matter; what counts in this case is that the effect, represented by the nominal phrase in the accusative case, frequently takes the plural form, emphasizing the distributive nature of the mental process. The prefix za-, among many other senses distinguished by Tabakowska (2003a:â•›166–172), can represent a construal of ‘excess’ with intransitive perfective verbs, being extended from the sense of ‘going beyond a boundary’. In the group of intensive-resultative verbs, Dickey (unpubl. manusc.:â•›15) classifies za… się (lit. ‘behind’… refl) verbs as absorbtives, as they construe a continuous process whose subject, by becoming deeply engrossed in the activity, loses control over it. As the mental activity occurs independently of the TR’s will, some adverse consequences, or, in other words, oblique results, may be expected to take place. In the analysis of the prefixed verbs and the objects that they take, one should be able to observe that the thinking activity may give either direct or oblique results, as distinguished by Dickey (2009, unpubl. manusc.), thus forming two endpoints of a continuum. The former – giving a direct, and usually positively loaded, effect of the mental process – is represented by the accusative case and is combined with wymyślić/ ać ‘think out’ or przemyśleć ‘think through’. Then comes domyślić/ać się ‘guess’, indicating the goal of the process in the genitive case. It is followed by pomyśleć o+LOC/ nad+INSTR ‘think about/over’ or rozmyślać o+LOC/nad+INSTR ‘ponder about’. Objects in both the locative, construing an indirect constant movement of the TR round the focal point, and the instrumental, not indicating the goal of the action, but serving wyprze-

do-

ACC

GEN

direct result

porozo+LOC/ nad+INST

podo-

rozzaREFL Intr

Clause

oblique result

Abbreviations: ACC – Accusative; GEN – Genitive; LOC – Locative; INST – Instrumental; REFL – Reflexive; and Intr – Intransitive.

Figure 1.╇ Relationship between prefixed verb and the affectedness of the object4

4. Domyślić się and zamyślić się are reflexive verbs, which may take complements, while rozmyślić się is reflexive and intransitive.

234 Małgorzata Fabiszak et al.

to manifest it (Janda 1993:â•›143), are not directly affected by the action, and thus appear to be more oblique. Neither is the clausal object that comes together with pomyśleć, że…‘think that…’ or domyślić się, że… ‘guess that…’ Rozmyślić się ‘change one’s mind’ and zamyślić się ‘be lost in thought’ constitute the end of the continuum, taking oblique objects. Their presence is not mentioned in sentences at all; however, the verbs themselves, as Dickey (2009:â•›27) points out, may indicate an adverse or harmful result of the process, which represents the most extreme degree of subjectification, as understood by Langacker (1999). Introspective and qualitative analysis of corpus examples, the results of which are represented above in Figure 1, allows us to formulate the following hypothesis: wy-, prze-, do- myślić (się) on the one hand, and po-, do-, roz-, za-myslić (się) on the other, are conceptually similar. This hypothesis will be explored with correspondence analysis and hierarchical cluster analysis in Section 5. First, however, we will devote some space to the description of the corpus and the coding procedure. At this juncture, it is also noteworthy that our research question is further specialized, as intransitive reflexive forms, which do not take any object, will be excluded from the present study due to its exclusive focus on the relation holding between the prefixed forms of Polish ‘think’ and the semantics of their objects.

3. The corpus The lexico-grammatical analysis of the lexemes under study has been conducted on the online version of the PWN Corpus of Polish. Glynn (2009:â•›84) stresses the importance of representativity and corpus size in lexical semantic studies: Content words repeat infrequently and lexical variation is typically sensitive to extra-linguistic factors. These two conditions mean that for a lexical semantic study to capture any degree of semantic subtlety of even the most common usages associated with a given lexeme, the corpus must be large and preferably representative of various types of language and register.

It is essential, however, that we be aware that “even the largest corpus in the world is but a microscopic fraction of actual language use” (Glynn, this volume). The PWN Corpus of Polish consists of 40 million words sampled from 386 books, 977 issues of 185 newspapers and magazines, 84 recorded (and transcribed) conversations, 207 websites, as well as several hundred leaflets. It is, therefore, relatively balanced both in terms of genre and topic distribution. It must be noted, however, that it is biased toward unspontaneous written language. Tables 1 and 2 show the percentage ratios of particular text types and topics in the corpus. Unfortunately, there is no dedicated tool that would allow the researcher to tag the genre and topic of specific word uses automatically. To avoid the misattribution

The semasiological structure of Polish myśleć ‘to think’ 235



Table 1.╇ Genre distribution in the PWN Corpus of Polish Source

Percentage of corpus

Number of text samples

fiction non-fiction newspapers and magazines spoken leaflets Internet (websites, blogs, chats, forums)

20 21 45.5 â•⁄4.5 â•⁄5.5 â•⁄3.5

195 192 997 issues/185 titles â•⁄84 272 files 207

Table 2.╇ The PWN Corpus of Polish: Topic distribution Subject matter

Percentage

Subject matter

Percentage

philosophy, religion history, geography literary criticism, linguistics sciences

â•⁄7 17 â•⁄9 â•⁄9

politics, economy social sciences applied sciences arts other

14 â•⁄5 â•⁄8 â•⁄5.5 25.5

of examples to the specific topics on the basis of limited co-text, we did not include these variables in our analysis. It is thus strictly a semantic-syntactic analysis. The tables above are only provided in order to give the reader an idea of what the corpus represents. The study has been designed in such a way so as to examine the relationship and potential correlation between the suffixes do-, po-, prze-, roz-, wy- and za-, the aspect, object form and object semantics. With that purpose in mind, the dataset has been manually tagged in order to measure the extent to which the lemmas in question may be synonymous.

4. Feature annotation As observed by Divjak (2006:â•›22), a project aimed at establishing the degree of similarity between lexical items requires “precise syntactic and semantic data on the distribution of the potentially near-synonymous lexemes over constructions and of their collocates over the slots of those constructions”. Therefore, after all the contextualized instances of the investigated lexemes were extracted from the corpus, each of them was “translated into metalanguage”, as Divjak (2006:â•›21) puts it. In other words, every occurrence of domyślać, domyślić (się) pomyśleć, przemyśleć, przemyśliwać, rozmyślać, rozmyślić, wymyślać, wymyślić and zamyślić was analysed and annotated for a number of formal and semantic properties. Laborious and time-consuming as it was, manual

236 Małgorzata Fabiszak et al.

tagging of the data was necessary for securing the presence of all the elements crucial to the semantic description of a lexeme. This approach, referred to as ‘usage-feature’ analysis (Glynn 2010c:â•›8), has proven successful in corpus-driven Cognitive Linguistic research (Gries 2003, 2006; Divjak 2006, 2010; Gries and Stefanowitsch 2006; Grondelaers et al. 2007; Glynn 2009, 2010a, in press; Speelman et al. 2009; Glynn and Fischer 2010). The decision as to which variables and features to code was made on the basis of relevant literature, including, among others, Vendler (1967), Divjak (2006), Gries (2006), and Glynn (2009, 2010b). The annotation used by Divjak (2006), Gries (2006), and Glynn (2009, 2010b) proved particularly informative. According to Divjak (2006:â•›23), what is essential is that “the main participants of events or situations are encoded”. At first, the occurrences were annotated for a limited, yet diverse, variety of morphological, syntactic and semantic features, including: tense, aspect, and voice; transitivity, mood as well as the subject’s and complement’s form, humanness, animacy, abstractness, etc. (see Gries 2006:â•›73, 75; Divjak 2006:â•›34–36; and Glynn 2010b:â•›245–249 for more examples). With time (and the growth of the coders’ expertise), new categories were added to the coding schema. The description of the morphological features now also includes the prefix, person and number of the verb. As for syntactic properties, apart from mood and transitivity, negation has been incorporated into the adopted usage-feature set. Finally, with regard to the semantics of subjects and objects attested in the corpus, the following categories were added: subject visibility, competence and specificity, as well as some further formal features such as object case/person/number, and (in the case of clausal complements) clause semantics. Given that it is the mutual dependence between the prefix, the aspect and the complement type that lies at the heart of the present analysis, every direct object, be it a noun phrase, a clause, or a reduced clause, was decomposed into its formal and semantic characteristics. Consequently, NP complements (coded for case and number) were labelled as human (e.g. Piotr ‘Peter’/detektyw ‘detective’), concrete (e.g. potrawa ‘dish’), or abstract (e.g. plan ‘plan’/rozwiązanie ‘solution’), while clausal complements were grouped into achievements (i.e. single moment actions e.g. die), accomplishments (i.e. durative, heterogeneous processes, e.g. reach a verdict), states (e.g. be, have), activities (i.e. durative and uncompleted actions, e.g. to be hiding in the shed), or hypothetical (i.e. conditionals or clauses in the future tense).5 Pronominal direct objects were tagged for case, number and person (if applicable) and their co-referents were classified according to the same principles as NP complements. In the analysis, however, it turned out that object form (NP or clause) and object semantics were the most informative. NP object case is not a feature independent of the prefix (a particular prefixed form takes a

5. The first four clausal categories were distinguished on the basis of Vendler (1967).

The semasiological structure of Polish myśleć ‘to think’ 237



Table 3.╇ Prefixed forms of myśleć and their co-occurrence with Object Forms Predicate

NP

Clause

Reduced Pronoun Narrative Intrans. Lexeme Lemma Clause total total

domyślać się domyślić się pomyśleć przemyśleć przemyśliwać rozmyślać rozmyślić się wymyślać wymyślić zamyślić się Total

â•⁄â•⁄70 â•⁄â•⁄28 â•⁄155 â•⁄115 â•⁄â•⁄12 â•⁄â•⁄56 â•⁄â•⁄â•⁄0 â•⁄168 â•⁄569 â•⁄â•⁄14 1187

â•⁄338 â•⁄237 â•⁄570 â•⁄â•⁄10 â•⁄â•⁄â•⁄5 â•⁄â•⁄38 â•⁄â•⁄â•⁄0 â•⁄â•⁄â•⁄0 â•⁄â•⁄78 â•⁄â•⁄20 1296

â•⁄3 â•⁄3 46 â•⁄0 â•⁄0 â•⁄0 â•⁄0 â•⁄0 â•⁄0 â•⁄1 53

â•⁄51 â•⁄22 â•⁄81 â•⁄86 â•⁄â•⁄7 â•⁄28 â•⁄â•⁄0 â•⁄36 373 â•⁄â•⁄5 689

â•⁄2 â•⁄1 57 â•⁄0 â•⁄1 â•⁄9 â•⁄0 â•⁄0 â•⁄0 â•⁄0 70

â•⁄78 â•⁄59 â•⁄89 â•⁄14 â•⁄â•⁄3 â•⁄49 â•⁄64 â•⁄59 â•⁄37 145 597

â•⁄542 â•⁄350 â•⁄998 â•⁄225 â•⁄â•⁄28 â•⁄180 â•⁄â•⁄64 â•⁄269 1057 â•⁄185 3892

â•⁄â•‹892 â•‹â•⁄ 998 â•‹â•⁄ 253 â•‹â•⁄ 244 1,326 â•‹â•⁄ 185 3892

particular object case). NP object number did not seem to interact in any regular ways with the prefixes. So that is why these two features were later disregarded. Altogether, a total of 3,982 tokens were extracted from the corpus as representative of the six investigated lemmas in their two aspectual forms. Table 3 illustrates the distribution of the lemmas in the dataset as well as the number of NP/pronominal/ clausal complements for every type. Table 3 shows that not all the prefixed forms are equally frequent, with only 28 examples of przemyśliwać and as many as 1,057 tokens of wymyślić. Relative to the representativeness of the corpus, we could claim that, visà-vis its relative frequency, wymyślić is the most conspicuous of the analysed lexemes. Moreover, the distribution of the same prefix between the two aspects is far from balanced. As many as 61% of the do- forms are Imperfective, as if the process of reaching the goal indicated by do- was more often focused on than the very act of having reached it. Even though the prefix prze- focuses on the period of time covered by the verb, it also emphasizes the completion and is thus far more commonly used in the Perfective Aspect (89% of cases). Since we focus on the verb-object interaction here, we disregard the intransitive uses of roz-. Considering its transitive uses, roz- is always Imperfective, po- is always Perfective, while za-, unlike po-, can potentially co-occur with either aspect. In the investigated corpus it is also restricted to the Perfective Aspect. For wy- the ratio is 80% Perfective to 20% Imperfective. This may suggest that it is only do- which can be either Perfective or Imperfective, while the other prefixes show a clear preference for one Aspect: po-, prze-, wy- and za- for the Perfective and roz- for the Imperfective. It can be explained by the processual, dispersed nature of roz-, as indicated in the introspective part of the study. As the aim of this paper is to explain the interaction of Prefix and Object grammar and semantics in the creation of meaning, the intransitive forms will be discarded from further analysis. Also, the Narrative selects almost exclusively for the po-prefix,

238 Małgorzata Fabiszak et al.

so there is no need to investigate their interaction with other prefixes. The Reduced Clauses are rare; hence, these occurrences are grouped with full Clause complements. In the cases where the semantics of the pronominal object could be identified and coded, the examples were included in further analysis. Those cases, however, whose semantics could not be analysed, were deleted. Following this, the pronominal objects were re-coded as NPs when they stood for NPs and as Clauses if they stood for clauses, as in the construction myśleć o tym, że … ‘to think about it that…’. As will be shown in the sections that follow, a careful analysis of all the annotated features and their subsequent submission to multivariate statistics have enabled us to identify “patterns of usage” (Glynn 2009). Apart from producing results corresponding to and, therefore, corroborating the hypothesis presented in Section 2, the exploratory statistics applied here will also reveal interesting variation in usage not predicted by the introspective analysis. This demonstrates that introspection does indeed need to be complemented by quantitative measures to produce more comprehensive results.

5. Multivariate analysis of the results of feature annotation In this section, our data are further explored with two multivariate techniques: correspondence analysis and cluster analysis (for descriptions of these methods see Glynn, this volume, and Divjak and Fieller, this volume). Then, the confirmatory method of logistic regression analysis is used to corroborate the results of the correspondence analyses. These will enable us to investigate the contribution of Object Semantics and other essential factors to the holistic meaning structure of the prefixed cognition verb myśleć. The section ends with a discussion of the interaction of all the analysed variables. First, a chi-square test is applied to the data to check if the variation between the lexemes is significant: Pearson’s chi-square test χ² = 3803.6, df = 55, p-value < 2.2e-16 The chi-square test demonstrates that there is significant variation between the lexemes under investigation. In Table 4, the inspection of Pearson’s residuals shows that the correlation between the prefix do- and Imperfective Aspect is the most important, as is that between po- and Perfective Aspect. In regard to Object Form, the strongest and most significant correlations hold between do- and Object Clause, and wy- and Object NP. Finally, with respect to Object Semantics, the prefix do- correlates importantly with Accomplishment, Activity and State, po- with Achievement and Hypothetical clauses, while wy- correlates with Concrete and Abstract, prze- with Abstract, and roz- with Human nominal objects.

The semasiological structure of Polish myśleć ‘to think’ 239



Table 4.╇ Pearson’s residuals for the prefixed verb forms of Polish myśleć ‘to think’ Imperfective Perfective Object Clause Object NP Object ABSTRACT Object ACCOMPLISHMENT Object ACHIEVEMENT Object ACTIVITY Object CONCRETE Object HUMAN Object HYPOTHETICAL Object STATE

do-

po-

prze-

roz-

wy-

za-

â•⁄17.014 –10.499 â•⁄11.915 –11.959 â•⁄–9.362 â•⁄â•⁄3.871 â•⁄â•⁄3.91 â•⁄â•⁄6.095 â•⁄–6.118 â•⁄–2.588 â•⁄–3.637 â•⁄12.882

–14.556 â•⁄â•⁄9.125 â•⁄10.229 –10.95 –13.081 â•⁄–0.009 â•⁄â•⁄4.404 â•⁄â•⁄4.426 â•⁄–2.245 â•⁄â•⁄0.122 â•⁄10.093 â•⁄â•⁄4.57

–3.739 â•⁄2.251 –6.088 â•⁄6.305 â•⁄8.166 –0.671 –1.931 –1.246 –2.708 –1.401 –2.06 –4.853

14.704 –9.035 –0.772 â•⁄0.865 –0.273 –0.795 â•⁄0.039 –1.165 –1.902 â•⁄5.578 â•⁄3.509 –2.847

â•⁄–4.415 â•⁄â•⁄2.611 –16.923 â•⁄17.488 â•⁄16.819 â•⁄–2.628 â•⁄–6.608 â•⁄–8.353 â•⁄â•⁄9.222 â•⁄â•⁄0.633 â•⁄–6.625 –12.313

–3.134 â•⁄1.902 â•⁄0.639 –0.609 –0.775 –0.823 â•⁄0.074 –0.124 –0.454 â•⁄0.813 â•⁄1.322 â•⁄0.086

Let us now turn to correspondence analysis in order to see how these factors interact with one another. Figure 2 presents the results of a multiple correspondence analysis. It employs a Burt matrix/‘joint’ method to correct for low explained inertia (Greenacre 1993). The explained inertia is 81.2% (Dim. 1 = 68.4, Dim. 2 = 12.8), which is a stable result in multiple correspondence analysis. As was predicted by the analysis of the results of Table 4, the Imperfective Aspect correlates highly with the do- and roz- prefixes. The combination of the goal-indicating do- with the Imperfective Aspect shows the focus on the processual nature of

roz–

1.50

IMPERF do–

0.75 ABSTR NP

0.00

wy–

ACT

HUM

ACCOM CLAUSE

prze– PERF–

CONCR

–0.75

HYPO

za–

–1

STATE ACH

–0.5

0

po–

0.5

1

Figure 2.╇ Multiple correspondence analysis: Prefixes of the Polish verb myśleć ‘to think’ and their correlation with Aspect, Object Form and Object Semantics

240 Małgorzata Fabiszak et al.

the verb domyślać się in the conceptualization. The prefix roz- indicates the dispersed nature of the verb it is attached to and, in combination with the Imperfective, emphasizes the extensive nature of the thinking process. As for the hypothesized correlation between wy-, prze-, do- myślić (się), on the one hand, and po-, do-, roz-, za-myślić (się), on the other (see Section 2 and Figure 1), Figure 2 partly confirms these assumptions, which were arrived at via theoretical and introspective reasoning. Firstly, the prefixes prze- and wy- in Figure 2 are grouped together relative to nominal objects of thought. Secondly, za- and po- also correspond to one another relative to the Perfective Aspect and hypothetical clausal objects of thought. Finally, there is a third correlation discernible between do- and roz-, which were originally expected to belong together with the previous group; here, they are clustered together relative to the Imperfective Aspect. In the next step of data analysis, we will combine two factors: Aspect and Prefix, with a view to visualizing more clearly the perfective and imperfective uses of the relevant prefixed predicates. Accordingly, the next plot presents the binary correspondence analysis of Prefix combined with Aspect, Object Form and Object Semantics. The binary correspondence in Figure 3 clearly captures the dispersion of object types relative to the prefixes. It is a stable analysis, with 95% explained inertia (Dim. 1: 67.16, Dim. 2: 27.84). The plot shows that nominal Abstract objects correlate closely with Perfective prze- and Perfective and Imperfective wy-, which are plotted to the left of the centre. Above this grouping, we can see that Concrete nominal objects are most closely correlated with the Perfective wy-, while Human nominal objects are in distinct correlation with Imperfective roz-. This is made evident by the semantic feature being pushed away from the rest of the plot and located just above the prefix in question. All these correlations are illustrated in examples (8a–e) below: (8) a. Przemyślałam jeszcze raz całą sytuacje od początku i doszłam do tego samego. ‘I thought this situation over once more and came to the same [conclusion].’ (prze+Perf+ObjNP+ObjAbstr) b. Jeżeli zorientuje się, że wróciłyśmy, wymyśli jakieś usprawiedliwienie. ‘If he realizes we have come back, he will invent some excuse.’ (wy+Perf+ObjNP+ObjAbstr) c. Bo jak facet 500 lat temu mógł wymyślic helikopter lub rower? ‘How could a guy invent a helicopter or a bike 500 years ago?’ (wy+Perf+ObjNP+ObjConcr) d. Mówi, że fryzjerstwo jest twórcze: wymyśla własne patenty, na przykład układanie na krem Nivea, dla efektu i z braku żelu. ‘He says that hairdressing is creative: he invents his own patents, for example, doing hair with the use of the Nivea cream, for effect and for want of gel.’ (wy+Imperf+ObjNP+ObjAbstr)



The semasiological structure of Polish myśleć ‘to think’ 241

e. Patrzyła na mnie i rozmyślała o Witku. ‘She was looking at me and thinking about Witek.’ (roz+Imperf+ObjNP+ObjHum) The mental predicate przemyśleć in (8a) designates a thorough, temporally extended activity coming to its end, which may bring a change to the object affected by the mental process. The choice of abstract objects of thought seems justifiable for such an in-depth analysis. It also stands to reason that the resultative, goal-oriented prefix wyattracts abstract and concrete nominals (8b, c), which profile the effect of the thinking process in a reified and comprehensive way. The imperfective form wymyślać, rather than focusing primarily on the effect of thinking, emphasizes the distributive nature of the process, in the example here additionally reinforced by the plural use of the nominal in the object position (8d). It also makes perfect sense (example (8e)) why the prefix roz-, accentuating the extensive nature of the mental activity, should tend towards objects designating humans, normally our loved ones. Now, when moving to the right-hand bottom quadrant of Figure 3, we can see how the Prefix do- combined with the Imperfective Aspect correlates with Activity and State, while do- combined with the Perfective Aspect is in close correlation with State and in distinct correlation with Accomplishment, as exemplified below (9a–d): (9) a. Albo nie chciała wtedy powiedzieć wprost, że się domyśla, że w tajemnicy przed nią popalał heroinę. ‘Or she didn’t want to say directly that she was coming to realize that he was clandestinely smoking heroin.’ (do+Imperf+ObjClause+ObjActivity) b. W pierwszej części filmu nikt się nie domyśla, że ten szczuplutki chłopiec o wąskiej twarzy i dużych ustach to kobieta. ‘In the first part of the film nobody realizes that this slim boy with a narrow face and lavish lips is a woman.’ (do+Imperf+ObjClause+ObjState) c. Twój rozmówca natychmiast domyśli się, że przeżywałeś jakiś dramat. ‘Your interlocutor will realize at once that you were experiencing some drama.’ (do+Perf+ObjClause+ObjState) d. W żaden sposób nie mogliśmy się domyślić , co ich tu sprowadziło. ‘We could in no way work out what brought them here.’ (do+Perf+ObjClause+ObjAccomplishment) The sentences above demonstrate that the verb myśleć, when coupled with the attainment prefix do- in either aspect, tends to co-occur with (1) objects designating states that affect other people in the surrounding world (examples (9b and c)), to which the conceptualiser is denied full access; (2) bounded or unbounded activities that happen beyond the speaker’s immediate field of attention (example (9a)); and (3) accomplishments whose genesis and course of development do not fall within the speaker’s known reality either (example (9d)). Therefore, it can be seen that the processual meaning of

242 Małgorzata Fabiszak et al.

Obj.Human Obj.Hypothetical

0.50 ROZ–Imperf Obj.Concrete

0.25

ZA–Perf WY–Perf ObjNP

0.00

Obj.Achievement ObjCLAUSE Obj.Activity

Obj.Abstract PRZE–Perf

–0.25

PO–Perf

DO–Imperf Obj.State DO–Perf

WY–Imperf

Obj.Accomplishment

–0.50

–1

–0.5

0

0.5

Figure 3.╇ Binary correspondence analysis: Prefix combined with Aspect, Object Form and Object Semantics

the verb and the semantic features of the said objects of thought, characterized by a certain degree of obscurity, are compatible. Considering the right-hand upper quadrant of the plot, we can see the correlation between the prefix po- and Hypothetical, Achievement and Activity clauses, which are illustrated in examples (10a–c): (10) a. Pomyślałem, że i ja mógłbym latać. ‘I thought that I could fly too.’ (po+Perf+ObjClause+ObjHypo) b. Pomyślałem, że niczego nie spostrzegł. ‘I thought that he hadn’t noticed anything.’ (po+Perf+ObjClause+ObjAch) c. Można było pomyśleć , że się o coś modli. ‘One could think that he was praying for something.’ (po+Perf+ObjClause+ObjActivity) This delimitative prefix is construed against the background of a variety of possible paths, one of which is selected and leads to the final point, becoming the focus of attention, to use Langacker’s parlance. The final point here is represented by clauses designating hypothetical events, achievements or activities. This shows that pomyśleć is more directly correlated with clauses, imposing upon them its delimitative nature. It is also noteworthy that activities and achievements are more directly observable and more easily enclosed in or confined to a single event of thought than accomplishments or states.



The semasiological structure of Polish myśleć ‘to think’ 243

Hypothetical clausal objects are attracted by the prefixes roz- and za-, as exemplified below (11a–b): (11) a. “Widocznie każdy musi wszystko przeżyć od nowa”, rozmyślał na głos Olejniczak. ‘“Apparently everyone has to re-live everything”, Olejniczak was thinking aloud.’ (roz+Imperf+ObjClause+ObjHypothetical) b. “Może warto spróbować…”, zamyślił się. ‘“Maybe it’s worth trying”, he thought.’ (za+Perf+ObjClause+ObjHypothetical) It is noteworthy that in Section 2 both these prefixes were hypothesized to be conceptually similar. They both profile a mental process, whereby the subject is absorbed in thought about a given object. Due to its dispersed character, the procedural intensifying prefix roz- designates an expanse of mental space affected by the thinking process, without actually impacting whatever constitutes the object of pondering. Here, the mind seems to be construed in a more processual manner. The intensive-resultative za-, on the other hand, construes a situation in which either the subject seems to be behind the curtain of thought, or his/her mind, viewed as a container, appears to be completely covered by or filled in with the mental state (cf. Tabakowska 2003a).6 Both these mental processes engross the subject to such an extent that any other activity is impossible. Hypothetical objects which correlate closely with these prefixes concern the unknown, the possible, the unrealized, which naturally intrigues humans and invites extensive (roz-) as well as deep (za-) consideration. Let us now consider the difference in the use of nominal and clausal objects. Both correspondence analyses reveal that this distinction is basic in the data. These two object types divide the prefixes into two discrete groups represented in the plots by two separate clusters on the right and left halves. Correspondence analysis offers no statistical confirmation as to the significance or accuracy of what it identifies. In order to obtain such information, we have to turn to logistic regression (see Speelman, this volume). The model below produces accurate and predictive results, which can be assessed on the basis of the C score (0.846) and the estimated R2 (0.513). Although not expressed as a probability, the C score of 0.85 can be understood as approximating a 85% success rate in predicting the behaviour of the data in taking a nominal or clausal object (see Speelman, this volume, for a detailed discussion on how to interpret the model statistics). The estimated R2 score at 0.513 is a very strong indication of a stable and predictive model, any figure above 0.3 being accepted as a strong result. The model was checked for overfitting and multicollinearity, neither of which posed a problem. 6. The prefix za- is also present in such words as zasłonięty ‘covered with’ and zapełniony ‘filled with’.

244 Małgorzata Fabiszak et al.

Variance inflation factor values were beneath 2.5, which is well below accepted levels of tolerance (Dodge 2008:â•›96). Deviance Residuals:€ Min€€€€€€1Q€€ Median€€€3Q€€€€€ Max€€ -2.2793€ -0.6885€ -0.5204€€0.5139€€2.0329€€ Coefficients: €€€€€€€€€€€ Estimate Std. Error z value (Intercept)€ 0.22609€€€ 0.37899€€ 0.597€ Aspect Perftive€ -0.56256€€€ 0.17132€ -3.284€ Prefix do-€€ -1.59438€€€ 0.37208€ -4.285 Prefix po-€€ -0.98245€€€ 0.34924€ -2.813€ Prefix prze-€ 1.86671€€€ 0.39706€€ 4.701 Prefix roz-€ -0.04704€€€ 0.42383€ -0.111€ Prefix wy-€€€ 2.29423€€€ 0.35414€€ 6.478 --‘***’ 0.001, ‘**’ 0.01, ‘*’ 0.05, ‘.’ 0.1

Pr(>|z|)€ 0.55080€€€€ 0.00102 **€ 1.83e-05 *** 0.00491 **€ 2.59e-06 *** 0.91162 9.27e-11 ***

Null deviance: 3795.0€ on 2738€ degrees of freedom Residual deviance: 2463.5€ on 2732€ degrees of freedom AIC: 2477.5 Number of Fisher Scoring iterations: 4 Obs 2739

Model L.R. 1331.48

d.f. 6

P 0

C 0.846

Dxy 0.692

R2 0.513

Brier 0.14

A closer look at the table of coefficients tells us how the model predicts the outcome as either clausal or nominal. In the table, negative coefficients predict the occurrence of clausal objects and positive coefficients predict the occurrence of a nominal object. The strongest predictor for the clausal object is the prefix do-. The second feature predicting clausal objects is po-. However, the coefficient score is close to zero, indicating that its role is minor, despite its statistical significance. We can now return to the the results of correspondence analysis in Figure 3 to better understand these findings. Although both po- and do- are present, we now know that in fact do- is the more important association in the cluster. Nominal complementation, in turn, is strongly predicted by the prefixes wy- and prze-, which again bears out the correlations visualized in Figure 3. The fact that the prefix roz- is the weakest predictor, neither significant nor important, also corresponds to the findings of the correspondence analysis, where it is located on the line separating the halves containing nominal and clausal objects, respectively.



The semasiological structure of Polish myśleć ‘to think’ 245

Overall, the above findings indicate that the attainment prefix do-, in particular, but also the delimiting po- are more importantly associated with processual objects, as designated by clausal complements. The resultative, goal-oriented prefix wy-, on the other hand, and the prefix prze- correlate importantly with the abstract category of things, profiled by nominal objects. This corroborates the results of the exploratory correspondence analyses presented above. It is also interesting in itself that no predictive model could be generated with the inclusion of object semantics. This may indicate that the semantics of the object of thought for these mental predicates can only be distinguished at a higher and more schematic level of analysis. Rather than drawing a fine-grained distinction between particular types of objects relative to particular verbs, it appears that, at least for some prefixes, a more coarse-grained preference can be identified – either for processual or reifying construal of the object. The semantically coarse-grained results of the logistic regression analysis are compatible with the schematic semantic characterization of the prefixes in question here. Taking the strongest predictors for either response variable feature, we can see that the attainment, process-oriented do- is attracted to clausal objects, whereas the resultative wy-, bringing about more or less concrete but objectifiable results, is more likely to be associated with nominal phrases. Having analysed and interpreted the correspondence analyses, which brought to light a number of revealing interdependencies between various semantic and formal features, and displayed interesting continua thereof, some of which have been confirmed by the Logistic Regression Analysis, we may turn to Hierarchical Cluster Analysis. The insights from the correspondence analyses and the logistic regression analysis will allow us to interpret the results of the cluster analysis. The cluster analysis, in Figure 4, shows that roz- and za-, prze- and wy-Imperf as well as do- and po- cluster with each other, whereas wy-Perf stands out from the rest. This clustering only partly correlates with the hypothesis from Section 2, where wy-, prze-, and do- clustered at one end of the continuum, while po-, do-, roz- and za- clustered at the other. However, the correspondence analysis conducted above allows us to account for this discrepancy. As was shown in examples (8a–c), wy- and prze- correlate with NP objects, but docorrelates with Clausal objects. This is why prze- combined with Perfective Aspect and wy- combined with Imperfective Aspect cluster together – they both take Abstract nominal objects. Wy- combined with Perfective Aspect is most importantly correlated with concrete nominal objects. This is why it occupies a separate branch in the cluster. The introspective analysis, which relied on the native speaker’s competence of what is acceptable in the language, could not account for the difference in the frequency of use of do- with clausal vs. nominal objects. Similarly, the analysis based on intuition revealed that po- and roz- can both take nominal objects, yet it failed to ascertain that this potential is highly significant only for roz-. This is probably the reason why the HCA shows a clustering of po- and do-, and not of po- and roz-. This

246 Małgorzata Fabiszak et al.

wy-Perf

57 52 6

92 78 5 po-Perf wy-Imperf

prze-Perf

100 88 2 za-Perf

roz-Imperf

0

100 81 1

100 87 5 do-Imperf

200

96 81 4

do-Perf

400

600 800

1000

au bp edge #

Figure 4.╇ Hierarchical cluster analysis (Distance: Euclidean, cluster method: ward)

correlation is also clearly visible in the correspondence analysis and is a result of the propensity of these prefixes to correlate with clausal objects such as Achievement, Activity and State. They are conceptually similar, as they both construe thinking as a process, which is metaphorically understood as a journey on/along the road/path (po-) leading to a goal (do-). The roz-, za- cluster is caused by the tendency of both these prefixes to co-occur with Hypothetical clausal objects. Its presence can be further justified by the schematic meaning of the prefixes, which indicate that the subject is construed as being deep in thought to such an extent that any other activity is hindered.

6. Conclusion The present paper describes the semasiological structure of the onomasiological field of prefixed think verbs in Polish relative to their object form, object semantics and aspect. These factors have been selected on the basis of previous pilot studies that revealed their significance for the research question. The aim of providing an accurate semantic description has been attained in a twofold manner. First, the prefixes were subjected to a detailed introspective investigation in light of a number of relevant theoretical approaches. In this phase, we projected the inter- and intra-category conceptual relations, constituting the background against which crucial decisions could be made regarding the annotation schema and the hypotheses to be tested at the quantitative stage of the study.



The semasiological structure of Polish myśleć ‘to think’ 247

The second step involved submitting the annotated data to multivariate statistical modelling in the form of two exploratory methods, correspondence analysis and hierarchical cluster analysis, and one confirmatory method, logistic regression analysis. The application of two mutually complementary phases of analysis ensured greater reliability of results. Employing pertinent exploratory methods enabled us to identify actual patterns of use in the object of our study, as well as patterns surfacing in multiple dimensions that no introspection could possibly bring to light. Importantly, the results thus obtained are replicable and falsifiable, which adds to the accuracy of the model produced. Further stages of research into the semantics of the Polish mental verbs should focus on the contribution of Subject grammar and Subject semantics as well as modality and negation to the construal of the mental process. So far, Fabiszak, Hebda and Konat (2012) have run a pilot study on the contribution of Subject form and Object form and semantics to the construal of the scene in the Polish verb wierzyć ‘to believe’, while Fabiszak and Hebda (2011) looked at the role of Subject, mood and negation in the meaning construction of wierzyć ‘to believe’. Kokorniak and Krawczak (2010), in turn, focus on nominal complementation of the verbs myśleć ‘think’ and sądzić ‘suppose’. The construal of prefixed think verbs in Polish relative to the grammatical subject person and adverbial modification is the object of study in Krawczak and Kokorniak (2012). Clausal that and zero complementation of the English verb think relative to an array of syntactic and semantic properties is analysed in Krawczak and Kokorniak (2010), while Krawczak and Fabiszak (2011) concentrate on the construal of the nominal as well as the clausal complementation of the verbs myśleć ‘think’ and wierzyć ‘believe’.

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Glynn, D. (2010b). Testing the hypothesis: Objectivity and verification in usage-based Cognitive Semantics. In D. Glynn, & K. Fischer (Eds.), Quantitative Cognitive Semantics: Corpus-driven approaches (pp. 239–270). Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110226423 Glynn, D. (2010c). Corpus-driven Cognitive Semantics: An overview of the field. In D. Glynn, & K. Fischer (Eds.), Quantitative Cognitive Semantics: Corpus-driven approaches (pp. 1– 42). Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110226423.1 Glynn, D. (Forthcoming). Mapping meaning: Corpus methods for Cognitive Semantics. Cambridge: Cambridge University Press. Glynn, D., & Fischer, K. (Eds.). (2010). Quantitative methods in Cognitive Semantics: Corpus-driven approaches. Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110226423 Goddard, C. (2003). ‘Thinking’ across languages and cultures: Six dimensions of variation. Cognitive Linguistics, 14, 109–140. DOI: 10.1515/cogl.2003.005 Greenacre, M. (1993). Correspondence analysis in practice. London: Academic Press. Gries, St. Th. (2003). Multifactorial analysis in Corpus Linguistics: A study of particle placement. London: Continuum Press. Gries, St. Th. (2006). Corpus-based methods and Cognitive Semantics: The many senses of to run. In St. Th. Gries, & A. Stefanowitsch (Eds.), Corpora in Cognitive Linguistics: Corpus-based approaches to syntax and lexis (pp. 57–99). Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110197709 Gries, St. Th., & Stefanowitsch, A. (Eds.). (2006). Corpora in Cognitive Linguistics: Corpus-based approaches to syntax and lexis. Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110197709 Grochowska, A. (1979). Próba opisu reguł łączliwości przedrostka prze- z tematami czasowniÂ� kowymi. [An attempt at the description of the combinatory rules of the prefix prze- with verb roots.] Polonica, 5, 59–74. Grondelaers, S., Geeraerts, D., & Speelman, D. (2007). A case for a cognitive Corpus Linguistics. In M. Gonzalez-Marquez, I. Mittleberg, S. Coulson, & M. Spivey (Eds.), Methods in Cognitive Linguistics (pp. 149–169). Amsterdam & Philadelphia: John Benjamins. Jackendoff, R. (1983). Semantics and cognition. Cambridge, MA: MIT Press. Janda, L. (1993). A geography of case semantics: The Czech dative and the Russian instrumental. Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110867930 Junker, M.-O. (2003). A native American view of the ‘Mind’ as seen in the lexicon of cognition in East Cree. Cognitive Linguistics, 14, 167–194. DOI: 10.1515/cogl.2003.007 Kokorniak, I., & Krawczak, K. (2010). Thinking about thinking: Constructions of Polish mental verbs in discourse. Paper presented at Syntax in Cognitive Grammar, Częstochowa. Krawczak, K., & Kokorniak, I. (2010). Verbs of cognition, their construal, and complementation in interactive events. Paper presented at the 4th International Conference of the German Cognitive Linguistics Association, Bremen. Krawczak, K., & Fabiszak, M. (2011). Cognition verbs in Polish, their construal and complement semantics. Paper presented at the 3rd Conference of the Scandinavian Association for Language and Cognition, Copenhagen. Krawczak, K., & Kokorniak, I. (2012). A corpus-driven quantitative approach to the construal of Polish think. Poznań Studies in Contemporary Linguistics, 48, 439–472. DOI: 10.1515/psicl-2012-0021

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Kustova, G. (2000). Niektóre problemy opisu predykatów mentalnych. [Some problems in the description of mental predicates.] In R. Grzegorczykowa, & K. Waszakowa (Eds.), Studia z semantyki porównawczej [Studies in comparative semantics] Vol. 1 (pp. 249–263). Warszawa: Wydawnictwo UW. Lakoff, G., & Johnson, M. (1980). Metaphors we live by. Chicago: University of Chicago Press. Langacker, R. (1991). Foundations of Cognitive Grammar. Vol. 2. Descriptive application. Stanford: Stanford University Press. Langacker, R. (1999). Losing control: Grammaticalization, subjectification, and transparency. In A. Blank, & P. Koch (Eds.), Historical semantics and cognition (pp. 147–175). Berlin & New York: Mouton de Gruyter. Lindner, S. (1983). A lexico-semantic analysis of English verb particle constructions. Trier: LAUT. Palmer, G. (2003). Talking about thinking in Tagalog. Cognitive Linguistics, 14, 251–280. Pasich-Piasecka, A. (1993). Polysemy of the Polish verbal prefix prze-. In E. Górska (Ed.), Images from the cognitive scene (pp. 11–26). Kraków: Universitas. Pawłowska, R. (1981). Znaczenie i użycie czasownika ‘myśleć’. [The meaning and use of the verb ‘think’.] Polonica, 7, 149–160. Piernikarski, C. (1975). Czasowniki z prefiksem po- w języku polskim i czeskim: Na tle rodzajów akcji w językach słowiańskich. [Verbs with the po- prefix in Polish and Czech: In the background of Aktionsarten in Slavic languages.] Warszawa: PWN. Przybylska, R. (2002). Stru ktura schematyczno-wyobrażeniowa prefiksu czasownikowego roz-. [Image-schematic structure of the verbal prefix ‘roz-’.] Polonica, 21, 269–286. Przybylska, R. (2006). Schematy wyobrażeniowe a semantyka polskich prefiksów czasownikowych do-, od-, prze-, roz-, u-. [Image schemata and the semantics of Polish verb prefixes do-, od-, prze-, roz-, u-.] Kraków: Universitas. Radden, G., & Dirven, R. (2007). Cognitive English grammar. Amsterdam & Philadelphia: John Benjamins. DOI: 10.1075/clip.2 Rudzka-Ostyn, B. (2000). Z rozważań nad kategorią przypadka. [Ruminating on the category of case.] Kraków: Universitas. Schlesinger, I. M. (1998). Cognitive space and linguistic case: Semantic and syntactic categories in English. Cambridge: Cambridge University Press. Śmiech, W. (1986). Derywacja prefiksalna czasowników polskich. [Prefix derivation of Polish verbs.] Wrocław: Ossolineum. Speelman, D., Tummers, J., & Geeraerts, D. (2009). Lexical patterning in a construction grammar: The effect of lexical co-occurrence patterns on the inflectional variation in Dutch attributive adjectives. Constructions and Frames, 1, 87–118. DOI: 10.1075/cf.1.1.05spe Szwedek, A. (2007). An alternative theory of metaphorisation. In M. Fabiszak (Ed.), Language and meaning: Cognitive and functional perspectives (pp. 312–327). Frankfurt/Main: Peter Lang. Tabakowska, E. (2003a). Space and time in Polish: The preposition za and the verbal prefix za-. In H. Cuyckens, T. Berg, R. Dirven, & K.-U. Panther (Eds.), Motivation in language: Studies in honor of Günter Radden (pp. 153–177). Amsterdam & Philadelphia: John Benjamins. Tabakowska, E. (2003b). The notorious Polish reflexive pronouns: A plea for Middle Voice. Glossos 4. Retrieved from [Accessed 9th November 2008]. Vendler, Z. (1967). Linguistics in philosophy. Ithaca, NY: Cornell University Press.



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A multifactorial corpus analysis of grammatical synonymy The Estonian adessive and adposition peal ‘on’ Jane Klavan

University of Tartu

In the present study, both monofactorial and multifactorial corpus methods are applied to the alternative use of the analytic adpositional construction and the synthetic case construction in present-day written Estonian. 600 examples from the fiction sub-corpora of written Estonian were annotated for 16 different (seven morphosyntactic and nine semantic) factors. In order to determine which factors are most influential in determining the choice between the two constructions, a logistic regression model was built to fit the data. The analysis confirmed the statistical influence of the following factors: lexical complexity, type of verb, word order, word class, and mobility. The results reported in this study align with previous research, which has shown that case affixes are used to express more abstract relations and adpositions more concrete ones. Keywords: adpositional construction, case construction, Finno-Ugric languages, logistic regression

1. Introduction1 To express a spatial scene where a vase is located on a table, one can either use the adessive case (example (1a)) or the adpositional construction with the postposition peal ‘on’ (example (1b)) in Estonian: (1) a. vaas on laual vase.sg.nom be-prs.sg3 table.sg.ad ‘the vase is on the table’. 1. I am indebted to Dylan Glynn for his valuable comments and his extensive help with the logistic regression analysis. Methodologically, the present chapter relies heavily on Glynn (2007, 2010).

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b. vaas on laua peal vase.sg.nom be-prs.sg3 table.sg.gen on.ad ‘the vase is on the table’. Among other things, I will be taking a closer look at one of the central claims made in the literature about the difference between the ways the two strategies, i.e. the synthetic vs. analytic way of expressing meaning, are used. It is claimed that case affixes are used to express more abstract relations and adpositions to express more concrete ones (e.g. Bartens 1978; Comrie 1986; Luraghi 1991:â•›66–67; Ojutkangas 2008; Hagège 2010:â•›37–38; Lestrade 2010). Adpositions are said to be semantically more specific than cases and they are used to express the less predictable spatial meanings; cases, on the other hand, are more abstract and used to express more frequent spatial meanings (Lestrade 2010). The chapter proceeds from the theoretical premises of both Construction Grammar (Goldberg 1995, 2006) and Cognitive Grammar (Langacker 1987, 2008), where one of the basic general assumptions is that of no-synonymy – when two constructions differ syntactically, then they also differ either semantically or pragmatically (Goldberg 1995:â•›67). At present, there is no detailed corpus study on this topic and the few previous studies that are available proceed from an approach based largely on introspection (Rannat 1991; Vainik 1995). Accordingly, the main aim of the chapter is to carry out a completely corpus-based analysis of the adessive case construction and the adpositional construction with the postposition peal ‘on’. The central focus will be on finding out how significant different morphosyntactic and semantic factors are in determining the use of either the adessive constructions or the adpositional constructions, and which factors are the most important ones. Both monofactorial and multifactorial statistical techniques are used to analyse the results. The monofactorial analysis is seen as a necessary and beneficial first step in the quantitative analysis of the results. The purpose is to move from more simple, univariate exploratory analysis to more complex but more powerful multivariate analysis. Monofactorial techniques make it possible to identify which variables are statistically significant, but by employing such a multivariate statistical technique as regression analysis, it is possible to determine the contribution of the different semantic and morphosyntactic variables to the alternation and calculate the relative strength of each individual variable. A number of researchers have successfully argued for the benefits of using multifactorial analyses (e.g. Gries 2003; Wulff 2003; Glynn 2007, 2010; Szmrecsanyi 2010). Gries (2003:â•›155), among others, emphasises that “variation phenomena are too multifaceted to be treated adequately by means of minimal-pair tests and the researchers own judgements”. The chapter was inspired by numerous other studies on different variation phenomena, including those specifically about the synthetic-analytic distinction (for dative alternation in English, see Bresnan et al. 2007, Bresnan and Ford 2010; for English comparative alternation, Mondorf 2003; for the English genitive

A multifactorial corpus analysis of grammatical synonymy 255



alternation, Rosenbach 2003, Szmrecsanyi 2010; for particle placement alternation in English transitive phrasal verbs, Cappelle 2009). The chapter consists of six sections. In the following section, an overview of the functions of the Estonian adessive case and the adposition peal is given. Section 3 describes the data sample; Section 4 gives an overview of the variables coded and presents the monofactorial results. The results of a multifactorial statistical (logistic regression) analysis are presented and discussed in Section 5; the chapter ends with a conclusion (Section 6).

2. The Estonian adessive case and the adposition peal ‘on’ 2.1

The Estonian adessive case

Estonian nouns and adjectives decline in fourteen cases; six of these cases are referred to as locative cases and can be divided into interior locative cases (illative, inessive, elative) and external locative cases (allative, adessive, ablative) (see Table 1). The Estonian adessive case belongs to the set of external locative cases and expresses, first and foremost, spatial or temporal relations. It normally takes the role of an adverbial or attribute in the clause (Erelt et al. 1995:â•›58). Estonian external locative cases express spatial relations of an open surface and they form a three-part series – allative, adessive, ablative – expressing direction, location and source, respectively (Erelt et al. 2007:â•›240; see Table 1). The present chapter focuses only on the adessive, although the other forms of external locative cases are also said to be synonymous with the respective forms of the adposition peal ‘on’ (direction: allative -le ~ peale ‘onto’; source: ablative -lt ~ pealt ‘off ’). Although the primary meaning of the locative cases was the expression of spatial relations, in modern Estonian they fulfil a number of abstract functions. For instance, it is more frequent for the Estonian adessive to mark the possessor or agent (examples (2c) and (2d)) than, for example, location (example (2a)); the following functions of the Estonian adessive case are relevant for the present analysis (Erelt et al. 2007:â•›250): Table 1.╇ Estonian locative cases as exemplified by the noun laud ‘table’ Interior Exterior

lative (direction)

locative (location)

separative (source)

illative laua-sse ‘into table’ allative laua-le ‘onto table’

inessive laua-s ‘in table’ adessive laua-l ‘on table’

elative laua-st ‘out of table’ ablative laua-lt ‘off table’

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(2) a. Location Vaas on laual. vase.sg.nom be-prs.3sg table.sg.ad ‘The vase is on the table’. b. Instrument Mari mängib klaveril mõnd lugu. Mari.nom play-prs.3sg piano.sg.ad some tune.sg.part ‘Mari plays some tunes on the piano’. c. Possessor Maril on kaks last. Mari.ad be-prs.3pl two child.sg.part ‘Mari has two kids’. d. Agent with finite verb forms See asi ununes mul kiiresti. this thing.sg.nom forget-prs.3sg me.sg.ad quickly ‘I quickly forgot about that thing’.

2.2

The Estonian adposition peal ‘on’

In addition to the locative cases, location and change of location in Estonian can be expressed with adpositions, adverbs, and nouns declined in interior and exterior locative cases (Erelt et al. 1993:â•›71). In Estonian reference grammars, adpositions are treated as uninflected words that are used together with nouns and express similar meanings as case endings. In comparison with adpositions, the meaning of cases is said to be much more abstract and the usage range much broader (Palmeos 1985; Erelt et al. 1995:â•›33–34; Erelt et al. 2007:â•›191). This is in line with the general claims made concerning the differences between adpositions and case affixes (Comrie 1986; Hagège 2010; Lestrade 2010). Nevertheless, as is stressed in the following sub-section, there are still instances where both the adessive case and the adposition peal ‘on’ are seen as semantic alternatives in Estonian. A distinctive morphological characteristic of Estonian adpositions is that like locative cases they constitute three-member sets that are semantically and grammatically divided into the lative, locative, and separative forms (see Table 2). The adposition Table 2.╇ The three-member sets of Estonian postpositions sees ‘in’ and peal ‘on’ Interior Exterior

lative (direction)

locative (location)

separative (source)

illative si-sse ‘into’ allative pea-le ‘onto’

inessive ‘in’ see-s adessive pea-l ‘on’

elative ‘out of ’ see-st ablative pea-lt ‘off ’

A multifactorial corpus analysis of grammatical synonymy 257



peal ‘on’ takes external locative case endings: peale – peal – pealt. In the present chapter, only the locative form peal ‘on’ is discussed. At the clause level, the Estonian adpositional phrase has two basic functions – that of an adverbial and adverbial modifier (Erelt et al. 1993:â•›137). The adposition peal ‘on’ is polysemous; relevant for the present study are the following senses: (3) a. Location Leib on laua peal. bread.sg.nom be-prs.3sg table.sg.gen on.ad ‘Bread is on the table’. b. Place Turu peal oli suur sagimine. market.sg.gen on.ad be-pst.3sg big commotion.sg.nom ‘There was a big commotion on the market’. c. Instrument Mängi klaveri peal ette! play-imp.2sg piano.sg.gen on.ad ahead ‘Play something on the piano!’

2.3

The parallel use of the Estonian adessive and the adposition peal ‘on’

When comparing the meanings of the adposition peal ‘on’ (examples in (3)) to those of the adessive (examples in (2)), it can be seen that these two forms are used as alternatives to each other, especially in the functions of expressing location, place and instrument. According to Palmeos (1985:â•›15), the analytic construction – genitive together with the adposition peal ‘on’ – expresses the same meaning as the synthetic adessive. At the same time, it has been claimed in Estonian reference grammars that the meaning of adpositions is more concrete and specific than that of the cases (Erelt et al. 2007:â•›191). This has also been mentioned by Palmeos (1985:â•›18), who notes that the analytic construction conveys the meaning more clearly than the synthetic one. This clarity of expression is partly due to the grammatical homonymy inherent in the Estonian language – in some cases, when using the synthetic construction, it is not clear whether we are expressing location or possession and sometimes, the use of the adessive to express location is not possible because the possessive reading is too strong. Nevertheless, there are still numerous instances where both the adessive case and the adposition peal ‘on’ can express more or less the same meaning. A small-scale corpus analysis showed that in the 5-million-word fiction sub-corpus of the Balanced Corpus of Estonian (2008), there are 314 different Landmarks used with both the adessive case and the adposition peal ‘on’. Furthermore, similar results of the parallel use of these two constructions were obtained with an open production task that

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studied the expression of different spatial relations in Estonian (Salm 2010). Klavan et al. (2011) have reported the results of a forced choice task and a production task, the aim of which was to determine which semantic factors play a role in the use of the adessive and adposition peal ‘on’. The results of these studies indicate that the adessive is used when there is an abstract relation between Trajector and Landmark and the Landmark is a place; the adposition peal ‘on’ is used when there is an unconventional spatial relation between Trajector and Landmark and when the Landmark is a thing. However, the two tasks also yielded results where there was no significant difference between the two locative constructions. The present study hopes to provide converging evidence and to shed new light upon this issue by building upon the previous work, but using a different methodology (mono- and multifactorial corpus analysis) and looking at other factors besides the semantic ones.

3. The data sample The data analysed in this chapter come from the corpus of present-day written Estonian. A data sample of 300 instances of the Estonian adessive case from the fiction sub-corpus of the Morphologically Disambiguated Corpus (2010; size 104,000 words) and 300 instances of the Estonian adposition peal ‘on’ from the fiction sub-corpus of the Balanced Corpus of Estonian (2008; size 5 million words) was collected. Based on the findings from the previous variation and spatial expression studies cited above, the data were manually coded for multiple variables or ‘predictors’, which are outlined in the following section. It is worth pointing out that in order to get the 300 suitable instances of the adessive case, it was necessary to manually work through 1,700 instances of this construction; the reason being that the adessive fulfils a number of other functions in Estonian besides expressing spatial relations.

4. Corpus-linguistic operationalizations and monofactorial results The original coding schema included more than 30 variables; in the present analysis only the sixteen most important ones are discussed. These sixteen variables can be divided into two groups and include the following: seven morphosyntactic factors (length of the Landmark phrase, lexical complexity of the Landmark, word order, verb lemma, syntactic function of the Landmark phrase, word class of Landmark and Trajector) and nine semantic factors (type of relation between Landmark and Trajector, type of Landmark, animacy, number and mobility of Landmark and Trajector, relative size between Landmark and Trajector). The following sub-sections give an overview of the operationalizations of these variable groups and their different levels.



A multifactorial corpus analysis of grammatical synonymy 259

The significance of each variable was also tested individually and these results are presented directly after the presentation of the respective variable. The monofactorial analysis of the results relies on Gries (this volume) and predominantly makes use of the Chi-squared test to evaluate the raw frequency counts encountered in the corpus. Following Gries (ibid.), I also computed the effect sizes and inspected the Pearson residuals for each variable in order to determine how strong the results of the Chisquare tests are and what exactly determines the difference between the frequency counts. As Gries (ibid.) points out, the effect size theoretically ranges from 0 (‘no effect’) to 1 (‘perfect correlation’).

4.1

Morphosyntactic factors

4.1.1 Length of the Landmark phrase Previous studies on grammatical alternation have shown that the more explicit form is favoured in cognitively complex environments (Mondorf 2003:â•›294). This phenomenon has also been referred to as Rohdenburg’s complexity principle (ibid.). Given thus the option of either using a synthetic or analytic locative construction, longer words have been found to opt for the analytical variant and shorter words/phrases for the synthetic variant (Cooper and Ross 1975; Hawkins 1994; Wasow 1997; Arnold et al. 2000; Mondorf 2003; Wulff 2003). Mondorf (2003:â•›251–253) argues for a presumably universal tendency, the phenomenon that she terms analytic support: In cognitively more demanding environments which require an increased processing load, language users – when faced with the option between a synthetic and analytic variant – tend to compensate for the additional effort by resorting to the analytic form.

Although Mondorf (2003) focuses on the English comparative construction, the claim is that this compensatory strategy can be extended to other kinds of variation phenomena that draw on the synthetic-analytic distinction. Since length constraints have been found to affect other syntactic variation phenomena as well (e.g. Cooper and Ross 1975; Hawkins 1994; Wasow 1997; Arnold et al. 2000; Wulff 2003), it was decided to code the present data for the length of the locative phrase. Measures of syntactic complexity can be efficiently operationalized by counting the number of graphemic words (Bresnan and Ford 2010). For the present analysis, length of the Landmark phrase was measured both in words and syllables. In line with Bresnan and Ford (2010:â•›9, fn. 8) length was transformed by the logarithm in order to compress extreme values and bring the distribution more closely into the logistic regression model assumption of linearity. The results show that the mean length of the Landmark phrase with the adessive (1.95) differed highly significantly from the mean length of the Landmark phrase

260 Jane Klavan

Table 3.╇ Length of the Landmark phrase in words Number of words in the Lm phrase

Adessive

peal

Total

1 word 2 words 3 words 4 words 5 words 6 words 7 words Total

114 123 â•⁄41 â•⁄15 â•⁄â•⁄2 â•⁄â•⁄2 â•⁄â•⁄3 300

192 â•⁄88 â•⁄13 â•⁄â•⁄5 â•⁄â•⁄2 â•⁄â•⁄0 â•⁄â•⁄0 300

306 211 â•⁄54 â•⁄20 â•⁄â•⁄4 â•⁄â•⁄2 â•⁄â•⁄3 600

with the postposition peal ‘on’ (1.46), t(78) = 4.78, p < .001. As seen from Table 3, the adessive was predominantly used with Landmark phrases that were two or more words long and the postposition peal with Landmark phrases that were one word long (examples (4a) and (4b)). If we take that a longer Landmark phrase implies a cognitively more complex environment (cf. Wasow 1997; Cappelle 2009:â•›149), Rohdenburg’s complexity principle does not hold here, i.e. the more explicit form (the postposition peal) was not favoured in a cognitively more complex environment. (4) a. ILU1980\stkt0001: Pihlakad kasvasid sellelsamal põllupeenral. rowan.pl.nom grow-pst.3pl this.sg.ad flowerbed.sg.ad ‘The rowans were growing on this flower bed’. b. MJ_A: Kai peal oli meeletu trügimine… pier.sg.gen on.ad be-pst.3sg mad.sg.nom pushing.sg.nom ‘On the pier people were pushing madly…’ According to Mondorf (2003:â•›254), who discusses the English comparative construction, one of the effects of the so-called more-support that reflects the general analytic support is that: a separate lexeme as degree marker rather than an inflectional suffix can serve both as an unambiguous signal indicating increased processing load to the reader and as a less condensed and more explicit way of structuring a complex phrase.

Since the synthetic variant in -er allows recognition only after the adjective and its inflection have been processed, complex environments should call for early recognition and hence the analytic variant would be used in English for the comparative construction (Mondorf 2003:â•›255). However, in the case of the Estonian adessive and the adposition peal ‘on’, this signalling argument does not work because both the adessive case marker and the postposition peal ‘on’ follow the locative phrase (see examples (4a)



A multifactorial corpus analysis of grammatical synonymy 261

Table 4.╇ Length of the Landmark phrase in syllables Number of syllables in the Lm phrase

Adessive

peal

Total

1 syllable 2 syllables 3 syllables 4 syllables 5 syllables more than 5 syllables Total

â•⁄â•⁄7 â•⁄64 â•⁄61 â•⁄45 â•⁄32 â•⁄91 300

â•⁄33 125 â•⁄31 â•⁄59 â•⁄17 â•⁄35 300

â•⁄40 189 â•⁄92 104 â•⁄49 126 600

and (4b)). Thus, quite the opposite effect may play a role in Estonian. Precisely due to the fact that in the case of Estonian locative phrases, the postposition only comes at the end of the phrase, the locative case is a better signal to indicate that what we have here is a long locative phrase expressing a support relation – in Estonian all of the words in the adessive locative phrase are marked for the adessive case, as sellelsamal ‘this’ in example (4a) above. In addition, the results also show that the mean length of the Landmark phrase in syllables was significantly different with the adessive (4.87) and the postposition peal (3.15), t(435) = 7.18, p < .001. The proportion of peal ‘on’ uses with Landmark phrases one or two syllables long was considerably higher than the proportion of adessive uses with Landmark phrases of the same length; when the Landmark phrase was more than 10 syllables long, the proportion of adessive occurrences was much bigger than that of peal ‘on’ (Table 4).

4.1.2 Lexical complexity of Landmark It was decided to also code the Landmark for what has been termed here as lexical complexity, with the levels of ‘compound’ and ‘single lexeme’, e.g. writing desk vs. desk. Table 5 shows that the number of occurrences where the Landmark word was a compound was significantly higher with the adessive (88 instances) than with the adposition peal ‘on’ (17 instances), χ²(1, N = 600) = 56.57, p < .001, φ = 0.31. This gives further indication of the adposition peal being preferred with shorter, less complex Landmark phrases, while the adessive tends to be used with longer and more complex Landmark phrases. Table 5.╇ Lexical complexity of Landmark Landmark word

Adessive

peal

Total

compound single lexeme Total

â•⁄88 212 300

â•⁄17 283 300

105 495 600

262 Jane Klavan

Table 6.╇ Position of the locative phrase within the clause Position of locative phrase

Adessive

peal

Total

final initial middle Total

129 â•⁄83 â•⁄88 300

111 â•⁄83 106 300

240 166 194 600

4.1.3 Word order: Position of the locative phrase Several researchers have discussed the principle of end-weight in relation to grammatical variation (Wasow 1997; Cappelle 2009:â•›149–150). This phenomenon states that “long, complex phrases tend to come at the ends of clauses” (Wasow 1997:â•›81). However, it is not entirely clear what is meant by ‘weight’. For example, it can either be length or complexity (cf. Wasow 1997; Cappelle 2009:â•›149). In the present chapter it is simply assumed that because the analytic adpositional construction with peal ‘on’ can create a heavier constituent effected by the extra lexeme (peal ‘on’), it weighs more than the synthetic adessive case. However, it should be noted that length is only one aspect of how the principle of end-weight can be operationalized. For the present study, the word order factor was coded according to the position of the locative phrase in the clause with the levels of ‘final’, ‘initial’ and ‘middle’. Estonian is a language with a relatively free word order and the locative phrases can come at the beginning of a clause (in which case the clause is referred to as an existential clause in Estonian reference grammars), at the end of a clause or in the middle of a clause. However, there was no significant difference between the two construction types in the present dataset (see Table 6), χ²(2, N = 600) = 3.02, p = .22. Contrary to the purported principle of end-weight, the locative construction with the adessive case was slightly more frequent in the final position. This can be, at least partly, explained by the fact that the mean length of the locative constructions with the adessive was longer than the mean length of the locative constructions with the postposition peal ‘on’ and that these longer Landmark phrases with the adessive predominantly occur in the final position within a clause (see Section 4.1.1 above). 4.1.4 Word order: Loc_Nom vs. Nom_Loc In addition to the position of the locative phrase within the clause, it was decided to code whether the locative phrase follows or precedes the Trajector phrase. This factor has two levels – ‘Nom_Loc’ and ‘Loc_Nom’. ‘Loc’ refers to the locative phrase and ‘Nom’ to the Trajector phrase. The relevant frequencies are given in Table 7. In general, it can be seen that the preferred word order is such that the locative phrase follows the Trajector (393 occurrences in total). Although the raw frequencies indicate that when the locative phrase precedes the Trajector, the adessive is used more often



A multifactorial corpus analysis of grammatical synonymy 263

Table 7.╇ Word order: Loc_Nom vs. Nom_Loc Loc_Nom vs. Nom_Loc

Adessive

peal

Total

Loc_Nom Nom_Loc Total

111 189 300

â•⁄96 204 300

207 393 600

Table 8.╇ Verb lemmas used with locative constructions Verb lemma

Adessive

peal

Total

action verbs existence verbs motion verbs posture verbs no verb Total

113 â•⁄40 â•⁄46 â•⁄51 â•⁄50 300

â•⁄91 â•⁄85 â•⁄35 â•⁄45 â•⁄44 300

204 125 â•⁄81 â•⁄96 â•⁄94 600

than the adposition peal ‘on’, statistically these results are not significant, χ²(1,  N = 600) = 1.66, p = .19.

4.1.5 Verb lemma Every instance of the adessive and the adposition peal ‘on’ was coded for the verb lemma used in these sentences. In total, there were 212 different verbs used with these locative constructions. The verbs were subcategorised into different groups based largely on Levin (1993) and include the following levels: ‘action verbs’ (e.g. tegema ‘to do’), ‘existence verbs’ (e.g. olema ‘to be’), ‘motion verbs’ (e.g. jooksma ‘to run’), and ‘posture verbs’ (e.g. istuma ‘to sit’). In addition, this factor also had the level of ‘no verb’ which was used for elliptical sentences where no overt verb lemma was expressed. The raw frequencies of these verb groups are given in Table 8. The Chi-squared test revealed that the frequencies of the two constructions significantly differed by verb lemma (χ²(4, N = 600) = 22.76, p < .001, φ = 0.19). The Pearson residuals show that existence verbs determine the difference between these frequency counts – the adpositional construction is significantly more often used with existence verbs like olema ‘to be’, asuma ‘to be situated’, and asetsema ‘to be placed’. 4.1.6 Syntactic function of the Landmark phrase Both the adessive and the adpositional construction can fulfil two syntactic functions – that of an adverbial and a modifier. It was therefore decided to code the syntactic function of the locative phrase in the dataset with precisely these two levels: ‘adverbial’ and ‘modifier’. The results show that there is a modest, but significant difference (Table 9), χ²(1, N = 600) = 5.78, p = .016, φ = 0.09. Although both the adessive

264 Jane Klavan

Table 9.╇ Syntactic function of the Landmark phrase Syn. function of Lm phrase

Adessive

peal

Total

adverbial modifier Total

264 â•⁄36 300

281 â•⁄19 300

545 â•⁄55 600

case and the postposition peal ‘on’ predominantly fulfil the function of an adverbial, the adessive case is slightly more frequently used in the function of a modifier, as in example (5). (5) ILU1980\stkt0023: Paigad küünarnukkidel ja hõlmadel tükkisid lahti … patch.pl.nom elbow.pl.ad and flap.pl.ad start-pst.3pl apart ‘Patches on the elbows and flaps started to come apart…’

4.1.7 Word class of Landmark and Trajector Different expression types have been found to affect the choice of syntactic alternatives (see, for example, Bresnan and Ford 2010). Both Landmarks and Trajectors were coded for the following types: ‘noun’, ‘pronoun’, ‘verb phrase’. The majority of Landmarks used with the adessive case and the postposition peal ‘on’ are noun phrases (Table 10). However, when the Landmark is a pronoun, the postposition peal ‘on’ is used more frequently. This difference is significant – χ²(1, N = 600) = 10.10, p = .001, φ = 0.13. This result is related to the variable length of the Landmark (see Section 4.1.1 above). Pronouns are short words and these results reflect, once again, the tendency to use the postposition peal ‘on’ with shorter Landmarks. Table 10.╇ Word class of Landmark Word class of Landmark

Adessive

peal

Total

noun pronoun Total

292 â•⁄â•⁄8 300

274 â•⁄26 300

566 â•⁄34 600

Word class of Trajector

Adessive

peal

Total

noun pronoun verb phrase Total

210 â•⁄49 â•⁄41 300

166 â•⁄82 â•⁄52 300

376 131 â•⁄93 600

Table 11.╇ Word class of Trajector

A multifactorial corpus analysis of grammatical synonymy 265



The majority of Trajectors used with both locative constructions are also noun phrases (Table 11). Nevertheless, curiously, the same tendency to use the adpositional construction with pronouns occurs and the difference is also significant, χ²(2, N = 600) = 14.76, p < .001, φ = 0.16.

4.2

Semantic variables

Numerous cognitive-functional studies on spatial language expressions have shown that various properties of Trajector and Landmark participating in the locative construction influence the use of spatial expressions (e.g. Talmy 1983; Herskovits 1986; Vandeloise 1991; Feist and Gentner 2003; Coventry and Garrod 2004; Carlson and Van der Zee 2005). In the vein of this research tradition, various semantic properties of Landmarks and Trajectors were coded in the present data.

4.2.1 Type of relation between Landmark and Trajector It has been suggested in previous work on cases and adpositional constructions that cases are semantically more abstract than adpositions (Bartens 1978; Comrie 1986; Luraghi 1991:â•›66–67; Ojutkangas 2008; Hagège 2010:â•›37–38; Lestrade 2010). Both the Estonian adessive and the adposition peal ‘on’ can express spatial and abstract relations between a Trajector and a Landmark. This variable was coded in the dataset with the levels of ‘abstract’ and ‘spatial’ in order to see if this general assumption of cases expressing abstract relations was also borne out in the present data. A relation was coded abstract when either the Trajector or Landmark was abstract or the relation itself was abstract, i.e. if there was a meaning transfer. There was a marginal significant difference, χ²(1, N = 600) = 5.04, p = .02, φ = 0.10; indeed, the adposition peal ‘on’ is more frequent with abstract relations in the present dataset (Table 12). However, one must bear in mind here that for the present analysis, only such occurrences where the alternation between the adessive and the adposition peal ‘on’ is possible were looked at. If we compare the general usage of these two constructions, we can easily see that the adessive case expresses abstract functions, where the use of an adposition is not possible (cf. Section 2 above, examples (2c) and (2d)). Table 12.╇ Type of relation between Landmark and Trajector Relation type

Adessive

peal

Total

abstract spatial Total

â•⁄49 251 300

â•⁄71 229 300

120 480 600

266 Jane Klavan

4.2.2 Type of Landmark It can also be predicted that there is a general difference between what types of Landmarks are used together with either the Estonian adessive case or the adposition peal ‘on’. Accordingly, Landmarks in the dataset were coded for their type, the levels of which were ‘location’ (e.g. street) and ‘object’ (e.g. table). The rationale of making a distinction between small easily manipulable objects and large static objects or locations is that location should lend itself more easily for abstraction and hence is more likely to be used with the adessive (Bartens 1978). On the other hand, as has been put forward in previous studies, adpositions are more concrete and specific than cases, and they convey the meaning of spatial location of an object more clearly and should thus be more frequent with small easily manipulable objects such as Landmarks (Bartens 1978; Palmeos 1985:â•›18; Comrie 1986; Luraghi 1991:â•›66–67; Ojutkangas 2008; Hagège 2010:â•›37–38; Lestrade 2010). The results of the Chi-squared test indicate that the frequency counts of the adessive and the adposition peal ‘on’ significantly differed by the type of Landmark (χ²(1, N = 600) = 11.21, p < .001, φ = 0.14) – the adessive tends to be used when the Landmark is a location and the adposition peal ‘on’ when it is an object (Table 13). 4.2.3 Animacy of Landmark and Trajector Since animacy is considered to be a very important cognitive category and is discussed in numerous linguistic and psycholinguistic studies (for overviews, see, for example, de Vega et al. 2002:â•›121–122; Feist and Gentner 2003:â•›2; Bresnan and Ford 2010:â•›10), it was decided to code this category for the Estonian adessive and adposition peal ‘on’ dataset as well. This variable has only two levels – ‘animate’ and ‘inanimate’. Unsurprisingly, the results show that the adposition peal ‘on’, rather than the adessive, is used in cases of animate Landmarks (Table 14).

Table 13.╇ Type of Landmark Landmark

Adessive

peal

Total

location object Total

169 131 300

128 172 300

297 303 600

Animacy of Landmark

Adessive

peal

Total

animate inanimate Total

â•⁄â•⁄2 298 300

â•⁄17 283 300

â•⁄19 581 600

Table 14.╇ Animacy of Landmark



A multifactorial corpus analysis of grammatical synonymy 267

The results of the Fisher’s exact test revealed a significant difference – p < .001; the odds ratio is 0.11. However, here it must be, once again, emphasised that the adessive has another important function in Estonian besides expressing space – that of expressing possession (see example (2c) above). Since animate objects are very apt to possessing things, the combination of an animate Landmark and the adessive case fulfils the function of the possessive construction. Therefore, if there is need in Estonian to talk about an object placed on top of an animate Landmark, this would be expressed with the adposition peal ‘on’. There was no significant difference between the adessive and the adposition peal ‘on’ for the variable animacy of Trajector (Table 15), χ²(1, N = 600) = 0.44, p = .51. The data do, however, confirm the general tendency of Trajectors to be more frequently animate than inanimate.

4.2.4 Number of Landmark and Trajector Another cognitively and typologically important category in grammar is number (Greenberg 1966), which also plays a role in certain grammatical variations (e.g. Bresnan and Ford 2010:â•›179). In the dataset, both Landmarks and Trajectors were coded either ‘plural’ or ‘singular’. When context and formal plural marking were in conflict or when there was ambiguity, the analysis proceeded from the context. The results (Table 16) show that there is no difference between the two locative constructions. Although the proportion of plural Landmarks is a little higher with the adessive construction, this difference is not significant: χ²(1, N = 600) = 2.84, p = .09. Interestingly, there is a difference in the use of the adessive and the adposition peal ‘on’ according to whether the Trajector is singular or plural – the proportion of adessive occurrences with a plural Trajector is higher than the proportion of the adposition peal ‘on’ occurrences with a plural Trajector (Table 17) and this difference is significant: χ²(1, N = 600) = 4.03, p = .04, φ = 0.08. This may be due to an interaction Table 15.╇ Animacy of Trajector Animacy of Trajector

Adessive

peal

Total

animate inanimate Total

167 133 300

175 125 300

342 258 600

Number of Landmark

Adessive

peal

Total

plural singular Total

â•⁄40 260 300

â•⁄27 273 300

â•⁄67 258 600

Table 16.╇ Number of Landmark

268 Jane Klavan

Table 17.╇ Number of Trajector Number of Trajector

Adessive

peal

Total

plural singular Total

â•⁄94 206 300

â•⁄72 228 300

166 434 600

Mobility of Landmark

Adessive

peal

Total

mobile static Total

116 184 300

178 122 300

294 306 600

Table 18.╇ Mobility of Landmark

with another variable – type of Landmark.2 Since the adessive tends to be used with locations and since locations are large, immobile objects such as streets or fields, one would expect to find more than one object (Trajector) located on such large locations, e.g. people/cars on the street vs. a person/a car on the street. Indeed, a little more than half of the occurrences with a plural Trajector have location as the type of Landmark in the dataset.

4.2.5 Mobility of Landmark and Trajector Following de Vega et al. (2002), both Landmarks and Trajectors in the dataset were coded for the variable mobility, the levels of which were ‘mobile’ and ‘static’. Mobile objects are those that do not have a fixed position in the environment, either because they move by themselves (e.g. humans, animals) or can be moved by an external agent (e.g. a table). Static objects (the majority of which in the dataset are also locations, but not all) have a fixed position in the environment (e.g. streets, trees). It can be seen from Table 18 that the adessive very frequently occurs with a static Landmark and the adposition peal ‘on’ with a mobile Landmark; this difference is also highly significant: χ²(1, N = 600) = 25.64, p < .001, φ = 0.21. There was no significant difference between these two constructions for the mobility of Trajector, χ²(1, N = 600) = 0.15, p = .69 (Table 19). 4.2.6 Relative size between the Landmark and the Trajector In Cognitive Linguistic analyses of spatial expressions, it has been claimed that Landmarks tend to be larger than Trajectors (Talmy 1983; Herskovits 1986; Langacker 1987; Vandeloise 1991). In order to validate this claim and to see whether this factor influences the use of the Estonian adessive case and the postposition peal ‘on’, the 2. I am indebted to Krista Ojutkangas for this suggestion (p.c.).

A multifactorial corpus analysis of grammatical synonymy 269



Table 19.╇ Mobility of Trajector Mobility of Trajector

Adessive

peal

Total

mobile static Total

268 â•⁄32 300

265 â•⁄35 300

533 â•⁄67 600

Table 20.╇ Relative size between the Landmark and the Trajector Relative size between Tr and Lm

Adessive

peal

Total

conventional same unconventional Total

193 â•⁄58 â•⁄49 300

140 â•⁄95 â•⁄65 300

333 153 114 600

relative size between the Landmark and Trajector was coded either as ‘conventional’ (Landmark > Trajector), ‘same’ (Landmark = Trajector) or ‘unconventional’ (Landmark < Trajector). The results indicate that in general, Landmarks tend to be indeed larger than Trajectors. Moreover, there is a difference between the adessive and the adposition peal ‘on’. The adessive is used when the Trajector is smaller than the Landmark and the adposition peal ‘on’ when the Trajector and the Landmark are of the same size or when the Trajector is bigger than the Landmark (Table 20). This difference is significant: χ²(2, N = 600) = 19.63, p < .001, φ = 0.18.

4.3

Summary of the variables

Many of the variables that are described and that have been put forward in the literature on variation were confirmed to have a significant effect on the use of the Estonian adessive and adposition peal ‘on’. Table 21 presents in a summary fashion all the variables argued to contribute to the alternation between the Estonian adessive and the adposition peal ‘on’; the p-values and effect sizes were obtained using the Chi-square test (see Gries, this volume). Out of the sixteen variables discussed, nine were highly significant, three marginally significant and four were not significant. The highly significant factors were the length of the Landmark phrase (in both words and syllables), the lexical complexity of Landmark, the verb lemma, word class of Landmark and Trajector, type, animacy and mobility of Landmark, and the relative size between Trajector and Landmark. The factors that were marginally significant were the syntactic function of the Landmark phrase, type of relation between Trajector and Landmark, and the number of Trajector; the factors that were not significant include the following: word order, animacy of Trajector, number of Landmark, and mobility of Trajector.

270 Jane Klavan Table 21. Variables that are argued to contribute to the alternation between the Estonian adessive and the adposition peal ‘on’ Variable name

Level for the adessive construction

Level for the adpositional construction

p-value

Effect size

Length of Lm phrase in words Length of Lm phrase in syllables Lexical complexity of Landmark Word order: Position of the locative phrase Word order: Nom_Loc/Loc_Nom Verb lemma Syntactic function of Lm phrase Word class of Lm Word class of Tr Type of relation between Tr & Lm Type of Lm Animacy of Lm Animacy of Tr Number of Lm Number of Tr Mobility of Lm Relative size Tr & Lm

2 or more words 4 or more syllables compound

1 word 1–3 syllables single lexeme

action verbs modifier

existence verbs

p < .001 p < .001 p < .001 p = .22 p = .19 p < .001 p = .02 p < .001 p < .001 p = .03 p < .001 p < .001 p = .51 p = .09 p = .04 p < .001 p < .001

– – 0.3 – – 0.2 0.1 0.1 0.2 0.1 0.1 0.1 – – 0.1 0.2 0.2

noun location

plural static Lm > Tr

pronoun pronoun abstract object animate

mobile Lm = Tr; Lm < Tr



A multifactorial corpus analysis of grammatical synonymy 271

One of the most surprising results among the less significant factors was the variable word order. Taking into consideration previous studies on grammatical variation, specifically the proposed end-weight principle (see Section 4.2.1), it was predicted that since the adposition peal ‘on’ adds an extra word to the locative phrase, thus making the whole locative phrase longer, it would prefer the final position within the clause. Instead, the locative phrases with the adessive occurred slightly more frequently in the final position. A possible explanation is the interaction between the length of the Landmark phrase and word order – longer Landmark phrases were used with the adessive in the dataset. It is clear, however, that this issue needs further research. Another morphosyntactic variable that seems to play at least a marginal role in the alternation between the two locative constructions is the syntactic function of the locative phrase. The first function is considerably more frequent, but if the locative phrase is used in the modifier function, it tends to be expressed by the adessive and not with the adposition. The results also show that there was a tendency for the adessive to occur when the Landmark was a location, and for the adposition peal ‘on’ to occur when it was an object. Unpredictably, the plurality of Trajector stood out – with plural Trajectors, the adessive construction was frequent. This interacts with the previous factor – type of Landmark – the adessive occurring with locations as Landmarks. Locations, in turn, tend to imply more than one Trajector. Out of the nine highly significant factors, five were morphosyntactic and four were semantic factors. Length of the Landmark phrase proved to be highly significant in a number of ways. First and foremost, the mean scores for the length of Landmark phrase both in words and syllables were different for the adessive and the adposition peal ‘on’. If the Landmark phrase is more than two words or more than four syllables long, the adessive is used; if the Landmark phrase is composed of only one word or is three or less syllables long, the adposition peal ‘on’ is used. The tendency to use the adposition with shorter Landmarks was also illustrated with the factor lexical complexity of the Landmark phrase – single lexemes were used with the adposition peal ‘on’ and compound words with the adessive. Unpredictably, there was a significant difference between the two constructions in the type of verb used – the adposition peal ‘on’ was frequently used with existence verbs. Another unpredictable significant factor was the word class of Trajector – the adposition peal ‘on’ was frequently used with pronominal Trajectors. From the semantic factors, type, animacy and mobility of Landmark, and the relative size between Trajector and Landmark were highly significant. Due to the fact that animate Landmarks with the adessive case express the possessor, the spatial support relation with animate Landmarks is expressed with the adposition peal ‘on’. The factor mobility of Landmark interacts with the type of Landmark – the adessive is used with static Landmarks, which in many cases are locations, and the adposition peal ‘on’ with mobile Landmarks, which in many cases are objects. Furthermore, the adessive is used when the Landmark is bigger than the Trajector; when the Landmark

272 Jane Klavan

and the Trajector are of the same size or when the Trajector is bigger than the Landmark, the adpositional construction was more frequent. Although the results of the monofactorial analysis indicate that a number of factors are significant in the alternation between the Estonian adessive and the adposition peal ‘on’, this way of analysing the data is not sufficient on its own. When speakers use either of these locative constructions, they probably do not consider the value of one factor only – in actual language use, all of the factors interact simultaneously and need to be analysed as such. Therefore, a multifactorial approach is necessary to determine which of the variables are more decisive and predictive for the choice of the construction. In the following section, I will present the results of a logistic regression analysis.

5. Multifactorial results. Logistic regression analysis Multiple logistic regression (Glynn 2007:â•›241–275; Baayen 2008:â•›195–208) is used to quantify the contribution of the factors presented above to the alternative use of the Estonian adessive and the adposition peal ‘on’. Being a confirmatory modelling technique, regression analysis gives probabilistic scores and calculates the explanatory power of the model (Glynn 2010:â•›257). I will not discuss here the details that lie behind this statistical technique. The interested reader is referred to elsewhere in this volume for a detailed overview of what the model does, what are its inner workings, its weaknesses and strengths; Glynn (2007, 2010), for example, gives an introduction to the mechanics of this technique. The results of the monofactorial analyses showed that many different factors were important in determining the difference between the adessive and the adpositional constructions. All of these factors were included in the regression modelling and several models were run with various combinations of these factors. Due to the concerns of multicollinearity, a number of factors could not be entered into the model simultaneously; this in turn increased the total number of models created. After comparing a range of models, the most significant and explanatory model was selected. The analysis was performed in R (version 2.10.1) and the model is presented below: Binominal Logistic Regression

Locative Phrase ~ Verb_Lemma + WO_LocNom + LM_LexComp + LM_WC + LM_Mobility

Deviance Residuals: Min

-2.1839

1Q

-1.0214

Median 0.2539

3Q

0.9923

Max

2.2529

A multifactorial corpus analysis of grammatical synonymy 273



Coefficients:

Estimate Std.Error

(Intercept)

z value Pr(>|z|)

-1.0388

0.3293

-3.155

Verb_Lemma Existence 1.4509

0.3347

4.334

Verb_Lemma Action Verb_Lemma Motion

Verb_Lemma Posture WO_LocNom Nom_Loc LM_LexComp Comp LM_WC Pron

LM_Mobility Mobile ---

0.3116 0.1471 0.3205 0.5132

-2.2415 2.0282 0.9781

0.2913 0.3485 0.3334 0.2061

1.070 0.422 0.962 2.490

0.3244

-6.911

0.1929

5.070

0.6405

3.167

0.00161 0.28471

**

1.46e-05 *** 0.67304 0.33626 0.01277

*

0.00154

**

4.83e-12 *** 3.97e-07 ***

Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 822.06 on 592 degrees of freedom

Residual deviance: 676.47 on 584 degrees of freedom AIC: 694.47

Number of Fisher Scoring iterations: 4 Summary of Model

Predictive Power of Model

D.f.: 8

C: 0.764

Model L.R .: 145.59 P: 0

Pseudo R²: 0.29

Somers’ Dxy: 0.527

Adding interactions and changing the order of the levels did not improve the model. The Nagelkerke R², a pseudo R² statistic for logistic regression, gives us an idea of the variability accounted for by the present model. As Glynn (2010:â•›259) points out, any figure above 0.3 is a sign of predictive power (for the model under discussion, the figure is just below 0.3–0.29). Another important score is the C-score (ROC), which is a scaled rank correlation between predicted and observed outcomes. Although not expressed in terms of probability of success, it can be interpreted as a rough indicator of such, where 1 represents prefect predictions and .5 pure chance. Although the score of C–0.764 does not indicate a predicatively strong model (.8 is typically taken as a predictive model), it does indicate that predictor variables explain a reasonable amount of the differences in use. The model was also checked for multicollinearity by calculating the variance inflation factors. Over dispersion does not appear to be a serious issue either. Although the indicators of the model’s explanatory power are all close to the lower boundary, it can be concluded that the model still bears some statistical significance and explanatory power and a cursory look at the results can be taken.

274 Jane Klavan

The model includes the factors type of verb (Verb_Lemma), word order (WO_ LocNom), lexical complexity of the Landmark phrase (LM_LexComplexity), word class of the Landmark (LM_WC) and mobility of the Landmark (LM_Mobility) and their different values or features – these predict the outcome of an example as either the adessive or the adpositional construction. In the list of the estimates of the coefficients, negative numbers predict the adessive construction and positive numbers the adpositional construction. Lexical complexity of the Landmark is the most important predictor for the adessive construction. This confirms the results of the monofactorial analysis, where we saw that when the Landmark word is a compound word, the adessive construction is used. Important predictors of the adpositional construction are the word class of the Landmark with the level of ‘pronoun’, verbs of existence, mobility of the Landmark with the level of ‘mobile’ and such a word order sequence where the locative phrase follows the Trajector. Glynn (2010:â•›260) points out that “[a]s a rule, any figure higher or lower than +/–1 is a relatively important predictor”. Since almost all of the significant levels or values are around +/–1, it can be concluded that in combination, the factors included in the model are fairly strong predictors. It seems, therefore, that although monofactorial results showed that for the present dataset a large number of factors were highly significant in determining the alternative use of the adessive and the adposition peal ‘on’ only five of these factors are predictive when we consider all of the factors together in combination, i.e. in a truly multifactorial situation what everyday language use no doubt is. One of the conclusions to be drawn from the fact that, in theory, the model could have more explanatory power is that there may be other factors not included in the present analysis that may play an even more significant role in determining the use of these two constructions. For instance, all of the discourse-functional variables, such as topic, register, preceding and subsequent mention of the adessive or adpositional construction, etc., and variables like idiolect and dialect are absent from the present analysis. Furthermore, the corpus data discussed in this study comes from a corpus of fiction, where the language used is that of edited written texts. Incorporating data from spoken or internet language (i.e. unedited texts) may provide very useful insights into the analysis and the model in general, which in turn would produce more coherent results that would predict the data more accurately. Nevertheless, both the monofactorial and multifactorial analyses of the present data also systematically indicate that there are significant differences between the Estonian adessive and the adposition peal ‘on’, as can be predicted if we proceed from the premises of Cognitive Grammar and Construction Grammar.



A multifactorial corpus analysis of grammatical synonymy 275

6. Conclusion The present chapter looked at the alternation between the Estonian adessive case and the adposition peal ‘on’ in the corpus of present-day written Estonian. Both the monofactorial and multifactorial analyses showed that the use of these two constructions is determined by a variety of morphosyntactic and semantic variables. More specifically, the multifactorial analyses of the data confirmed the statistical influence of the following factors: lexical complexity of Landmark, type of verb, word order, word class of Landmark, and the mobility of Landmark. Adessive tends to be used when the Landmark is lexically more complex, when it is static, and when the locative phrase precedes the Trajector. Adposition peal ‘on’ tends to be used together with verbs of existence and pronominal Landmarks, when the Landmark phrase is lexically simple, when the Landmark is animate and mobile, and when the locative phrase follows the Trajector. Even though the results of the corpus analysis confirmed the prediction that there are differences in the use of the adessive and the adposition peal ‘on’, we should be careful about drawing any far-reaching conclusions because the model obtained as a result of running the logistic regression analysis is only marginally powerful. This may indicate that there are other more important factors that better predict the alternation between the adessive and the adpositional construction which are absent from the present analysis (e.g. discourse-functional factors, idiolect, dialect). The corpus analysis results discussed in the present chapter do not facilitate a very good comparison with the results obtained by Klavan et al. (2011), since the latter included in their studies only semantic factors, thus excluding morphosyntactic ones. Nevertheless, as the logistic regression analysis showed, at least one of the semantic factors was an important predictor – mobility of Landmark; static Landmarks predict the adessive construction and mobile Landmarks the adpositional construction. Klavan et al. (2011) showed, in turn, that with locations as Landmarks the adessive is used, and with objects as Landmarks the adposition peal ‘on’ is used; since locations are predominantly static and objects mobile, there is converging evidence that the type of Landmark does influence the alternative use of the adessive and the adposition peal ‘on’. It is hoped that the chapter succeeded in demonstrating the necessity and utility of using a combination of methodologies in studying grammatical (and other) variation phenomena.

276 Jane Klavan

References Arnold, J. E., Wasow, T., Losongco, A., & Ginstrom, R. (2000). Heaviness vs. newness: The effects of complexity and information structure on constituent ordering. Language, 76(1), 28–55. Baayen, H. (2008). Analyzing linguistic data: A practical introduction to statistics using R. Cambridge: Cambridge University Press. DOI: 10.1017/CBO9780511801686 Balanced Corpus of Estonian (2008). Retrieved from Bartens, R. (1978). Synteettiset ja analyyttiset rakenteet lapin paikanilmauksissa [Suomalais-ugrilaisen Seuran toimituksia 166]. Helsinki: Suomalais-Ugrilainen Seura. Bresnan, J., Cueni, A., Nikitina, T., & Baayen, H. (2007). Predicting the dative alternation. In G. Bouma, I. Kraemer, & J. Zwarts (Eds.), Cognitive foundations of interpretation (pp. 69– 94). Amsterdam: Royal Netherlands Academy of Science. Bresnan, J., & Ford, M. (2010). Predicting syntax: Processing dative constructions in American and Australian varieties of English. Language, 86(1), 168–213. DOI: 10.1353/lan.0.0189 Cappelle, B. (2009). Contextual cues for particle placement: Multiplicity, motivation, modelling. In A. Bergs, & G. Diewald (Eds.), Context in construction grammar (pp. 145–191). Amsterdam & Philadelphia: John Benjamins. Carlson, L., & Van der Zee, E. (2005). Functional features in language and space: Insights from perception, categorization, and development. Oxford: Oxford University Press. Comrie, B. (1986). Markedness, grammar, people, and the world. In F. R. Eckman, E. A. Moravcsik, & J. R. Wirth (Eds.), Markedness (pp. 85–106). New York: Plenum. DOI: 10.1007/978-1-4757-5718-7_6 Cooper, W. E., & Ross, J. R. (1975). World order. In R. E. Grossman, J. L. San, & T. J. Vance (Eds.), Chicago linguistic society: Papers from the parasession on functionalism (pp. 63– 111). Chicago: Chicago Linguistic Society. Coventry, K. R., & Garrod, S. C. (2004). Saying, seeing, and acting: The psychological semantics of spatial prepositions. New York: Psychology Press. de Vega, M., Rodrigo, M. J., Ato, M., Dehn, D. M., & Barquero, B. (2002). How nouns and prepositions fit together: An exploration of the semantics of locative sentences. Discourse Processes, 34(2), 117–143. DOI: 10.1207/S15326950DP3402_1 Erelt, M., Kasik, R., Metslang, H., Rajandi, H., Ross, K., Saari, H., Tael, K., & Vare, S. (1993). Eesti keele grammatika II: Süntaks [The grammar of Estonian II: Syntax]. Tallinn: Eesti Teaduste Akadeemia Keele ja Kirjanduse Instituut. Erelt, M., Kasik, R., Metslang, H., Rajandi, H., Ross, K., Saari, H., Tael, K., & Vare, S. (1995). Eesti keele grammatika I: Morfoloogia [The grammar of Estonian I: Morphology]. Tallinn: Eesti Teaduste Akadeemia Eesti Keele Instituut. Erelt, M., Erelt, T., & Ross, K. (2007). Eesti keele käsiraamat [Handbook of Estonian]. Tallinn: Eesti Keele Sihtasutus. Feist, M., & Gentner, D. (2003). Factors involved in the use of in and on. In R. Alterman & D. Kirsh (Eds.), Proceedings of the twenty-fifth annual meeting of the Cognitive Science Society (pp. 390–395). Boston MA: Cognitive Science Society. Glynn, D. (2007). Mapping meaning: Toward a usage-based methodology in cognitive semantics. Unpublished PhD thesis, Katholieke Universiteit Leuven.



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Glynn, D. (2010). Testing the hypothesis: Objectivity and verification in usage-based cognitive semantics. In D. Glynn, & K. Fischer (Eds.), Quantitative Cognitive Semantics. Corpus-driven approaches (pp. 239–270). Berlin: Mouton de Gruyter. DOI: 10.1515/9783110226423 Goldberg, A. (1995). Constructions: A construction grammar approach to argument structure. Chicago: University of Chicago Press. Goldberg, A. (2006). Constructions at work: The nature of generalization in language. Oxford: Oxford University Press. Greenberg, J. (1966). Language universals, with special reference to feature hierarchies. The Hague: Mouton de Gruyter. Gries, St. Th. (2003). Grammatical variation in English: A question of ‘structure vs. function’? In G. Rohdenburg, & B. Mondorf (Eds.), Determinants of grammatical variation in English (pp. 155–173). Berlin: Mouton de Gruyter. Hagège, C. (2010). Adpositions. Oxford: Oxford University Press. DOI: 10.1093/acprof:oso/9780199575008.001.0001 Hawkins, J. A. (1994). A performance theory of order and constituency. Cambridge: Cambridge University Press. Herskovits, A. (1986). Language and spatial cognition: An interdisciplinary study of the prepositions in English. Cambridge: Cambridge University Press. Klavan, J., Kesküla, K., & Ojava, L. (2011). Synonymy in grammar: the Estonian adessive case and the adposition peal ‘on’. In S. Kittilä, K. Västi, & J. Ylikoski (Eds.), Studies on case, animacy and semantic roles (pp. 113–134). Amsterdam: John Benjamins. Langacker, R. W. (1987). Foundations of Cognitive Grammar. Volume I: Theoretical prerequisites. Stanford: Stanford University Press. Langacker, R. W. (2008). Cognitive Grammar: A basic introduction. Oxford: Oxford University Press. DOI: 10.1093/acprof:oso/9780195331967.001.0001 Lestrade, S. (2010). The space of case. Unpublished PhD dissertation, Radboud University Nijmegen. Levin, B. (1993). English verb classes and alternations: A preliminary investigation. Chicago: University of Chicago Press. Luraghi, S. (1991). Paradigm size, possible syncretism, and the use of adpositions with cases in flective languages. In F. Plank (Ed.), Paradigms: The economy of inflection (pp. 57–74). Berlin: Mouton de Gruyter. Mondorf, B. (2003). Support for more-support. In G. Rohdenburg, & B. Mondorf (Eds.), Determinants of grammatical variation in English (pp. 251–304). Berlin: Mouton de Gruyter. DOI: 10.1515/9783110900019 Morphologically Disambiguated Corpus (2010). Retrieved from Ojutkangas, K. (2008). Mihin suomessa tarvitaan sisä-grammeja? Virittäjä, 112(3), 382–400. Palmeos, P. (1985). Eesti keele grammatika II: Kaassõna [The grammar of Estonian II: Adposition]. Tartu: TRÜ trükikoda. Rannat, R. (1991). Noomeni sünteetiliste ja analüütiliste vormide kasutus [The use of the synthetic and analytic forms of the noun]. Unpublished BA dissertation, University of Tartu. Rosenbach, A. (2003). Aspects of iconicity and economy in the choice between the s-genitive and the of-genitive in English. In G. Rohdenburgand, & B. Mondorf (Eds.), Determinants of grammatical variation in English (pp. 379–411). Berlin: Mouton de Gruyter.

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Salm, S. (2010). Kaassõnade ‘sees’ ja ‘peal’ ning vastavate kohakäänete kasutust mõjutavad tegurid [The factors influencing the use of Estonian adpositions sees ‘in’ and peal ‘on’ and the corresponding locative cases]. Unpublished BA dissertation, University of Tartu. Szmrecsanyi, B. (2010). The English genitive alternation in a cognitive sociolinguistic perspective. In D. Geeraerts, G. Kristiansen, & Y. Peirsman (Eds.), Advances in cognitive sociolinguistics (pp. 141–166). Berlin & New York: Mouton de Gruyter. Talmy, L. (1983). How language structures space. In H. Pick, & L. P. Acredolo (Eds.), Spatial orientation: Theory, research and application (pp. 225–282). New York: Plenum Press. DOI: 10.1007/978-1-4615-9325-6_11 Vainik, E. (1995). Eesti keele väliskohakäänete semantika kognitiivse grammatika vaatenurgast [The semantics of Estonian external locative cases from the perspective of Cognitive Grammar]. Tallinn: Eesti Keele Instituut. Vandeloise, C. (1991). Spatial prepositions: A case study from French. Chicago: University of Chicago Press. Wasow, T. (1997). Remarks on grammatical weight. Language Variation and Change, 9(1), 81– 105. DOI: 10.1017/S0954394500001800 Wulff, S. (2003). A multifactorial corpus analysis of adjective order in English. International Journal of Corpus Linguistics, 8(2), 245–82. DOI: 10.1075/ijcl.8.2.04wul

A diachronic corpus-based multivariate analysis of “I think that” vs. “I think zero” Christopher Shank, Koen Plevoets, and Hubert Cuyckens Bangor University / University College Ghent / University of Leuven

This corpus-driven study seeks to explain the choice between the zero complement and the that complement constructions, when occurring with the mental state predicate think. Previous studies have identified a range of factors that are argued to explain the alternation patterns. Such studies have also proposed that there is a diachronic drift towards zero complementation. Based on a sample of 9,720 think tokens, from both spoken and written corpora, from between 1560–2012, we test the hypothesis of diachronic change and the effect of eleven proposed factors on the constructional alternation. Using logistic regression, we demonstrate that, contrary to previous studies, there is in fact a diachronic decrease in zero complementation. Moreover, the study also demonstrates the importance of understanding the interaction of the various factors that explain the near-synonymous relation, including, especially, between the spoken and written modes. Keywords: complementation, logistic regression, mental state verb, near-synonymy, that/zero alternation

1. Introduction This chapter uses a corpus-based approach in conjunction with logistic regression analysis to understand the near-synonymous motivation for the diachronically varied alternation of the complementizer zero and that constructions with the verb think. The analysis examines the periods from 1560 to 2010, in both written and spoken genres, as exemplified in the examples below. (1) I think that Powder is a vile bragger, he doth nothing but cracke.  (CED, 1560–1673) (2) I think you can marry non but me; seinge we are sworne to be true.  (CED, 1560–1673)

280 Christopher Shank, Koen Plevoets, and Hubert Cuyckens

In previous studies, it has been suggested that this alternation is being lost and that the zero form is generalizing to substitute the that form (Rissanen 1991; Thompson and Mulac 1991; Palander-Collin 1999). The current chapter seeks to test this hypothesis by means of a stepwise logistic regression analysis of (n = 5801) tokens of think, the most frequently used complement-taking verb of cognition, spanning the time period from 1560 to 2012. The literature has also put forward a number of motivating factors promoting the zero form. Logistic regression determines the importance of different factors by treating the alternation as a choice that it attempts to predict based on the behaviour of the factors. Our regression model tests whether the factors proposed in the literature do indeed predict the zero form, the potential impact that these individual factors may or do have upon each other when combined in terms of their overall predictive power from both a synchronic and diachronic perspective, and finally their ability to predict the zero form over time. Determining the interaction of time with each of the structural conditioning factors, this study adds an innovative diachronic perspective to existing research into zero/that alternation by testing the effect of time as a factor on the selection of the zero complementizer. Logistic regression represents an established technique in the attempts to understand near-synonymous constructions. Some recent applications of the technique to questions of constructional near-synonymy include Heylen (2005), Bresnan et al. (2006), Grondelaers et al. (2007; 2008), Divjak (2010), Glynn (2010), Speelman and Geeraerts (2010), Klavan (this volume), Levshina (this volume), Speelman (this volume), inter alia. This study extends the principle to diachronic research. Although the analysis is restricted to formal usage-features, it is believed that these formal characteristics of use are sufficient to adequately distinguish the two semantically extremely similar forms. Moreover, it is hoped that these differences can be charted over time. We start off with a review of the literature dealing with that/zero alternation in order to characterize the construction under investigation and to review the factors that have previously been said to condition the use of either that or zero complementation. In Section 3, our data and methodology are explained. After presenting our results in Section 4, we offer a conclusion in Section 5.

2. Review of the literature The increase in structural/clausal flexibility that emerged in English starting in the late ME and EModE periods had a profound impact on many facets of early English syntax especially in regards to the fixation of SVO word order, clause combining, and complementation patterns. One of more important shifts, especially in regards to grammaticalization research, has concerned the observed decrease in the frequency of the that-complementizer and a corresponding increase in the zero complementizer form



A diachronic corpus-based multivariate analysis 281

(Rissanen 1991; Hopper and Traugott 1993; Finegan and Biber 1995, and Palander-Â� Collin 1999). The most often cited study is that of Rissanen (1991) who used the Helsinki corpus to examine the development and use of the that/zero alternation in think, know, say, and tell constructions with object clauses in Late Middle and Early Modern English. His analysis revealed a steady increase in the deletion of that as an object clause link in think constructions from 14% in the years 1350 to 1420 up to nearly 70% by the period of 1640 to 1710. Other researchers such as Finegan and Biber (1995) have expanded upon Rissanen’s claims regarding the that/zero-alternation by analyzing a similar data set taken from the Archer Corpus to examine the period from 1650 to 1990. This type of analysis has illustrated the role variables such as genre plays in such alterations by demonstrating how more formal genres such as sermons, medical articles, and personal letters often retained the that-complementizer form. Initially, researchers used early corpus-based methodologies to document the diachronic increase in the zero complementizer in a number of different verbs (e.g. say, tell, think, know) from ME through PDE, then turned their attention to factors in both the matrix and complement clauses that might be motivating the observed and ongoing structural/clausal changes. With regards to matrix clause features, the subject has drawn attention from a number of authors. Thompson and Mulac (1991) utilized chi-square tests to demonstrate the impact that the higher relative frequency of a verb (e.g. think and guess) and the presence of I or you (versus other subject forms) as the subject of the matrix verb also facilitate the presence of the zero complementizer. Their findings were further complemented and built upon by Rissanen (1991) and Biber and Finegan (1995) who showed, via a simple proportional contrastive analysis, that the subject type (i.e. pronominal subjects), the person of the subject governing the object clause (especially 1st person), and again in the text type (especially with regards to informality), also contributed to a decline in the frequency of the that-clause. Other studies that have shown that pronouns, particularly ‘I’ or ‘you’, favour the use of zero include Elsness (1984), Tagliamonte and Smith (2005) and Torres Cacoullos and Walker (2009). Another matrix clause factor that has received attention in the literature is the absence of additional material in the matrix clause. It is believed that matrix clauses containing elements other than a subject and a (simplex) verb are more likely to be followed by that. Such elements may be adverbials (Thompson and Mulac 1991a; Torres Cacoullos and Walker 2009); negations or periphrastic forms in the verbal morphology of the matrix clause predicate (Thompson and Mulac 1991a; Torres Cacoullos and Walker 2009). The presence of intervening material between matrix and complement has been widely discussed as a factor favouring that (Finegan and Biber 1985; Rissanen 1991; Rohdenburg 1996; Tagliamonte and Smith 2005; Torres Cacoullos and Walker 2009). Adjacency of matrix and complement clause is believed to minimize syntactic and

282 Christopher Shank, Koen Plevoets, and Hubert Cuyckens

cognitive complexity (Torres Cacoullos and Walker 2009). Besides the risk of ambiguity, which Rohdenburg (1996:â•›160) regards as a special type of cognitive complexity, the presence of intervening material has been related to a heavier cognitive processing load. In the words of Rohdenburg (1996:â•›161), “any elements capable of delaying the processing of the object clause and thus the overall sentence structure favour the use of an explicit signal of subordination”. Another factor which has received attention in the literature on zero/that alternation is the subject of the complement clause. It has been suggested that pronominal subjects as opposed to full NPs favour the use of zero (Elsness 1984; Finegan and Biber 1985; Rissanen 1991; Thompson and Mulac 1991a; Rohdenburg 1996; Tagliamonte and Smith 2005; Torres Cacoullos and Walker 2009). (3) Bill, I understand you have a special guest with you. 

(COCA)

(4) Well, I’m not, because I understand that most of his girlfriends have either (COCA) been, you know, like the hooker or porn star types.  The high discourse topicality of pronouns has been proposed as an explanatory principle (Thompson and Mulac 1991a:â•›248), as well as Rohdenburg’s (1996:â•›151) complexity principle, which entails that “in the case of more or less explicit grammatical options the more explicit one(s) will tend to be favoured in cognitively more complex environments”. While Elsness (1984) regards I and you as particularly conducive to zero complementation, Torres Cacoullos and Walker’s (2009:â•›28) multivariate study results in the following ordering of subjects from least to most favourable to that: it/ there < I < other pronoun < NP. Elsness (1984) adds that short NPs and NPs with definite or unique reference are more likely to select the zero variant than longer and indefinite NPs. In Kearns (2007a:â•›494), first and second person subjects (i.e. I, you but also we) are compared to third person subjects, but identical rates of zero and that are found for both data sets. Kearns (2007:â•›493; 2007b:â•›304) also examines the length of the complement clause subject as a possible factor, operationalizing it in terms of a three-way distinction between pronouns, short NPs (one or two words) and long NPs (three or more words). The study reveals significant differences, including one between short and long NPs. Finally, other factors that have been shown to be influential with regards to increasing the frequency of the zero form have included “appropriate light heavy weight distribution pattern in the matrix and complement clause”, an “anaphoric relationship or givenness of the complement clause” (summarized in Kaltenböck 2004:â•›52), coreferentiality of either tense or person between the matrix and complement clauses, and the absence of the harmony of polarity between the matrix and complement clauses (Torres Cacoullos and Walker 2009). A considerable amount of the corpus-based research into the loss of the complementizer with the matrix verb think, while informative and clearly important, has, however, been inherently limited in terms of actual

A diachronic corpus-based multivariate analysis 283



Table 1.╇ Zero and that in Early Modern English: Subject types (Risannen 1991:â•›281) Model 1 (1500–1570) Pronoun Say Tell Know Think Total

Model 3 (1640–1710)

other

Pronoun

other

zero

that

zero

that

zero

that

zero

that

37 â•⁄6 18 16 77

47 13 12 â•⁄7 79

â•⁄7 â•⁄2 â•⁄5 â•⁄6 20

33 â•⁄7 â•⁄5 â•⁄6 51

â•⁄80 â•⁄47 â•⁄22 â•⁄48 197

â•⁄8 25 13 â•⁄2 48

22 â•⁄9 â•⁄7 19 57

22 25 â•⁄4 â•⁄9 60

explanatory or predictive power due to what we believe are a number of underlying methodological issues. For example, the seminal and often cited work done by Rissanen (1991) and Finegan and Biber (1995) on that deletion utilized the Helsinki Corpus, which covers a period ranging from c730 to 1710 and also contains only 1.5 million words, a small corpus by today’s standards. The sample sizes that these authors worked with were often less than 30 tokens per period which had the unfortunate effect of severely limiting the generalizability of their results. An example of this type of limitation is presented below in Table 1. In addition to small sample sizes, a number of the individual factors which were deemed to be predictive of the zero form were developed by contrasting and comparing the simple percentages of occurrences of a feature or variable in the resulting data sets, as a high percentage of occurrence was assumed to predict the presence of the zero complementizer. This type of methodological approach may reveal general structural trends and patterns but it does not give any substantive insight into the actual significance a given factor is actually playing in positively or negatively influencing the that/zero deletion process. It also does not allow for any valid inferences to be made concerning the diachronic validity of a particular factor remaining a significant predictor over time. More recent studies have benefited from larger written and spoken corpora (e.g. the Cobuild, Brown and Santa Barbara corpora) which have allowed for larger samples to be extracted and analyzed. These improvements have also coincided with the incorporation by researchers of statistical techniques such as chi-square testing into their research design and methodologies. The results from these newer studies, however, are limited by the fact that a chi-square test only reveals if a relationship exists between two variables (i.e. the presence of a structurally predictive variable for the zero complementizer form and the presence of the zero complementizer form in a given sentence). It does not indicate which specific outcome or which diachronic direction is being predicted (the variable could actually have the opposite effect in that it could actually be predicting, contra expectations, the that complementizer form).

284 Christopher Shank, Koen Plevoets, and Hubert Cuyckens

In addition, the results presented in the synchronically-oriented studies are often used to make inferences about diachronic patterns and the effects of specific motivating factors; factors which were initially proposed or hypothesized by looking at small samples sizes (n < 30) and simply comparing the occurrence of a particular factor within a data set. It is with these types of methodological limitations and/or concerns in mind that we have designed our study. To address these aforementioned problems, our study utilizes an empirically motivated framework, a range of large diachronic corpora, and a statistical technique (regression analysis).

3. Data and methods of the current study Our analysis was based on tokens retrieved from the following written and spoken corpora (Tables 2 and 3). The Wordsmith concordance program was used first to identify the total number of inflected forms of think (i.e. think, thinks, thinking and thought) in both the written and spoken corpora from 1560–2012 per period. These results were then used to calculate the overall percentage of each inflected form relative to one another within the different periods. The percentages were then applied to the extracted subsets in order to ensure that the subsets would be proportionally similar in terms of inflected forms to the larger corpora from which they were taken. This two-step process resulted in Table 2.╇ Written corpora Sub-period of written English

Time span

Corpus

Number of words

Early Modern English (EModE)

1560–1710

â•⁄â•⁄2,848,314 Innsbruck Corpus of Letters CEECS I Corpus (1560–onward) CEECS II Corpus Corpus of English Dialogues (CED) Corpus of Early Modern English Texts (CMET) Lampeter Corpus (Early Modern English portion-up to 1710)

Late Modern English (LModE)

1710–1920

â•⁄15,413,159 Corpus of Late Modern English texts Extended Version (CLMETEV) Lampeter Corpus (Early Modern English portion (1710–onward)

Present-Day English (PDE)

1920–2009

The Time Corpus (Time) The Corpus of Contemporary American English – written component (COCA)

500,000,000

A diachronic corpus-based multivariate analysis 285



Table 3.╇ Spoken corpora Sub-period of spoken English

Time span

Early Modern English 1560–1710 (EModE)

Corpus

Number of words

Corpus of English Dialogues (CED) Old Bailey Corpus (OBC)

â•⁄â•⁄â•⁄â•‹980,320

Late Modern English (LModE)

1710–1913

Old Bailey Corpus (OBC)

113,253,011

Present-Day English (PDE)

1920–2012

The Corpus of Contemporary American English – spoken components (COCA) American National Corpus – spoken components (ANC) London-Lind Corpus (L-Lund) Alberta Corpus – 2010 component (Alberta)

133,180,448

Table 4.╇ Total number of tokens for think retrieved from the written and spoken corpora Date Written data

Total number of verbal forms

Date Spoken data

Total number of verbal forms

1560–1579 1580–1639 1640–1710 1710–1780 1780–1850 1850–1920 1920–1989 1990–2009 Total

(n = 100) (n = 638) (n = 1346) (n = 1440 ) (n = 1201) (n = 1297) (n = 280) (n = 317) (n = 6619)

1560–1579 1580–1639 1640–1710 1710–1780 1780–1850 1850–1913 1980–1993 1994–2012 Total

(n = 68) (n = 481) (n = 451) (n = 537 ) (n = 556) (n = 527) (n = 229) (n = 252) (n = 3101)

the following datasets for the verb think: (n = 3101 tokens from the written English corpora and n = 6619 tokens from the spoken English corpora). The full set (n = 9,720) of extracted sentences were analyzed and divided into those containing either a that-clause or a zero complementizer. The distribution of the remaining written (n = 2,217) and spoken (n = 3,584) sentences and resulting data sets are presented in Table 5 and Table 6. A comparison of the diachronic relative frequency patterns of the that versus zero forms per million words with the verb think indicates that the frequency of the zero form has remained relatively constant vis-à-vis the that-complementizer from 1560 to 2010 in both spoken and written genres. The zero form is clearly the more frequent

286 Christopher Shank, Koen Plevoets, and Hubert Cuyckens

Table 5.╇ think in written corpora. Distribution of that-clauses and zero complementizer clauses from EModE to PDE in written corpora Period 1560–1579 1580–1639 1640–1710 1710–1780 1780–1850 1850–1920 1920–1989 1990–2009 Total

think-that

think-zero

think-that

think-zero

n

N

n

N

(n = 21) (n = 18) (n = 65) (n = 79) (n = 103) (n = 101) (n = 40) (n = 24) (n = 451)

214.00 â•⁄59.23 174.51 123.19 151.66 175.47 109.44 106.20

(n = 17) (n = 133) (n = 200) (n = 290) (n = 316) (n = 359) (n = 204) (n = 247) (n = 1766)

173.24 437.65 558.27 535.29 545.23 680.69 561.92 912.90

n: absolute frequency; N: normalized frequency per million

Table 6.╇ think in spoken corpora. Distribution of that-clauses and zero complementizer clauses from EModE to PDE in spoken English Period 1560–1579 1580–1639 1640–1710 1710–1780 1780–1850 1850–1913 1980–1993 1994–2012 Total

think-that

think-zero

think-that

think-zero

n

N

n

N

(n = 8) (n = 29) (n = 10) (n = 22) (n = 12) (n = 16) (n = 97) (n = 129) (n = 323)

â•⁄92.97 â•⁄86.37 â•⁄23.75 â•⁄45.64 â•⁄26.09 â•⁄47.50 449.18 471.64

(n = 28) (n = 116) (n = 212) (n = 412) (n = 439) (n = 418) (n = 857) (n = 779) (n = 3261)

â•⁄324.78 â•⁄345.48 â•⁄447.47 â•⁄854.10 â•⁄938.68 1305.45 3152.25 3139.33

n: absolute frequency; N: normalized frequency per million

form from 1560 to 2012 and this comports with all previous literature on think and claims regarding diachronic that/zero variation patterns. The (n = 2217) written and (n = 3584) spoken sentences containing either a that or zero complementizer clause were then coded for 26 features within three categories: corpus information, matrix clause features and complement clause features. The features included information such as the time period of the corpus (e.g. 1710–1780), the inflected form of the token and the full context in which it appeared. The matrix

A diachronic corpus-based multivariate analysis 287



1000.00 912.90

800.00 558.27

600.00 400.00 200.00

Written data – freq of the that –complemtizer

680.69 545.23

535.29

561.92

437.65 214.00 173.24

174.51

123.19

151.66

175.47

109.44

106.20

Written data – freq of zero complementizer

59.23

1990–2009

1920–1989

1580–1920

1780–1850

1710–1780

1640–1710

1580–1639

1560–1579

0.00

Figure 1.╇ Think in written data – that versus zero distribution per million words

3152.25

3139.33

Spoken data – freq of that –complementizer Spoken data – freq of zero complementizer

1305.45

449.18

471.64

1980–1993

47.50

1850–1913

26.09

1780–1850

1710–1780

1640–1710

1580–1639

447.47 92.97 324.78 345.38 86.37 45.64 23.75

938.68

1990–2012

854.10

1560–1579

3600.00 3200.00 2800.00 2400.00 2000.00 1600.00 1200.00 800.00 400.00 0.00

Figure 2.╇ Think in spoken data – that versus zero distribution per million words

and complement clauses of each extracted token were also coded for features such as person, tense, polarity, the length of the subject (pronoun / np-short 1–2 words / np-long 3+ words), and coreferentiality (or lack thereof). In addition, the presence (or absence) of additional elements within the matrix clause (elements between the subject and the matrix verb) was also noted along with intervening elements (between the matrix clause and the complementizer) and the location of the intervening elements (either pre/before or post/after the complementizer and before the complement clause subject). Once the coding process was completed, the data were submitted to the multiple logistic regression analysis modelled with the factors that have been claimed in the

288 Christopher Shank, Koen Plevoets, and Hubert Cuyckens

Table 7.╇ Factors which favour the presence of the zero complementizer (summarized in Kaltenböck 2004:â•›52) 1. Matrix clause subjects are either I or you. (Elsness, 1984; Thompson and Mulac 1991; Tagliamonte and Smith 2005; Kearns 2007a) 2. The absence of extra elements in the matrix clause (viz. auxiliaries, indirect objects, adverbials) which reduce the ability of the matrix to function as an epistemic phrase by additional semantic content (cf. Thompson and Mulac 1991; Rohdenburg 1996) 3. The absence of intervening elements between the matrix and complement clause, making explicit boundary marking (disambiguation) with that unnecessary (Rissanen 1991; Tagliamonte and Smith 2005) 4. Pronominal subject of the complement clause, co-referential with the matrix clause subject (Elsness 1984; Torres Cacoullos and Walker 2009) 5. The length of the matrix clause subject (pronoun > np-short > np-long) (Thompson and Mulac 1991; Rissanen, 1991) 6. The length of the complement clause subject (it > pronoun > np-short > np-long) (Thompson and Mulac 1991; Rissanen, 1991; Rohdenburg 1996) 7. Coreferentiality of tense between the matrix and complement clauses (Torres Cacoullos and Walker 2009) 8. Coreferentiality of polarity between the matrix and complement clauses (Torres Cacoullos and Walker 2009)

literature (see Section 2) to favour the presence of the zero complementizer. Table 7 lists the factors that were included in our analysis.1 The statistical technique for our analysis is stepwise logistic regression analysis (which was run with the stepAIC-function in the R library MASS).2 The stepwise selection procedure was both-ways. The maximal model contained all main effects

1. In fact, we ran multiple analyses which also incorporated factors such as a pronominal subject (versus NP) in the matrix clause (Elsness 1984), a pronominal subject (versus NP) in the complement clause (Thompson and Mulac 1991; Rissanen 1991), and a 1st or 2nd person as the complement clause subject (Thompson and Mulac 1991). All factors cited in Section 3 were first analyzed in separate models and then also in various small subsets of factors, in order to get a better understanding of their relative potential in explaining the that/zero complementizer. These exploratory steps eventually led to the factors in Table 7. We would like to thank Dylan Glynn for his helpful comments in this respect. 2. The logical extension for our many predictors would be to fit a mixed-effects model. However, none of the factors in our data is a random effect, so we opted for a straightforward logistic regression, as explained in Speelman (this volume). The stepwise selection procedure then serves to identify the important predictors. The general outline of this methodology was suggested to us by Stefan Th. Gries, for which we express our gratitude.



A diachronic corpus-based multivariate analysis 289

plus the two-way interactions with mode and period (together with the interaction between period and mode itself).3 The resulting model after stepwise selection contained 9 main effects and 8 interactions which predict the zero form; see Table 8 for the model summary.4 The model fits well with the predicted variation (C-statistic, or the area under the ROC) just above the threshold of 80%. The rather modest explained variation (as expressed in Nagelkerke’s pseudo-R²) of 27% is just below the baseline of 30% (see Speelman, this vol., for how to interpret the model diagnostics of the C-statistic or Nagelkerke’s R²).5 The next section discusses the coefficients.

4. Discussion of the results Because of the rather complex structure of our regression model (with 9 main effects and 8 interactions), we interpret the results in Table 8 with the visual aid of so-called effect plots (obtained with the R library effects; see Gries 2013:â•›303). Furthermore, we divide the discussion into the main effects, the interactions with mode and the interactions with period. In 4.1, we present the nine main effects of period, mode, matrix-internal elements, intervening elements between the matrix and complement clause, complement clause subject length, I or you as the matrix clause subject, harmony of tense, subject coreferentiality and harmony of polarity, which predict the use of the zero form. In 4.2 we discuss the four statistically significant interactions with mode, viz. interactions with intervening elements between the matrix and complement, the absence of intervening elements between the matrix and complement clauses, subject coreferentiality, and the length of the complement clause subject. In 4.3, we finally offer the diachronic picture of the conditioning factors for zero use, i.e.

3. Mode is the distinction between written and spoken language. In the results of the statistical analysis, however, its label has been changed to TYPE. 4. The ANOVA type III tests revealed that the main effect of coreferentiality of tense (CC.T. co.ref) and the two interactions of mode with matrix-internal elements (mat.int:TYPE) and with the length of the complement clause subject (CC.length:TYPE) are “border-significant” (i.e. slightly higher than 0.05). This is reflected in Table 8 in the fact that some levels of these factors are not significant or are also border-significant. As the (stepwise) selection of the factors was based on Akaike’s Information Criterion and not on Likelihood-Ratio testing, the discussion of the results in Section 4 will nevertheless cover all effects. 5. The model was also checked for multicollinearity and although TYPE and period revealed variance inflation factors of 5.4 and 5.2, respectively, the rest of the predictors received scores of approximately 4 or under. Given the complexity of the model, we feel the assumption of orthogonality is met. See Speelman (this volume) for an explanation of the question of multicollinearity in logistic regression.

Estimate Error z value (Intercept) 7.14770 0.85237 8.386 mat.int: mat int -1.12456 0.14464 -7.775 CC.length: Pronoun -2.79835 0.86310 -3.242 CC.length: NP Short -3.99093 0.86946 -4.590 CC.length: NP Long -4.79996 0.95717 -5.015 interv: interv -2.55597 0.55110 -4.638 I.or.U: non -0.89387 0.09886 -9.042 Mode: written -2.26338 0.46837 -4.832 CC.Pol.co.ref: non -1.35818 0.39459 -3.442 CC.Pcoref: coref 1.08250 0.28079 3.855 CC.T.co.ref: non -0.15270 0.08981 -1.700 Period -0.54998 0.11807 -4.658 interv: interv * Mode: written -1.38356 0.30941 -4.472 mat.int: mat int * Mode: written -0.33652 0.18580 -1.811 Mode: written * CC.Pcoref: coref -1.38028 0.34021 -4.057 Mode: written * Period 0.31019 0.05057 6.134 CC.Pol.co.ref: non * Period 0.29591 0.06973 4.243 CC. length Pro * Period 0.33643 0.12078 2.786 CC. length NP short * Period 0.44723 0.12154 3.680 CC. length NP long * Period 0.48836 0.13219 3.694 interv: interv: * Period 0.17660 0.08285 2.132 CC.length: Pro * Mode: written 0.78566 0.37388 2.101 CC.length: NP Short * Mode: written 0.38367 0.36568 1.049 CC.length: NP Long * Mode: written 0.16318 0.40981 0.398 ------------------------------Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Coefficients:

Table 8.╇ Stepwise regression analysis; 9 main effects and 8 two-way interactions Pr(>|z|) < 2e-16 7.55e-15 0.001186 4.43e-06 5.31e-07 3.52e-06 < 2e-16 1.35e-06 0.000577 0.000116 0.089100 3.19e-06 7.77e-06 0.070107 4.97e-05 8.59e-10 2.20e-05 0.005343 0.000234 0.000220 0.033043 0.035610 0.294098 0.690489 *** *** ** *** *** *** *** *** *** *** . *** *** . *** *** *** ** *** *** * *

290 Christopher Shank, Koen Plevoets, and Hubert Cuyckens

A diachronic corpus-based multivariate analysis 291 Table 8. (continued) Deviance Residuals:

Min -3.1176

1Q 0.2271

Median 0.3528

3Q 0.4883

Max 2.8074

Null deviance: 4557.8 on 5800 degrees of freedom Residual deviance: 3607.8 on 5777 degrees of freedom AIC: 3655.8 Model L.R.: 949.99 d.f.: 23

C: 0.803 R2: 0.278

Legend: The following coding abbreviations have been utilized in the regression analysis: mat.int = absence of matrix internal elements, CC.length = length of complement clause subject, interv = lack of intervening elements between matrix and complement clauses, I. or U. = Subject pronoun I or you, CC.Pol.co.ref = polarity between the complement and matrix clauses, and CC.Pcoref= coreferentiality of person between the complement and matrix clauses.

292 Christopher Shank, Koen Plevoets, and Hubert Cuyckens

the interactions with period. It shows that there are significant changes across time in the extent to which mode, the absence of intervening elements between the matrix and complement clauses, length of the complement clause subject, and harmony of polarity predict the use of zero.

4.1

Main effects

The first step in our process involved determining whether the factors proposed in the literature indeed predict the zero complementizer form. The results from this initial procedure are presented in Figures 3–6. As it gives the overall picture of the diachronic change, we begin by examining the main effect of time or ‘period’ as a predictor of the zero form.

Main effect: Period

Figure 3a shows that there is a steady loss of the zero form from the earliest period of 1560 to the most recent period of 2012. The decrease is gradual but statistically significant. This finding is most noteworthy as it runs counter to previous claims that there is a diachronic increase in zero complementation.

Main effect: Mode

1.0

Predicted probability of SubC = ’zero’

Predicted probability of SubC = ’zero’

The analysis of the effect of mode (i.e. spoken versus written language) upon the presence of the zero form reveals that the zero form occurs significantly more often in the spoken rather than the written data (Figure 3b). This is consistent with claims in the literature that zero complementation is especially common in spoken language. This confirms findings from previous studies (cf. Finegan and Biber 1985; Rissanen 1991).

0.8 0.6 0.4 0.2 0.0 1

2

3

4 5 Period

a. Period

6

7

8

1.0 0.8 0.6 0.4 0.2 0.0 Spoken

b. Mode (or Type)

Figure 3.╇ Main effects – structural factors predicting the zero form

Type

Written

A diachronic corpus-based multivariate analysis 293



Although the difference between the main effects of spoken versus written data is slight, it will become apparent in 4.2, where we discuss the interactions of the other factors with it, that the effects of conditioning factors may differ quite vastly depending on the mode.

Main effect: Absence of matrix internal elements

In Figure 4a, the analysis reveals that the absence of elements within the matrix clause is a good predictor for the zero form; when the matrix clause does not contain any material in addition to the subject and the verb, the probability of the zero form is significantly greater compared to matrix clauses that do contain extra material.

Main effect: Absence of intervening elements

In Figure 4b, we see that the absence of intervening material between the matrix and complement clause is an even stronger predictor for the zero form. When intervening material is present, the zero complementizer rate drops to just above 60%. Thus, when there are elements separating the matrix clause from the complement clause, there is almost a 40% chance that that will be realized. This adds support to the validity complexity principle proposed in the literature (cf. Rohdenburg 1996).

Main effect: Length of the complement clause subject

1.0

Predicted probability of SubC = ’zero’

Predicted probability of SubC = ’zero’

In Figure 5a, we turn our attention to the complement clause subject, examining the role that the weight of the subject (i.e. it, pronoun, NP-short and NP-long) plays in predicting the presence of the zero form. The results in this plot confirm the order that Torres Cacoullos and Walker (2009) previously arrived at; the subject pronoun it is more likely to occur with the zero form than other pronouns, which are still better

0.8 0.6 0.4 0.2 0.0 abs

mat.int

a. Matrix internal elements

Written

1.0 0.8 0.6 0.4 0.2 0.0 abs

interv

b. Intervening elements

Figure 4.╇ Main effects – structural factors predicting the zero form

interv

1.0

Predicted probability of SubC = ’zero’

Predicted probability of SubC = ’zero’

294 Christopher Shank, Koen Plevoets, and Hubert Cuyckens

0.8 0.6 0.4 0.2 0.0 it

pro

np-short

np-long

1.0 0.8 0.6 0.4 0.2 0.0 I or U

a. Length of Complement

non

I.or.U

CC.length

b. Subject I or you

Figure 5.╇ Main effects – structural factors predicting the zero form

predictors of zero than short noun phrases and long noun phrases. This shows that the shorter and referentially lighter complement clause subjects are better predictors of the zero form.

Main effect: I or you

Turning our attention back to the main clause subject, we now examine the effect of the subject pronouns I or you as a predictor (Figure 5b). As with complement clause length, our results confirm previous literature (see Elsness 1984; Thompson and Mulac 1991; Tagliamonte and Smith 2005; Kearns 2007; Torres Cacoullos and Walker 2009) that the 1st and 2nd person is indeed a better predictor than other subject forms (i.e. 3rd person and plural forms) for the presence of the zero form.

Main effect: Cotemporality

In Figure 6a, we examine the effect of cotemporality, i.e. whether a construction in which the verbs of the matrix and complement clauses have the same tense is more likely to be used with the zero complementizer. In the plot above, there is not much difference between cotemporality and non-cotemporality, and Table 8 indeed revealed this effect to be border-significant. Nevertheless, the coefficient for non-cotemporality was negative, demonstrating that cotemporality tends to favour the zero form.

Main effect: Coreferentiality of person between matrix and complement clause

Figure 6b presents the effect of another type of ‘harmony’ between the matrix and complement clause, viz. coreferentiality between the respective subjects. Structures with coreferential subjects are slightly more likely to get a zero form than those with non-coreferential subjects.

A diachronic corpus-based multivariate analysis 295



0.6 0.4 0.2 0.0

a. Cotemporality

1.0

1.0

0.8

0.8

0.6 0.4 0.2 0.0

b. Coreferentiality of Person

Predicted probability of SubC=’zero’

0.8

Predicted probability of SubC=’zero’

Predicted probability of SubC=’zero’

1.0

0.6 0.4 0.2 0.0

c. Harmony of polarity

Figure 6.╇ Main effects – structural factors predicting the zero form

Main effect: Harmony of polarity between the matrix and complement clauses

The main effect of harmony of polarity between the matrix and complement clauses (Figure 6c) is that it is the disharmonious patterns that significantly predict the zero form. When there is harmony of polarity between the matrix and complement clauses, the zero form is slightly less likely to occur than with a mixed, i.e. disharmonious, pattern. This refines Torres Cacoullos and Walker’s (2009) finding that harmony of polarity is not a significant conditioning factor for the zero form. Now that we have completed our discussion of the main effects, we look at the interaction with the spoken or written mode.

4.2

Mode

In this section, we see that mode has an impact on the strength of other factors. Recall that although there was a significant difference in the main effect between spoken and written language, the difference was not that great. This section, however, reveals that some factors may be better predictors for the zero form in one mode as opposed to the other mode.

Mode: Absence of intervening elements

Figure 7a allows us to compare the conditioning effect of intervening elements between matrix clauses and the complement clause in the spoken and written modes. Recall that absence of intervening elements was a very good predictor overall. The interaction confirms this earlier finding; in both panels we observe a dramatic difference in complementizer use between the presence and absence of material. A notable difference, however, resides in the extent to which the presence of intervening material in the written mode predicts the zero form. When there is intervening material in the written mode, we are much less likely to get the zero form than in the spoken mode, so much so that the explicit complementizer that in fact becomes more likely; the zero rate drops to below 0.4. It may be that writers are more led by the complexity

296 Christopher Shank, Koen Plevoets, and Hubert Cuyckens

abc TYPE : spoken

0.8 0.6 0.4 0.2

TYPE : spoken

1.0 Predicted probability of SubC=’zero’

Predicted probability of SubC=’zero’

1.0

abc

interv TYPE : written

mat int TYPE : written

0.8 0.6 0.4 0.2 0.0

0.0 abc

abc

interv

a. Intervening elements

mat int mat.int

interv

b. Internal elements

Figure 7.╇ Mode and structural factors predicting the zero form

principle than speakers and feel the need to insert that to make clause boundaries clearer when intervening material risks impairing clarity.

Mode: Absence of matrix internal elements

Figure 7b presents the results for the effect of elements between the matrix clause subject and verb in the spoken and written modes respectively. We see that the absence of matrix-internal elements is a good predictive factor for both spoken and written data. The steepness of the plot lines shows that the difference in predictive power between the presence and absence of matrix internal elements is comparable for both modes; however, in the written mode, less zero is used overall. This is indicated by the lower points for both the spoken and written levels.

Mode: Coreferentiality of person between the matrix and complement clause

The analysis of the effect of the coreferentiality of person between the matrix and complement clause subjects reveals an interesting difference with regard to mode (Figure 8a). Coreferentiality of person leads to higher levels of zero in the spoken data. In the written data, confidence intervals show that the difference between coreferentiality and non-coreferentiality is not significant.

Mode: Length of the complement clause subject

The final factor that we examine in this section is the effect that the length of the complement clause subject has as a predictor of the zero form relative to mode. As before, the plot in Figure 8b shows that within the spoken data the following cline exists: it > pro > np-short > np-long. A comparison between the two modes shows that short and long NPs tend more strongly towards that in the written mode than in the

A diachronic corpus-based multivariate analysis 297

non TYPE : spoken

it

0.8

0.6

0.4

0.2

0.0 non

coref

TYPE : spoken

1.0

Predicted probability of SubC = ’zero’

Predicted probability of SubC = ’zero’

1.0

coref TYPE : written

0.8

0.6

0.4

0.2

0.0 it

pro np-short np-long

CC.Pcoref

a. Coreferentiality of person

pro np-short np-long TYPE : written

CC. length

b. Length of the complement subject

Figure 8.╇ Mode and structural factors predicting the zero form

spoken mode. Overall, the length of complement clause subject has a stronger effect on written data than on spoken data. Again, the complexity principle, i.e. the need to mark off clause boundaries, may motivate writers’ choice of the that-complementizer as opposed to the zero form. In addition, the concern with clarity fostered by standardization and prescriptivism may also play a role. We now turn to the final stage of our analysis and look at the effect of the structural factors across the eight time periods (i.e. 1560–2012). Thus, in the following sections, we discuss the interactions with period which came out as significant.

4.3

Period

The interaction effects with period were significant with the following factors: mode, absence of intervening elements, complement clause length, and cotemporality of polarity between the matrix and complement clauses. This final step in the analysis offers a diachronic perspective; it shows whether the import of a given factor becomes stronger or weaker over time.

Period: Mode

Figure 9a shows the effect of mode over time. In the earliest periods, the zero form was far more prevalent in the spoken data relative to the written data but over time, as the zero form has gone down in the spoken mode and increased in the written mode, in PDE the two modes are at the same predictive level. As Figure 9a shows, the endpoints in PDE for both modes are almost identical which suggests that nowadays mode, in and of itself, is no longer a good or a significant predictor of the zero form with these verbs anymore.

298 Christopher Shank, Koen Plevoets, and Hubert Cuyckens

1 2 TYPE : spoken

3 4 5 6

7 8

0.8

0.6

0.4

0.2

0.0

1 2

TYPE : written

1 2 3 4 5 6 7

8

interv : abs

1.0

Predicted probability of SubC = ’zero’

Predicted probability of SubC = ’zero’

1.0

7 8

0.8

0.6

0.4

0.2

0.0

1 2 3 4 5 6 7

Period

a. Mode (or Type)

3 4 5 6 interv : interv

8

Period

b. Intervening elements

Figure 9.╇ Period and structural factors predicting the zero form

Period: Absence of intervening elements

The analysis of the diachronic effect of the absence of intervening elements between the matrix and complement clauses (Figure 9b) gives a result which confirms what has been argued in the literature on that/zero variation, namely that the absence of intervening elements is a strong predictor of the zero form. The results show that this trend is decreasing over time; however, it still remains quite robust relative to the presence of intervening elements. The values in the right panel suggest that intervening elements predict the explicit that-complementizer throughout all periods, although the effect gets weaker, but this finding is somewhat less robust, as shown by the larger confidence intervals.

Period: Length of the complement clause subject

In Figure 10a, the analysis of the effect of the length of the complement clause subject over time shows a clear division between it and other pronouns versus NPs in that the former two have been and still remain the stronger predictors of the zero form while the latter (i.e. NPs) are actually increasing in their own respective predictive abilities of the zero form. Still, they have yet to reach the level of it or other pronouns. Furthermore, an examination of the start and endpoint for it and other pronouns shows that they are higher compared to NPs at any stage of their development and that it and other pronouns remain the stronger predictive factors in PDE.

Period: Harmony of polarity between the matrix and complement clauses

The final significant effect over time to be discussed in this section is the interaction between harmony of polarity and period. Figure 10b shows that when there is harmony of polarity, there is a distinct tendency towards more that over time; harmony

A diachronic corpus-based multivariate analysis 299



Predicted probability of SubC = ’zero’

3 4 5 6

7 8

CC.length : pro

1 2

0.8 0.6 0.4 0.2 1.0

CC.length : np-short

CC.length : np-long

0.8 0.6 0.4 0.2 0.0

1 2 3 4 5 6 7

8

1.0

1.0

0.0

Predicted probability of SubC = ’zero’

1 2 CC.length : it

CC.Pol.co.ref : coref

7 8

0.8

0.6

0.4

0.2

0.0

1 2 3 4 5 6 7

Period

a. Length of the complement subject

3 4 5 6

CC.Pol.co.ref : non

8 Period

b. Harmony of polarity

Figure 10.╇ Period and structural factors predicting the zero form

of polarity used to be a stronger predictor of the zero form than it is now. This trend is the opposite in the non-harmonious data; here, the level of zero use has actually increased over time.

5. Discussion This study has shown that, contrary to claims and speculation in the literature to the effect that there has been an overall diachronic tendency towards more zero complementizer use at the expense of that-complementation, the most frequent complement-taking mental verb in Present-Day English think, in fact, exhibits a diachronic decrease in zero complementation and a concomitant increase in that use. This trend can be observed both as a main effect when the data for this verb is aggregated and the interactions via mode (i.e. spoken and written data) are explored. The rigorous methodological approach developed and utilized in this study, and the attention given to ensuring sufficiently large and representative sample sizes from each period, has also highlighted the fundamental problems seen in previous work on this topic which have often relied heavily upon descriptive statistical processes. As evidenced by our initial presentation of findings in Section 3, a reliance on descriptive statistics (often presented in the literature in conjunction with a chi-square test) can unintentionally obscure important interactions between factors or variables and/or not reveal the stability or robustness of diachronic trend-lines or patterns. From a descriptive perspective, it would appear that the zero form for think is robust or is at least remaining consistent over time and thus one could reasonable infer that the factors which have been proposed to facilitate the zero form are either

300 Christopher Shank, Koen Plevoets, and Hubert Cuyckens

equally predictive or also remain significant over time. It is only when a methodology such as the one used in this study is applied that the true role of the various factors becomes apparent along with the diachronic robustness of the predicted or expected trends and/or patterns vis-à-vis a dependent variable such as the presence of the zero complementizer. In addition to invalidating the long-standing assumption that this particular complement-taking verb has diachronically developed towards higher levels of zero complementation, this study also highlights the need to differentiate between individual factors when examining complementation patterns. It became apparent, firstly, that the extent to which the factors mentioned in the literature actually predict zero use may differ considerably in terms of predictive power, as was revealed by the analysis of interactions between various factors and mode (i.e. spoken versus written data) or period (i.e. time). The effect of intervening elements of material between the matrix and complement clause was a case in point. As we observed in Figure 4, a strong predictor overall, when intervening material was present the zero complementizer rate dropped to just above 60%. Its predictive power, however, is revealed to be much stronger in the written mode than in the spoken mode; when intervening material is present in the written mode, that is favoured. This effect was also shown to be quite robust and stable over time (i.e. period) with a slight decrease seen in PDE (Figure 9). The apparent significance, however, of the length of the complement clause subject was not limited to just one mode. This factor was significant in both the written and spoken data sets. Our results therefore suggest that the following cline may be present in terms of predicting the zero form: it > Pro > NP-short > NP-long zero ---------------------------------that This cline, however, when examined diachronically, also revealed a small but consistent decrease for both the it and pro subject forms over time towards PDE. This general decline was seen with a great majority of the factors tested in this study. Finally, the analysis of mode revealed that the zero form occurs overall significantly more often in the spoken rather than the written data. Yet, once again, by diachronically examining the effect of mode over time (i.e. period) we see that in PDE this previously significant finding now essentially disappears. In the most recent period, the trend lines indicate that both modes are equally predictive of the presence of the zero form and that mode has lost any real significance as a predictive factor. We believe that these results have shown the strength of the methodology and approach. Having established the structural factors that lie behind the choice of the complementizer for think and having demonstrated that this alternation is not merely a diachronic phenomenon, two important steps should now be taken. Firstly, the data set needs to be extended to include a larger set of mental state verb types. This may



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reveal additional differences in the way that /zero alternation has evolved with similar verbs of cognition, as well as shedding more light on how the effect of a conditioning factor may differ from verb to verb. Secondly, the addition of a range of semantic and pragmatic features to the analysis may offer more direct insights into the differences between the two forms. Although the manual annotation involved may necessitate smaller samples, extending the analysis in this manner will further explain the role of the alternation.

6. Conclusion In this chapter we have tried to demonstrate the advantages of utilizing a rigorous empirically oriented framework and statistical analysis when exploring the diachronic development of clause combining and complement clause patterns with the verb think. Our approach has allowed us to test a range of motivating factors for actual diachronic significance, to calculate the cumulative effects of these factors/variables against each other and over time, and to determine what factors, if any, retain any predictive power for the presence of the zero complementizer form. In addition, our methodology has permitted us to identify the importance that the absence of intervening elements of material between the matrix and complement clauses, the length of the complement clause subject and the effects of mode and period play in predicting the presence of the zero form Finally, our use of a regression analysis has allowed us to assess the effect of factors, or lack thereof, across mode and over time. Our findings indicate that, contrary to expectations and predictions, there is a steady statistically significant loss of the zero form from the earliest period of 1560 to the most recent period of 2012. It is based on these findings and our overall results that we believe the approach demonstrated in this chapter has real potential for helping us to understand the role or roles that structural factors play in distinguishing near-synonymous forms in some aspects of diachronic language change.

References Aijmer, K. (1997). I think – an English modal particle. In T. Swan, & O. Jansen Westvik (Eds.), Modality in Germanic languages: Historical and comparative perspectives (pp. 1–47). Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110889932.1 ANC = American National Corpus (2002). Linguistic Data Consortium, University of Pennsylvania. Bolinger, D. (1972). That’s that. (Janua linguarum. Series Minor, 155). The Hague: Mouton de Gruyter.

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Bresnan, J., Cueni, A., Nikitina, T., & Baayen, H. (2007). Predicting the dative alternation. In G. Bouma, I. Kraemer, & J. Zwarts (Eds.), Cognitive foundations of interpretation (pp. 69– 94). Amsterdam: Royal Netherlands Academy of Science. Brinton, L. J., & Traugott, E. C. (2005). Lexicalization and language change. (Research Surveys in Linguistics.) Cambridge: Cambridge University Press. DOI: 10.1017/CBO9780511615962 BROWN = Francis, W. N., & Kucera, H. (1979). The Brown Corpus. Department of Linguistics, Brown University. Bybee, J. (2002). Cognitive processes in grammaticalization. In M. Tomasello (Ed.), The new psychology of language Vol. II (pp. 145–167). New Jersey: Lawrence Erlbaum CEECS I & II = Corpus of Early English Correspondence Sampler (CEECS) . CEMET = Corpus of Early Modern English texts (Extended version). See De Smet (2005). CLMETEV = Corpus of Late Modern English texts (Extended version). See De Smet (2005). COCA = Davies, M. (2008). The Corpus of Contemporary American English (COCA): 1990– present. Retrieved from . De Smet, H. (2005). A Corpus of Late Modern English. ICAME Journal, 29, 69–82. Divjak, D. (2010). Structuring the lexicon: A clustered model for near-synonymy. Berlin & New York: Mouton de Gruyter Elsness, J. (1984). That or zero: A look at the choice of the object clause connective in a corpus of American English. English Studies, 65, 519–533. DOI: 10.1080/00138388408598357 Finnegan, E., & Biber, D. (1995). That and zero complementizers in Late Modern English: Exploring Archer from 1650–1990. In B. Aarts, & C. Meyer (Eds.), The verb in contemporary English: Theory and description (pp. 241–257). Cambridge: Cambridge University Press. Glynn, D. (2010). Testing the hypothesis: Objectivity and verification in usage-based Cognitive Semantics. In D. Glynn, & K. Fischer (Eds.), Quantitative Cognitive Semantics: Corpus-driven approaches (pp. 239–270). Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110226423 Gries, S. Th. (2013). Statistics for linguistics with R: A practical introduction. 2nd revised edition. Berlin & Boston: Mouton de Gruyter. DOI: 10.1515/9783110307474 Grondelaers S., Speelman, D., & Geeraerts, D. (2008). National variation in the use of er “there”. Regional and diachronic constraints on cognitive explanations. In G. Kristiansen, & R. Dirven (Eds.), Cognitive Sociolinguistics: Language variation, cultural models, social systems (pp. 153–204). Berlin & New York: Mouton de Gruyter. Grondelaers, St., Geeraerts, D., & Speelman, D. (2007). A case for cognitive corpus linguistics. In M. Gonzalez-Marquez, I. Mittelberg, S. Coulson, & M. Spivey (Eds.), Methods in Cognitive Linguistics (pp. 49–169). Amsterdam & Philadelphia: John Benjamins. Heylen, K. (2005). A quantitative corpus study of German word order variation. In S. Kepser, & M. Reis (Eds.), Linguistic evidence: Empirical, theoretical and computational perspectives (pp. 241–264). Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110197549.241 Kaltenböck, G. (2004). That or no that – that is the question: On subordinator suppression in extraposed subject clauses. Vienna English Working Papers, 13, 49–68. Kearns, K. (2007a). Epistemic verbs and zero complementizer. English Language and Linguistics, 11, 475–505. DOI: 10.1017/S1360674307002353 Kearns, K. (2007b). Regional variation in the syntactic distribution of null finite complementizer. Language Variation and Change, 19, 295–336. DOI: 10.1017/S0954394507000117 LAMPETER = Lampeter Corpus of Early Modern English Tracts (1641–1732). Retrieved from .



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Palander-Collin, M. (1999). Grammaticalization and social embedding: I THINK and METHINKS in Middle and Early Modern English. Helsinki: Tome LV. Quirk, R., Greenbaum, S., Leech, G., & Svartvik, J. (1972). A grammar of contemporary English. London: Longman. Rissanen, M. (1991). On the history of that/zero as clause object links in English. In K. Aijmer, & B. Altenberg (Eds.), English corpus linguistics: Studies in honor of Jan Svartvik (pp. 272– 289). London & New York: Longman. Rohdenburg, G. (1996). Cognitive complexity and increased grammatical explicitness in English. Cognitive Linguistics, 7, 149–182. DOI: 10.1515/cogl.1996.7.2.149 Speelman, D., & Geeraerts, D. (2010). Causes for causatives: The case of Dutch ‘doen’ and ‘laten’. In T. Sanders, & E. Sweetser (Eds.), Causal categories in discourse and cognition (pp. 173– 204). Berlin & New York: Mouton de Gruyter. Tagliamonte, S., & Smith, J. (2005). No momentary fancy! The zero ‘complementizer’ in English dialects. English Language and Linguistics, 9, 289–309. DOI: 10.1017/S1360674305001644 Thompson, S. A., & Mulac, A. (1991). A quantitative perspective on the grammaticalization of epistemic parentheticals in English. In E. Traugott, & B. Heine (Eds.), Approaches to grammaticalization (pp. 313–339). Amsterdam & Philadelphia: John Benjamins. TIME = Davies, M. (2007). TIME Magazine Corpus (1920s–2000s). Retrieved from . Torres Cacoullos, R. & Walker, J. A. (2009). On the persistence of grammar in discourse formulas: A variationist study of that. Linguistics, 47, 1–43. DOI: 10.1515/LING.2009.001 Traugott, E. C., & Dasher, R. B. (2002). Regularity in semantic change. Cambridge: Cambridge University Press. Traugott, E. C., & Konig, E. (1991). The semantics-pragmatics of grammaticalization revisited. In E. C. Traugott, & B. Heine (Eds.), Approaches to grammaticalization, Volume 1. Focus on theoretical and methodological issues (pp. 189–218). Amsterdam & Philadelphia: John Benjamins. DOI: 10.1075/tsl.19.1

Section 2

Statistical techniques

Techniques and tools Corpus methods and statistics for semantics Dylan Glynn

University of Paris VIII

The use of corpora in semantic research is a rapidly developing method. However, the range of quantitative techniques employed in the field can make it difficult for the non-specialist to keep abreast with the methodological development. This chapter serves as an introduction to the use of corpus methods in Cognitive Semantic research and as an overview of the relevant statistical techniques and software needed for performing them. The discussion and description are intended for researches in semantics that are interested in adopting quantitative corpus-driven methods. The discussion argues that there are fundamentally two corpus-driven approaches to meaning, one based on observable formal patterns (collocation analysis) and another based on patterns of annotated usage-features of use (feature analysis). The discussion then introduces and explains each of the statistical techniques currently used in the field. Examples of the use of each technique are listed and a summary of the software packages available in R for performing the techniques is included. Keywords: collocation analysis, corpus linguistics, semantics, statistics, usage-feature analysis (behavioural profile)

1. Introduction This chapter offers an explanation of the corpus methods represented in the book and a brief overview of the various statistical techniques employed. It is designed as a resource for those less familiar with the field, but also as a reference for those already working with corpus-driven methods in Cognitive Semantics. Specifically, corpus-Â� driven Cognitive Semantics is understood as the work beginning with Dirven et al. (1982), Schmid (1993, 2000), Geeraerts et al. (1994, 1999) and Gries (1999, 2003), and currently represented in the edited volumes of Gries and Stefanowitsch (2006), Stefanowitsch and Gries (2006), Lewandowska-Tomaszczyk and Dziwirek (2009), Glynn and Fischer (2010), Geeraerts et al. (2010), Divjak and Gries (2012), Gries and

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Divjak (2012), Pütz et al. (2012), Reif et al. (2013), Glynn and Sjölin (2014), and in the monographs Hilpert (2008, 2012), Divjak (2010a), Gilquin (2010), Dziwirek and Lewandowska-Tomaszczyk (2011), Hoffmann (2011), and Glynn (forthc.). In this chapter, corpus-driven Cognitive Semantics is argued to divide into two methodologies, or analytical approaches, based either on the formal analysis of collocations or the semantic analysis of features. This proposed distinction is described in Section 2. Following this, Section 3 describes the quantitative techniques used in such research. It lists and explains the techniques and offers examples of how they are used, giving detailed references on where the application of each technique is explained in the literature.

2. Collocations and features: Two approaches to corpora A common misconception amongst cognitive linguists is that corpus-driven research, and indeed, the quantitative analysis of corpus data, does not involve any close analysis of actual examples. This is not necessarily true at all. Within Cognitive and Functional Linguistics, broadly speaking, there is a wide range of approaches to corpus data, from simply counting the number of occurrences of a given form in a given context to the development of complex computational models trained on enormous text banks. For corpus-driven research in semantics, where the ‘meaning’ of a given linguistic form is in question, it is possible to broadly identify at least two approaches. All the studies in the first section of this book fall into one of these two categories. The first of these is based on formal, and therefore, observable, patterns. We can term this approach ‘collocation analysis’. Secondly, the corpus analysis can be based on patterns of annotated features, which we term ‘feature analysis’. In the former, the analysis seeks to identify formal patterns so as to interpret them as indices of meaning structure and in the latter, the analysis seeks to directly identify semantico-pragmatic patterns through close manual annotation. Although the approaches can be combined (cf. Stefanowitsch and Gries 2008), they tend to be used separately and possess distinct strengths and weaknesses. The first ‘type’ of corpus-driven research, collocation analysis, is more established and is typical of mainstream Corpus Linguistics. Collocation studies identify the co-occurrence of linguistic forms in a given sample of naturally occurring language. Firth’s (1957:â•›179) now famous phrase, “you shall know a word by the company it keeps”, is a succinct way of capturing the aim of this approach. When extended to other parts of language, such as syntactic patterns or indeed text types and genres, the large-scale study of collocation is a powerful tool for making generalisations about language use. Cognitive and Functional Linguistics are particularly concerned with why a given form is used and so it follows that in order to answer research questions



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of this nature, inferences as to the semantic, functional, or conceptual motivation for the collocation must be made in post hoc interpretation. Despite this subjective step in the use of collocation analysis in Cognitive-Functional Linguistic research, the analytical approach has important advantages. To the extent that one can retrieve forms automatically, one can consider extremely large samples, making studies (relatively) representative of a given language or part of language. Secondly, forms are objectively identifiable, making this step largely independent of subjective analysis. However, this statement warrants qualification. Even if a form is objectively identifiable, linguists are typically interested in only certain uses of a given form and, often, these specific uses cannot be retrieved automatically. In such situations, the decision as to which occurrences are representative of the category is typically a question for debate (cf. Perek, this volume, 61–86). Moreover, collocation studies rely on some measurement of association. Raw frequency of co-occurrence can be misleading because if one of the forms is extremely frequent, then relatively high co-occurrence may just be a result of the overall high frequency of that form. The problem of how to determine the degree of association, or ‘attraction’, is fundamental. Common ways of measuring the degree of association for lexical co-occurrence are the mutual information (MI) score, the z-score (standard score), the t-score and the log-likelihood. Many Corpus Linguistics programs, both on-line and stand-alone, automatically generate some of these scores. Collostructional analysis is one alternative to such measures. Developed by Stefanowitsch and Gries (2003, 2005) and Gries and Stefanowitsch (2004a, 2004b) and described in Hilpert (this volume, 391–404), it is a suite of methods that use the Chi-squared or Fisher exact test to compute degree of association. These techniques allow the researcher to consider the co-occurrence, not just of lexemes, but also of syntactic patterns. Collostructional analysis has proven popular in Cognitive Linguistics. One of the newest advances in the use of collocation is the application of Word Space modelling to semantic research questions within computational linguistics. The principle is to extend the analysis of collocation beyond one or two words or even syntactic patterns, to whole lines, paragraphs and even entire texts. Such approaches give rich collocation-based behavioural profiles of a given linguistic form. The implications for such analytical techniques in semantics are only now being realised. This methodology is not represented in the volume. Peirsman et al. (2010) and Sagi et al. (2001) are examples of the application of these methods to research in semantic relations. The number of studies employing a collocation approach, even restricted to Cognitive Linguistics, is enormous. A small sample of recent studies includes Newman and Rice (2004, 2006), Deignan (2005), Delorge (2009), Pęzik (2009), Van Bogaert (2010), Colleman (2010) and Zeschel (2010). Applications of collostructional analysis include Wulff (2006), Wulff et al. (2007), Hilpert (2008, 2009) and Gilquin (2010). In general terms, it is possible to identify a second quantitative approach in corpus-driven Cognitive Semantics, one that focuses on the manual analysis of

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usage-features. Although less traditional in the mainstream of Corpus Linguistics, the general principle has a long tradition in Cognitive Linguistics (Dirven et al. 1982; Rudzka-Ostyn 1989, 1995; Fillmore and Atkins 1992; Geeraerts et al. 1994) and, more recently, is gaining currency in Functional Linguistics (Fischer 2000; Scheibman 2002; Kärkkäinen 2003; Pichler 2013). The principle of combining the results of this usage-feature analysis with multivariate statistics begins with Geeraerts et al. (1999) and Gries (2003). It is termed the behavioural-profile approach by Gries and Divjak (2009) and Divjak and Gries (2009) and multifactorial usage-feature analysis by Glynn (2009, 2010b).1 The principle is simple: for a large sample of a given linguistic phenomenon, various formal, semantic, and/or social ‘linguistic features’ (or ‘ID tags’ in the terminology of Gries and Divjak 2009) are identified and ascribed to each occurrence. It is worth noting that the method per se has also been independently developed in social psychology and computational linguistics. In the former, it is termed the analysis of components (cf. Scherer 2005; Fontaine et al. 2013) and in the latter, sentiment analysis (Wiebe et al. 2005; Verdonik et al. 2007; Daille et al. 2011; Balahur and Montoyo 2012; Read and Carroll 2012; Taboada and Carretero 2012). The approach consists of the repeated application of what is essentially a ‘traditional’ linguistic analysis to hundreds, or even thousands, of naturally occurring examples. This procedure results in a quantified usage-profile of the linguistic phenomenon in question. Usage-feature analysis is employed, with varying degrees of statistical sophistication, to examine phenomena of all kinds, from syntactic variation and semantics (Heylen 2005a; Bresnan et al. 2007; Speelman et al. 2009), to discourse studies and conversation analysis (Scheibman 2002; Kärkkäinen 2003; Flores Salgado 2011; De Cock 2014a, 2014b), and even gesture research (Zlatev and Andrén 2009; Morgenstern et al. 2011). The limitations of the approach are twofold. Firstly, the detailed manual analysis is as subjective as any traditional linguistic analysis and is open to the same vagaries, theoretical biases and human error. Secondly, the manual analysis, or annotation, of examples is meticulous and laborious. This, combined with the simple practical reality of limited resources, means that samples are relatively small. The resulting sample

1. Since Multifactorial Usage-Feature Analysis (Behavioural Profile Approach) is less known in corpus circles, a selection of current examples of its use include: Geeraerts et al. (1999), Gries (1999, 2003, 2006, 2010), Szmrecsanyi (2003, 2010), Wulff (2003, 2009), Heylen (2005a), Divjak (2006, 2010a, 2010b), Divjak and Gries (2006, 2009), Bresnan et al. (2007), Grondelaers et  al. (2007, 2008), Glynn (2009, 2010a, 2010b, 2014a, 2014b, forthc.), Janda and Solovyev (2009), Speelman et al. (2009), Speelman and Geeraerts (2010), Krawczak and Glynn (2011, in press), Krawczak and Kokorniak (2012), Levshina (2012), Levshina et al. (2013a, 2013b), Krawczak (2014a, 2014b), and Deshors (2014). Doctoral dissertations focusing on developing the method include Gries (2000), Grondelaers (2000), Heylen (2005a), Glynn (2007), Arppe (2008), Robinson (2010b), Deshors (2011), Levshina (2011), Barnabé (2012), Klavan (2012), and Diehl (2014).

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Table 1.╇ Observational differences in collocation and feature analysis of corpora Stage 1: Analysis of data Stage 2: Interpretation of analysis

Collocation

Feature

objective subjective

subjective objective

size makes it more difficult to be sure of representativity and harder to obtain statistically significant results. The advantages of the approach are also twofold. Firstly, the method allows the operationalisation and quantification of traditional linguistic analyses. This is no trivial matter because it permits hypothesis testing and produces falsifiable results for research questions not easily approached using traditional corpus methods (c.f. Geeraerts 2010; Glynn 2010b; Stefanowitsch 2010). Secondly, an important strength lies in the possibility of treating the results obtained through the usage-feature analysis with multivariate statistics. This is especially important for non-modular theories of linguistics, such as Cognitive Linguistics, because multivariate statistics permits an analysis to handle the complexity of the interaction of the different dimensions of language structure simultaneously (such as lexis, syntax, phonology, society, etc.), creating a multidimensional and socio-conceptually realistic profile of the use of a linguistic form or the role of a linguistic function. Geeraerts (2011) compared the two corpus approaches, underlining that both are subjective, but are at different stages in their application. Table 1 summarises Geeraerts’ point about subjectivity. Juxtaposing the two analytical approaches like this is, of course, a simplification. At the first stage of analysis, collocation studies are often not entirely objective because of questions such as what constitutes a ‘form’. Firstly, forms are polysemous and only certain uses may be relevant for a given study. In such a situation, manual selection is often the only solution. Secondly, the forms themselves are typically composite and so formal variation itself can cause category issues. In other words, is a given formal variant an example of the form in question or is it a ‘different’ form? Again, in such situations, subjective categorisation enters the analysis. Turning to feature analysis, the subjective first step is not always particularly subjective. Often, feature analysis is largely based on observable phenomena. For example, grammatical features can be crucial to usage-feature analysis and are annotated automatically, or if done manually, are done so objectively. At the stage of interpretation the same objective-subjective blurring occurs. For collocation analysis, as Desagulier (this volume, 145–178) shows, statistical analysis can help add a degree of objectivity to interpreting the collocation patterns observed. A similar caveat is needed for the usage-feature method. Although multivariate statistics may help us to objectively distinguish semantico-pragmatic patterns from non-patterns, we still must decide if those patterns answer the research question at hand, which is an inherently subjective step.

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3. Statistical techniques and tools Often one of the most confusing issues in the application of quantitative techniques to linguistic research is the myriad of different techniques available. This section is primarily intended for the reader who has some experience with quantitative methods, presenting an overview of the techniques relevant to corpus linguistic research. For the reader who has little experience in quantitative techniques, the overview will be technical, but it is hoped, still informative. It is important to understand that statistics is a rapidly growing science with constant new advances as well as many uncertainties and conflicts. Perhaps more importantly, we must also remember that statistical techniques are only analytical tools. No statistical technique will identify a linguistic fact or explain any linguistic structure. Nevertheless, statistical tools can be used by linguists to help look for language structure – assuming one knows where to look. They can also be used to confirm the probability that the results of an analysis are not a chance occurrence. Statistics can help linguists struggle with what they have been doing for centuries, describe and explain language, but they are only tools in that endeavour. Just as there is sometimes a misconception that statistics can answer linguistic questions, there exists a misconception that quantitative corpus-driven research is devoid of ‘real’ linguistic analysis. Nothing is further from the truth. Corpus-driven linguists deal with real language and in large quantities. The ‘numbers’ presented in corpus-driven research are not the analysis; they are a quantitative summary of the analysis, which must, in turn, be interpreted. Corpus-driven linguists, for the most part, deal with language in a relatively close and fine-grained way; they just deal with large quantities of it. One of the aims of this book is to showcase and explain the use of a small set of statistical techniques that can be helpful for traditionally trained linguists in their research. The aim is not to teach statistics or the computer programs for performing statistical analyses, but simply to introduce some of the possibilities. In this section, we begin with a short description of the computer applications available for performing statistics, and then briefly consider a fundamental theoretical question for the statistical sciences – type of data. This question is essential to understand before one can decide which statistical techniques are appropriate in a given situation. This is followed by a systematic summary of the techniques currently used in the field, examples of their use, as well as examples of texts that explain how they are used. The description ends with a detailed list of the different commands and packages for performing these statistical techniques in the programming suite R.

Statistical software

There are many computer applications, commercial and otherwise, that enable the researcher to perform statistical analysis. In this volume, the statistical program that



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is used by most authors is R. This program is, in fact, a powerful programming suite with enormous potential. The explanatory chapters all use R and the reader is taken step-by-step through the necessary “code”, or command lines, needed to perform the analyses. No attempt is made to demonstrate the full functionality of the program, merely to offer a working knowledge of how to perform specific analyses. This volume focuses upon R for three reasons. Firstly, it is a free and cross-platform program. Secondly, since it is open source, as soon as new statistical techniques develop, new software modules are written and uploaded for the public. Thirdly, the programme is one of the two most commonly used programs for statistics in the social sciences (there are, of course, many more, especially devoted to specific techniques). The other most frequently used program in the social sciences is SPSS. Like R, it is also an extremely powerful tool, as widely used, but also includes a graphic user interface (unlike R). Since R is equally powerful, arguably more up to date, entirely free and used by the majority of authors in the book, the only negative is its command-line interface. However, in the following chapters, the command-line is given simple step-by-step instructions and, it is hoped, will not pose too many problems for the beginner. It is true that the command-line may seem daunting at first, but if the steps are followed line-by-line, the only difference with ‘button-for-button’ (as in a graphic interface application) is one of familiarity. Other important application suites include SAS, Statistica, and Stata, which are all powerful and versatile. SAS is command-line, like R and in some ways, R can be seen as the open-source version of SAS. It is arguably the most complete statistical programming suite, but is rarely used in the social sciences. Statistica and Stata are comparable to SPSS. They too have graphic user interfaces, are relatively user friendly and, just like SPSS, are costly. Statistica is restricted to the Windows operating systems, but has a relatively large and helpful online community. Stata is cross-platform, but is probably less common than Statistica. It is not really possible to say which suite is the best, since certain techniques are extremely well covered in one suite and not the other. Due to its being open source, R is surely the suite with the most options and also the quickest to respond to developments within the domain of statistics, but, of course, that does not mean its implementation of those techniques is the best. If the reader is familiar with any of these other programs, the descriptions of the statistical techniques in the book, as well as their interpretation and application, will still be useful. Lastly, it should be noted that a graphic user interface is under development for R. This is not drawn upon because its development is not yet complete and the commands/R sessions described in this book are sufficiently straightforward that readers who are not familiar with statistics or command-line will not have problems following.

Types of data

Before choosing a statistical technique, one must first know what ‘type’ of data one is dealing with. This is because different types of data require different statistical

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techniques. The most basic distinction is between what is called continuous data and categorical data. The former typically come from measurements and therefore make a continuum, for example 1.0, 1.1, 1.2 … 1.8, 1.9, 2.0. This kind of data is probably the most common and comes from diverse sources such as age, time, height, dosage, temperature, response times, and, arguably, grammatical judgements. Continuous data are typical in psychology and psycholinguistics. The second kind of data is categorical, also called ‘discrete data’, ‘tabular data’ or ‘count data’. It is this kind of data, as corpus linguists, with which we are most often concerned. Such data include, for example, the frequency of occurrence of a linguistic form, the number of times it occurs in a given tense, or in a given register. In these examples, the data are said to be nominal because each of the occurrences is independent from the other. However, categorical data can also be ordered. This is the case when, for example, the categories follow a natural sequence or ranking, such as young, middle-aged, and old or when a sentence is short, medium or long in length. Ordered categorical data share properties of both nominal categorical and continuous data. Grammatical judgements, on a scale of 1 to 7, for example, could be argued to be continuous or ordered categorical. Technically, it is ordered because a respondent cannot enter 3.5, for example, but is forced to make a discrete choice upon what is, in reality, a continuous scale of acceptability. However, if we assume that no respondent would perceive differences to the degree of 3.5, then we can treat the scale as a true measurement, and therefore, continuous. Table 2.╇ Types of data in statistics Data type

Example of data

Continuous 1, 1.1, 1.2 … 1.8, 1.9, 2 1, 2, 3, 4, 5, 6, 7 Ordered short, medium, long cold, warm, hot Nominal apples, peaches, pears y’all, you lot, youse

Description

Example of use

Sequential (ordered) but non-discrete / continuous Sequential (ordered) but discrete / non-continuous Independent and discrete categories

Response times in Psycholinguistics Different periods in diachronic linguistics Different lexemes in Corpus Linguistics

Although there is occasionally debate on the issue, most statistical techniques are designed for one of the kinds of data. For example, least squares estimation and linear regression are used for continuous data and maximum likelihood and logistic regression for categorical, just as principle components analysis is used for continuous data and correspondence analysis for categorical. Table 2 summarises the differences.

Statistical techniques for corpus linguistics

Statistics is an immense science – there are countless tests and corrections for those tests. There are even more exploratory techniques with various algorithms that each technique can employ and different ways for representing results of those exploratory techniques. Confirmatory analysis has again as many different techniques, but this



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time, seemingly endless sets of diagnostics to check the validity of the results. It must be stressed that the techniques presented here only scratch the surface of what is possible, but also of what problems exist. We begin with significance tests and association measures. Although not statistical techniques per se, they are tools that are important to the field. We then cover exploratory methods, the results of which cannot be used to make claims about structure beyond the sample. In other words, what is found with these techniques may be restricted to the corpus or the extract of the corpus being examined. These exploratory techniques do not test hypotheses or make predictions about the population (real language). The description then turns to confirmatory techniques, which are more complex in their application but which make predictive claims and can test hypotheses in terms of statistical significance or the probability that observed structures exist in real language beyond the sample.

Sample, significance and independence

Establishing that the occurrence of something in a given sample is more or less common than would be expected by chance or that two sets of data are more different than would be expected by chance are basic steps in inductive research. Pearson’s Chisquared test and Fisher’s Exact test are omnipresent in research based on samples of categorical data. Gries (this volume) explains these tests and shows how to apply them in R. Other tests useful for corpus data include the exact binomial test, McNemar’s paired Chi-squared test, and the proportions test. These are used for investigating relations in frequency tables. An excellent explanation of these tests and their commands in R can be found in Dalgaard (2008: Ch. 8) and Baayen (2008:â•›Section 4.1.1). See also Gries (2009b:â•›125–127, 158–176; 2013:â•›165–172), Everitt and Hothorn (2010: Ch. 3), and Adler (2010:â•›360–367).

Collocation and association measures

Within Cognitive Linguistics, collostructional analysis has proven to be one of the most important methods for investigating collocations. Developed by Stefanowitsch and Gries (2003, 2005) and Gries and Stefanowitsch (2004a, 2004b), the principle can be combined with a range of association measures for determining the degree of collocational ‘strength’ (the measure is typically calculated with a p-value obtained from a Fisher exact test, log-transformed). These calculations are not yet implemented in most corpus annotation or concordance software. However, Stefan Gries has developed R scripts (semi-automated sets of commands) for performing the tests.2 Hilpert (this volume, 391–404) explains three varieties of collostructional analysis: collexeme analysis, distinctive collexeme analysis, and covarying collexeme analysis. 2. For more information, contact Stefan Th. Gries. His contact details can be found on his website: http://www.linguistics.ucsb.edu/faculty/stgries/.

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Examples of use include Wulff (2003), Hilpert (2008), Stefanowitsch and Gries (2008), Colleman (2009), and Gilquin (2010). The aim of quantifying degree of association between two forms in terms of frequency is not unique to the collostructional suite. Corpus Linguistics has developed an array of calculations to determine relative degree of association, especially between individual words. The most common are the mutual information (MI), the z-score, the t-score, and the log-likelihood. There is important variation in the results obtained from using any one test over another. Evert (2009) offers a detailed discussion on the matter; see also Wiechmann (2008), Wulff (2010) and Desagulier (this volume, 145–178). The z-score and the t-score are both explained with the R-code in Johnson (2008: Ch. 3) and Dalgaard (2008: Ch. 5). The freely available Ngram Statistics Package extracts sequences from a corpus and calculates a range of association measures. All these scores are used extensively in collocation-based corpus linguistics.

Cluster analysis

Cluster analysis is a diverse family of techniques, which, as the name suggests, cluster data. K-means clustering is used when one knows how many clusters there should be in advance; the technique ‘sorts’ the data accordingly. More common in semantic research is hierarchical clustering, which is used as an exploratory technique for the identification of clusters in the data. Importantly, by identifying clusters, it also sorts the data into the clusters it has ‘discovered’. The technique begins with a set of features and then uses them to group the features of a given variable (for instance, a list of senses, concepts, words, or constructions). It represents the results in a dendrogram, a kind of plot that depicts groups in an intuitively transparent way as dependencies clustered in branches. Cluster analysis is an excellent technique for determining which forms are similar to each other and which are different. It is explained by Divjak and Fieller (this volume, 405–442). Other explanations using R code include Crawley (2007:â•›742–744), Baayen (2008:â•›138–148), Johnson (2008: Ch. 6), and Ledolter (2013: Ch. 15). Härdle and Simar (2007: Ch. 11), Izenman (2008: Ch. 12), Drenan (2009: Ch. 25), Everitt and Hothorn (2010:â•›18), Afifi et al. (2011: Ch. 16) and Marden (2011: Ch. 12) represent detailed, yet approachable, explanations without R code. Everitt et al. (2011) is surely the most comprehensive work devoted to the technique, and although quite technical, is a systematic and excellent reference for using cluster analysis. The book provides no explanations for performing the analysis, but does give information on which software packages are available for many of the analyses it describes. Examples of use in Cognitive Linguistics include Schulze (1991), Chaffin (1992), Myers (1994), Sandra and Rice (1995), Ravid and Hanauer (1998), Rice et al. (1999), Gries (2006), Divjak (2006, 2010а), Divjak and Gries (2006), Gries and Hilpert (2008), Valenzuela Manzanares and Rojo López (2008), Janda and Solovyev (2009), Louwerse and Van Peer (2009), Robinson (this volume, 87–116), Glynn (2010a, 2014a, 2014b,



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this volume, 117–144), Levshina (2012), Szmrecsanyi (2013), and Krawczak and Glynn (in press).

Correspondence analysis

Correspondence analysis is an exploratory technique that helps identify associations in the data, such as patterns in the combinations of linguistic features. The technique is designed for dealing with complex interactions where it is not known a priori which dimension, be that syntax, semantics, pragmatic, or social context, that structures the behaviour of the data. For instance, it can help find which semantic features typically occur with a set of grammatical forms or constructions, but also how these two dimensions interact relative to social variation. It visualises these associations in biplots, which, although arguably difficult to interpret, represent rich depictions of complex structures. Glynn (this volume, 443–486) explains the application and interpretation of two varieties of correspondence analysis: binary correspondence and multiple correspondence analysis. There exist several comprehensive books devoted to the technique: Benzécri (1980, 1992), Murtagh (2005), Greenacre (2007 [1993], 2010), and Le Roux and Rouanet (2010). Amongst these, Greenacre (2007) is probably the standard book of reference. Useful introductions include Le Roux and Rouanet (2004: Chs. 2 and 5), Everitt (2005: Ch. 5), Härdle and Simar (2007: Ch. 13), Baayen (2008: Ch. 5), Izenman (2008: Ch. 17), and Husson et al. (2011: Chs. 2 and 3). The last of these, Husson et al. (2011), is particularly clear and includes some of the most recent developments. Examples of use include Arppe (2006), Glynn (2007, 2009, 2010a, 2010b, 2014a, 2014b, this volume, 117–144), Szelid and Geeraerts (2008), Plevoets et al. (2008), Glynn and Sjölin (2011), Krawczak and Glynn (2011), Barnabé (2012), Krawczak and Kokorniak (2012), Nordmark and Glynn (2013), Levshina et al. (2013b), Desagulier (this volume, 145–178; in press), Delorge et al. (this volume, 39–60), Fabiszak et al. (this volume, 223–252), and Krawczak (2014a, 2014b; in press).

Multidimensional scaling

This technique is similar to correspondence analysis in its functionality and output. It identifies correlations between levels (features) in frequency tables. Explanation in R can be found in Rencher (2002: Ch. 15, Section 1), Everitt (2005: Ch. 5), Baayen (2008:â•›136–138), Drenan (2010: Ch. 23), Maindonald and Braun (2010 [2003]:â•›383– 384), and Everitt and Hothorn (2009: Ch. 17; 2011:â•›121–127). A new volume, which is one of the most comprehesive applied works on the technique to date and one that includes explanation in R, is Borg et al. (2013). Adler (2010:â•›525, 541ff., 564) lists the wide range of functions in R for applying multidimensional scaling, but without examples of use. Härdle and Simar (2007: Ch. 15) and Izenman (2008:â•›13) offer more detailed explanations of how the technique functions. See Le Roux and Rouanet (2004:â•›12– 14) and Cadoret et al. (2011) for comparison between multidimensional scaling and

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correspondence analysis. Borg and Groenen (2005) is a complete description, containing both mathematical theory and details of application and interpretation. Cox and Cox (2001) is equally detailed, though more concerned with mathematical theory. Nevertheless, the work includes helpful chapters on biplots and correspondence analysis. Examples of its use within the field include Bybee and Eddington (2006), Clancy (2006), Croft and Poole (2008), Szmrecsanyi (2010), Hilpert (2012), Heylen and Ruette (2013), and Ruette et al. (in press, forthc.). Although not a corpus study, Berthele (2010) is another recent example.

Configural frequency analysis

This is a simple and powerful technique, yet surprisingly uncommon outside the German linguistic tradition. It can be seen as a simplified log-linear analysis (see below) or as multiple Chi-squared tests; indeed, it functions by creating log-linear combinations of factors to predict cell frequencies typically based on Chi-squared tests. The technique offers possibilities for significance testing in multivariate models where no clear response variable exists, by identifying which correlations in a multiway frequency table are significant. The main limitation for the application of this technique is sample size. For a given analysis, all cells must have at least one occurrence and a minimum of 20% should have more than 5 occurrences. An excellent explanation, though with no R code, can be found in Tabachnick and Fidell (2007: Ch. 16). Gries (2009b:â•›240–252) offers a clear explanation of how to implement it, but note that this is omitted from the newest version of his book (Gries 2003). Von Eye (2002) is a textbook devoted to the subject and von Eye et al. (2010) represents the state-of-the-art. Hierarchical configuration frequency analysis has been used by Stefanowitsch and Gries (2005, 2008), Wulff et al. (2007), Hilpert (2009, 2012), Jing-Schmidt and Gries (2009), Schmidtke-Â� Bode (2009), Berez and Gries (2010), Hoffmann (2011), and Kööts et al. (2012).

Linear discriminant analysis

Discriminant analysis is a classification technique that functions in a similar way to logistic regression and classification tree analysis (see below). However, linear discriminant analysis requires normally distributed data and continuous predictor variables, two conditions that are rarely met in Corpus Linguistics.3 Venables and Ripley (2002:â•›331–338), Crawley (2007:â•›744–747), Baayen (2008: 154–160), Adler (2010:â•›440–444) and Maindonald and Braun (2010:â•›385–391) offer explanations appropriate for the intermediate user. Everitt (2005:â•›Ch 7), Härdle and Simar (2007: Ch. 12), Tabachnick and Fidell (2007: Ch. 9), Izenman (2008: Ch. 8) and Afifi et al. (2011: Ch. 11) offer more substantial descriptions of discriminant analysis, 3. Cf. Stevens (2001), Arppe (2008:â•›164), Baayen (2008:â•›154), Heylen et al. (2008), and Hoffman (2011:â•›95) for discussion on the problems associated with the implementation of discriminant analysis. See also Divjak (2010a:â•›138) who defends its use.



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but offer no explanation for performing the analysis in R. Given the criteria are met, the method is a powerful classification technique and has been used by Gries (2003), Wulff (2003), and Divjak (2010a) in the field.

Classification tree analysis

An alternative to linear discriminant analysis is a data mining technique designed for categorical data called classification tree analysis. It is closely related to another technique termed regression tree analysis, which is used for continuous data. Together they are referred to as CART (or classification and regression tree analysis). The classification tree analysis technique employs an algorithm called recursive partitioning. For a given binary response variable (a vs. b), the algorithm begins with this alternation and asks which of the predictors (the other variables in the model) is best at predicting the choice between the two alternatives in the response variable. The algorithm continues this process for each of the two branches until all the predictor variables are ‘used up’. This re-occurring branching gives us a ‘tree’ that shows how the different variables predict the outcome, a vs. b. Classification tree analysis is explained and presented with R code in Crawley (2007: Ch. 21), Baayen (2008:â•›148–154), and Adler (2010:â•›406–117, 446–452). Other substantial descriptions include Venables and Ripley (2002: Ch. 9), Everitt and Hothorn (2010: Ch. 9), Maindonald and Braun (2010: Ch. 11), and Marden (2011: Ch. 11). The method has enjoyed some popularity in Cognitive Linguistic research, being both straightforward to apply and to interpret. Within the field, examples of its use include Klavan et al. (2011), Robinson (2012; this volume, 87–116), and Levshina et al. (this volume, 205–222). Bootstrapping regression trees and, what is termed, the random forests technique, represent an important avenue for the development of these techniques. Bootstrapping is a widely used technique that randomises the data in order to test explanatory strength and, thus, to ascertain confidence scores for the observed data through comparison with the randomised version of the data. The application of such techniques to classification tree analysis is opening up a new set of statistical alternatives to logistic regression analysis (see below). See Everitt and Hothorn (2010:â•›170–173), Strobl et al. (2009a), Adler (2010:â•›414–417), and Maindonald and Braun (2010:â•›369–372) for a description. Such techniques have yet to be applied in the field.

Regression analysis

In its various forms, regression analysis is one of the most widely used and powerful techniques in statistics. The importance of regression techniques lies in their ability to ‘predict outcomes’. The outcome is the term used to refer to a linguistic choice or a linguistic variant. This can be any kind of linguistic phenomenon, from lexemes, gestures, grammatical constructions and phonological patterns to the meanings of words, pragmatic functions, even gender, period, sociolect or dialect. The principle

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of how a regression analysis works is simple. The regression analysis takes our linguistic analysis of the data and builds a model that attempts to predict the behaviour of whatever phenomenon we are interested in explaining. If the model can predict which linguistic phenomenon (choice or variant, for example) is used, based on the linguistic analysis, then we can say that the analysis is accurate and, at least adequate, in distinguishing the phenomena under consideration. The linguistic choice or variety is understood as the response variable, which is ‘predicted’ by the independent variables, or the factors and features of the linguistic analysis. The model provides a great deal of information about how the linguistic analysis predicts the behaviour of the response variable but three pieces of information are crucial. Firstly, it tells us which of the linguistic factors and features are statistically significant in predicting the outcome. Secondly, it tells us the effect size of those features and factors; in other words, the relative importance of that factor or feature in predicting the outcome. Lastly, it tells us how accurately a combination of all the significant factors and features distinguish between the linguistic phenomena (the forms, uses or varieties being investigated). The following sections summarise several types of regression that are designed for categorical outcomes. This family of regression techniques are typically referred to as logistic regression. The standard references for logistic regression modelling include Agresti (2013 [1990, 2002], also 2007) and Hosmer and Lemeshow (2013 [1989, 2000]). Harrel (2001, also 2012) and Faraway (2006, also 2002) are also widely used reference books for the technique. Two other useful references include Hilbe (2009) and Menard (2010, also 2002). Once the basics have been mastered, and perhaps even before then, these books should be consulted. Especially useful is Thompson (2009), an unpublished and freely downloadable book that accompanies, step-by-step, Agresti’s work, with the R code needed to perform most of what his books cover. A note of caution is needed for the reader with little experience in statistics. None of the aforementioned books are designed for novice users, but they need to be consulted before regression analysis is used in research. Actually performing regression analysis is not particularly difficult. The complexity of confirmatory modelling lies not in applying the techniques (fitting the models), but in knowing which of the many algorithms and options one should use for the data and also applying and understanding the diagnostics of the model. Since confirmatory modelling tests hypotheses, one runs the risk of what is termed a Type I Error. This is statistics parlance, more or less, for demonstrating something to be true, when it is not. Before one reports findings obtained with regression modelling, one should always have the results thoroughly checked by a statistician.



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Binary logistic regression

Currently, the most common regression analysis for categorical data is binary logistic regression. This technique takes one or more ‘predictor’ or ‘explanatory’ variables and attempts to predict the outcome of a binary response variable, such as the use of one sense or near-synonym over another (start vs. begin, for instance). The regression analysis ‘models’ the data, permitting it to indicate which features, or ‘levels’, are most important in distinguishing the binary outcome. It also indicates the statistical significance of each of these predictions. Finally, scores for the overall success of the model in predicting the outcome can be obtained. As one of the most widely employed techniques in categorical statistics, there exists a diverse range of tutorials and textbooks devoted to it. Specifically designed for linguists, Speelman (this volume, 487–533) offers a concise introduction to applying the technique, so too does Baayen (2008: Ch. 6), Dalgaard (2008: Ch. 2008), Johnson (2008: Ch. 5), and Gries (2009b:â•›291–306; 2013: Ch. 5). Speelman and the latter two explanations include R code. Crawley (2005: Ch. 16) also includes lucid explanations of much of the R code needed. More general explanations, which remain accessible to the relative beginner, include Chatterjee and Hadi (2006: Ch. 12), Faraway (2006: Chs. 2–4), Gelman and Hill (2007: Ch. 5), Sheather (2009: Ch. 8), Everitt and Hothorn (2010: Ch. 7), Maindonald and Braun (2010: Ch. 8), Azen and Walker (2011: Chs. 8, 9), and Field et al. (2012: Ch. 8). As mentioned above, the ‘standard’ references for the technique include Harrell (2001), Faraway (2006), Hilbe (2009), Menard (2010: Chs. 8, 9), Agresti (2013: Chs. 4–7; 2007: Chs. 4, 5), and Hoshmer and Lemshow (2013). The technique is widely used in sociolinguistics and has a well-established tradition in Cognitive Linguistics. A few examples of use include Szmrecsanyi (2003, 2006), Heylen (2005b), Grondelaers et al. (2007, 2008), Speelman et al. (2009), Divjak (2010a), Glynn (2010b, this volume, 117–144), Robinson (2010a, 2010b, this volume, 87–116), Speelman and Geeraerts (2010), Deshors (2011, 2014), Levshina (2011), and Deshors and Gries (this volume, 179–204).

Loglinear analysis

Multiway frequency analysis or loglinear analysis is a technique not yet widely used in the field. Unlike binary logistic regression, loglinear analysis is not limited to determining the difference between a maximum of two possibilities. Therefore, it can be used to predict the behaviour of several senses, lexemes, or constructions. The technique is similar to configural frequency analysis, described above. Where configural frequency analysis examines configurations of sets of cells in a multiway frequency table, log-linear analysis looks at the interaction of variables that make up the multiway frequency table. Another way to think of loglinear analysis is to think of it as a logistic regression analysis without a response variable (start vs. begin, for instance).

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Instead of this response variable, one attempts to predict the actual frequencies for each variable with the minimal number of factors. Gries (this volume) offers a brief introduction to the technique, where it is termed “Poisson regression”. Adler (2010:â•›394–395, 444) offers a very short explanation, but suggests a range of functions in R that can be used for fitting loglinear models (Adler 2010:â•›227, 425, 437–438, 543, 557–558, 569). Thompson’s (2009: Chs. 8, 9) R manual for Agresti (2002) has two detailed chapters devoted to the technique. Short explanations include Oakes (1998: Ch. 5), Agresti (2007: Ch. 7; 2013: Chs. 9, 10), Faraway (2006:â•›61–67, 93–95), Dalgaard (2008: Ch. 15), Gries (2009b:â•›240–248; 2013:â•›324– 327), Tarling (2009: Ch. 7), Braun (2010:â•›258–266), Afifi et al. (2011: Ch. 17), Azen and Walker (2011: Ch. 7), Smith (2011: Ch. 4), Field et al. (2012: Ch. 18), and Ledolter (2013: Ch. 7). Von Eye and Mun (2013) is a new volume devoted to the technique and includes practical explanations in R. However, the book is relatively theoretical and may prove challenging for learners. For users of SPSS, Tabachnick and Fidell (2007: Ch. 16) present a thorough explanation. Kroonenberg (2008) is an approachable, non-technical, volume devoted to the topic, and Christensen (1997) is older and more technical, but comprehensive. Finally, Hilbe (2011) offers a less orthodox discussion, contextualising loglinear modelling as a means for identifying multivariate dependencies. With an example-based discussion, the author reveals how the approach ties in with other techniques. Within the field of Cognitive Linguistics, Krawczak and Glynn (in press) and Glynn (forthc.) are examples of its use.

Multinomial logistic regression

This extension of binary logistic regression (explained above) is also called polychotomous logistic regression, or polytomous logistic regression. The principle is the same as for binary logistic regression, save that there are multiple nominal outcomes. The technique, however, still requires a base line for the model, that is, an outcome that serves as the point of reference for the ‘other’ outcomes (start vs. begin, set off and commence, for example). Arguably the most approachable descriptions to date are Hilbe (2009: Ch. 10), Orme and Combs-Orme (2009: Ch. 3), and Ledolter (2013: Ch. 11), but see also Agresti (2007: Ch. 6). Arppe (2008) represents a detailed study on possible alternatives to this technique. For SPSS users, Tarling (2009: Ch. 6) and Azen and Walker (2011: Ch. 10) include a step-by-step example-based explanation. For Stata uses, Long and Freese (2006) is clear; its explanations are also useful independent of the statistical package used. The application of multinomial logistic regression is not straightforward and the technique has not yet enjoyed wide use in the field. However, as quantitative approaches to semantics continue, its application is likely to be an important contribution. Arppe (2008), Nordmark and Glynn (2013), Krawczak (2014a, 2014b, in press), and Glynn (forthc.) represent examples of its application in Cognitive Linguistics.



Techniques and tools 323

Ordinal logistic regression

Also referred to as ordered multinomial logit regression or proportional odds regression, the technique is a special case of logistic regression where the response is multiple and ordered, such as ‘short’, ‘medium’, ‘long’ or ‘young’, ‘older’, and ‘oldest’. At least three ways of modelling ordinal regression exist; the most common is called the proportional method. The principle is straightforward. Rather than a binary response, one has a series of response variables. For example, for an ordered list of choices A, B, C or D, one attempts to predict the outcome of A versus B, C, or D, then in turn A or B versus C and D, and finally A or B or C versus D. If these response variables A, B, C, and D are ordered, this can be interpreted as determining what factors predict that ordering. The most accessible explanations of such modelling can be found in Baayen (2008: Ch. 6), Hilbe (2009: Ch. 9), Orme and Combs-Orme (2009), and Tarling (2009: Ch. 8). O’Connell (2006) is a user-friendly textbook devoted to the technique, but intended for users of SPSS. Long and Freese (2006) is comparable for users of Stata. Agresti (2013:â•›86–98) offers a description of some of the basic issues and tests involved with ordered categories, and Agresti (2007: Ch. 6) offers a more detailed description, though somewhat theoretical. In terms of theory, Agresti (2010) represents a comprehensive work of reference. Johnson and Albert (1999) is a detailed and somewhat technical book devoted to the subject. This is a good reference, but has little explanation on application and only includes a software guide for program MATLAB.

Mixed-effects logistic regression

Sometimes also called multilevel modelling or hierarchical modelling, this technique is similar to ‘normal’ logistic regression, except that the model accounts for both ‘fixed’ effects (that is, the predictors in the model) and ‘random’ effects (or factors we know a priori are ‘noise’ in the model). For example, if one is looking at examples from a small set of sources, such as a set of authors in a diachronic corpus or speakers in discourse analysis, one does not want the individual traits of those authors or speakers influencing the outcome of the analysis. These unwanted effects are treated as ‘random’ in the model. Put simply, mixed-effects regression analysis accounts for those ‘unwanted’ factors, and ‘neutralises’ their effects, preventing them from skewing results. The principle can be applied to any form of regression, including the ordinal and multinomial regression explained above. Speelman (this volume, 487–533) offers a succinct explanation. An older, but thorough, description can be found in Edwards (2000: Ch. 4). Gellman and Hill (2006) offer an extremely detailed, yet approachable, book on the matter. Crawley (2007: Ch. 19), Baayen (2008: Ch. 7), Maindonald (2008: Ch. 10), Sheather (2009: Ch. 10), and Tarling (2009: Ch. 9) give clear introductions to the method, as does Johnson (2008:â•›255–260). See also Frawley (2007: Ch. 19), who gives one of the clearest explanations on how to distinguish random variables from fixed

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variables, and Maindonald and Braun (2010: Ch. 10), who offer a thorough description of the interpretation of the output in R. Finally, Hox (2010) is a work devoted to the technique. It is broad in its coverage, with a theoretical orientation, but it remains approachable for the faux-débutant, serving as an excellent book of reference. Mixed models are beginning to become more common in the Cognitive Linguistic literature; examples include Bresnan et al. (2007), Divjak (2010b), Klavan (2012), Levshina et al. (2013a; this volume, 205–222); Krawczak and Glynn (in press), and Glynn (2014a). Table 3 summarises the different techniques described here. Although the table systematically covers the techniques for categorical data, it does not include any techniques for continuous data. Moreover, it does not include many of the recent advances and variants, such as random forest classification or hierarchical configural frequency analysis. Tabachnick and Fidell (2007:â•›29–31) offer an excellent breakdown of many of the multivariate techniques available; so too does Baayen (2008:â•›Appendix B). Tummers et al. (2005), Heylen et al. (2008) and Gilquin and Gries (2009) offer extensive discussions on the quantitative state-of-the-art in Cognitive Linguistics. Just as the number of different statistical techniques can be overwhelming for someone first learning, so too can the number of packages and commands available for performing them in R. Packages are modules that expand R’s functionality and the commands are the computer prompts to make them operate. One of R’s most important strengths is the fact it is a vibrant community, with countless active internet fora and just as many people writing packages to refine and advance the application of every imaginable statistical technique. The downside to this, of course, is that a simple search request on the Internet can result in in an overload of information and options. In response to this problem, Table 4 represents a concise reference list for the functions and packages in R for performing the multivariate techniques described above. It is far from complete, being designed as a quick reference for the intermediate user who wishes to get started on a method with which he or she is not yet familiar. Also included are references for tutorials and textbooks on the functions and packages. A complete list would be impossible since many of the techniques have a number of packages devoted, or partially devoted, to them and other techniques have many variants. Moreover, it must be remembered that for the confirmatory techniques, there also exist large numbers of diagnostic and visualisation options, most of which are performed with the use of other more general or more specific packages and functions. Certain books can be recommended for the reader who wishes to go back and investigate the basics that this volume skips, and also for the reader who wishes to delve deeper into the kinds of methods presented here. Baayen’s (2008) Analyzing Linguistic Data is an excellent place to start. Another highly recommended guide for starting statistical analysis using R in Linguistics is Dalgaard’s (2008)’s Introducing Statistics with R. If used in combination with Baayen (2008), one should be able to move on

Techniques and tools 325 Table 3. Quantitative techniques and their usage in corpus-based Cognitive Linguistics Technique

Type

Object collocation

Example of application

Explanation

T-score, Z-score, MI score

measure

strength

identifying multi-word patterns – Biber (2009) identifying constructional variants – Wong (2009)

Evert (2009), Biber & Jones (2010)

Chi-squared test, univariate Fisher’s exact Test

probability / independence

synonymy, constructional – Wulff (2006) polysemy, lexical – Robinson (2010)

Dalgaard (2008), Everitt & Hothorn (2009), Gries (this volume)

Collostructional analysis

univariate

collocation strength

synonymy, constructional – Hilpert (2008) synonymy, constructional – Gilquin (2010)

Stefanowitsch & Gries (2003), Gries & Stefanowitsch (2004a), Hilpert (this volume)

Hierarchical cluster analysis

multivariate associations btw. objects of single variable

polysemy, lexical – Gries (2006) synonymy, lexical – Divjak (2010a)

Baayen (2008), Everitt et al. (2011), Divjak & Fieller (this volume)

Multidimensional multivariate associations btw. objects of scaling multiple variables

synonymy, morphological – Croft & Poole (2008) relations between variants Berthele (2010)

Baayen (2008), Izenman (2008), Everitt & Hothorn (2010)

Correspondence analysis

synonymy, concepts – Szelid & Geeraerts (2008) polysemy, constructional – Glynn (2009)

Le Roux & Rouanet (2010), Husson et al. (2011), Glynn (this volume)

Configural multivariate associations btw. objects of frequency analysis multiple variables

polysemy, constructional – Hilpert (2009) synonymy, constructional – Hoffmann (2011)

von Eye (2002), Tabachnick & Fidell (2007), Gries (2009b)

Discriminant analysis

synonymy, constructional – Gries (2003) synonymy, lexical – Divjak (2010a)

Tabachnick & Fidell (2007), Baayen (2008), Maindonald & Braun (2010)

Classification tree multivariate identify factors that lead to analysis an outcome / prediction

polysemy, lexical – Robinson (2012a) synonymy, lexical – Levshina et al. (this vol.)

Venables & Ripley (2002), Everitt & Hothorn (2010), Maindonald & Braun (2010)

Loglinear analysis multivariate predict correlation multiple response variables

synonymy, constructional – Krawczak & Glynn (in press) Kroonenberg (2008), Hilbe (2011), polysemy, lexical – Glynn (forthc.) Smith (2011)

Binary logistic regression

multivariate predict outcome binary response variable

synonymy, constructional – Szmrecsanyi (2003) synonymy, lexical – Speelman & Geeraerts (2010)

Ordinal logistic regression

multivariate predict outcome ranked response variable

synonymy. lexico–constructional – Klavan (2012) Baayen (2008), Tarling (2009), synonymy, constructional – Glynn & Krawczak (forthc.) Orme & Combs-Orme (2009)

multivariate associations btw. objects of multiple variables

multivariate identify factors that lead to an outcome / prediction

Orme & Combs-Orme (2009), Everitt & Hothorn (2010), Speelman (this volume)

Multinomial multivariate predict outcome logistic regression multiple response variables

synonymy, lexical Arppe (2008) synonymy, lexical – Krawczak (2014a)

Long & Freese (2006), Tarling (2009), Orme & Combs-Orme (2009)

Mixed-effects multivariate predict outcome logistic regression include random variables

synonymy, constructional – Divjak (2010b) synonymy, constructional – Levshina et al. (this vol.)

Baayen (2008), Maindonald & Braun (2010), Smith (2011)

326 Dylan Glynn

Table 4.╇ Functions and packages for categorical multivariate statistics in R Technique

Function

Package

R code tutorial

Hierarchical cluster analysis

hclust

stats*

Crawley (2007:â•›738ff.); Zhao (2013)

agnes

cluster

Kaufman & Rousseeuw (2005); Maechler (2013)

pvclust

pvclust

Suzuki & Hidetoshi (2006); Suzuki (2013)

kmeans

stats*

Crawley (2007:â•›742ff.); Zhao (2013)

clara

cluster

Kaufman & Rousseeuw (2005); Maechler (2013)

pamk

fpc

Hennig (2013)

corresp

MASS*

Venables & Ripley (2002:â•›326ff.); Ripley (2013)

ca

ca

Greenacre (2007); Neandić & Greenacre (2007)

anacor

anacor

de Leeuw & Mair (2009a, 2013a)

MASS*

Venables & Ripley (2002:â•›329f.); Ripley (2013)

K-means cluster analysis Binary correspondence analysis

Multiple correspond- mca mjca ence analysis Multidimensional scaling

ca

Greenacre (2007); Neandić & Greenacre (2007)

MCA

FactoMineR

Lê et al. (2008); Husson et al. (2013)

cmdscale

stats*

Baayen (2008:â•›136ff.); Johnson (2008:â•›208ff.)

sammon

MASS*

Maindonald & Baun (2010:â•›284f.)

smacofSym

smacof

de Leeuw & Mair (2009b, 2013b)

cfa

Funke et al. (2007); von Eye & Mair (2008)

Configural frequency cfa hcfa analysis Linear discriminant Analysis

Classification tree analysis / Random forest classification

cfa

Gries (2010:â•›248ff.); von Eye et al. (2010:â•›265ff.)

cfa2

cfa24

No tutorials available, cf. Schönbrodt (2013)

lda

MASS*

Baayen (2008:â•›167ff.); Maindonald & Braun (2010:â•›385ff.)

discrim

ade4

Chessel et al. (2004); Chessel & Dufour (2013)

rda

klaR

Roever et al. (2013)

rpart

rpart

Zhao (2012:â•›32ff.); Therneau et al. (2013)

tree

tree

Venables & Ripley (2002:â•›266)

ctree

party

Zhao (2013:â•›29ff.)

cforest

party

Strobl et al. (2009a, 2009b)

randomForest randomForest Maindonald & Braun (2010:â•›351ff.);

Liaw & Wiener (2002) Loglinear analysis

glm

MASS*

Maindonald & Braun (2010:â•›258ff.); Baguley (2012)

loglm

MASS*

Thompson (2009:â•›142ff.); Baguley (2012)

quasipois

aod

Lesnoff & Lancelot (2013)

4. The package cfa2 is not currently in the CRAN repository for R but can be found in the RForge repository. This repository is typically used for packages still under development. A simple command listed on the Rforge site for the package will install a package as effortlessly as installation using the ‘normal’ method in R.

Techniques and tools 327



Table 4.╇ (continued) Technique

Function

Package

R code tutorial

Binary logistic regression

glm

MASS*

Baayen (2008:â•›195ff.); Everitt & Hothorn (2010:â•›122ff.)

lrm

rms†

Harrell (2001:â•›257ff.; 2012:â•›221ff.); Baayen (2008:â•›195ff.)

MCMClogit

MCMCpack

Martin et al. (2010)

polr

MASS*

Faraway (2006:â•›117ff.); Maindonald & Braun (2010:â•›270ff.)

lrm

rms†

Baayen (2008); Johnson (2008)

clm

ordinal

Christensen (2012)

multinom

nnet

Faraway (2006:â•›106); Thompson (2009:â•›118)

polytomous

polytomous

Arppe (2014)

mlogit

mlogit

Field et al. (2012:â•›325); Croissant (2013)

lmer

lme4

Baayen (2008:â•›278ff.); Bates (forthc.:â•›1ff.)

glmmPQL5

MASS*

Johnson (2008:â•›255ff.); Thompson (2009:â•›179ff.)

MCMCglmm

Hadfield (2010)

Ordinal logistic regression

Multinomial logistic regression Multilevel logistic regression (mixed effects) *

MCMCglmm

Recommended package for the base installation. This means it comes ‘pre-installed’.

†

In older textbooks and tutorials, this package is called Design. The package rms is simply a new version. The command line to use the package is unchanged and so older descriptions remain helpful.

from what is covered in this volume on all three fronts – developing knowledge of R, the basic statistical principles and tests, as well as advanced statistical analysis. Gries’ (2009a) Quantitative Corpus Linguistics with R is another book to consider. Although an excellent book, it is designed more for corpus linguistics per se than multivariate analysis. More in line with the focus of this volume is Gries’ (2009b) Statistics for Linguistics Using R. It covers the basics thoroughly and introduces some multivariate statistical techniques. A new edition, Gries (2013), expands the chapter on precisely the techniques covered in this volume Johnson’s (2008) Quantitative Methods in Linguistics is good for a debutant level statistics textbook using R – it explains both the command line and statistics lucidly and concisely. However, it ‘orders’ the different statistical techniques relative to different subfields of linguistics. This could be misleading for the novice and not particularly logical for the reader with some knowledge in the field, since most of the techniques are not at all restricted to the subfield Johnson ascribes to them. However, the expla-

5. The function glmmPQL uses a so-called penalised quasi-likelihood, which has lost favour in the research community (Crawley 2007:â•›655). Although the functions lmer and MCMCglmm are more up to date in this regard, glmmPQL in the MASS package still works perfectly well, especially when learning since some of the command line is closer to other regression functions a learner may have already mastered.

328 Dylan Glynn

nations of the techniques are clear, especially concerning the issues that lie between the very basic and more advanced study, such as understanding data distribution and samples. Slightly more advanced books, though approachable, are Everitt and Hothorn (2010; 2011). These volumes are excellent textbooks for researchers with an introductory knowledge in statistics and/or with R, but who wish to adopt multivariate techniques – veritable handbooks. Although the examples are not linguistic, they are clear and well chosen. The statistical techniques covered are all explained through the use of examples. The demonstration of the R code is systematic and complete. Finally, Keen (2010) offers a thorough coverage of the graphic possibilities in R. Appropriate for novice and expert alike, the book is practically orientated with detailed examples of the R code.

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Therneau, T., Atkinson, E., & Foundation, M. (2013). An introduction to recursive partitioning using the RPART routines. Available at: http://cran.r-project.org/web/packages/rpart/ vignettes/longintro.pdf. Thompson, L. (2009). S-PLUS (and R) manual to accompany Agresti’s categorical data analysis (2002). Available at: home.comcast.net/~lthompson221/Splusdiscrete2.pdf. Tummers, J., Heylen, K., & Geeraerts, D. (2005). Usage-based approaches in Cognitive Linguistics: A technical state of the art. Corpus Linguistics and Linguistic Theory, 1, 225–261. DOI: 10.1515/cllt.2005.1.2.225 Valenzuela Manzanares, J., & Rojo López, A. M. (2008). What can language learners tell us about constructions? In S. De Knop, & T. De Rycker (Eds.), Cognitive approaches to pedagogical grammar? A volume in honour of René Dirven (pp. 197–230). Berlin & New York: Mouton de Gruyter. Van Bogaert, J. (2010). A constructional taxonomy of I think and related expressions: Accounting for the variability of complement-taking mental predicates. English Language and Linguistics, 14, 399–428. DOI: 10.1017/S1360674310000134 Venables, W., & Ripley, B. (2002). Modern applied statistics with S (4th ed.). Heidelberg: Springer. DOI: 10.1007/978-0-387-21706-2 Verdonik, D., Rojc, M., & Stabej, M. (2007). Annotating discourse markers in spontaneous speech corpora on an example for the Slovenian language. Language Resources and Evaluation, 41, 147–180. DOI: 10.1007/s10579-007-9035-7 von Eye, A. (2002). Configural frequency analysis: Methods, models, and applications. Mahwah: Erlbaum. von Eye, A., & Mair, P. (2008) A functional approach to configural frequency analysis. Austrian Journal of Statistics, 37, 161–173. von Eye, A, Mair, P., & Mun, E.-Y. (2010). Advances in configural frequency analysis. London: Guilford Press. von Eye, A, & Mun, E.-Y. (2013). Log-linear modeling: Concepts, interpretation, and application. Hoboken: John Wiley. Wiebe, J., Wilson, T., & Cardie, C. (2005). Annotating expressions of opinions and emotions in language. Language Resources and Evaluation, 39, 165–210. DOI: 10.1007/s10579-005-7880-9 Wiechmann, D. (2008). On the computation of collostruction strength: Testing measures of association as expressions of lexical bias. Corpus Linguistics and Linguistic Theory, 4, 253– 290. DOI: 10.1515/CLLT.2008.011 Wong, M. (2009). Gei constructions in Mandarin Chinese and bei constructions in Cantonese: A corpus-driven contrastive study. International Journal of Corpus Linguistics, 14, 60–80. DOI: 10.1075/ijcl.14.1.04won Wulff, S. (2003). A multifactorial corpus analysis of adjective order in English. International Journal of Corpus Linguistics, 8, 245–82. DOI: 10.1075/ijcl.8.2.04wul Wulff, S. (2006). Go-V vs. go-and-V in English: A case of constructional synonymy? In St. Th. Gries, & A. Stefanowitsch (Eds.), Corpora in Cognitive Linguistics: Corpus-based approaches to syntax and lexis (pp. 101–126). Berlin & New York: Mouton de Gruyter. Wulff, S. (2009). Rethinking idiomaticity: A usage-based approach. London: Continuum. Wulff, S. (2010). Marrying cognitive-linguistic theory and corpus-based methods: On the compositionality of English V NP-idioms. In D. Glynn, & K. Fischer (Eds.), Quantitative Cognitive Semantics: Corpus-driven approaches (pp. 223–238). Berlin & New York: Mouton de Gruyter.



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Wulff, S., Stefanowitsch, A., & Gries, St. Th. (2007). Brutal Brits and persuasive Americans: Variety-specific meaning construction in the into-causative. In G. Radden, Köpcke, K.-M., Berg, Th., & Siemund, P. (Eds.), Aspects of meaning construction (pp. 265–281). Amsterdam & Philadelphia: John Benjamins. Zeschel, A. (2010). Exemplars and analogy: Semantic extension in constructional networks. In D. Glynn, & K. Fischer (Eds.), Quantitative Cognitive Semantics: Corpus-driven approaches (pp. 201–221). Berlin & New York: Mouton de Gruyter. Zhao, Y. (2013). R and data mining: Examples and case studies. Unpublished manuscript. Available at: http://www.rdatamining.com. Zlatev, J., & Andrén, M. (2009). Stages and transitions in children’s semiotic development. In J. Zlatev, M. Andrén, C. Lundmark, & M. Johansson Falck (Eds.), Studies in language and cognition (pp. 380–401). Newcastle: Cambridge Scholars.

Statistics in R First steps Joost van de Weijer and Dylan Glynn Lund University and University of Paris VIII

The R Project for Statistical Computing is one of the most comprehensive and widely used software options for statistical analysis. Moreover, it is open source, freely available and entirely cross-platform. It is for these reasons that the following chapters all employ R to demonstrate the application and interpretation of statistics. Like the commercially available software SAS, but unlike three other widely used suites (SPSS, Stata, and Statistica), R is principally used in command line. The need to work with commands rather than a graphical user interface can be a challenge for novice users, especially when combined with the task of learning statistics. However, commands given in a step-by-step fashion is arguably simpler than a graphic interface, which can overwhelm the novice user with options. This chapter is an introduction to R focusing on how to import data and make sure those data are in the correct format for analysis. Knowledge of each of these steps is assumed in the following chapters. Keywords: dataframe, cross-tabulation, formatting data, importing data

1. Installing R R is freely available from www.r-project.org. On the site, one will find the CRAN server link where the various versions (Linux, MacOSX and Windows) can be downloaded. Follow the instructions to install R onto a personal computer.

2. Commands Once R has been installed on the computer, you can launch it by double-clicking the program’s icon. A window entitled “R Console” should open. In this window, you will see some introductory text, followed by an empty line that starts with a “>” sign. This

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sign is called the prompt. Unlike many other programs, R does not have a graphical interface with drop-down menus or dialogue windows to do an analysis. Instead, you need to tell the program what to do by typing commands directly in the console window. Numerous examples of commands are given throughout this book. Commands can be simple or complex. An example of a command is given below. This command tells R to read a text file and thus load the data into its working memory. The actual command below will not work since the location of the file is not specified, but it serves to explain the principle behind using command line. mydata = read.table("dataframe.txt")

For many users new to R, working with commands is difficult at first. Commands have a very strict structure (called syntax). If they are not entered entirely correctly, they do not work. The source of the error can be small (a missing comma, for instance) and the resulting error message is usually not very helpful to a beginner trying to determine what the problem actually is. Nevertheless, writing and memorising commands gets easier through practice. A helpful strategy is to keep and maintain a personal collection of command examples that you have used before and which are useful for the kinds of analysis you typically carry out. Let us examine the above command line by identifying its constituent elements. The central element is the word read.table. This is one of many functions that are built in into R and it is used for importing external data. More examples of the read.table function are discussed/explained below in Section 4. A function, such as read.table, is a way of telling the program to do something, in this case load the data, which is in the format of a table, into R. Note that read.table is followed by an opening parenthesis and, a bit further on at the end, a closing parenthesis. The text within the parentheses is the name of a data file, enclosed in quotation marks. The action that is specified by the function is often performed ‘on something’; here, the data file called dataframe.txt which is stored on the computer. This part of the command is called the argument . Then notice the part to the left of the read.table command in the example above. The result of the action performed by the command is saved internally in R under the name mydata. Practically, this means that the content of the external data file is copied, and saved in R under a new name. This name is more or less arbitrarily chosen. There are some restrictions on the choice of names, but almost anything will do, as long as it starts with a letter and does not contain any special characters. The name could as well have been olddata, sunday2112, pilotstudy, or xxx. It is up to you to choose the name, choose something short and easy to remember. Data or results that are saved in R are usually referred to as objects. Once an object has been created, it will be available until the program is quit or until it is manually deleted from R. An object can be a single number, a series of numbers, a complete data file, a graph, the output of an analysis, and so on. These are all stored in the so-called



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workspace. In order to see a listing of what is in the workspace, type the command ls(). In order to delete or remove and object type remove() with the name of the object between the parentheses.

3. The data file Creating a data file that will be loaded into R is an important step in the analysis and one that often leads to confusion when first learning how to use R. The idea is to take the data, from whatever their source, and put them in a plain text file. This step needs extreme care since text files can include hidden formatting and other information that will prevent the data from being loaded. Typically, data are held in a spreadsheet file (such as those produced by MS Office’s Excel, Open Office’s Calc or iWork’s Numbers) or a database (such as those produced by MS Office Word’s Access, Open Office’s Base, and Apple’s FileMaker). When just beginning, the tabular layout of a spreadsheet is arguably the easiest. This is because when data are displayed in a spreadsheet, one can easily see whether all cells are complete, whether the columns are aligned properly and how many cases there are. Once one is confident that the data are all clear and there are no empty cells and so forth, one can copy and paste the data directly into a plain text file. It is important that the file itself does not contain any ‘formatting’. If the file contains formatting or invisible mark-up, R may not be able to read the file. There are many text-editing programs that can contain hidden formatting (such as WordPad for Windows and TextEdit for MacOSX). However, other text editors automatically ‘strip’ any formatting, hidden or otherwise (such as NotePad in Windows and TextWrangler in MacOSX). If the data are contained in a database, one needs to export the data to a plain text file. This option is also available in the spreadsheet programs. Exporting data helps to eliminate the problem of hidden formatting and mark up. If the data contain diacritics or non-roman characters, this option is the safest one because it is usually possible to specify the encoding used in the text file (unicode is the preferred option here). The data in the text file, whether taken from a database or a spreadsheet, normally exists in one of two formats: a flat or ‘raw’ dataframe form, where each row represents a case and each column represents a variable, and a cross-tabulation or a contingency table where this information is summarised numerically. An example of the flat or ‘raw’ dataframe format is illustrated in Table 1. In most spreadsheets and databases, the data can be saved as a tab or comma delimited textfile, which means that there is a tab or a comma between each column. On screen, the columns in the textfile may not look perfectly straight, but this does not necessarily mean there is a problem – remember, there is no formatting. R reads any type of column delimitation. In the commands, it is assumed the data are tab-delimited. The flat dataframe layout of the data normally results from the

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Table 1.╇ Example of a flat dataframe verb tense person figurativity run past 1 literal run past 1 metaphor jog future 2 metaphor run past 2 literal literal skip past 2 jog future 1 literal

Table 2.╇ Example of a cross-tabulation jog run skip

future 2 0 0

past 0 3 1

pers.1 1 2 0

pers.2 1 1 1

literal 1 2 1

metaphor 1 1 0

manual analysis of examples in a database or spreadsheet. In this format, the numbers of occurrences are not indicated, but instead each occurrence is listed in a large ‘flat’ file. This format of the data is the preferred format for multivariate statistics. One of the most common problems faced when starting statistical analysis in R is that the annotation or concordance tool used to obtain the data exports the results in a numerical table (described below). Typically, such tables have omitted much of the important information and cannot be used in most multivariate analyses. It is important to make sure that whatever corpus tool being used the data can be exported to the flat dataframe format. The second typical format for data is a numerical tabulation. We refer to this as a cross-tabulation or a contingency table. In contrast to the raw dataframe, this format is a numerical summary of the data and is typically a result of manually counting occurrences or the results of questionnaires. However, the format can also be generated by a number of spreadsheet, database, annotation and concordance programs. An example of a cross-tabulation is shown in Table 2. Using the first column in Table 1 as the row names, the data in Table 2 are the equivalent to those above. It is important to note that this table would look considerably different if we were to take a different column in Table 1 and use it to create the row names. This data format is sometimes also referred to as a frequency table, contingency table, xtab, or pivot table.

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4. Importing the data into R 4.1

Importing data from a flat dataframe

The two formats of data are loaded into R differently. We will begin with the raw datafile. The most common command for importing data into R is read.table(), which was introduced in Section 1. Here we present this command again, but now with two additions. mydata = read.table("dataframe.txt", header=TRUE, sep="\t")

In this example, there are three arguments to the command rather than just one as in the earlier example. The arguments have been separated by commas. The first argument, "dataframe.txt" is the filename. The second argument, header=TRUE, indicates that the first line of the data file contains the variable names, as is the case in Table 1. If this argument had been omitted, then the fields in the first line of the data file would have been interpreted as values rather than as names, and the columns would have been labelled automatically instead (V1, V2, etc.). The third argument, sep="\t", indicates that the columns are separated by tabs. Had the columns been separated by commas instead, then the third argument would have been sep=",". The object that has been created with the read.table() command above is called a dataframe, and it has been named mydata. However, these commands will still not work – we have to add one further piece of information. We need to tell R where to find the data file. There are four possibilities: mydata = read.table(file.choose(), header=TRUE, sep="\t") mydata = read.table("clipboard", header=TRUE, sep="\t") mydata = read.table("users/linguist/data/dataframe.txt", header=TRUE, sep="\t") setwd("/Users/linguist/data") mydata = read.table("dataframe.txt", header=TRUE, sep="\t")

In the first alternative, the name of the file has been replaced by file.choose(). This argument causes a dialogue window to open from which the data file can be chosen. With the second alternative, it is assumed that the data have been copied to the clipboard and R takes the data from there. This is similar to the copy and paste function common in applications such as MS Word and Excel. Depending of the operating system and the version of R being used, the second option often results in problems. The third option tells R to go to a specific location and open the file. That location can be on the hard drive of a personal computer, on a server, or even on the Internet. The location is indicated as a path, where slashes “/” represent folders. This location

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or path needs to be between inverted commas. In MacOSX and Linux, the command given above indicates that the data file is in a folder called ‘data’, which is in a folder called ‘linguist’, which in turn is in a folder called ‘Users’, which is on the boot drive of the system. In Windows, one needs to add the name of the disk or volume typically indicated by a lowercase letter followed by a colon, “c:” being the default label for a boot drive. Therefore, for Windows, the equivalent command line looks like this: mydata = read.table ("c:users/linguist/data/dataframe.txt", header=TRUE, sep="\t")

The fourth alternative, finally, consists of two commands. The first command sets the so-called working directory, which is the path to the folder in which the datafile is stored. The second command imports the data into a dataframe object. If you do not know what the current working directory is, you can find out by typing the command getwd(). The object that is being created with read.table() is called mydata. It is important to check that the dataframe created from a data file has been properly imported into R. It is not uncommon that something goes astray during the process of importing, and not always does this result in an error message in R. Therefore, next we provide examples of commands that can help make sure that the newly imported data is in order. The simplest way of seeing what the data looks like in R is by typing the name of the object. We called our data object mydata. mydata

Typing the name of the object, here mydata, will display the contents of the entire object. However, if the object is a flat dataframe, this will result in the entire dataset being displayed, which can be extremely cumbersome. In the case of a flat dataframe, a better option is to look at the first few rows, using the command head(): head(mydata)

This command will display the column names of the dataframe (these are the names that were in the first row of the data file; the headers in a spreadsheet and the cell labels in a database), followed by the first six rows. There is a corresponding command, tail(), that displays the last six rows of the dataframe. A second command that is useful in this regard is summary(). This command generates a numerical summary of the dataframe. This is also useful for spotting spelling mistakes and so forth in the analysis. Remember that R treats lowercase and uppercase letters as distinct items and does not ignore invisible characters such as a space or a tab. It is rare that a flat dataframe is without any mistakes. After importing data, one must typically return to the database or spreadsheet and correct many small typographic errors.

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summary(mydata)

A third command that provides information about a dataframe is the command str(). This command offers information about the structure of a dataframe. When applied to the data from Table 1, we receive the following output: str(mydata) 'data.frame' : $ verb : 2 2 1 2 3 1 $ tense : 2 2 1 2 2 1 $ person : $ figurativity: 1 2 2 1 1 1

6 obs. of 4 variables: Factor w/ 3 levels "jog","run","skip": Factor w/ 2 levels "future","past": int 1 1 2 2 2 1 Factor w/ 2 levels "literal","metaphor":

The first line of the output shows that mydata is a dataframe with six observations (rows) and four variables (columns). The next four lines show the four variables and three types of information about them. First of all, they show their names. Second they show what type of variables they are. Here, three of the four variables are labelled as Factor, which is the usual type for categorical variables. Additionally, the str() command shows how many levels these variables have, that is, the number of features that these variables possess. The variables tense and figurativity have two levels, while verb has three. The fourth variable, person, is labelled as int, which means that the values of that variable are whole numbers. The numbers 1 and 2 are labels for first and second person, respectively. This has revealed an important error. R has assumed that this variable is numerical because the labels used in the analysis were numbers. One solution is to add a letter to the label in the spreadsheet or database, the other is to change it in R. This is further explained in Section 5.3.

4.2

Importing cross-tabulations

If the data are in a cross-tabulated format, as exemplified in Table 2, loading the data is a little different. There are two ways to load the data in this case. Firstly, one can repeat the command used above in Section 4.1 to load the data from a flat dataframe, but add the argument row.names = 1. mydata = read.table(file.choose(), header=TRUE, sep="\t", row.names=1)

The read.table command is not designed for data in this format, so R does not always treat the data as it should (for example, the str() and summary() commands do not work). Nevertheless, for most purposes, loading the data in this way does not

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Table 3.╇ Layout for read.ftable() command verb

future 2 0 0

jog run skip

past 0 3 1

1stPers 1 2 0

2ndPers 1 1 1

literal 1 2 1

metaphor 1 1 0

pose any problems. If one wishes to see that the cross-tabulation has been correctly loaded, enter the object name: mydata

This brings up the cross tabulation for inspection. A second, more orthodox, way to load a cross-tabulation is to use the command read.ftable(). Notice an “f ” has been added to the function read.table. mydata = read.ftable(file.choose(), sep="\t")

This command tells R that the data are in the cross-tabulated format. Note that the header=TRUE argument has been removed. The read.ftable command is sensitive to the actual layout of the data, especially to how the row and column names are placed in the text file. For this command to work, the name of the first row must be located on a previous line, independent from the column names. One must also remember to add a ‘blank’ first column beneath the first row-name. Table 3 exemplifies this layout. Both commands, read.table and read.ftable(), expect a blank line (a return carriage) at the end of the text file, beneath the table.

4.2.1 Transpose a contingency table Sometimes it is useful to transpose a cross-tabulation. Transposition means that the entire data object is rotated by 90 degrees. That is, the rows become columns and the columns become rows. For a raw dataframe, this is rarely useful, but for cross-tabulations, since the data are summarised as a given variable and its levels are relative to another variable (or variables and levels), inverting the table means that a statistical technique may actually examine the data from a different perspective. Transposition can be done in R using the command t(), as in the following example: mydata2 = t(mydata)

The object mydata2 is now an inverted or transposed version of the of the original cross-tabulation.

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5. Making changes to a dataframe in R It is not uncommon that information in a dataframe needs to be changed or that new information needs to be added. A possible way of doing this is to make changes directly in the data file and to re-load the data, but for various reasons it might be desirable to keep the data file unchanged, and to do the modifications to the dataframe in R instead.

5.1

Creating objects

To begin, the principle of creating objects in R needs to be explained. Two synonymous signs are used for creating object, “=” and “<-”. The signs can be used interchangeably. The item that is to the left of the sign is the new object, and it equates whatever is to the right. In Section 4.1 above, we created an object mydata using this sign. This object is stored in the memory of the computer and remains there until one quits R or one removes the object with the command rm() or remove(). For example, when changing the data in R, one option is to make a duplicate of those data. Of course, if something goes wrong, one can always re-load from the data file. Moreover, having too many data objects in R uses up precious memory. However, to help us understand how objects can be created, let us duplicate our data: mydata.copy = mydata

Now there are two identical copies of the data in R, one labelled mydata, the other labelled mydata.copy. One does not normally use this functionality to duplicate data, but to create a new object; for example, the results of a statistical analysis, which one wishes to store in order to plot or to run further analyses upon at a later stage. Working with large datasets or running many analyses can result in sluggish performance from the computer since all this information is stored in the active memory. Therefore, objects not in use should be removed. To remove an object, type rm(). The following line removes the duplicated data. rm(mydata.copy)

5.2

Changing a variable name

The name of one or more variables in a dataframe can be changed using the command colnames(). In order to do this, one must also know the number of the column with the name that needs to be changed. In the example dataframe, there are four columns. To see the names of all four columns, type: colnames(mydata)

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To change the name of a column, in this case the first one, type: colnames(mydata)[1] = "newname"

5.3

Changing a variable type

A common manipulation is to change the variable type. An example is when the levels of a categorical variable have been coded as numbers, as was the case with the variable person in Table 1. The levels of this variable have been coded as 1 and 2 for first and second person, respectively. Automatically, this variable was imported as an integer variable, in other words, a numeric variable. As a consequence, certain commands that are appropriate for a categorical variable do not work (e.g., the levels() command) if no action is undertaken. More importantly, this variable is not numerical, it is categorical; the example sentence was either in the 1st person or the 2nd person. Letting R assume it is a numerical variable will lead to errors in any subsequent statistical analysis. The solution is to change the variable type for person from integer to factor using the factor() command: mydata$person.fact = factor(mydata$person)

Note that we gave the transformed variable a new name (person.fact), which automatically created a new variable in the dataframe. While it is possible to keep the original name after transformation, there is a risk involved of inadvertently running the same transformation once again, and thus doubling the effect of the transformation. This risk is avoided by using a new name for the transformed variable. If one wishes to replace the numerical variable with the same variable but understood by R as a factor, use the command: mydata$person = factor(mydata$person)

5.4

Changing values in a dataframe

There are many situations where values for a given variable need to be changed. These may be values that were not entered correctly in the first place, values that need to be rescaled, and so on. Here we illustrate how to change values in a dataframe by first adding a new variable to mydata that divides the verbs into two groups, and then changing some of the values of that new variable. Suppose, for instance, that we would like to add a variable to mydata that indicates verb type, and that the verbs jog and run belong to type "A" while skip belongs to type "B". Here we do that in two steps. In the first step we create the new variable, call it verbtype, and assign it the value "A" for all cases in the dataset:

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mydata$verbtype="A"

In the second step, we change the values of verbtype into "B", but do that only for the cases where the variable verb equals skip. This can be done using square brackets ([]) notation. In R, square brackets are often used to identify the position of a value, as we saw above with the colnames() command. To find a value in a dataframe, we need to specify the row(s) that contain a specific value, and the column(s). In other words, we need to include two things within the square brackets: the row(s) and the column(s). Within square brackets, the row is always specified first, followed by a comma, followed by the specification of the column. Schematically: [which row(s)? , which column(s)?]

In our example, the changes need to apply only to the rows where the variable verb equals skip, and only in the column that contains the variable verbtype: mydata[mydata$verb=="skip","verbtype"]

If we give this as a command to R, we get the value of the variable verbtype for the cases where the variable verb equals skip. Now this value is still "A", but it needs to be changed to "B". Setting the new value is easy: mydata[mydata$verb=="skip","verbtype"]="B"

We can check the result by typing the name of the dataframe: mydata

which shows:

1 2 3 4 5 6

verb run run jog run skip jog

tense person figurativity verbtype past 1 literal A past 1 metaphor A future 2 metaphor A past 2 literal A past 2 literal B future 1 literal A

Learning to use the square brackets notation is very helpful when working with R. It is a flexible way of manipulating dataframes, or getting information out of a dataframe.

5.5

Creating a subset of the dataframe

It happens frequently that certain cases need to be excluded from an analysis. These may be cases containing missing values, outliers, or cases with incorrect values. In

354 Joost van de Weijer and Dylan Glynn

R, there are several ways of creating a subset of a dataframe. Here we present one of them, namely using the subset() command. Suppose, by way of illustration, that we would like to exclude all cases for the verb to skip from mydata. We could establish this by telling R subset(mydata,mydata$verb!="skip")

where the operator != means is not equal to. Note, that the quotes around the word "skip" are obligatory and that they must be straight quotes (not ‘curly’). It sometimes happens, when code is copied and pasted into R from a text source that the quotes are curled and not straight. In this case, R will not recognise the command. If, on the other hand, we would like to restrict the dataset to the verb skip only, then we would write: subset(mydata,mydata$verb=="skip")

In this second example of the subset() command, pay attention to the double == sign. This is also obligatory, or the command will not work.

5.6

Merging dataframes

Two dataframes can be merged in two ways, either the second dataframe is appended below the first one, or it is added next to it. In the first merge, we add new cases to the first dataframe; in the second we add new variables. Merging two dataframes is easy, as long as the two dataframes match. If we append one dataframe to the other one, both dataframes need to have the same number of columns, and the column names need to be identical. The command for appending one dataframe to another one is rbind() (‘row bind’): rbind(dataframe1,dataframe2)

If we want to add the second dataframe to the right of the first one, and the two dataframes have the same number of rows, we can use the cbind() command (‘column bind’): cbind(dataframe1,dataframe2)

If two dataframes do not match completely, the commands rbind() and cbind() produce errors. An alternative, for partly matched dataframes, is the command merge(). This command allows one to specify which rows or columns in the first dataframe are to be matched with those in the second.

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5.7

Reordering the levels of a factor

In a categorical variable, there are different features or types that makes up the variable. For example, in the variable verb, we have three types run, skip, and jog. These are referred to as levels and may be shown using the command levels(). To display the levels of the variable verb, for instance, type: levels(mydata$verb)

The output shows the three verbs, which, by default, have been ordered alphabetically, i.e., jog, run and skip. This same order would also be applied when the verbs were to be displayed in a graph or a table, or when choosing one of the verbs as a reference to which the others are being compared. In these cases, the default order may need to be changed into something else. One way of establishing this is by adding an option to the factor() command. Suppose, for instance, that the three verbs were to be reordered as skip, jog and run instead, we could write: mydata$verb=factor(mydata$verb, levels =c("skip","jog", "run"))

The effect of this command is that the verbs will now be displayed in the specified order. Re-ordering the levels is especially important in regression analysis where the first level serves as the reference level to the others (see Speelman, this volume 487– 533). If only the reference level needs to be set without affecting the order of the levels, there is a second and simpler alternative, namely the relevel() command. If, for instance, we would like to keep the original alphabetical order, but make the verb run the reference level of the three, then we could write: mydata$verb = relevel(mydata$verb,ref="run")

5.8

Counting frequencies

The most basic command for obtaining frequency information from a dataframe was mentioned above. The command summary() is the first port of call for examining frequencies in a dataframe: summary(mydata)

This command tells R to display a summary of the frequencies for each level of each variable in the dataframe. However, it can only list the frequencies of up to 7 levels. This means that if a variable has many different tags, features or levels, we need to

356 Joost van de Weijer and Dylan Glynn

look specifically at the variable itself. For this, we use the table () command. When applied to the variable verb in mydata, this will be: table(mydata$verb)

This command tells R to list all the levels in the variable verb and their frequencies.

6. Converting data formats We have seen that there are two data formats, the dataframe and the cross-tabulation. The data file shown in Table 1 is an example of a flat or raw dataframe. Every row represents a single case. Often this is the format of a data file that is imported into R. It shows the data as they were collected by the researcher. However, we often want to display the frequency of occurrences in a flat dataframe, in which case we need to convert it to a contingency table or cross-tabulation. Moreover, this numerical format is needed for certain common statistical techniques, such as chi-square tests, cluster analysis, or correspondence analysis.

6.1

Converting a raw dataframe into a two-way contingency table

The table() command can be applied to two columns in a flat dataframe, resulting in a two-dimensional contingency table. The contingency table expresses the relation between the two variables, that is, how often the levels of the first variable co-occur with the levels of the second variable. If we were merely looking at the variables verb and tense (the first two columns in Table 1), then the following would create a contingency table: xtab = table(mydata$verb,mydata$tense)

which displays the following output: xtab future past jog 2 0 run 0 3 skip 0 1

However, this kind of command is of limited use with complex dataframes since it is for two-way contingency tables. In order to summarise a more complex dataframe, we need to concatenate or ‘stack’ the columns. In other words, we make a string of two-way contingency tables, all relative to the same variable and put them together in a row.

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Table 4. ╇ Data from Table 1 converted to a stacked contingency table verb

future

past

1stPrs

2ndPrs

literal

metaphor

jog run skip

2 0 0

0 3 1

1 2 0

1 1 1

1 2 1

1 1 0

6.2 Creating a stacked contingency table The data in mydata are organised in more than two columns. That means that, in principle, multiple two-way contingency tables can be constructed, displaying the relations between the variable in the first column and each of the subsequent variables. These contingency tables can be collected in one larger table with the first variable in the first column and the other variables in the columns to the right. In this case, we say that the contingency tables have been stacked next to each other. This is how Table 2 was created. For explanatory purposes, it is represented here as a stacked contingency Table 4. In R, one can create a stacked contingency table from a flat dataframe with the cbind() command that we also used earlier for combining dataframes. For instance, cbind(table(mydata$verb,mydata$tense), table(mydata$verb,mydata$person))

combines the two contingency tables of verb by tense and verb by person. The result looks like this: future past 1 2 jog 2 0 1 1 run 0 3 2 1 skip 0 1 0 1

In this way, all combinations of columns can be stacked next to each other, yielding the results displayed in Table 2. In the appendix, we provide a script that does this automatically for an entire dataframe, and which also labels the columns with appropriate names. The script is called tablebind. If one wants to use this script, copy it into a text file on the computer and save it in the working directory as tablebind.R. In R, give the command: source("tablebind.R")

This command makes tablebind() available as a new R-command, which takes the flat dataframe as its argument. In order to run it, type: tablebind(mydata)

358 Joost van de Weijer and Dylan Glynn

This command yields the output displayed in Table 2. Note that the first column in the dataframe is the one upon which the cross-tabulation will be calculated. If one wants to generate a contingency table that calculates figurativity, for example, then the order of the columns in the original dataframe will have to be changed accordingly. Section 7 explains in more detail how to run scripts like this and offer other options for storing them.

7. Making charts In R, it is possible to make almost any type of chart, and adjust the layout to the smallest detail. The variety of possibilities is too large to describe in this introduction. Here we provide just a few examples. The generic command for making a chart in R is plot(). When this command is applied to two continuous variables, we get a scatter plot. When applied to a categorical variable, we get a bar chart. If we apply this command to the variable verb in mydata, for instance, we get a chart that shows the frequencies of the verbs in the dataframe. plot(mydata$verb)

The chart opens in a new window, called the Quartz-window in MacOSX (Figure 1). Sometimes, plots can be hidden behind the console. The window menu will bring the plot to the front. There are several ways in which the layout of a chart can be changed. The first is to set the overall graphical parameters of the chart with the command par(). The command par()

gives an overview of all the parameters and their settings. The background colour of a graph, for instance, is abbreviated as bg. To see the current setting for this parameter, type: par("bg")

which gives the default colour of the graph background. Each of these parameters can be modified. Changing the background colour to, say, light grey, is established by: par(bg="lightgrey")

Modifications in the graphical parameters stay in effect for as long as the Quartz window is open. Once this window has been closed, the old settings are restored in a new window.

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0.0

0.5

1.0

1.5

2.0

2.5

3.0



Jog

Run

Skip

Figure 1.╇ Barplot using plot()

The second way of adjusting the chart layout is to specify additional options in the plot command. These options make it possible, among other things, to change the scales of the axes, change the plotting symbols, add labels, and add a title. The following example expands the limits of the Y-axis scale in the bar chart from Figure 1 from 0 to 5, adds the label ‘Verb’ to the X-axis, adds the label ‘Frequency’ to the Y-axis, and adds the title ‘Barchart Example’: plot(mydata$verb, ylim=c(0,5), xlab="Verb", ylab="Frequency", main="Barchart Example")

Note that the command has been written out on several lines. Finally, extra elements (legend, arrows, stars, text, lines) can be added separately. Once the graph is finished, it can be saved as a file. In MacOSX, one simply saves the file by choosing the menu “File” and then the option “Save”. The file is saved as a .pdf by default, giving optimal quality. Many applications, such as Preview or Adobe Acrobat have export options, which allow the file to then be saved under any format and at resolutions defined by the user. Under Windows, there is a list of options such as .pdf, .png, .jpg etc., under which the image file can be saved. Alternatively, the file can be written to a file directly from the Console window. The following three commands show an example of saving the bar chart as a .pdf-file: pdf("barchart.pdf") plot(mydata$verb) dev.off()

360 Joost van de Weijer and Dylan Glynn

The same procedure can be followed for .jpg, .png and other file types. Vector formats such as .pdf offer the best quality, but certain versions of MS Word do not accept .pdf images or automatically convert them to poor quality bitmap images. In which case, saving the image as a high quality .png file is the best option. For .png, a resolution of at least 600 dpi is recommended, but more is better. R possesses a rich inventory of possibilities for visualising results. For any command, if one types a ? before the command and enters this, a screen will appear with a help file. This will give the arguments that the command accepts, as well as an example of its use and hyperlinks to other related commands. Experiment by typing the command: ?plot

8. Working with scripts More often than not, an analysis consists of a series of commands. The first command could read in the data, for example, the second command calculates some descriptive statistics, and the third command makes a plot of the results. In that case, it is a good idea to save them in a so-called script file. In order to make a script, select File > New Document from the R menu. A new window will open in which one can add commands, exactly as they are typed in the console window. An example is shown below: mydata=read.table("datafile.txt") str(mydata) summary(mydata)

Commands can be run directly from the script window. Click once on the command that one wishes to run, then type command-Enter (Macintosh) or Control-r (Windows). The command and its output are then automatically displayed in the Console window. There are several advantages of working with scripts. One advantage is that one builds up a collection of scripts with commands that are often used. A second advantage is that scripts can contain personal comments. Comments can be anything from the date that the script was created, to the purpose of the script or the explanation of a complex command. The following is an example of a very short script, which includes the example command that we saw above, with a comment added giving information on the date the script was created: # Example R-script, created December 2011 mydata=read.table("datafile.txt")

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The first line starting with the hash-sign (“#”) is the comment. The second line is the command. Comments have no effect if run, they are there only for additional information or explanation and are ignored by R. A third advantage of working with scripts is that script files allow one to write very long commands on multiple lines. Commands to make plots, typically, become very long. Writing them on separate lines (as was shown above in Section 6) usually makes the structure of the command more transparent, and makes it easier, if there were something wrong with the command, to spot the error. Finally, R offers the possibility of syntax colouring, which also can help with seeing the structure in R commands. Syntax colouring means that different parts of the script are shown in different colours. A specific colour is reserved for a comment, another colour for a command keyword, a third colour for numbers, and so on. For these reasons, script files can be a great help in learning to work with R. Script files are normally saved on the computer with the extension .R.

9. Extending functionality with packages When R is installed for the first time it contains many basic functions for doing analyses and making plots. These base functions can be complemented with other functions that are geared towards more special-purpose analyses, such as the ones described in this book. Many so-called packages exist that contain functions used within a specific discipline, or for producing specific types of plots, or doing specific types of analysis. An incredibly rich collection of packages for performing all kinds of statistical analyses exists, and this collection is constantly being improved upon and added to. The packages are small and download quickly. To use a package, it must first be installed, that is, it must be downloaded from the R-website and saved to the computer. One way of installing a package is with the install.packages() command. The following example shows how to install the package called ca, for doing correspondence analysis described in Glynn (this volume): install.packages("ca")

This will firstly produce a prompt asking the user to choose a server (CRAN mirror) and a list of different options will appear. Once a server has been selected, the package can be installed. Another way to install packages is to the use the menu options. Under MacOSX, it will be found under the menu “Packages & Data > Package Installer” and under Windows “Packages > Install packages(s)”. Under MacOSX, choose the server and then simply type the first letters of the name of the package and it should appear. Then

362 Joost van de Weijer and Dylan Glynn

select “install”. It is recommended that the option in the radio button “install dependencies” be checked. Under Windows, the procedure is the same except that one must scroll through a long list to locate the desired package but install dependencies is set to default and does not be worried about. An extremely common point of confusion for new users is the difference between installing and loading packages / libraries. The packages contain the libraries that R needs to perform its tasks. One only needs to install a package once on a computer, but the library associated with it, must be loaded each time R is booted. Loading a package can be done with the library() command: library(ca)

Once loaded, a package is available until R is quit. Remember that it must be re-loaded with the library() command each time. Error messages that result from unloaded packages can be one of the most frustrating experiences for novice users. A good way of preventing this from happening is to add the library() command to the R-script.

10. Going further This short introduction is designed to help new users get started with R. There are many things to discover in R, and it will probably take some time to get a good grasp of the kinds of commands, packages and graphs that are useful for the kind of analysis for which one wants to use R. To conclude, we offer three pieces of advice that we found helpful on the way of becoming experienced R users. First, as mentioned above in Section 7, there is a built-in help function that shows information about the syntax of a command, some examples, and often links to other related commands. A call for help on a command is obtained with help() or with ?(), placing the command in parentheses. Second, the Internet is a good place to search for help. There are numerous sites with blogs, tutorials, and user fora. Here one can find R code, pose questions, and see graphs. For the less experienced users, we can recommend the site Quick-R, which contains many clear examples. Furthermore, the R-website also offers a manual. Finally, the number of books on statistics using R within many different disciplines grows steadily. Books for linguistic analysis are Baayen (2008), Dalgaard (2008), Johnson (2008) and Gries (2009, 2012). Focusing on graphics, Keen (2010) and Mittal (2011) are accessible to beginners and are relatively complete. Other introductory books include Crawley (2007), Everitt & Hothorn (2009), Maindonald & Braun (2010) and Adler (2010).



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References Adler, J. (2010). R in a nutshell: A desktop quick reference. Sebastopol: O’Reilly Media. Baayen, H. (2008). Analyzing linguistic data: A practical introduction to statistics using R. Cambridge: Cambridge University Press. DOI: 10.1017/CBO9780511801686 Crawley, M. (2007). The R book. Chichester: John Wiley. DOI: 10.1002/9780470515075 Dalgaard, P. (2008). Introductory statistics with R (2nd ed.). Dordrecht: Srpinger. DOI: 10.1007/978-0-387-79054-1 Everitt, B. S., & Hothorn, I. (2009). A handbook of statistical analyses using R (2nd ed.). Boca Raton: Taylor & Francis. Gries, St. Th. (2009). Quantitative corpus linguistics with R: A practical introduction. London: Routeledge. DOI: 10.1515/9783110216042 Gries, St. Th. (2012). Statistics for linguistics with R: A practical introduction. Berlin & New York: Mouton de Gruyter. Keen, K. (2010). Graphics for statistics and data analysis with R. Boca Raton: CRC Press. Johnson, K. (2008). Quantitative methods in linguistics. Oxford: Blackwell. Maindonald, J., & Braun, J. (2010). Data analysis and graphics using R (3rd ed.). Cambridge: Cambridge University Press. Mittal, H. V. (2011). R graphs cookbook. Birmingham: Packt.

Appendix: The tablebind-script This script can be copied or carefully entered into R and saved as a function, explained in Section 7. The script and the data file can be downloaded from http://dx.doi.org/10.1075/hcp.43. 13wei.additional. tablebind=function(df.flat) { if(ncol(df.flat)<3) return("Dataframe needs at least three columns.") for(i in 1:ncol(df.flat)) df.flat[,i]=factor(df.flat[,i]) df.stacked.ncol=0 for(i in 2:ncol(df.flat)) df.stacked.ncol=df.stacked.ncol+length(levels(df.flat[,i])) k=1 df.stacked.colnames=rep("X",df.stacked.ncol) for(i in 2:ncol(df.flat)) for(j in 1:length(levels(df.flat[,i]))) {df.stacked.colnames[k]= paste(colnames(df.flat[i]), levels(df.flat[,i])[j],sep=".") k=k+1 }

364 Joost van de Weijer and Dylan Glynn

df.stacked=table(df.flat[,1],df.flat[,2], exclude=c(NA),useNA="no") for(i in 3:ncol(df.flat)) df.stacked=cbind(df.stacked,table(df.flat[,1],df.flat[,i], exclude=c(NA),useNA="no")) df.stacked=data.frame(df.stacked) colnames(df.stacked)=df.stacked.colnames return(df.stacked) }

Frequency tables Tests, effect sizes, and explorations Stefan Th. Gries

University of California, Santa Barbara

This chapter provides an overview of statistical tests to analyze frequency data. Specifically, it discusses the use, logic, and interpretation of chi-squared tests of two-dimensional frequency tables as well as the computation of effect sizes for such tables, followed by several extensions and follow-up procedures that are not usually discussed (such as the analysis of sub-tables of tables and the Marascuilo procedure). In addition, there is a brief discussion of how Poisson/ count regression can be used to analyze frequency data with more than two dimensions. Keywords: chi-squared test, frequency data, Marascuilo procedure, Poisson regression

1. Introduction 1.1

Discrete vs. continuous data

Usage-based linguistics is essentially a distributional science in the sense that linguists explore the distribution of linguistic elements at every level of linguistic analysis: phonology, morphology, syntax, semantics, pragmatics and text linguistics etc. Corpus linguistics is no exception to this. More specifically, corpus linguists explore: – the frequencies of occurrence of linguistic elements in corpora, for example, frequency lists; – the dispersion of linguistic elements in corpora as in, for example, measures of dispersion; – the frequencies of co-occurrence of linguistic elements in corpora as in, for example, collocation, collocational frameworks, n-grams, colligations/collostructions etc.

366 Stefan Th. Gries

Very often, the data we study as linguists are discrete in nature. That is, the linguistic elements we study come in different categories and, trivially, if two elements are labeled the same, they belong to the same category, and if they are labeled differently, they belong to different categories. In statistical approaches, this kind of scenario is usually described with the terminology of variables (or factors) and their levels. For example, when direct objects are studied, it may be interesting to describe them in terms of which part of speech the direct object’s head is. In other terminology, each direct object studied is then described with regard to the variable Part of Speech by assigning a particular variable level to it; depending on what the direct objects look like, the following levels are conceivable: Part of Speech: lexical noun, Part of Speech: pronoun, Part of Speech: semipronoun, (such as matters or things), etc. Trivially, if direct objects are categorized this way, then a direct object whose head is categorized as Part of Speech: pronoun is, for the purposes of this analysis, identical to another one whose head is categorized as Part of Speech: pronoun and different from one whose head is categorized as Part of Speech: lexical noun. On other occasions, the observed variables are actually not discrete, but continuous, but for the purposes of an analysis they may be grouped into two or more categories such as: – when the lengths of subjects falling between 1 and 30 syllables, for example, are classified as falling into the categories Length: short (such as shorter than the median length) and Length: long (i.e. longer than the median length); – when the frequencies of closed-class words falling between 1 and 100,000, for example, are classified into the categories Frequency: low (such as between 1 and 50 occurrences), Frequency: intermediate (such as between 51 and 1,000 occurrences), and Frequency: high (such as between 1,001 and 100,000 occurrences). For the kinds of statistical methods to be discussed below, it does not really matter whether the variables involved in a particular study are genuinely discrete or categorical in nature or have just been converted to discrete variables: the methods as well as their results and potential implications are the same. The analysis of multidimensional frequency tables – i.e., tables reporting observed co-occurrence frequencies of three or more features with regard to which elements have been classified – has a lot to offer to linguists in general and cognitive linguists in particular. For example, frequency effects play an important role in most flavors of Cognitive Linguistics and/or Construction Grammar: – absolute token frequencies and conditional token probabilities are correlated with (degree of) cognitive entrenchment and unit status (cf. Schmid 2000), age and speed of the acquisition of constructions (cf. Brooks and Tomasello 1999 or



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Goldberg, Casenhiser, and Sethuraman 2004), and phonological reduction (cf. Bybee and Scheibman 1999); – type frequencies are correlated with degrees of productivity and grammaticalization (cf. Bybee 1985); – conditional probabilities as they can be derived from corpus frequencies are correlated with processing/parsing strategies (cf. Saffran, Aislin, and Newport 1996 or Saffran and Wilson 2003); etc. But multidimensional frequency tables of course also arise in studies whose target is not frequency effects per se but where just the interrelations of several variables is studied on the basis of corpus or experimental data. The general idea in the analysis of two- or more-dimensional frequency tables is to determine whether the frequencies observed in cells of the table are distributed in a way that is significantly different from a random distribution and, if that is the case, what is (most) responsible for the significant difference and what is not. The entities that are included in an analysis because they are potentially responsible for significant differences will be called predictors, and I use predictors here to refer to three different things: – levels of variables; – individual variables; – interactions of n variables. The first two of these three different kinds of predictors are probably obvious from what has been said so far, but the third may not be. An interaction of n variables is defined as a non-additive, or unpredictable, joint effect of the n variables (on a dependent variable). Consider a case where the referents subject and object NPs have been coded with regard to a variable Clause (whether they are subjects or objects in a main or a subordinate clause) and their Givenness in discourse (on a scale from 0 to 10). Let us assume: – referents of subjects are more given than referents of objects; – referents of subjects and objects in main clauses are more given than referents of subjects and objects in subordinate clauses. From this, one would expect the referents of subject NPs in main clauses to be most given because they combine the two features – ‘given’ and ‘being in a main clause’ that co-occur with high values of Givenness. If they turn out to be least given, however, then this would be a two-way interaction between the variables GramRelation (with the levels subject and object) and Clause (with the levels main and subordinate). Before we turn to the actual analysis of frequencies of discrete data, I first need to make a few general remarks that apply to virtually all evaluations of frequency tables, in fact to most statistical methods in general.

368 Stefan Th. Gries

1.2

Methodological preliminaries

The most central methodological issue that needs to be discussed briefly is how one of the most fundamental principles of scientific reasoning bears upon statistical analyses of frequency data. This most fundamental principle is entia non multiplicanda praeter necessitatem, which is known as Occam’s razor, or sometimes also as the principle of parsimony. It prohibits the inclusion of unnecessary explanatory notions into an analysis or, from the reverse perspective, it requires the analyst to show for each explanatory notion he wants to include that it is in fact necessary to include it. For statistical analyses of frequency data, this means that a researcher (i) tries to build a model of the observed data, i.e. a quantitative representation of the potentially relevant relations in the data that contains all predictors under consideration, and then (ii) must successively determine whether the predictors currently included in the model may in fact be included in the model or whether they have to be eliminated from consideration because their influence is too small to be statistically reliable/significant or conceptually noteworthy/substantial. This means that, especially in the area of multifactorial studies, the first statistical analysis is hardly ever the last because once a first statistical model has been built, Occam’s razor dictates it be tested for parsimony; in the domain of regression modeling, this process of slimming down predictors is often referred to as model selection. This principle is usually recognized in multifactorial studies (to varying degrees, though), where many researchers now routinely go through a model selection process in which in a stepwise fashion predictors are excluded from consideration until a model consists only of predictors that are significant themselves or that figure in higher-order interactions that are significant. However, for both mono- and multifactorial applications, this principle is not as often recognized for predictors that are neither interactions of variables or variables but variable levels. The above definition of predictors requires that the inclusion of different variable levels should ideally be scrutinized for whether variable levels must be kept apart just as the inclusions of separate variables and interactions should be. Note, though, that a conflation of variable levels must make sense conceptually: it is not useful to create a new combination of variable levels that looks nicer statistically but is conceptually senseless (cf. below for an example) – modeling is usually only a means to an end, not an end in itself. The principle of parsimony is therefore a very important methodological guideline and will surface in different forms below.

2. How to analyze frequency tables This section constitutes the main part of this chapter. In Section 2.1, I discuss the simpler case of two-dimensional tables, whereas in Section 2.2, I explain the more

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complex case of multidimensional tables. The discussion will be based on the open source software R, which can be downloaded from .

2.1

Two-dimensional tables

2.1.1 2-by-2 tables The simplest case of two-dimensional tables are 2-by-2 tables, in which one nominal or categorical variable is cross-tabulated with another nominal or categorical variable. As an example, let us consider the question of whether the disfluencies uh and uhm are differently frequent directly before nouns and verbs. That is, one variable is Disfluency, with the levels uh and uhm, and the other variable is Part of speech of the following word, with the levels noun vs. verb. The analysis of such tables is very straightforward. First, the data must be entered into a matrix in R. To that end, the function matrix can be used, which requires (i) the observed frequencies in a column-wise fashion (c(30, 50, 70, 20)) and (ii) the number of columns the table has (ncol=2): x<-matrix(c(30, 50, 70, 20), ncol=2)

While this creates the matrix of the frequencies, it is useful to add row and column labels. The function list takes two vectors, first the row names, and second, the column names: attr(x, “dimnames”)<-list(Disfluency=c(“uh”, “uhm”), POS=c(“Noun”, “Verb”))

To see whether the data entry has been successful, the data plus the row and column totals can then be inspected using the function addmargins: addmargins(x) POS Disfluency Noun Verb Sum uh 30 70 100 uhm 50 20 70 Sum 80 90 170

Table 1.╇ Fictitious data on the correlation of Disfluency and Part of speech 1 uh uhm Totals

Noun

Verb

Totals

30 50 80

70 20 90

100 â•⁄70 170

370 Stefan Th. Gries

Such matrices are typically evaluated using a so-called chi-squared test (exceptions to this will be discussed below). This test requires that all observations are independent of each other and that 80+% of the expected frequencies are larger than 5. If this is the case, one can use the function chisq.test, which in the standard form to be discussed here requires the matrix to be tested (x) and an argument to be explained below (correct=FALSE); the result of the test should be saved into a new data structure, e.g., x.test: x.test<-chisq.test(x, correct=FALSE)

Nothing is returned, but the data structure x.test now contains all the results. Three things must now be done. First, one should inspect the frequencies that would have been expected by chance – i.e. when there is no correlation by the kind of disfluency and the part of speech of the following word – by calling the part of the test results that contain the expected frequencies: x.test$exp POS Disfluency Noun Verb uh 47.05882 52.94118 uhm 32.94118 37.05882

(One can also compute each expected frequency of a cell manually by dividing the product of the cell’s row and column total by the total of the table, e.g., 100·80÷170 = 47.05882, etc.). Obviously, the expected frequencies are all greater than 5. Therefore, the next step is to determine whether the observed result from Table 1 is significant – i.e. different enough from the expected result shown above – by calling the overall result: x.test Pearson’s Chi-squared test data: x X-squared = 28.3671, df = 1, p-value = 1.004e-07

In this example, there is a highly significant correlation between the kind of disfluency and the part of speech that follows: p is much smaller than the critical value of p = 0.05. However, the fact that there is an overall significant result does not reveal which of the four cells are most responsible for this effect and how. To identify these cells, one should inspect the so-called Pearson residuals, which are computed as in (1). (1) Pearson residuals =

observed – expected √expected

Frequency tables 371



x.test$res POS Disfluency Noun Verb uh -2.486729 2.344511 uhm 2.972210 -2.802227

First, if the Pearson residual in a cell is positive/negative, then the observed frequency in that cell is greater/less than the expected frequency in that cell. Second, the more the Pearson residual deviates from 0, the stronger that effect. In this case, therefore, the strongest effect is the preference of uhm before nouns, followed by the dispreference of uhm before verbs. The final step is to compute an effect size. An effect size quantifies the strength of the observed correlation independently of the sample size. In the case of 2-by-2 tables, one standard effect size is Φ (phi), which theoretically ranges from 0 (‘no effect’) to 1 (‘perfect correlation’) and is computed as shown in (2). In this case, the correlation is intermediately strong. (2) Φ =

χ2 n

sqrt(x.test$stat/sum(x)) X-squared 0.4084912

The final question to be addressed is what to do when too many expected frequencies are too small. While sparse data are always problematic in the sense that one does not want to base potentially far-reaching generalizations on small data sets, there is a test that can be used to test such tables for significance, too, which is called the Fisher-Â� Yates exact test. The R function that computes this test is fisher.test and its most important argument is just the matrix containing the data: fisher.test(x) Fisher’s Exact Test for Count Data data: x p-value = 9.66e-08 alternative hypothesis: true odds ratio is not equal to 1 95 percent confidence interval: 0.08256479 0.35287555 sample estimates: odds ratio 0.1734529

In this case, where the sample size and the expected frequencies are unproblematic anyway, the p-value provides the same kind of result: the distribution of the two

372 Stefan Th. Gries

disfluencies before the two parts of speech is most likely not random, but there is more. The output also provides another kind of effect size for 2-by-2 tables, the socalled odds ratio. The odds ratio is one of several measures that expresses how much the distribution of a binary variable changes in response to another binary variable. In this case, the odds ratio quantifies the ratio of the frequency of uh before nouns (30/50) to the frequency of uh before verbs (70/20): (30/70)/(50/20) [1] 0.1714286

The result is similar, but not identical, to the one provided by R, which uses a more refined estimation algorithm (and also provides a confidence interval that is not addressed here (cf. Gries 2013:â•›Section 3.1.5 for explanation and exemplification)). The logic, however, is the same: the more the odds ratio differs from 1, the stronger the effect. Sometimes, a scholar might not report odds ratios of 0.5 and 1.5 but logged odds ratios as shown below: log(0.5) [1] -0.6931472 log(1.5) [1] 0.4054651

One reason for this is that odds ratios are often difficult to compare to each other: A beginner might look at two odds ratios of 0.5 and 1.5 and – erroneously – think they reflect equally strong effects because they are equally far away from 1. This is false as the logs of the odds ratios show: the more a logged odds ratio deviates from 0, the stronger the effect, which is why an odds ratio of 0.5 reflects a stronger effect than an odds ratio of 1.5. (In addition, logged odds ratios are also important in the context of logistic regression, a topic I cannot discuss here; cf. Gries 2013:â•›203–301 for detailed explanation.)

2.1.2 Larger two-dimensional r-by-c tables Thankfully, the logic of 2-by-2 tables also applies to two-dimensional tables with more than two rows (i.e. r > 2) and/or two more columns (i.e. c > 2). Consider Table 2 for an extended version of the above disfluencies example. Table 2.╇ Fictitious data on the correlation of Disfluency and Part of speech 2 uh uhm silence Totals

Conjunction

Noun

Verb

Totals

â•⁄30 â•⁄50 â•⁄20 100

70 20 â•⁄5 95

â•⁄90 â•⁄40 â•⁄10 140

190 110 â•⁄35 335

Frequency tables 373



The data are entered in the same way as before: x<-matrix(c(30, 50, 20, 70, 20, 5, 90, 40, 10), ncol=3) attr(x, “dimnames”)<-list(Disfluency=c(“uh”, “uhm”, “silence”), POS=c(“Noun”, “Verb”, “Conjunction”))

And the requirements of the test (in terms of the proportion of expected frequencies being not smaller than 5) analysis is also no different: x.test<-chisq.test(x, correct=FALSE) x.test$exp POS Disfluency Noun Verb Conjunction uh 56.71642 53.880597 79.40299 uhm 32.83582 31.194030 45.97015 silence 10.44776 9.925373 14.62687 x.test Pearson’s Chi-squared test data: x X-squared = 45.2273, df = 4, p-value = 3.566e-09 x.test$res POS Disfluency Noun Verb Conjunction uh -3.547512 2.196002 1.1892280 uhm 2.995361 -2.004245 -0.8805362 silence 2.955245 -1.563384 -1.2097935

The expected frequencies are unproblematic: all of them are even larger than 9. Hence, the p-value of the chi-squared test can be taken seriously, which points to an association between the kind of disfluency and the part of speech of the following word. The nature of this association then becomes clear from the residuals: uh is dispreferred before nouns (negative residual of ≈–3.55) whereas uh is preferred before verbs (positive residual of ≈2.2) and before conjunctions (positive residual of ≈1.2). Two things remain to be done. First, one again needs to compute an effect size, which for r-by-c tables with r > 2 and/or c > 2 is called Cramer’s V. Its formula is shown in (3), where min(r, c) means ‘take the numbers of rows and columns and pick the smaller of the two’. (3) V =

χ2 n × (min(r, c) – 1)

The effect size is now smaller than before:

374 Stefan Th. Gries

sqrt(x.test$stat/(sum(x) * (min(dim(x))-1))) X-squared 0.2598142

Second, one should explore whether the data can, or in fact must, be simplified as a consequence of Occam’s razor, the principle that requires analysts to adopt the simplest possible model. In this case, for example, the observed data distinguish three parts of speech – nouns, conjunctions, and verbs – but the (signs of the) residuals reveal that verbs and conjunctions behave alike so maybe a two-way distinction – nouns vs. non-nouns – is sufficient. To test heuristically which distinction to adopt, the data are entered again, but this time the two levels of the part of speech that are suspected to behave the same are conflated: x.2<-matrix(c(30, 50, 20, 70+90, 20+40, 5+10), ncol=2) attr(x.2, “dimnames”)<-list(Disfluency=c(“uh”, “uhm”, “silence”), POS=c(“Noun”, “Not noun”)) addmargins(x.2) POS Disfluency Noun Not noun Sum uh 30 160 190 uhm 50 60 110 silence 20 15 35 Sum 100 235 335

Then, the analysis is repeated on the new merged data set: x.2.test<-chisq.test(x.2, correct=FALSE) x.2.test Pearson’s Chi-squared test data: x.2 X-squared = 43.1801, df = 2, p-value = 4.203e-10 x.2.test$res POS Disfluency Noun Not noun uh -3.547512 2.314141 uhm 2.995361 -1.953958 silence 2.955245 -1.927790 sqrt(x.2.test$stat/(sum(x.2) * (min(dim(x.2))-1))) X-squared 0.3590205

Frequency tables 375



The chi-square value has hardly changed and the effect size has even gone up considerably. Both of these facts suggest that the real distinction for the disfluencies in this corpus may not be between nouns, verbs, and conjunctions, but just between nouns and non-nouns, but this would have to be tested more rigorously (using, e.g., model comparisons).

2.1.3 Additional applications This section deals with two unfortunately less well-known, but nevertheless very useful methods in the analysis of different kinds of two-dimensional r-by-c columns.

Testing a subtable of a table

This section is concerned with the question of what to do when one has an r-by-c subtable, but wishes to evaluate an s-by-d table with s ≤ r and d ≤ c. As an example, I will use a study of the frequencies with which four emotion metaphors are distributed over four registers (cf. Lohmann 2009 for an example). Lohmann studied the degree to which certain supposedly very pervasive conceptual metaphors are attested in different genres. Consider Table 3 for a (fictitious) example of the kind of data such a study may yield (I will explain the bold-faced figures below.) If one entered the data … x<-matrix(c(8, 31, 44, 36, 5, 14, 25, 38, 4, 22, 17, 12, 8, 11, 16, 24), ncol=4) attr(x, “dimnames”)<-list(Register=c(“acad”, “spoken”, “fiction”, “news”), Metaphor=c(“Heated fluid”, “Light”, “NatForce”, “Other”))

and did a chi-squared test on this table, then one would find a significant result (with χ2 = 19.5151; df = 9; p = 0.02115). However, let us assume that one found these data in a study, but that one is also only interested in whether spoken conversation differed from fiction in the use of the metaphors Emotion is light and Emotion is a natural force, i.e., the bold-faced figures in Table 3. Contrary to what quite a few Table 3.╇ Fictitious distribution of emotion metaphors in different genres Metaphor Register

Emotion is a heated fluid in a container

Emotion is light

Emotion is a natural force

Other Totals

Academic writing Spoken conv. Fiction News Totals

â•⁄â•⁄8 â•⁄31 â•⁄44 â•⁄36 119

â•⁄5 14 25 38 82

â•⁄4 22 17 12 55

â•⁄8 11 16 24 59

â•⁄25 â•⁄78 102 110 315

376 Stefan Th. Gries

people seem to think, one cannot simply extract this table from the overall table – i.e., pretend one had done a study oneself with just the variable levels and frequencies one is interested in – and run a chi-squared test on it. Thus, the following (slightly shortened) code and result is wrong:

subtable<-matrix(c(14, 25, 22, 17), ncol=2) chisq.test(subtable, correct=FALSE) # WRONG! Pearson’s Chi-squared test data: matrix(c(14, 22, 25, 17), ncol = 2) X-squared = 3.3016, df = 1, p-value = 0.06921

This test is wrong because its chi-square value is based on the marginal totals of the subtable (e.g. 39 vs. 39 for Emotion is light, etc.), but does not take the overall observed frequencies of Emotion is light into consideration (e.g. 82 vs. 55, etc.). The correct test is, unfortunately, slightly more lengthy and involves the following steps (following Bortz, Lienert, and Boehnke 1990:â•›Section 5.4.4). First, one computes the chi-squared test that compares the observed row sums of the subtable (36 vs. 42) to the ones expected from the proportions of row sums of the whole table (78 vs. 102, i.e., 78/180 vs. 102/180): chisq.test(c(36, 42), p=c(78, 102)/180)[c(1,7)] $statistic X-squared 0.2526975 $expected [1] 33.8 44.2

Second, one computes the chi-squared test that compares the observed column sums of the subtable (39 vs. 39) to the ones expected from the proportions of column sums of the whole table (82 vs. 55, i.e. 82/137 vs. 55/137): chisq.test(c(39, 39), p=c(82, 55)/137)[c(1,7)] $statistic X-squared 3.151996 $expected [1] 46.68613 31.31387

Third, one computes the frequencies that would have been expected in the subtable if the cells were distributed proportional to the expected marginal totals according to the usual two-dimensional chi-square formula mentioned above, by dividing the product of the cell’s row and column total by the total of the table, as shown in Table 4.

Frequency tables 377



Table 4.╇ Expected frequencies (when the cells are proportional to the expected marginal totals) Spoken convers. Fiction Totals

Emotion is light

Emotion is a natural force

Totals

(33.8 × 46.69) / 78 ≈ 20.23 (44.2 × 46.69) / 78 ≈ 26.46 46.69

(33.8 × 31.31) / 78 ≈ 13.57 (44.2 × 31.31) / 78 ≈ 17.74 31.31

33.8 44.2 78

Emotion is a natural force

Totals

Table 5.╇ Contributions to chi-square Emotion is light Spoken convers. Fiction Totals

20.23)2

13.57)2

(14 – / 20.23 ≈ 1.92 (22 – / 13.57 ≈ 5.24 (25 – 26.46)2 / 26.46 ≈ 0.08 (17 – 17.74)2 / 17.74 ≈ 0.03 46.69 31.31

33.8 44.2 78

As the penultimate step, one computes each table cell’s contribution to the chisquare value by dividing the squared difference between the observed and the expected cell frequency by the expected frequency, as shown in Table 5. (By the way, these correspond to the squared Pearson residuals mentioned in (1).) In R, this can be done much more simply: exp.temp<-matrix(c(20.23, 26.46, 13.57, 17.74), ncol=2) sum(((subtable-exp.temp)^2)/exp.temp) [1] 7.266921

The final step is then, at last, to compute the difference of this last chi-square value and the sum of the other two. This difference is the required chi-square value and then provides the desired p-value: 7.266921-(0.2526975+3.151996) # chi-square [1] 3.862227 pchisq(3.862227, prod(dim(subtable)-1), lower.tail=F) # p-value [1] 0.04938474

This chi-square value corresponds – disregarding rounding errors – to what an R function for this method written by the author would provide, as the last row indicates: sub.table(x, 2:3, 2:3) # the data and the rows/columns for the sub-table […]

378 Stefan Th. Gries



$‘Chi-squared tests’

Chi-square Df p-value 7.2682190 3 0.06382273 0.2526975 1 0.61518204 3.1519956 1 0.07583417 3.8635259 1 0.04934652

Cells of subtable to whole table Rows (within sub-table) Columns (within sub-table) Contingency (within sub-table)

As is now obvious, the data in the subtable actually produce a significant result: the two kinds of metaphors are differently frequent in the two registers. Note again that the wrong approach from above – just applying a separate chi-squared test to the subtable – did not return a significant result, which should demonstrate how important it is to apply the correct methods.

The Marascuilo procedure

In order to determine how many different variable levels to retain in either a unidimensional vector of frequencies or percentages, one can use the so-called Marascuilo procedure. Since this procedure can be applied to a simple vector of frequencies or percentages, it can also be used for a 2-by-c table, where it tests which of the c variable levels of the column variable are better conflated. To explore this procedure, we consider the alternation of particle placement exemplified in (4). (4) a. He picked up the book. b. He picked the book up. Just like many other constituent order alternations in English, the choice of one order by a speaker is determined by many different factors and usually made unconsciously. One of the factors governing particle placement is the information status of the referent of the direct object (cf. Kruisinga and Erades 1953; Chen 1982; Gries 2003): on the whole, it seems as if new referents prefer to occur after the particle (i.e. as in (4a)) whereas given referents prefer to occur before the particle (i.e. as in (4b)). However, since given vs. new is only the most simplistic classification of information status, one may want to include at least one additional level such as Status: inferable, which characterizes referents which have not been mentioned before in the preceding discourse, but which a hearer can infer on the fly from linguistic or contextual knowledge. Consider Table 6 for an example data set. The first step in applying the Marascuilo procedure is as discussed above, i.e. enter the data and perform a chi-squared test for two-dimensional tables to determine whether there is a correlation between information status and the constituent order: x<-matrix(c(37, 13, 63, 37, 20, 40), ncol=3) attr(x, “dimnames”)<-list(“Constituent order”= c(“Verb-Object-Particle”, “Verb-Particle-Object”), “Information status”=c(“given”, “inferable”, “new”)) x.test<-chisq.test(x, correct=FALSE)

Frequency tables 379



Table 6.╇ Particle placement: Constituent order and Information status Verb-Object-Particle Verb-Particle-Object Totals

given

inferable

new

Totals

37 13 50

â•⁄63 â•⁄37 100

20 40 60

120 â•⁄90 210

x.test$exp Information status Constituent order given inferable new Verb-Object-Particle 28.57143 57.14286 34.28571 Verb-Particle-Object 21.42857 42.85714 25.71429 x.test Pearson’s Chi-squared test data: x X-squared = 21.0914, df = 2, p-value = 2.631e-05 x.test$res Information status Constituent order given inferable new Verb-Object-Particle 1.576841 0.7748272 -2.439750 Verb-Particle-Object -1.820780 -0.8946933 2.817181 sqrt(x.test$stat/(sum(x) * (min(dim(x))-1))) X-squared 0.3169151

The result is fairly obvious: there is a not particularly strong, but still highly significant, correlation or interaction between the two variables in the expected direction: given and new referents prefer to occur before and after the particle, respectively. In addition, inferable referents pattern more like given referents – they prefer to occur before the particle – but less strongly so. According to Occam’s razor, one should now test whether all three levels of Information status are required especially since in this case a conflation of Information status: given and Information status: inferable as a counterpart to Information status: new would make sense – whereas a conflation of Information status: given and Information status: new as a counterpart to Information status: inferable would not. The Marascuilo procedure requires three steps. First, one computes the percentages of the variable with two levels, in this case the column variable Constituent order: prop<-prop.table(x, 2) # the 2 means ‘column-wise’, 1 would mean ‘row-wise’

380 Stefan Th. Gries

prop Information status Constituent order given inferable new Verb-Object-Particle 0.74 0.63 0.3333333 Verb-Particle-Object 0.26 0.37 0.6666667

Second, one computes all pairwise differences between the percentages of one constituent order in the three information states: – 0.74 – 0.63 = 0.11 (given – inferable); – 0.74 – 0.333 = 0.407 (given – new); and – 0.63 – 0.333 = 0.297 (inferable – new). Third, one compares each of the three differences to a threshold value that must be computed with the rather complicated formula shown in (5) (for a significance value of p = 0.05): (5)

χ2

p = 0.05; df = levels – 1

perc1 × (1 – perc1)

×

Σâ•›column1

+

perc2 × (1 – perc2) Σâ•›column2

For the comparison (given – inferable), this translates into (6): (6)

5.9915 ×

0.74 × 0.26 50

+

0.63 × 0.37 100

= 0.1924091

Since the observed percentage difference of 0.11 is not larger than the critical percentage difference for p = 0.05 at df = 3 – 1 = 2 of approximately 0.19, the difference between the percentages of Information status: given and Information status: inferable is not significant. Again, this procedure is somewhat labor-intensive, but can be computed easily using R. The output of applying such a function (mar) to the matrix x returns, among other things, the following results for the pairwise comparisons: mar(x) […] $‘pairwise comparisons’ comparisons diffs crit.ranges decisions 1 given-inferable 0.1100000 0.1924091 ns 2 given-new 0.4066667 0.2127105 * 3 inferable-new 0.2966667 0.1901492 *

The results of the Marascuilo procedure at least suggest that one should conflate Information status: given and Information status: inferable into a new category Information status: non-new, evaluate that matrix, and report and interpret those results:

Frequency tables 381



x2<-matrix(c(100, 50, 20, 40), ncol=2) attr(x2, “dimnames”)<-list(“Constituent order”= c(“Verb-Object-Particle”, “Verb-Particle-Object”), “Information status”=c(“non-new”, “new”)) x2.test<-chisq.test(x2, correct=FALSE) x2.test$exp Information status Constituent order non-new new Verb-Object-Particle 85.71429 34.28571 Verb-Particle-Object 64.28571 25.71429 x2.test Pearson’s Chi-squared test data: x2 X-squared = 19.4444, df = 1, p-value = 1.036e-05 x2.test$res Information status Constituent order non-new new Verb-Object-Particle 1.543033 -2.439750 Verb-Particle-Object -1.781742 2.817181 sqrt(x2.test$stat/(sum(x2) * (min(dim(x2))-1))) X-squared 0.3042903

Both the chi-square value and the effect size hardly change as a result of the elimination of one variable level, and given this loss of one df, the p-value is even much smaller than before. (Note that other statistical approaches may come to different conclusions, which does not, however, obviate the need for some kind of test of whether the three levels of Information status need to be kept separate and for an explicit discussion of which test was used.) This is a clear case in which Occam’s razor not only makes the results better, but in which it also may lead to new findings: if the researcher had not already expected that given and inferable were very similar – unless the researcher wanted to test whether they are the same, he or she should have just coded one non-new information status – then Occam’s razor has helped to reveal this patterning.

2.2

Multidimensional tables

Two-dimensional frequency tables have probably the most widespread use of all frequency tables. However, most linguistic choices are not determined by only a single variable, and while the analysis of multidimensional frequency tables is somewhat

382 Stefan Th. Gries

more complex, a growing number of linguists have realized that very often only a multifactorial study will reveal the most important generalizations and avoid erroneous interpretations arising from the omission of important predictor variables (cf. the well-known example of Simpson’s paradox; cf. Sheskin 2011:â•›718–720). Multidimensional frequency tables can be analyzed in many different ways, which often makes it difficult for the beginner to choose one method over another: loglinear models/Poisson regression, binary or multinomial logistic regression, (multiple) correspondence analysis, association rules, … are among the most frequent methods but I cannot discuss them all here. Binary logistic regression is a very widely used method but, as the name suggests, it is restricted to dependent variables with only two levels (cf. Gries 2013:â•›Section 5.3 for in-depth discussion as well as Baayen 2008:â•›Section  6.3.1; Johnson 2008:â•›Section 5.4; and Speelman, this volume). I will therefore discuss one example of a Poisson regression (which could also be investigated with a binary logistic regression). Let me begin, however, with the warning that this chapter cannot discuss all the tricky details of regression model selection so readers are advised to brush up their knowledge in this area and/or study additional materials (especially those readers who do not know linear regressions already); I find Crawley’s (2005, 2012) books most instructive, and Faraway (2006) also provides a good, though more technical, introduction. In this section, I will discuss an example from a recent corpus study published in the ICAME Journal (Hommerberg and Tottie 2007). Their study explores two complementation patterns of the verb try in British and American English: try to vs. try and. Their goal is “to show how native speakers of present-day British and American English actually use the two constructions”, and they use a data set from the Cobuild Direct Corpus, whose size and composition is summarized in Table 7. The variables Variety and Mode are self-explanatory; the variable Try refers to whether speakers/writers used try to or try and, and the variable Clause refers to whether the VP containing try is itself part of a to-clause (as in we’re going to try (to/ and) (Hommerberg and Tottie 2007:â•›56). I will assume that Table 7 is in R’s workspace as a data frame called x. The str command summarizes the structure of the table as follows: str(x) ‘data.frame’: 16 obs. of 5 variables: $ VARIETY: Factor w/ 2 levels “american”,“british”: 1 1 1 1 ... $ MODE : Factor w/ 2 levels “spoken”,“written”: 1 1 2 1 1 ... $ TRY : Factor w/ 2 levels “and”,“to”: 1 1 2 2 1 1 2 2 1 ...

Frequency tables 383



Table 7.╇ The data studied by Hommerberg and Tottie (2007) Variety

Mode

Try

Clause

Freq.

american american american american american american american american british british british british british british british british

spoken spoken spoken spoken written written written written spoken spoken spoken spoken written written written written

and and to to and and to to and and to to and and to to

other to other to other to other to other to other to other to other to

120 â•⁄90 381 174 â•⁄10 â•⁄26 219 167 503 706 150 133 â•⁄49 127 230 144

$ CLAUSE : Factor w/ 2 levels “other”,“to”: 1 2 1 2 1 2 1 2 ... $ FREQ : int 120 90 381 174 10 26 219 167 503 706 ...

Several things are needed for a Poisson regression. First, the relevant R function is glm, which is short for generalized linear model. Second, the function takes two main arguments, the first of which is a formula that specifies which dependent variable – the observed frequencies of occurrence – and which predictors – which independent variables and which of their interactions – to include. Formulae in R are written as “dependent variable ~ predictors/independent variables”, where n independent variables combined with asterisks mean ‘include the independent variables and their interactions’ while n independent variables combined with colons mean ‘include the interaction of these independent variables’. The second argument is family=poisson, which instructs R to compute a Poisson regression with a log-link and not a ‘normal’ linear regression with a Gaussian identity function. In essence, this ensures that the regression cannot predict negative values (which would not make sense since frequencies cannot be negative; cf. Crawley 2012:â•›Section 13.3 for discussion). Given the discussion of model selection, the first step of the actual analysis consists of fitting a maximal model in which all predictors are included. The following code computes such a model, stores it into a data structure m1, and summarizes this data structure (the output here is abbreviated and minimally altered).

384 Stefan Th. Gries

m1<-glm(FREQ ~ VARIETY*MODE*TRY*CLAUSE, family=poisson) summary(m1) […] Coefficients: Estimate Std.Error z value Pr(>|z|) (Intercept) 4.78749 0.09129 52.444 < 2e-16 *** VARIETYbrit 1.43310 0.10159 14.106 < 2e-16 *** MODEwrt -2.48491 0.32914 -7.550 4.36e-14 *** TRYto 1.15531 0.10468 11.037 < 2e-16 *** CLAUSEto -0.28768 0.13944 -2.063 0.03911 * VARIETYbrit:MODEwrt 0.15614 0.36157 0.432 0.66586 VARIETYbrit:TRYto -2.36526 0.14005 -16.889 < 2e-16 *** MODEwrt:TRYto 1.93118 0.33989 5.682 1.33e-08 *** VARIETYbrit:CLAUSEto 0.62671 0.15116 4.146 3.38e-05 *** MODEwrt:CLAUSEto 1.24319 0.39737 3.129 0.00176 ** TRYto:CLAUSEto -0.49606 0.16678 -2.974 0.00294 ** VARIETYbrit:MODEwrt:TRYto 0.82503 0.38592 2.138 0.03253 * VARIETYbrit:MODEwrt:CLAUSEto -0.62985 0.43542 -1.447 0.14803 VARIETYbrit:TRYto:CLAUSEto 0.03675 0.21309 0.172 0.86307 MODEwrt:TRYto:CLAUSEto -0.73053 0.42051 -1.737 0.08235 . VARIETYbrit:MODEwrt:TRYto:CLAUSEto -0.23079 0.48373 -0.477 0.63328 […] Null deviance: 2.1620e+03 on 15 degrees of freedom Residual deviance: -8.7486e-14 on 0 degrees of freedom […]

The main part of the output above is a table, which lists the included predictors, their coefficient estimates and their significance tests. The most relevant columns are the first (with the name of the predictor), the second headed Estimate, and the last with the p-value for the predictor. The row for the intercept shows 4.78749 as an estimate, the antilog of which is 120, the observed frequency of the combination of the alphabetically first factor levels: Variety: american Mode: spoken Try: and Clause: other.

Frequency tables 385



The estimates that R outputs then for the predictors reflect the difference between the listed predictor and a reference level. For individual variables, the reference level is the alphabetically first, unlisted level. For instance, the value of 1.43310 for Variety: british means that the model estimates that, compared to the reference level of Variety: american, Variety: british increases (positive sign) the estimated frequencies. For instance, the value of –2.48491 for Mode: written means that the model estimates that, compared to the reference level of Mode: spoken, Mode: written reduces (negative sign) the estimated frequencies (and more strongly so than Variety: british increases them). Another way to understand the meanings of the coefficients is to compute the predictions of the model, for example, for Variety: british Mode: written Try: to Clause: other, all one needs to do is to add up all coefficients whose predictors are part of this configuration and antilog the sum: exp(4.78749+1.43310-2.48491+1.15531+0.15614-2.36526+ 1.93118+0.82503) [1] 230.0002 # rounding difference only

This predicted frequency corresponds to the observed frequency because this is the maximal model that contains all predictors. According to Occam’s razor, insignificant predictors must now be weeded out. Crucially, the elimination of insignificant predictors always begins with the highest-order interactions and, as long as there are still insignificant predictors, proceeds to lower-order interactions and then to individual variables. Crucially, a predictor is not removed even if it is significant when it still participates in a higher-order interaction. In this case, there is only one four-way interaction – Variety: Mode: Try: Clause – and it is not significant. Thus, one now updates the first model by removing that interaction: m2<-update(m1, ~. -VARIETY:MODE:TRY:CLAUSE)

However, one must now first check whether this simplification of the model was justified. This is how it is done: anova(m1, m2, test=”LRT”) […] Resid. Df Resid. Dev Df Deviance P(>|Chi|) 1 0 0.00000 2 1 0.22492 -1 -0.22492 0.6353

R evaluates the difference between the two models, and because they do not differ from each significantly (p = 0.6353), Occam’s razor requires one to adopt the simpler one, m2. One can then inspect this simpler model (with summary(m2)) and it becomes obvious that the only three-way interaction that is not significant is Variety: Try: Clause. Hence:

386 Stefan Th. Gries

m3<-update(m2, ~. -VARIETY:TRY:CLAUSE) anova(m2, m3, test=”LRT”) […] Resid. Df Resid. Dev Df Deviance Pr(>Chi) 1 1 0.22492 2 2 0.22633 -1 -0.0014192 0.9699

When this new model m3 is inspected, it is clear that it cannot be simplified any further: each predictor is significant or participates in a significant interaction (Variety: Mode is not significant, but participates in Variety: Mode: Try, which is). summary(m3) […] Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) 4.79421 0.08228 58.268 < 2e-16 *** VARIETYbrit 1.42477 0.08915 15.981 < 2e-16 *** MODEwrt -2.59755 0.23561 -11.025 < 2e-16 *** TRYto 1.14646 0.09105 12.592 < 2e-16 *** CLAUSEto -0.30343 0.10550 -2.876 0.00403 ** VARIETYbrit:MODEwrt 0.29069 0.22849 1.272 0.20330 VARIETYbrit:TRYto -2.34943 0.10553 -22.263 < 2e-16 *** MODEwrt:TRYto 2.05052 0.23742 8.637 < 2e-16 *** VARIETYbrit:CLAUSEto 0.64521 0.10658 6.054 1.42e-09 *** MODEwrt:CLAUSEto 1.40279 0.21997 6.377 1.80e-10 *** TRYto:CLAUSEto -0.47355 0.10385 -4.560 5.11e-06 *** VARIETYbrit:MODEwrt:TRYto 0.67402 0.22825 2.953 0.00315 ** VARIETYbrit:MODEwrt:CLAUSEto -0.82045 0.17546 -4.676 2.92e-06 *** MODEwrt:TRYto:CLAUSEto -0.90750 0.20548 -4.417 1.00e-05 *** […] Null deviance: 2161.98713 on 15 degrees of freedom Residual deviance: 0.22633 on 2 degrees of freedom […]



Frequency tables 387

Often such data are summarized in the form of a table that, simplifying a bit, conveniently summarizes each independent variable’s significance in one p-value. This table, a so-called ANOVA table, can be created as follows (cf. Gries 2013:â•›266, 271, for explanation). library(car) options(contrasts=c(“contr.sum”, “contr.poly”)) Anova(m3, type=”III”, test=”LR”) # the results are not shown here options(contrasts=c(“contr.treatment”, “contr.poly”))

The table now combines predictors involving the same variables but different variable levels and confirms more succinctly what was already shown above: each predictor in m3 but Variety: Mode is significant. How are the results interpreted? They are interpreted as already hinted at above, on the basis of the coefficients. Since I cannot discuss all the findings in detail, some comments must suffice. The data show, trivially, compared to the reference combination of Variety: american Mode: spoken Try: and Clause: other, setting Variety to british increases the predicted counts (the coefficient for Variety: british is positive), compared to the reference combination of Variety: american Mode: spoken Try: and Clause: other, setting Mode to written decreases the predicted counts (the coefficient for Mode: written is negative), etc. More interesting, however, are the interactions that qualify these main effects. As just one example, consider the interaction Variety: british Try: to. This strong and highly significant interaction means that, while setting both Variety to british and Try to to increases the estimated counts (by the antilog of 1.42477 + 1.14646 ≈ 2.57123), their joint effect does not boost the counts accordingly, but decreases them by nearly the same amount (by the antilog of –2.34943); thus, compared to the predicted frequency for Variety: american Mode: spoken Try: and Clause: other, 120.81, the predicted frequency for Variety: british Mode: spoken Try: to Clause: other, is increased by 24.8%, the antilog of 2.57123 – 2.34943. But then there is also a significant interaction Variety: british Mode: written Try: to … It is clear that complex interactions like these and the degree to which they are significant or not can hardly be recognized by just eye-balling the data and are usually only comprehensible on the basis of well-designed graphs (e.g. bar plots of predicted frequencies). This concludes the discussion of this example here. Many issues of Poisson regressions could not be covered for reasons of space (such as testing the assumptions of Poisson regressions or how to handle over-/underdispersion). The method is powerful when applied to complex data sets and definitely worth exploring in more detail.

388 Stefan Th. Gries

3. Conclusion This brief chapter could, of course, not do justice to all the complexities that can and do arise in the study of frequency tables. I hope, however, that the above brief remarks and examples have shown how useful a statistically correct and comprehensive exploration of such data can be and also has hopefully whetted the reader’s appetite to explore such techniques in more detail (and also their graphical exploration, which I could not address here at all) both in this volume and in the works referred to throughout this paper.

References Baayen, R. H. (2008). Analyzing linguistic data: A practical introduction to statistics using R. Cambridge: Cambridge University Press. DOI: 10.1017/CBO9780511801686 Bortz, J., Lienert, G. A., & Boehnke, K. (1990). Verteilungsfreie Methoden in der Biostatistik (2nd ed.). Heidelberg: Springer. DOI: 10.1007/978-3-662-22593-6 Brooks, P., & Tomasello, M. (1999). How children constrain their argument structure constructions. Language, 75, 720–738. DOI: 10.2307/417731 Bybee, J. L. (1985). Morphology: A study of the relation between meaning and form. Amsterdam & Philadelphia: John Benjamins. DOI: 10.1075/tsl.9 Bybee, J. L., & Scheibman, J. (1999). The effect of usage on degrees of constituency: The reduction of don’t in English. Linguistics, 37, 575–596. DOI: 10.1515/ling.37.4.575 Chen, P. (1982). Discourse and particle movement in English. Studies in Language, 10, 79–95. DOI: 10.1075/sl.10.1.05che Crawley, M. (2005). Statistics: An introduction using R. New York: John Wiley. DOI: 10.1002/ 9781119941750 Crawley, M. (2012). The R book (2nd ed.). Chichester: John Wiley. DOI: 10.1002/9781118448908 Faraway, J. J. (2006). Extending the linear model with R: Generalized linear, mixed effects and nonparametric regression models. Boca Raton, FL: Chapman and Hall. Goldberg, A. E., Casenhiser, D., & Sethuraman, N. (2004). Learning argument structure generalizations. Cognitive Linguistics, 14, 289–316. Gries, St. Th. (2003). Multifactorial analysis in corpus linguistics: A study of particle placement. London & New York: Continuum. Gries, St. Th. (2013). Statistics for linguistics with R: A practical introduction. Berlin & New York: Mouton de Gruyter. DOI: 10.1515/9783110307474 Hommerberg, C., & Tottie, G. (2007). Try to and try and? Verb complementation in British and American English. ICAME Journal, 31, 45–64. Johnson, K. (2008). Quantitative methods in linguistics. Malden, MA & Oxford: Blackwell. Kruisinga, E., & Erades, P. A. (1953). An English grammar. Vol. I. Groningen: P. Noordhoff. Lohmann, A. (2009). The register-specificity of metaphor. Paper presented at the workshop ‘Corpus, colligation, register variation’ of the 31st DGfS-Tagung. Saffran, J. R., Aslin, R. N., & Newport, E. L. (1996). Statistical learning by 8-month-old infants. Science, 274, 1926–1928. DOI: 10.1126/science.274.5294.1926



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Saffran, J. R., & Wilson, D. P. (2003). From syllabus to syntax: Multilevel statistical learning by 12-month old infants. Infancy, 4, 273–284. DOI: 10.1207/S15327078IN0402_07 Sheskin, D. J. (2011). Handbook of parametric and non-parametric statistical procedures (5th ed.). Boca Raton, FL, London & New York: CRC Press. Schmid, H.-J. (2000). English abstract nouns as conceptual shells: From corpus to cognition. Berlin & New York: Mouton de Gruyter.

Collostructional analysis Measuring associations between constructions and lexical elements Martin Hilpert

Université de Neuchâtel

This chapter offers a practical introduction to a set of corpus-linguistic analytical methods that are referred to collectively as ‘collostructional analysis’. The overarching aim in conducting a collostructional analysis is to find out which lexical items form collocations with a given grammatical construction. The purpose of such an undertaking, in the context of this book, is to facilitate the semantic analysis of grammatical constructions. The chapter discusses several case studies in order to show that the semantic description of grammatical constructions benefits from a quantitative analysis of the lexical material that occurs with the respective constructions. A final discussion surveys advantages and pitfalls of collostructional methods. Keywords: collocations, quantitative analysis

1. Introduction This chapter offers an introduction to collostructional analysis for the non-initiated. It explains how it works, how it is used, and how its results can be interpreted. In doing so, it may serve as a primer for the original series of papers in which the different collostructional methods are presented (Stefanowitsch and Gries 2003, 2005; Gries and Stefanowitsch 2004a, 2004b). These papers should be referred to not only for theoretical background detail, but also for further case studies and discussion of the statistics that are implemented in the respective methods. Unlike the original papers, this chapter discusses a few practical aspects of conducting collostructional analyses that are meant to facilitate the process of getting started with one’s own projects. The overarching aim in conducting a collostructional analysis is to find out which lexical items are “typical” of a given grammatical construction. For example, given a construction such as English keep on V-ing, which verbs typically occur in this

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constructional frame? As is explained in more detail below, simple raw frequency counts sometimes do not provide a revealing answer to this question. Rather than asking which elements occur most often, collostructional analysis uses relative frequency counts to determine which elements occur more frequently in a construction than would be expected by chance. A sceptic might wonder why an analysis of constructional collocates should be useful. A collocational analysis of constructions is motivated by the insight that the meaning of a construction tends to harmonize with the meanings of the lexical elements that typically occur in it. For instance, a verb will only be acceptable within a given construction if its arguments are compatible with the roles specified by the construction; this is referred to as the Semantic Coherence Principle (Goldberg 1995:â•›50). The English ditransitive construction, which conveys the constructional meaning of a transfer, thus overwhelmingly occurs with transfer verbs such as give or send; the English way-construction, which evokes the effortful creation of a path through obstacles, occurs with verbs such as make, work, and push. Analyzing the mutual dependencies between constructions and lexical elements can yield insights into the meaning of constructions, which is one of the basic aims of Construction Grammar. In practical terms, if a research project has the goal of describing the semantics of a grammatical construction, collostructional analysis is a good methodological choice for the job. Collostructional analysis is not a single method, but is actually a cover term for three related methods of corpus-linguistic inquiry. Each of these methods investigates the mutual associations between grammatical constructions and lexical items: – Collexeme analysis (Stefanowitsch and Gries 2003) is used to investigate which lexical items typically occupy a given slot in a single grammatical construction such as the keep on V-ing construction. – Distinctive collexeme analysis (Gries and Stefanowitsch 2004a) contrasts two or more constructions with regard to the lexical items that occur with them. This is especially useful for the comparison of constructions that are roughly synonymous. Pairs of constructions such as the ditransitive vs. the prepositional Dative, will vs. be going to, or active vs. passive can be fruitfully contrasted with regard to the main verbs that characterize each respective variant. – Covarying-collexeme analysis (Gries and Stefanowitsch 2004b; Stefanowitsch and Gries 2005) reveals dependencies between lexical items that occupy two different slots within the same construction. To illustrate, the English object-to-subject raising construction (Proust is tough to read) holds a slot for an adjective and another one for a verb in the infinitive. A covarying-collexeme analysis can determine typical adjective-verb combinations, which then allow conclusions about the semantic frames that are most strongly associated with the construction. Each of the three methods is presented in a separate section below. Before that, a few remarks on practical matters are in order. Any collostructional analysis begins with

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the choice of an appropriate corpus and concordancing software. The next step in the work process is an exhaustive extraction of the construction that one is interested in. All examples are needed in order to obtain usable results. Depending on the form of the construction, this may not be trivial. While it is fairly easy to retrieve all examples of be going to V, even from an untagged corpus, finding all examples of the ditransitive construction or all examples of object-to-subject raising is more difficult. In most cases, it is advisable to cast a wide net first and weed out false positives by manual checking. This will often take some time. A practical way to handle this process is to put all concordance lines in a spreadsheet file, noting for each example in a separate column whether or not it instantiates the target construction. A cleaned-up concordance with all examples of the target construction is the basis for all three methods that are outlined below (and in fact for many other corpus-linguistic methods as well). In this chapter, the model construction that will serve to illustrate all three analytical methods is a subtype of the English it-extraposition construction (Kaltenböck 2005), in which an expletive subject it is followed by a copula, a predicative adjective and a to-infinitive clause: (1) a. It is hard to be a corpus linguist. b. It is important to give evidence. c. It is tempting to speculate about grammar. The following sections discuss how collostructional analysis can be used for a semantic analysis of the it’s ADJ to V-construction. All steps are outlined in such a way that they can be re-created directly by the reader, and in fact this is encouraged. Alternatively, a package with all the datasets discussed in this chapter is available upon request from the author. The first analytical step would be to extract all examples of the it’s ADJ to V-construction from a corpus such as the BNC, which can be freely accessed online (Davies 2004). The construction is fairly frequent; a corpus search for the pronoun it followed by a form of the copula and a to-infinitive yields 17,216 instances after manual clean-up.

2. Collexeme analysis Collexeme analysis (Stefanowitsch and Gries 2003) is the most basic of the three collostructional methods. It is used to find out which lexical items in a given slot are most strongly attracted to a grammatical construction, such as maybe the preferred adjectives of it’s ADJ to V. With a spreadsheet of a complete concordance, this question is easy to answer. In the BNC, it’s ADJ to V occurs with 462 different adjective types in total. Table 1 shows the ten most frequent types. These raw frequencies are a start, but more information is needed. As was mentioned above, a collexeme analysis determines whether a given lexical item occurs

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Table 1.╇ The ten most frequent adjectives in the it’s ADJ to V-construction Adjective

Tokens

possible difficult important necessary easy impossible hard interesting better essential

2,434 1,949 1,844 1,367 1,139 â•⁄â•‹995 â•⁄â•‹979 â•⁄â•‹453 â•⁄â•‹340 â•⁄â•‹338

Table 2.╇ Token frequencies in the BNC and in the it’s ADJ to V-construction Adjective

Corpus frequency (BNC)

Construction frequency (it’s ADJ to V)

possible difficult important necessary easy impossible hard interesting better essential

33,654 21,608 38,715 17,863 13,935 â•⁄6,822 15,285 â•⁄9,417 20,811 â•⁄8,633

2,434 1,949 1,844 1,367 1,139 â•⁄â•‹995 â•⁄â•‹979 â•⁄â•‹453 â•⁄â•‹340 â•⁄â•‹338

with a construction more often than expected. In order to state whether 453 tokens of interesting are anything out of the ordinary, the token frequencies of the adjectives in Table 1 need to be compared against their overall token figures in the BNC. How are these frequencies obtained? One possibility would be to consult a word frequency list from the BNC, several of which can be found on the Internet. Another possibility would be to conduct another corpus search, this time for all 462 adjective types that are found in it’s ADJ to V. Whichever option is chosen, the results should be organized in a table that lists each adjective with its full corpus frequency and its frequency in it’s ADJ to V. Table 2 shows the uppermost part of such a table. With this table in place, it is almost time to run the collexeme analysis. Saved in .txt format with tab stops, it constitutes the most important input. In addition, it is necessary to include two numbers: the first one is the token frequency of it’s ADJ to



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V (17,216); and the second one is the combined token frequency of all elements that could potentially occur in it’s ADJ to V, which means essentially all adjectives that occur in the BNC (13,704,818). This figure is best obtained through a tag-sensitive search for all adjectives, or again from a BNC word list. The most convenient way to run a collostructional analysis is to use the open source software R, together with a script written by Stefan Th. Gries that is available upon request (Gries 2004). The script prompts the user for the following four items: – – – –

The name of the construction one wishes to study (type: it’s ADJ to V). The combined frequency of all potential collexemes (type: 13704818). The combined frequency of all construction tokens (type: 17216). A table with the three columns ‘adjective’, ‘corpus_frequency ’, and ‘construction_ frequency’ (the script will open a pop-up window that allows the selection of the .txt file).

Armed with these pieces of information, the script generates a table that lists all adjectives that are found in the construction together, with their observed and expected frequencies and a measure of their attraction to the construction. This measure, which uses the Fisher’s exact test and reflects p-values resulting from that test, is referred to in the following as collostructional strength – the higher it is, the stronger the mutual attraction. Table 3 shows the most strongly attracted collexemes of it’s ADJ to V. In this particular case, the nine most strongly attracted collexemes are actually all found within the ten most frequent adjectives, so one might wonder whether the additional effort of a collostructional analysis is warranted. However, several points suggest that it is. First, throughout the table, one can see diverging values of collostructional strength and construction frequency; essential is less frequent than better, but more strongly associated with it’s ADJ to V. Second, the values of collostructional strength can be used to distinguish between elements that are significantly attracted to the construction (a value that is larger than 1.3 indicates significant attraction at the p-level of 0.05; the value Infinite indicates that the probability of error is infinitely small) and those that are not, which is information that construction frequencies alone cannot provide. The adjectives embarrassing and artificial (not shown in the table) both occur four times in the database, but only the former is significantly attracted to the construction. Lastly, the analysis identifies elements with construction frequencies that are significantly lower than those expected by chance. These elements, for instance, economic, clear, and modern (not shown in the table), can be said to be repelled by the construction. Given the high overall frequencies of these adjectives, they should occur in the construction more often than they do. The following examples from the BNC are thus unidiomatic, unusual examples of it’s ADJ to V.

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Table 3.╇ Collexemes of the it’s ADJ to V-construction Collexeme

Corpus frequency

Construction frequency

Expected frequency

Collostruction strength

difficult easy essential hard important impossible interesting necessary possible advisable tempting better reasonable useful best wise convenient fair safe … …

21,608 13,935 â•⁄8,633 15,285 38,715 â•⁄6,822 â•⁄9,417 17,863 33,654 â•⁄â•⁄â•‹530 â•⁄â•⁄â•‹666 20,811 â•⁄6,072 â•⁄9,960 26,088 â•⁄1,896 â•⁄1,966 â•⁄8,166 â•⁄6,330 … …

1,949 1,139 â•⁄â•‹338 â•⁄â•‹979 1,844 â•⁄â•‹995 â•⁄â•‹453 1,367 2,434 â•⁄â•‹135 â•⁄â•‹141 â•⁄â•‹340 â•⁄â•‹207 â•⁄â•‹198 â•⁄â•‹259 â•⁄â•‹106 â•⁄â•⁄â•‹95 â•⁄â•‹143 â•⁄â•‹130 … …

27.15 17.51 10.85 19.2 48.64 â•⁄8.57 11.83 22.44 42.28 â•⁄0.67 â•⁄0.84 26.15 â•⁄7.63 12.51 32.78 â•⁄2.38 â•⁄2.47 10.26 â•⁄7.95 … …

Infinite Infinite Infinite Infinite Infinite Infinite Infinite Infinite Infinite 262.84 261.67 246.38 213.62 159.61 136.88 132.50 112.83 108.11 106.87 … …

(2) a. It is economic to make the accumulators faster than the store elements. b. It is clear to see at most training clubs that praise is in very short supply. c. Babies aren’t very nice for the first couple of years of their lives either, though it is modern to say the opposite. Once the results of a collostructional analysis have been obtained, it is the task of the analyst to make sense of the data. Lists such as the one in Table 3 can be interpreted qualitatively to assess the constructional semantics. A particularly revealing result would be to find that there are groups of semantically closely-related items that are attracted to the construction under investigation. In the case of it’s ADJ to V, one can identify adjectives that make reference to different scales, such as ease (difficult, easy, hard), possibility (possible, impossible), importance (important, essential, necessary), and advisability (advisable, better, best, wise). Further adjectives instantiating these scales are found if more collexemes are inspected than just the top twenty. When lists of attracted collexemes are broken down into sets of semantically related items, these groupings should be done on the basis of close examination of actual examples in



Collostructional analysis 397

their contexts. It is necessary to look beyond the mere list of attracted elements, since lexical items typically can be used in a range of different meanings. Another important part of a collexeme analysis is to consider the repelled items in detail. The relative absence of certain lexical items in a construction can yield clues about the constraints that govern its usage, and so a characterization in negative terms can be very useful. Before we turn to the next section, a few problematic issues need to be mentioned. One problem that can be observed in Table 3 concerns items that are very strongly attracted to a construction. For no less than nine adjectives in it’s ADJ to V, the collexeme analysis returns an infinitely strong value of collostruction strength. This is an issue that will frequently arise in constructions with low type frequencies. To illustrate, a collexeme analysis of what Schmid (2000) calls shell nouns (the fact that CLAUSE, the decision to V, etc.) is very likely to register infinite collostructional strength for nearly all participating nouns because these form such a small and relatively closed set. This is not a problem for collostructional analysis per se, but it has to be noted that not all constructions are fruitfully investigated in this way. Good candidates for a collexeme analysis are semantically general constructions (be going to, the caused-motion construction, the ditransitive construction, etc.) with a type frequency of 100+ elements. The latter figure, of course, varies with the size of the corpus that is chosen. Even when such a threshold is surpassed, as is the case for several shell noun constructions, the analysis may still suffer if most of the types occur almost exclusively within those constructions, and not much in other contexts. A second problem concerns polysemous elements such as the adjective hard, which is very frequent in the it’s ADJ to V construction. In the construction, it is always used in the sense of ‘difficult’. Nonetheless, its corpus frequency also reflects all those instances in which it means ‘solid’. The inclusion of these instances weakens its collostructional strength. Polysemous items are therefore at a disadvantage in a collexeme analysis. There is no easy way to address this problem, as manual coding for different word senses is often not a feasible option. The best strategy is to be on the lookout for polysemous collexemes and to consider carefully where a collexeme analysis might disfavor a particular element. There are several other criticisms of collostructional analysis that have been raised and that would merit discussion, the interested reader is in particular referred to the criticisms in Bybee (2010) and the responses in Gries (2012).

3. Distinctive collexeme analysis Distinctive collexeme analysis (Gries and Stefanowitsch 2004a) contrasts constructions in their respective collocational preferences. The method is particularly suited for the study of semantically related constructions, such as, for example, the ditransitive construction and the prepositional dative construction. A distinctive collexeme

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analysis can bring to light the fact that two constructions, which, at first glance appear to be synonymous, do in fact display subtle differences. How then could an analysis of this kind be used for the study of it’s ADJ to V? In order to apply it, an alternative construction has to be identified, so that there are two constructions to compare. For instance, it might be fruitful to contrast it’s ADJ to V against a corresponding construction with a non-extraposed predicative adjective, as illustrated in (3). (3) a. It is hard to be a corpus linguist. b. [To be/Being/The life of] a corpus linguist is hard. If one is interested in the question of when and why speakers choose to use an extraposed adjective with an expletive subject pronoun it rather than a non-extraposed predicative construction, looking at the respective collocational preference partly answers the ‘when’ question and at least provides hints for the ‘why’ question. In order to run a distinctive collexeme analysis, both constructions need to be exhaustively extracted from the same corpus. The data from the collexeme analysis of it’s ADJ to V in the previous section can thus simply be re-used, but it has to be complemented by a full concordance of what is referred to here as the X is ADJ construction. The BNC holds 65,823 tokens of this construction that are distributed across 5,733 different adjective types. Table 4 contrasts the ten most frequent adjective types in it’s ADJ to V and X is ADJ. For the computation of a distinctive collexeme analysis, this data needs to be brought into a slightly different format, which is shown in Table 5. The input data for a distinctive collexeme analysis consists of the respective token frequencies for all adjective types that are attested in either of the two constructions (5,754 in total), saved Table 4.╇ The ten most frequent adjectives in it’s ADJ to V and X is ADJ Adjective

it’s ADJ to V

Adjective

X is ADJ

possible difficult important necessary easy impossible hard interesting likely better … …

2,434 1,949 1,844 1,367 1,139 â•⁄â•‹995 â•⁄â•‹979 â•⁄â•‹453 â•⁄â•‹357 â•⁄â•‹340 … …

right available wrong concerned true different necessary dead good possible … …

1,229 1,032 â•⁄â•‹905 â•⁄â•‹859 â•⁄â•‹853 â•⁄â•‹823 â•⁄â•‹796 â•⁄â•‹771 â•⁄â•‹682 â•⁄â•‹657 … …

Collostructional analysis 399



Table 5.╇ Token frequencies in it’s ADJ to V and X is ADJ Adjective

Construction frequency (it’s ADJ to V)

Construction frequency (X is ADJ)

possible difficult important necessary easy impossible hard interesting better essential … …

2,434 1,949 1,844 1,367 1,139 â•⁄â•‹995 â•⁄â•‹979 â•⁄â•‹453 â•⁄â•‹340 â•⁄â•‹338 … …

657 279 652 796 383 316 â•⁄86 136 269 391 … …

in .txt format with tab stops. The script prompts the user for the frequencies of both constructions and the location of the data file. While some asymmetries can already be gleaned from Tables 4 and 5, a distinctive collexeme analysis can give some more tangible guidelines for a semantic contrast of the two constructions. Table 6a shows the ten most distinctive collexemes of it’s ADJ to V. It can be seen that the results of the collexeme analysis are largely reproduced. The semantic scales of possibility, ease, advisability, and importance all reappear, suggesting that these parameters are central enough to the constructional semantics to figure in a contrast with a predicative construction. Table 6a.╇ The top ten distinctive collexemes of it’s ADJ to V Distinctive collexemes

Observed (it’s ADJ to V)

Observed (X is ADJ)

Expected (it’s ADJ to V)

Expected (X is ADJ)

Coll. strength

difficult easy hard important impossible necessary possible interesting best tempting

1,949 1,139 â•⁄â•‹979 1,844 â•⁄â•‹995 1,367 2,434 â•⁄â•‹453 â•⁄â•‹259 â•⁄â•‹141

279 383 â•⁄86 652 316 796 657 136 109 â•⁄â•⁄4

461.92 315.55 220.80 517.48 271.8 448.44 640.84 122.11 â•⁄76.30 â•⁄30.06

1766.08 1206.45 â•⁄844.20 1978.52 1039.20 1714.56 2450.16 â•⁄466.89 â•⁄291.70 â•⁄114.94

Infinite Infinite Infinite Infinite Infinite Infinite Infinite 188.19 â•⁄92.70 â•⁄89.70

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Table 6b.╇ The top ten distinctive collexemes of X is ADJ Distinctive collexemes

Observed (it’s ADJ to V)

Observed (X is ADJ)

Expected (it’s ADJ to V)

Expected (X is ADJ)

Coll. strength

available concerned different dead right clear high present true successful

â•⁄0 â•⁄0 â•⁄0 â•⁄0 92 â•⁄1 â•⁄0 â•⁄0 51 â•⁄0

1,032 â•⁄â•‹859 â•⁄â•‹823 â•⁄â•‹771 1,229 â•⁄â•‹433 â•⁄â•‹378 â•⁄â•‹372 â•⁄â•‹853 â•⁄â•‹341

213.96 178.09 170.63 159.85 273.88 89.98 â•⁄78.37 â•⁄77.12 187.42 â•⁄70.70

â•⁄818.04 â•⁄680.91 â•⁄652.37 â•⁄611.15 1047.12 â•⁄344.02 â•⁄299.63 â•⁄294.88 â•⁄716.58 â•⁄270.30

104.87 â•⁄87.18 â•⁄83.51 â•⁄78.21 â•⁄43.65 â•⁄41.86 â•⁄38.24 â•⁄37.63 â•⁄37.16 â•⁄34.49

The most distinctive collexemes of the predicative X is ADJ construction are shown in Table 6b. They include adjectives denoting truth values (right, true), but mostly consist of reasonably frequent adjectives that can only be predicated over referential nominals, i.e. not with a non-referential it. This concerns the elements available, concerned, dead, high, present, and successful. These do not occur in it’s ADJ to V and consequently show up in Table 6b as distinctive for X is ADJ. As was mentioned above, a distinctive collexeme analysis can be usefully applied when a theoretical point hinges on the fact that two constructions are non-synonymous. Collocational differences can be used to make this point, and they allow the analyst to flesh out the semantic contrasts between the two constructions.

4. Covarying-collexeme analysis The analyses in the previous sections have established that the it’s ADJ to V-construction selects for adjectives that concern semantic frames such as possibility, ease, advisability, and importance. As yet, it has not been asked with what kinds of verbs the construction might occur preferentially, and whether there could be any interdependencies between certain kinds of adjectives and certain kinds of verbs. A covarying-collexeme analysis addresses precisely this point. Given a construction with two slots that can be lexically filled, can we determine combinations of elements that occur more often than would be expected by chance? In the data at hand, the examples of it’s ADJ to V contain 6,257 different combinations, the ten most frequent of which are shown in Table 7. Also shown are the respective overall frequencies of the participating adjectives and verbs.

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Table 7.╇ The ten most frequent adjectives and verbs (ADJ-V) combinations of it’s ADJ to V Combination

Tokens

ADJ frequency

V frequency

interesting to note difficult to see easy to see important to note important to remember hard to see fair to say hard to imagine hard to believe possible to make

244 218 190 164 152 149 103 102 â•⁄93 â•⁄90

â•⁄â•‹453 1,949 1,139 1,844 1,844 â•⁄â•‹979 â•⁄â•‹143 â•⁄â•‹979 â•⁄â•‹979 2,434

â•⁄â•‹479 1,032 1,032 â•⁄â•‹479 â•⁄â•‹200 1,032 â•⁄â•‹448 â•⁄â•‹283 â•⁄â•‹224 â•⁄â•‹345

Table 8.╇ Input for a covarying-collexeme analysis of it’s ADJ to V Adjective

Verb

absurd absurd absurd absurd absurd absurd absurd absurd absurd absurd … …

suppose suppose suppose think think think assume be blame compare … …

A cursory look at Table 7 already reveals that adjectives denoting ease and difficulty (difficult, easy, hard) co-occur with verbs that denote cognitive processes (see, imagine, believe); the adjective important co-occurs with verbs that can be used to introduce a statement (note, remember). A covarying-collexeme analysis can identify those combinations that are significantly more frequent than expected, given the respective frequencies of their participating elements. This in turn may guide an analysis of the semantic frames that are associated with the construction that is studied. Again, the input has to be brought into a specific format, which is shown in Table 8. What is needed is a table with two columns in which all observations are listed. In the present case, this means that the table has 17, 216 lines, each of which consists of an

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Table 9.╇ The top twenty covarying collexemes of it’s ADJ to V Combination

Observed

Expected

Coll. strength

interesting to note fair to say important to remember true to say reasonable to assume hard to believe hard to imagine important to note unrealistic to expect reasonable to suppose easy to see important to realise important to stress interesting to compare easy to forget reasonable to expect hard to see unreasonable to expect good to be important to recognize

244 103 152 â•⁄49 â•⁄55 â•⁄93 102 164 â•⁄23 â•⁄30 190 â•⁄54 â•⁄45 â•⁄33 â•⁄33 â•⁄25 149 â•⁄14 â•⁄51 â•⁄41

12.60 â•⁄3.72 21.42 â•⁄1.33 â•⁄1.89 12.74 16.09 51.31 â•⁄0.19 â•⁄0.76 68.28 â•⁄8.03 â•⁄5.89 â•⁄2.21 â•⁄3.04 â•⁄1.02 58.69 â•⁄0.13 â•⁄8.38 â•⁄6.64

278.86 133.29 105.44 â•⁄75.72 â•⁄66.40 â•⁄55.89 â•⁄54.33 â•⁄43.98 â•⁄43.92 â•⁄40.76 â•⁄39.73 â•⁄35.36 â•⁄33.87 â•⁄29.78 â•⁄28.47 â•⁄27.58 â•⁄26.31 â•⁄25.82 â•⁄25.16 â•⁄24.67

adjective and a verb, separated by a tab stop. Whilst the computation of the other collostructional analysis usually takes a matter of seconds to complete, a covarying-collexeme analysis with the dataset just described may take longer to run. The most important results of the analysis are presented in Table 9. The combinations are listed alongside their observed frequencies in the database, which in each case exceed the value that is expected by chance. All combinations that are shown display a significant mutual attraction, as can be read off the rightmost column. Perhaps more tellingly than the analyses in the previous sections, the covarying-collexeme analysis brings out the rhetorical discursive functions of the it’s ADJ to V-construction, which are also discussed by Kaltenböck (2005:â•›145). Many of the combinations in Table 9 fulfil a function that can be described as setting the stage for a new piece of information in discourse. Phrases such as It is interesting to note / fair to say / important to remember / etc. do not carry focal information in themselves and are usually less prominently stressed than the material that follows. But in addition, the table lists combinations such as hard to believe / hard to imagine / hard to see, which a speaker can use to signal a negative epistemic stance towards a following proposition. In addition, there are combinations with the verbs expect and suppose that pertain to



Collostructional analysis 403

the validity of an inference. A full semantic analysis of it’s ADJ to V should attempt to flesh out these types in more detail and describe their interrelations. An in-depth look at the covarying collexemes of a construction can thus yield more detailed insights than a study that concentrates on just a single slot of that construction.

5. Concluding remarks The preceding sections have surveyed a number of research questions that can be addressed through different collostructional analyses. Hopefully, some readers will be encouraged to read further, to familiarize themselves further with the methods, and run their own analyses. Besides what has been presented in this chapter, further ways to apply collostructional analyses have been suggested. For example, collostructional analysis can be used for the study of sociolinguistic variation (Wulff et al. 2007) and language change (Hilpert 2006, 2012). The value of any collostructional analysis ultimately depends on the way it is brought to bear on a question of theoretical interest. Much as with other statistical methods, the hard task is not the running of the numbers, but the development of a research question that the chosen technique can answer. Used in this way, collostructional analysis is a tool that can substantially advance our understanding of grammatical constructions and their meanings.

References Bybee, J. L. (2010). Language, usage and cognition. Cambridge: Cambridge University Press. DOI: 10.1017/CBO9780511750526 Davies, M. (2004). BYU-BNC: The British National Corpus. Available via http://corpus.byu.edu/ bnc. Goldberg, A. E. (1995). Constructions. A construction grammar approach to argument structure. Chicago: University of Chicago Press. Gries, St. Th. (2004). Coll.analysis 3. A program for R for Windows 2.x. Gries, St. Th. (2012). Frequencies, probabilities, association measures in usage-/exemplar-based linguistics: Some necessary clarifications. Studies in Language, 36(3), 477–510. DOI: 10.1075/sl.36.3.02gri Gries, St. Th., & Stefanowitsch, A. (2004a). Extending collostructional analysis: A corpus-based perspective on ‘alternations’. International Journal of Corpus Linguistics, 9(1), 97–129. DOI: 10.1075/ijcl.9.1.06gri Gries, St. Th., & Stefanowitsch, A. (2004b). Co-varying collexemes in the into-causative. In M. Achard, & S. Kemmer (Eds.), Language, culture, and mind (pp. 225–36). Stanford: CSLI. Hilpert, M. (2006). Distinctive collexemes and diachrony. Corpus Linguistics and Linguistic Theory, 2(2), 243–56. DOI: 10.1515/CLLT.2006.012

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Hilpert, M. (2012). Diachronic collostructional analysis. How to use it, and how to deal with confounding factors. In J. Robinson, & K. Allan (Eds.), Current methods in historical semantics (pp. 133–160). Berlin & New York: Mouton de Gruyter. Kaltenböck, G. (2005). It-extraposition in English: A functional view. International Journal of Corpus Linguistics, 10(2), 119–159. DOI: 10.1075/ijcl.10.2.02kal Schmid, H.-J. (2000). English abstract nouns as conceptual shells: From corpus to cognition. Berlin/New York: Mouton de Gruyter. DOI: 10.1515/9783110808704 Stefanowitsch, A., & Gries, St. Th. (2003). Collostructions: Investigating the interaction between words and constructions. International Journal of Corpus Linguistics, 8(2), 209–243. DOI: 10.1075/ijcl.8.2.03ste Stefanowitsch, A., & Gries, St. Th. (2005). Covarying collexemes. Corpus Linguistics and Linguistic Theory, 1(1), 1–43. DOI: 10.1515/cllt.2005.1.1.1 Wulff, S., Stefanowitsch, A., & Gries, St. Th. (2007). Brutal Brits and persuasive Americans: Variety-specific meaning construction in the into-causative. In G. Radden, K.-M. Köpcke, T. Berg, & P. Siemund (Eds.), Aspects of meaning construction (pp. 265–281). Amsterdam: John Benjamins.

Cluster analysis Finding structure in linguistic data Dagmar Divjak and Nick Fieller University of Sheffield

Cluster analysis is an exploratory data analysis technique, encompassing a number of different algorithms and methods for sorting objects into groups. Cluster analysis requires the analyst to make choices about dissimilarity measures, grouping algorithms, etc., and these choices are difficult to make without an understanding of their theoretical implications and a very good understanding of the data. This chapter provides an introduction to the distance measures and clustering algorithms most commonly used for cluster analytic work. Different from Baayen (2008), Johnson (2008) and Gries (2009), its main aim is to equip the researcher with at least a basic understanding of what is happening when a dataset is explored with the help of a particular cluster analytic technique. Keywords: clustering algorithms, distance measures

1. Introduction We organisms are sensorimotor systems. The things in the world come in contact with our sensory surfaces, and we interact with them based on what that sensorimotor contact “affords”. (…) At bottom, all of our categories consist in ways we behave differently toward different kinds of things, whether it be the things we do or don’t eat, mate with, or flee from, or the things that we describe, through our language, as prime numbers, affordances, absolute discriminables, or truths. And isn’t that all that cognition is for – and about?  (Stevan Harnad 2005: To Cognize is to categorize: Cognition is categorization)

One of the key concepts in cognitive linguistics is categorization. To be able to categorize things is a necessary and innate capacity: we need to be able to recognize, distinguish and understand in order to survive. Our categories signal, for example, whether the mushroom we pick is edible or not, and whether the animal we encounter

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is harmless or dangerous. Survival is the main goal of cognition. Categorization is equally fundamental in language. Growing up, we not only learn which categories are relevant for us to function in our environment. We also acquire the categories of our language and learn to use a limited number of words and rules to name a large number of different items and to express an unlimited number of experiences. And things do not stop with language. As is the case in other disciplines, categorization is also important in the scientific study of language. As early as the 5th century BC, Sanskrit grammarians grouped words into classes – that would later become known as parts of speech – distinguishing between inflected nouns and verbs and uninflected pre-verbs and particles. Categorization efforts have been carried out across linguistic sub-disciplines, ranging from phonology, morphology, syntax and semantics, to discourse analysis and pragmatics. Despite its long history, even for parts of speech there is currently no generally agreed-upon classification scheme that would apply to all languages, or even a set of criteria upon which such a scheme should be based. In some cases, linguists are only now trying to organize entities into groups so that they can be compared and described. With desktop computers replacing filing cabinets, it has become easy for linguists to create very large databases that contain information on a multitude of properties. At the same time, this complexity may make it too difficult for the human analyst to detect any structure. One way of solving this issue is by running a cluster analysis. Cluster analysis (a term first used by Tryon in 1939) is a multivariate analysis technique that organizes information about how similar objects or entities are so that groups, or clusters, can be formed. Pioneered in machine learning, cluster analysis has found its way via sociolinguistics (e.g. Shaw’s 1974 work on dialectal boundaries) to linguistics, where it has now been used to describe a wide range of linguistic phenomena (see references elsewhere in this volume). It is also reaching beyond linguistics into other Arts and Humanities disciplines, aiding, for example, in the classification of texts according to relevant dimensions (see Alviar 2008 for the application of cluster analysis in the style characterization of New Testament texts). Cluster analysis is an exploratory data analysis technique, encompassing a number of different algorithms and methods for sorting different objects into groups in such a way that the similarity between two objects of the same group is maximal and the similarity between two objects that belong to different groups is minimal. In other words, cluster analysis can be used to discover structures in data and it does this without explaining why that structure exists. Cluster analysis is thus not a routine single statistical test based on probability theory; instead, it is a data analytic technique, a collection of different algorithms that put objects into clusters according to well-defined similarity rules. It is mostly used when we do not have any a priori hypotheses, but are in the exploratory phase of our research. Yet in contrast to other exploratory methods of this type such as Principal Components Analysis and Multidimensional scaling, cluster analysis requires the analyst to make choices, about dissimilarity



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measures, grouping algorithms, etc., and these choices are difficult to make without having an understanding of their theoretical implications and a very good understanding of the data. This latter requirement is particularly important, since in contrast to many other statistical methods, there seem to be fewer diagnostics informing of the weaknesses of any classification solution proposed. Before getting started, it is important to stress the focus of this chapter. Like Baayen (2008:â•›Section 5.1.5), Johnson (2008:â•›Ch. 6) and Gries (2009:â•›Ch. 5.5) before us, this chapter provides an introduction to the distance measures and clustering algorithms most commonly used (for an idea of the amazing variety of functions for cluster analysis that R has to offer, see http://cran.r-project.org/web/views/Cluster. html). Our main aim is, however, to equip the researcher with at least a basic understanding of what is happening behind the scenes when s/he explores his/her data with the help of a particular cluster analytic technique using R (without actually answering the one unanswerable question: “which method of clustering is best?”). Slightly more technical details may not suit all readers on first reading. To avoid letting linguistic opinions overshadow statistical decisions, we have opted to illustrate our chapter with a topic that would hardly raise any interest in linguistic circles, i.e. the relatedness of languages, based on the words they use to express the numbers 1 through 10. Cluster analysis only works on data that is “prepared” in some way. In general, this preparation equals “operationalizing” parameters deemed relevant in the description of the data, an issue we will elaborate on in Section 2.1. Although cluster analysis is relatively simple and can use a variety of input data, many aspects rely on ad hoc and intuitive justification: only certain particular aspects of the techniques are supported by established statistical theory. Therefore, most of the guidelines for using cluster analysis are rules of thumb. Once decisions have been made on key steps of the cluster analysis, topics we will go into in Sections 2.2 and 2.3, the cluster analysis technique provides a degree of objectivity in determining clusters or groups of similar entities. This has the advantage of identifying which elements of the analysis are subjective and then specifying precisely what follows from these subjective decisions, as we will do in Sections 2.4 and 2.5.1

1. This allows two types of comparisons. On the one hand, comparisons can be made between analyses based on different subjective decisions applied to the same entities; on the other hand, comparisons can be made between structures of different sets of entities based on matching subjective inputs. In other words, two cluster analyses cannot be compared/contrasted unless they have been applied to the same set of objects or have used the same similarity measure and clustering algorithm.

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2. Steps in conducting a cluster analysis There are several basic cluster analysis steps: – – – –

data collection and selection of the variables for analysis (Section 2.1) generation of a similarity matrix and clustering algorithm (Sections 2.2 and 2.3) decision about the number of clusters and their interpretation (Section 2.4) validation of the cluster solution (Section 2.5)

These steps are interrelated. The type of variable selected for analysis will impose restrictions on the choice of how to measure similarities, and the choice of clustering algorithm will influence the interpretation of the clusters detected.

2.1

Coding and standardization of variables

An important contribution to the statistical analysis of linguistic data, of any data really, is made by the variables used to capture the phenomenon. A common myth is that corpus linguists do everything automatically, which would make corpus linguistic techniques unsuited for the study of meaning. Yet at the heart of the corpus-based study of linguistic phenomena is the manual annotation of examples. This requires the analyst to read and analyze the examples one by one, just as s/he would do with a list of examples collected in a notebook or written out on cards. One of the main differences between a corpus linguist and other linguists is that the corpus linguist selects a random sample from a representative and balanced collection of texts that represent one or more varieties of the language s/he is studying. The corpus linguist then works with that sample and is not allowed to include additional sentences that would nicely illustrate his/her point, nor to remove sentences that disprove his/her account. An additional challenge the corpus linguist faces is that s/he needs to operationalize linguistic parameters in such a way that they can be applied consistently to a large number of examples and can be fed into a computer for statistical analysis. In other words, the corpus linguist has to decide how to put his/her variables onto a numeric scale of some sort, in a way that the variables and variable levels cover all instances encountered in the examples. This typically implies an initial analysis of the data, since not everything is quantified naturally. Let us consider, as an example, the popular linguistic issue of discovering family relations between languages. Given that cardinal numerals seem to only slowly change their form, and certainly keep their meaning, they testify to older stages of the language. For this particular example, we limit ourselves to cardinal numerals from 1 to 10 in some Romance, Germanic and Slavonic languages (see Tables 1, 2 and 3).2 2. The study was inspired by a study looking at numerals from one to ten in 11 languages, published in Wichern and Johnson (2007). The larger dataset, comprising 51 languages, was collected by Nick Fieller from phrasebooks and exchange students.

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English

French

Occitan

Catalan

Spanish

Asturian

Galician

Portugese

Italian

Romanian

Table 1.╇ Numerals in some Romance languages

one two three four five six seven eight nine ten

un deux trois quatre cinq six sept huit neuf dix

un dos tres quatre cinc sièis sèt uèch nòu dètz

un dos tres quatre cinc sis set vuit nou deu

uno dos tres cuatro cinco seis siete ocho nueve diez

ún dos tres cuatro cinco seyes siete ocho nueve diez

um dous três catro cinco ceis sete oito nove dez

um dois três quatro cinco seis sete oito nove dez

uno due tre quattro cinque sei sette otto nove dieci

unu doi trei patru cinci sase sapte opt noǔa zece

English

Dutch

German

Frisian

Norwegian

Danish

Swedish

Icelandic

Table 2.╇ Numerals in some Germanic languages

one two three four five six seven eight nine ten

een twee drie vier vijf zes zeven acht negen tien

ein zwei drei vier fünf sechs sieben acht neun zehn

ien twa trije fjouwer fiif seis sân acht njoggen tsien

en to tre fire fem seks sju atte ni ti

en to tre fire fem seks syv otte ni ti

ett två tre fyra fem sex sju åtta nio tio

einn tveir Þrír fjórir fimm sex sjö átta níu tíu

If we measure the similarity between number words, could we use that information to deduce family relationships? And how can we do that? Which variables would we use? Variables can be any of several different types. Recognizing which type a variable belongs to is important because this affects what choices of analyses are open to the investigator at a later stage. The initial distinction is between categorical, ordinal and numerical variables. Within these, various levels of refinement are possible. A simple, and certainly imperfect idea, yet one that yields a lot of useful information, is to use current spelling in terms of initial letters (pronunciation specifics could be added, as we will demonstrate in Section 2.5); other measures, e.g. number

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English

Ukranian

Russian

Bulgarian

Macedonian

Serbo-Croat

Bosnian

Slovene

Czech

Polish

Slovak

Table 3.╇ Numerals in some Slavonic languages

one two three four five six seven eight nine ten

один два три чотыре пять шістъ сімъ вісім девятъ десятъ

один два три четыре пять шесть семь восемь девять десять

едно две три четири пет шест седем осем девет десeт

един два три четири пет шест седум осум девет десет

jedan dva tri četiri pet šest sedam osam devet deset

jedan dva tri cxetiri pet sxes sedam osam devet deset

ena dve tri štiri pĕt šest sedem osem devet deset

jedna dvĕ tři čtyři pĕt šest sedm ost devĕt deset

jeden dwa trzy cztery pięć sześć siedem osiem dziewięć dziesięć

jeden dva tri štyri päť sesť sedem osen deväť desäť

of syllables or last letters, output nonsense. If the spelling of the first letter is our variable of interest, we would have over 30 different variable levels that lack any intrinsic ordering, making it a classical example of a categorical variable (sometimes called a nominal variable), i.e. a variable that has two or more categories, but there is no intrinsic ordering to the categories. There are plenty of categorical variables in linguistics. Think of, for example, masculine/feminine/neuter gender or imperfective/ perfective aspect. There is no intrinsic ordering to these categories, no agreed way to order these from highest to lowest or from smallest to largest, etc. If the variable has a clear ordering, then that variable would be an ordinal variable, as described below. Categorical variables do not have numeric values so it is not possible to perform arithmetic calculations (such as calculation of averages) on them either. A categorical variable with two categories (i.e. a binary variable) may be coded as taking values 0 and 1 but this is merely convention. Even if male is coded as 0 and female as 1, it still makes no sense to calculate an average gender. Ordinal variables are similar to categorical variables. The difference between the two is that ordinal variables do show a clear ordering. Ordinal linguistic variables do not spring to mind as easily as categorical variables do, probably because they require some form of data analysis. Let us consider the following example. Suppose you have a variable that encodes the level of control you have over an action, with three categories, for example “low” for verbs like forget, “medium” for actions like find and “high” for verbs like copy. In addition to being able to classify control-situations into these three categories, you can order the categories as low, medium and high. Although we can order situations according to the level of control we have over them, the spacing, i.e. the size of the difference, between the levels may well be inconsistent. The difference between medium and high control may well be much bigger than the difference

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between low and medium control. As with categorical variables it is not possible to perform arithmetic calculations on ordinal variables unless they are given numerical scores to reflect the ordering. However, assigning values 1, 2, 3, … will presume that the difference between the first two levels is the same as that between the second and third. Whether this is appropriate is a subjective decision based on the expertise of the linguist. Often, assigning scores to ordinal variables (i.e. converting them to numerical variables) is the only way of taking the ordering into proper account when analysing ordinal data. An alternative would be to ignore the ordering and treat it as a mere categorical variable. Numerical variables are the easiest to handle in statistics. A distinction is sometimes made between interval and ratio numerical variables. Interval variables are measured on a scale that does not have an unambiguous zero point (such as temperatures) while ratio variables are on a scale with a clear zero. This distinction is rarely important but may matter: e.g. saying the temperature today is twice as warm as yesterday is nonsensical since it depends on the scale used (0F or 0C), while an object is always twice as long as another whatever units are employed. However, it is possible to say that the difference between two values of an interval variable (e.g. temperature) is twice that between two others; this makes many common arithmetic operations possible on interval variables. Numerical variables may take only discrete values (e.g. integers) or they may be continuous, i.e. take any value within a range recorded to as many decimal values as desired. Variables may be restricted to taking only positive values (e.g. counts or frequencies or percentages) or they might be able to take both positive and negative values, e.g. ones derived as differences between other measures.3

2.2

Calculation of distances (similarities) between objects

Let us return to our example in which we have decided to use the spelling of the first letter of the cardinal numeral as the variable of interest. In order to decide which languages are more similar, we need more than just a variable to explore the cardinal numerals; we also need a way to assess similarity or dissimilarity between the numerals. In the context of cluster analysis, the term similarity has its everyday meaning of how similar entities are. More specifically, similarity is a numerical measure of how similar

3. To illustrate the restrictions imposed by the type of variable on choices available at later stages of the analysis it is useful to consider which familiar summary statistics can be calculated for the various types. For categorical variables only the mode (or the most commonly occurring value) can be used. For ordinal variables the median can also be used as a descriptive statistic. For any numerical variable, whether interval or ratio, all the commonly used statistics such as mean, variance, standard deviation, analysis of variance, regression etc. can be used but it is only for ratio variables that it is possible to use coefficients of variations or geometric mean or logarithms.

412 Dagmar Divjak and Nick Fieller

entities are: the larger that number, the more similar they are. The term distance or dissimilarity is the converse, i.e. how unlike the entities are. Here, objects are more dissimilar if the numerical measure is larger. In some situations it is more natural to think of similarities between objects, e.g. we could regard two words as being similar if they have similar meanings. In a totally different context we might think it more natural to concentrate on dissimilarities or distances, e.g. difference in percentages of occurrence of two words in a given corpus. Commonly, similarities are based upon a combination of several properties or variables. For example, we might want a similarity between words to be based not just on meaning but on frequency of usage, number of syllables, overlap of phonemes or almost any conceivable property of the word, provided we could put that property onto a numeric scale of some sort. The numeric scale might be very coarse, e.g. 0, 1, 2 or 3 corresponding respectively to not at all, slightly, fairly and very similar in meaning (all subjective judgements, note), or it might be a more continuous measure with many possible numeric values, such as a percentage. Let us look at the Germanic numerals. As we can see in Table 4, if we take the single first letter at face value, the numeral one begins with e in virtually all Germanic languages listed, except Frisian and English. Two is spelled with a t in all languages except German. The first letter of nine is n in all languages, and so on. We could decide to indicate identity in spelling with 1 and non-identity or difference with 0 for each of the numerals. Given that we are looking at 10 numerals in each language, we can sum 1’s (same) and 0’s (different) to get overall a similarity/dissimilarity score out of ten per language-pair. On this count, the similarity between Dutch and German, two neighbouring languages, is 5 out of 10, since 5 numerals share an identical first letter, scoring 1 each, and 5 do not, scoring 0 each. On a similar count, the similarity between Swedish and Danish is 9 out of 10, with only the numeral 8 having a differently spelled first letter. As mentioned before, similarities and dissimilarities are closely related. A distance between a pair of towns also reveals how close they are. Numerically it is easy Table 4.╇ A dissimilarity matrix for the spelling of the first letter in Germanic numerals from 1 to 10 English Dutch German Frisian Norwegian Danish Swedish Icelandic

English

Dutch

German

Frisian

Norwegian

Danish

Swedish

0 7 5 2 2 2 2 2

7 0 4 6 5 6 5 5

5 4 0 4 3 4 3 3

2 6 4 0 1 2 1 1

2 5 3 1 0 1 0 0

2 6 4 2 1 0 1 1

2 5 3 1 0 1 0 0



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to construct a similarity from a dissimilarity. For example, a percentage of agreement can be converted to a percentage of disagreement by subtraction from 100%. The 0, 1, 2, 3 scale coding for not at all, slightly, fairly and very similar referred to above can be converted to a measure of dissimilarity by subtracting the ranks from 3. This yields 0, 1, 2, 3 indicating very, fairly, slightly and not at all dissimilar. The reason for emphasising that similarities and dissimilarities can be calculated from each other is that, although it may be more natural to think of a similarity between objects in many situations, most computer packages such as R will require a list of dissimilarities, rather than similarities. In our example, we can subtract similarities from 10. The dissimilarity between Swedish and Danish, for example, is 1, since only the numeral 8 has a differently spelled first letter, the nine remaining numerals being identical in the spelling of the first letter. If we collect the dissimilarities for all language pairs, we obtain a dissimilarity matrix (Table 4). The way in which the similarity or distance between objects is calculated will determine how objects are grouped together by a computer algorithm into a system of clusters, sub-clusters, subsubclusters, etc. In particular, if the measure of similarity depends upon severable variables or properties it matters crucially what relative weights are given to the various properties. For example, we might regard frequency of usage as being twice as important as the number of syllables in reflecting the semantic similarity between words, so we would want the variable ‘usage’ to be given twice the influence or weight of ‘number of syllables’ in an overall measure of similarity. Of course, this is a subjective decision based upon expert knowledge. In fact, giving equal weight to all properties is also a subjective decision even though it might look as if an attempt at objectivity has been made. The sections below describe a few ways of combining properties or variables into measures of similarity or dissimilarity (or distance). In most cases, it is assumed that the variables are given equal weight (i.e. are regarded as equally important) but this is for convenience and it should not be overlooked that using equal weightings implies a specific decision of equal importance. Which of the various measures is “best” in any given situation is again a subjective decision but some restrictions on which measures can be used are imposed by the type of data available, e.g. whether the variables are categorical or whether they are continuous ratio data or whether there are some of each type; we will take this up in some detail below.

2.2.1 Categorical variables Some measures of similarity for categorical variables are designed specifically for binary categorical variables. At first sight this may appear to be a severe restriction, but in principle it is always possible to define a set of “dummy” binary variables to indicate which category an object has. Most recent computer packages handle this step, if it is required, internally and automatically so that the process is hidden from

414 Dagmar Divjak and Nick Fieller

the user; therefore, we will not describe it here. Furthermore, there is a drawback to converting categorical variables with large numbers of categories into dummy binary ones, and so it is generally better to use measures designed specifically for multi-level categorical variables. For categorical variables we focus on two measures, the application of which is not limited to nominal variables, i.e. Matching coefficients for binary variables and the Jacard coefficient. After a brief description of their mathematical properties, we will illustrate how this works on a simple example. Matching coefficients for binary variables: If all the variables measured in an individual observation are binary, then the simple matching coefficient is the total number of matches (of both 1s and 0s) divided by the number of variables. This gives equal weight to positive and negative matches. This is reasonable for variables such as gender with 1 coding for male and 0 for female or where 1 and 0 code for presence and absence and a co-absence is of some significance, but it might be misleading in others. In cases where co-absences are non-informative, a modification of the simple matching coefficient is the Jacard coefficient obtained by ignoring those variables with negative matches in the calculation, i.e., it is calculated from the total number of positive matches divided by the number of variables where at least one of the two individuals has value 1 for that variable. If all variables match negatively then the similarity is conventionally taken to be 0. Apart from these two basic matching coefficients, other modifications have been suggested which affect the weights given to variables where only one of a pair of binary variables is present for a particular individual. Some of these are discussed in detail by Gower and Legendre (1986). To illustrate the calculation of the Matching Coefficients with a simple example, consider Table 5 which gives the values of two categorical variables on six languages. Here, the two variables are Family (with possible values Germanic and Slavic) and Alphabet (with possible values Latin and Cyrillic). These variables can be represented as binary variables by coding Germanic as 1 and Slavic as 0, and Latin as 1 and Cyrillic as 0, giving the result shown in Table 6. The choice of which values are coded as 1 and which as 0 is arbitrary here and will not affect the result. This may not always be Table 5.╇ An example of two categorical variables measured on six languages Language

Family

Alphabet

English German Dutch Russian Polish Serbian

Germanic Germanic Germanic Slavic Slavic Slavic

Latin Latin Latin Cyrillic Latin Cyrillic

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Table 6.╇ An example of two binary variables measured on six languages Language

Family

Alphabet

English German Dutch Russian Polish Serbian

1 1 1 0 0 0

1 1 1 0 1 0

Table 7.╇ Table of similarities between languages based on two binary variables with a simple matching coefficient English German Dutch Russian Polish Serbian

English

German

Dutch

Russian

Polish

Serbian

1 1 1 0 â•⁄â•‹0.5 0

1 1 1 0 â•⁄â•‹0.5 0

1 1 1 0 â•⁄â•‹0.5 0

0 0 0 1 â•⁄â•‹0.5 1

â•⁄â•‹0.5 â•⁄â•‹0.5 â•⁄â•‹0.5 â•⁄â•‹0.5 1 â•⁄â•‹0.5

0 0 0 1 â•⁄â•‹0.5 1

the case, for example, where 1 indicates presence and 0 absence of some property of attribute. Whether co-absence of a property carries the same significance as co-presence is not obvious and can only be decided within the context of the example. The value of the simple matching coefficient used to measure the similarity between English and German is (1+1)â•›/â•›2 = 1: the two languages match for the variables Family and Alphabet and this sum is then divided by 2 because there are two variables in total. The similarity between English and Polish is (0+1)â•›/â•›2 = 0.5 since there is no match on the first variable but there is on the second. Between English and Russian the similarity is 0 because there are no matches on either of the variables. The complete table of similarities is given in Table 7. Note that Table 7 is symmetrical about the main diagonal: the similarity between Russian and Polish, for example, is the same as that between Polish and Russian. The calculations above have naturally led to measures of similarity. There are, however, occasions where it is more convenient to work with measures of dissimilarity, not least when computer packages such as R require it for entry into further automatic statistical analysis. The measure of similarity used is necessarily between 0 and 1 (since it is scaled by the total number of possible matches) with 1 indicating maximum similarity. This makes it easy to convert the values to a measure of dissimilarity by subtracting them from 1, giving values where 0 indicates minimum dissimilarity and 1 maximum dissimilarity. The result is shown in Table 8.

416 Dagmar Divjak and Nick Fieller

Table 8.╇ Table of dissimilarities between languages based on two binary variables with the complement of a simple matching coefficient English German Dutch Russian Polish Serbian

English

German

Dutch

Russian

Polish

Serbian

0 0 0 1 â•⁄â•‹0.5 1

0 0 0 1 â•⁄â•‹0.5 1

0 0 0 1 â•⁄â•‹0.5 1

1 1 1 0 â•⁄â•‹0.5 0

â•⁄â•‹0.5 â•⁄â•‹0.5 â•⁄â•‹0.5 â•⁄â•‹0.5 0 â•⁄â•‹0.5

1 1 1 0 â•⁄â•‹0.5 0

Table 9.╇ Table of dissimilarities between languages based on two binary variables with the complement of a Jacard matching coefficient English German Dutch Russian Polish Serbian

English

German

Dutch

Russian

Polish

Serbian

0 0 0 1 â•⁄â•‹0.5 1

0 0 0 1 â•⁄â•‹0.5 1

0 0 0 1 â•⁄â•‹0.5 1

1 1 1 0 0 0

â•⁄â•‹0.5 â•⁄â•‹0.5 â•⁄â•‹0.5 0 0 0

1 1 1 0 0 0

If we ignore “negative” matches, i.e. a match between zeroes as zeroes indicate absence of similarity here, then the only changes in Table 7, derived from the simple matching coefficient, involve pairs where at least one match (but not all) is negative; in this case this affects Russian and Polish and Serbian and Polish. The exclusion of cases where all variables match “negatively” is justified because in those cases the distance is maximal and conventionally taken as 1. The results are shown in Table 9.

2.2.2 Numerical variables For numerical variables, whether interval or ratio, it is usual to define distances, since most of the definitions are easily described in geometric terms. It is presumed that all the variables measured on an object are in the same units. This might mean that they are all percentages or all lengths measured in centimetres or weights in grams, or it could mean that they are standardised in some other way (for numerical variables this could be done by dividing by their standard deviations, and for categorical variables by dividing by their range, for example). Although we have described special coefficients for binary variables, practical experience indicates that the various measures described below can also be used for collections of binary variables provided that there are more than ten to twenty binary variables. The results of the analyses seem interpretable and are supported by other available evidence. Some basic and widely-applied methods include:

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A Manhattan distance

Euclidean distance B

Figure 1.╇ The Euclidean and Manhattan distances

Euclidean distance. The ordinary geometric distance between two points, A and B, marked on a piece of paper, as illustrated in Figure 1, is the Euclidean distance. With only two variables it is possible to represent all the individuals in a collection by points whose coordinates are given by the values. The Euclidean distance between two points is then obtained by summing the squared differences between the pairs of corresponding values for the two individuals and taking the square root of the sum. When there are several variables the procedure is the same except that the sum is over the squared differences of corresponding values of all variables. City block distance. The Manhattan or City-block is the sum of the absolute differences between the pairs of corresponding values for two individuals (rather than the sum of the squares for Euclidean distance). It would be the distance needed to travel on a rectangular grid of streets and avenues between two locations, as Figure 1 shows, and as such is always larger than the Euclidean distance, If the Manhattan distance measure is applied to binary variables and then divided by the number of variables, the resulting distance is identical to that obtained by applying the simple matching coefficient. Mahalanobis distance. A generalisation of the Euclidean distance is the Mahalanobis distance. Essentially, the aim is to make appropriate allowance for differing variances of different variables and the correlations between pairs of those variables. The effect is that less weight is given to differences in values on variables with large variances (so the large differences on these do not overwhelm the overall measure) and additionally to compensate for “duplication of information” when two variables are highly correlated. Other measures. As well as the two most commonly-used measures described above, many other possibilities have been proposed. Some of these are highly specific to

418 Dagmar Divjak and Nick Fieller

particular applications and others are based on some theoretical statistical property (such as chis-quared distances, distances based on a measure of correlation, and special formulae when the variables are angles). The correlation-based measures are particularly useful when the numerical variable has been derived from an ordinal categorical one, since their use lessens the dependence upon the particular numerical scores used for the ordered categories. A full discussion is given by Gower and Legendre (1986). Mixed variables. When some of the variables are numerical and some are categorical the possibilities are: (i) to convert some of the variables to be of the same type as the remainder and use one of the measures defined above or, (ii) to use a weighted sum of similarities calculated separately for variables of the same type or, (iii) to use a weighted sum of individual similarities calculated from pairs of variables in the most appropriate way. A special technique for the last of these, the Gower universal similarity coefficient, defines particular ways of doing this so that the resulting set of similarities has desirable mathematical properties, which would, however, be beyond the scope of this chapter. To illustrate some of these measures we continue the example introduced above with measures of three numerical variables: number of letters in the alphabet, number of speakers in millions and number of countries where the language is among the official languages. The values are given in Table 10. Notice that these variables are measured in totally different units and we use this to illustrate the pitfalls present unless some form of standardisation is used. The Euclidean distance between English and German as reflected by these variables is √[(26 – 30)2 + (360 – 120)2 + (7 – 3)2] = 240.067. That between English and Polish is √[(26 – 30)2 + (360 – 40)2 + (7 – 1)2] = 320.081. The complete distance matrix is given in Table 11. For illustration and again temporarily ignoring the fact that the variables are measured in different units, the City-Block or Manhattan distance between English and German is |26 – 30| + |360 – 120| + |7 – 3| = 4 + 240 + 4 = 248. Here the vertical Table 10.╇ An example of three numerical variables measured on six languages Language

Number of letters in the alphabet

Number of speakers in millions

Official language in number of countries

English German Dutch Russian Polish Serbian

26 30 26 33 32 30

360 120 â•⁄28 155 â•⁄40 â•⁄â•⁄8.7

7 3 6 5 1 3

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Table 11.╇ Distance matrix of Euclidean distances between languages English German Dutch Russian Polish Serbian

English

German

Dutch

Russian

Polish

Serbian

â•⁄0 240.1 332.0 205.1 320.1 351.3

240.1 â•⁄0 â•⁄92.1 â•⁄35.2 â•⁄80.0 111.3

332.0 â•⁄92.1 â•⁄0 127.2 â•⁄14.3 â•⁄19.9

205.1 â•⁄35.2 127.2 â•⁄0 115.1 146.3

320.1 â•⁄80.0 â•⁄14.3 115.1 â•⁄0 â•⁄31.4

351.3 111.3 â•⁄19.9 146.3 â•⁄31.4 â•⁄0

Table 12.╇ Distance matrix of Manhattan distances between languages English German Dutch Russian Polish Serbian

English

German

Dutch

Russian

Polish

Serbian

â•⁄0 248.0 333.0 214.0 332.0 359.3

248.0 â•⁄0 â•⁄99.0 â•⁄40.0 â•⁄84.0 111.3

333.0 â•⁄99.0 â•⁄0 135.0 â•⁄23.0 â•⁄26.3

214.0 â•⁄40.0 135.0 â•⁄0 120.0 151.3

332.0 â•⁄84.0 â•⁄23.0 120.0 â•⁄0 â•⁄35.3

359.3 111.3 â•⁄26.3 151.3 â•⁄35.3 â•⁄0

bars indicate the absolute value of the difference (i.e. larger minus smaller). Table 12 contains the complete distance matrix. The Manhattan distances are generally a little greater than the Euclidean distances but a serious drawback to both is that it matters crucially what units are used for the individual variables. If the number of speakers is measured in billions rather than millions then the measures are not only changed substantially but the relative orderings of them are changed. So, a language which appeared to be “closest” to a given one (i.e. its nearest neighbour) might appear to be a distant neighbour if the units of one variable are changed. To demonstrate this, consider the data in Table 13. Table 13.╇ An example of three numerical variables measured on six languages Language

Number of letters in the alphabet

Number of speakers in billions

Official language in number of countries

English German Dutch Russian Polish Serbian

26 30 26 33 32 30

0.360 0.120 0.028 0.155 0.040 0.0087

7 3 6 5 1 3

420 Dagmar Divjak and Nick Fieller

These are the same as in Table 7 but with the number of speakers expressed in billions not millions. The table of Euclidean distances calculated from these figures is given in Table 14. Table 14.╇ Distance matrix of Euclidean distances between languages English German Dutch Russian Polish Serbian

English

German

Dutch

Russian

Polish

Serbian

0 5.662 1.054 7.283 8.491 5.668

5.662 0 5.001 3.606 2.830 0.111

â•⁄1.054 â•⁄5.001 â•⁄0 â•⁄8.127 11.012 â•⁄7.019

7.283 3.606 8.127 0 5.115 5.146

â•⁄8.491 â•⁄2.830 11.012 â•⁄5.15 â•⁄0 â•⁄4.031

5.668 0.111 7.019 5.146 4.031 0

It is clear that not only the distances are changed in value but the relative ordering between the distances is substantially changed as well. For example, when measuring the number of speakers in millions (Table 11) the most similar pair is Russian and German with a Euclidean distance between them of 40.0. If we measure the number of speakers in billions, then the Russian-German pair is only the fourth closest; the closest pair is now German and Serbian. Similar changes are seen with the Manhattan distances but the Mahalanobis distances remain entirely unchanged and are identical to those in Table 13. We do not give these two tables here but the R code to produce them is provided in the Appendix. Similarly, it is easy to check that the Gower measure (given in Table 16) is unaltered by a change of units of a single variable. This comparison illustrates why the basic similarity measures should only be used when all the variables are measured in the same units. However, situations arise frequently in practice where inevitably the variables are in different units. In this case, variables should be standardised. One method is to divide each variable by its standard deviation. This can be done in R with the function scale(.) setting datamatrix<-scale(datamatrix), where datamatrix consists entirely of numerical values of the variables. A slightly better way is to use a Mahalanobis distance which additionally compensates for correlations between variables. It is not realistic to calculate a Mahalanobis distance by hand, even for the small example used here, but it can be done in a good computer package such as R. It does, however, require a little ingenuity since none of the standard libraries provides a function for calculating all pairwise distances between points. The complete table (calculated using the R code given in Appendix) is given in Table 15. Finally, for mixed variables, i.e. when some are binary and some are numerical, the Gower coefficient essentially combines a measure based on binary variables with one based on numerical ones. There is a facility for specifying separate weightings for each variable but this goes beyond the scope of the description here. It can be added that the continuous variables are individually scaled but no allowance is made for

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Table 15.╇ Distance matrix of Mahalanobis distances between languages English German Dutch Russian Polish Serbian

English

German

Dutch

Russian

Polish

Serbian

0 2.034 2.934 3.096 2.888 2.731

2.034 0 2.426 2.534 0.904 1.111

2.934 2.426 0 3.091 2.992 1.684

3.096 2.534 3.091 0 2.889 2.434

2.888 0.904 2.992 2.889 0 1.376

2.731 1.111 1.684 2.434 1.376 0

Table 16.╇ Distance matrix of Gower distances between languages English German Dutch Russian Polish Serbian

English

German

Dutch

Russian

Polish

Serbian

0 0.384 0.222 0.783 0.754 0.848

0.384 0 0.267 0.572 0.360 0.463

0.222 0.267 0 0.706 0.545 0.625

0.783 0.572 0.706 0 0.427 0.236

0.754 0.369 0.545 0.427 0 0.342

0.848 0.463 0.625 0.236 0.342 0

correlations. For completeness we give the resulting distance table (Table 16) which was calculated from R using the code given in the Appendix. The data used are those obtained by combining the categorical variables from Table 5 with the numerical ones in Table 10.

2.2.3 Choice of similarity measure In many cases, the choice of similarity measure is also restricted by the type of data involved, i.e. categorical or numerical (although in some cases it is possible to convert one type to another). Where there is a choice between available measures, there may be little practical difference in the resulting analyses. The aspect that is most likely to affect the analysis, however, concerns the choice of weights given to the various properties measured. At its extreme, basing an analysis on similarity of meanings will be entirely different from an analysis based on numbers of syllables, i.e. whether the weights given to the properties ‘meaning’ and ‘number of syllables’ are 1 and 0, or 0 and 1, respectively. If it is desired to include both properties then it is up to the investigator to make a decision on the appropriate weights to use. Necessarily, this is a matter of subjective judgement determined by the objective of the analysis. Recall that giving equal weights is likewise a purely subjective judgement and needs to be justified by the study objectives. Particular care must be given to cases where variables are measured in different units. If all of the variables are numerical then they should be standardised to a similar scale. This is generally best done by using Mahalanobis distances

422 Dagmar Divjak and Nick Fieller

(which also compensates for correlations) but a partial alternative is to use the Gower coefficient, which does standardise the variables. Even after standardisation it is still necessary to consider the relative weights of the variables and individual weights for each variable can be specified when using the Gower metric in function daisy(.).

2.3

Cluster formation

All forms of cluster analysis are essentially algorithmic. That is, they are defined by the algorithm which actually produces “clusters” of similar objects. The choices that have to be made are, firstly, how to calculate the distance between clusters. Secondly, it has to be decided how to form clusters, i.e. whether to grow the clusters from the separate objects (agglomerative clustering), to divide the complete set of objects into successively smaller groups (divisive clustering), or to aim for a specific number of clusters and try to find the best division of the objects into that number of groups (k-means or partitioning clustering).4 We will discuss each of these options in turn, starting with agglomerative algorithms.

2.3.1 Agglomerative algorithms An agglomerative algorithm starts by regarding the n separate objects as n separate “clusters”. Then, the first step is to join the two objects which are closest together to form a cluster of size 2. Next, either another pair is joined together to form another size 2 cluster, or if there is a single object closer to the first size 2 cluster than any other pair, then it is joined to form a size 3 cluster. The process carries on until finally all the objects are joined together. Different from the results of PCA or MDS, the outcome of a cluster analysis can be illustrated in one picture, a tree diagram (or dendrogram).

Cluster B

Nearest neighbours

Cluster A

Average distance Furthest neighbours

Figure 2.╇ Different methods for defining distance between clusters 4. We will not discuss so-called Model-based approaches that assume a variety of data models and apply maximum likelihood estimation and Bayes criteria to identify the most likely model and number of clusters, e.g. the Mclust() function in the mclust package.

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To measure the distance between objects or clusters, possibilities are the minimum, maximum and average distance between two points in different clusters. This is illustrated in Figure 2. “Average” could be the straightforward arithmetic mean, or the median, or some other measure based on the squared distance between cluster means divided by a measure of internal spread within the clusters, usually the average squared distance of elements from their cluster means. Using the squared distance rather than just the raw distance ensures that clusters are kept compact and do not become too spread out. Let us explore these options in some detail and look at what family relations they propose for our cardinal numerals, the (dis)similarity between which is assessed on the basis of current spelling in terms of initial letters.

Danish

English

Icelandic

Swedish

Norwegian

Frisian

0

1

Height 2

German

3

Dutch

4

Dendrogram of agnes (x = germanic, method = “single”)

Germanic Agglomerative coefficient = 0.66

Figure 3.╇ Agnes clustering of Germanic cardinal numerals using a Single linkage amalgamation algorithm5

A nearest neighbour or single linkage algorithm will tend to produce clusters where some objects are separated by a large distance although there is a string of objects in between them. This is the case because in single linkage, the distance between two 5. agnes() will let you start from a datamatrix of values of variables and then calculate a distance matrix internally, hence requiring specification of the distance metric, but also allows you to feed in a distance matrix. Other routines such as hclust() require you to calculate the distance matrix separately first using dist() or daisy().

424 Dagmar Divjak and Nick Fieller

clusters is computed as the distance between the two closest elements in the two clusters. The result is rather like a railway network where two stations may be connected even though they are far apart, just because there are several intermediate stops. To be more specific, in the case of single linkage or nearest neighbour algorithms, the result reminds of a family tree with the most closely related (e.g. siblings) joined together at the first level, then separate families of siblings joined at the next level to form cousins and so on to produce a complete genealogy showing descendants from a single source. At each generation, the numbers of clusters (or families) become smaller but individual clusters contain members more distantly related. Furthermore, the clusters formed at one generation are subclusters of the next higher generation and so the analysis is a hierarchical cluster analysis. Let us look at the Germanic cardinal numbers from a single linkage point of view (Figure 3). A dendrogram is a visual representation of the distances at which clusters are combined. It is read from top to bottom. Horizontal lines show joined clusters. The position of the line on the scale indicates the distance at which clusters are joined. When you read a dendrogram, you want to determine where the distances between clusters that are combined are large; hence you look for large distances between sequential vertical lines. From this dendrogram we can read that the most closely related are three of the Scandinavian languages: Norwegian, Swedish and Icelandic, in which cardinal numbers are spelled by and large identically. Next, Frisian and Danish are added. These appear on different sides of the first cluster but this is irrelevant for the dendrogram structure. The horizontal ordering of clusters in the dendrogram is arbitrary: a dendrogram can be compared to a children’s mobile, suspended from a high point with clusters allowed to rotate freely. When it is taken down and laid on the table the horizontal ordering that the clusters end up in is accidental. In a third step, English is linked to the cluster including Frisian and Danish. Then German is added to the amalgam, and finally, Dutch, making Dutch the most dissimilar to the others of all Germanic languages included in the cardinal numbers sample. Furthest neighbour or complete linkage algorithms use the maximum pairwise distance between elements as a measure of distance between clusters. These algorithms should generally produce more compact clusters, as can be seen in Figure 4 where English and Frisian as well as Dutch and German now each form a cluster. Finally, algorithms based on some form of average linkage use the average distance between two points in different clusters; usually the average is taken as the straightforward arithmetic mean. These results will be intermediate in scale – in our case virtually identical to the single linkage result – between single and furthest linkage methods, as Figure 5 illustrates. Here, the only difference with the dendrogram resulting from single linkage (Figure 3) is to be found in the way in which Frisian and Danish are linked to the first cluster: while single linkage adds Danish first, followed by Frisian, average linkage adds both at the same time.

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German

Danish

Icelandic

Swedish

Norwegian

Frisian

English

0

1

2

Dutch

Height 3 4

5

6

7

Dendrogram of agnes (x = germanic, method = “complete”)

Germanic Agglomerative coefficient = 0.77

Figure 4.╇ Agnes clustering of Germanic cardinal numerals using a Complete linkage amalgamation algorithm

Danish

Icelandic

Swedish

Norwegian

Frisian

English

0

1

2

German

Height 3

4

Dutch

5

Dendrogram of agnes (x = germanic, method = “average”)

Germanic Agglomerative coefficient = 0.69

Figure 5.╇ Agnes clustering of Germanic cardinal numerals using an Average linkage amalgamation algorithm

426 Dagmar Divjak and Nick Fieller

Generally, clusters produced by single linkage will be more “spread out” than those produced by complete linkage, with those from average linkage somewhere in between. This is because for a new member to join a cluster on single linkage it only has to be close to one single member of the cluster; this can result in a long string of elements, each close to its neighbours but one end a long way from the other. With complete linkage a new member has to be close to all other members of the group, keeping the clusters more compact. The attentive reader will have noticed that all dendrogram plots list the agglomerative coefficient (AC), a measure of the clustering structure of the dataset that can range from 0 to 1. An AC close to 1 indicates that a very clear structuring has been found whereas an AC close to 0 indicates that the algorithm has not found a natural structure. This measure is sensitive to sample size, i.e. the value grows with the number of observations. For this reason, the AC should not be used to compare datasets of very different sizes. Given that we used the same datasets for all three clusterings, we can conclude that the combination of the Euclidean distance measure with the Complete Linkage algorithm yields the best results, the AC being equal to 0.77, thus outperforming Average Linkage (with AC = .69) and Single Linkage (with AC = .66). One more method, Ward’s Method, needs to be mentioned here. Ward’s is a variant of the agglomerative methods outlined above and is widely used. This technique allows two clusters to merge if the increase in sum of squared distances of the members of the new cluster from their mean is smaller than for any other possible merger between two clusters. Use of squared distances penalises spread out clusters and so results in compact clusters without being as restrictive as complete linkage. However, in many practical examples the differences between the resulting analyses applied to the same data are surprisingly superficial: with regards to the general picture, they are much the same with only a few differences of detail. In cases where there are substantial differences in the composition of clusters, thought must be given to why such differences occur and which of the methods is the most appropriate for the research questions of interest.

2.3.2 Divisive algorithms In principle, the process of forming clusters can work in reverse, i.e. starting by dividing a single large family into two and so on, again leading to a hierarchical analysis. The aim at each step is to divide the most heterogeneous cluster into two more homogeneous clusters. Heterogeneity and homogeneity are measures based on the various alternatives suggested above. In most cases this requires exhaustive examination of all possibilities and so is computationally very expensive for even medium-sized data sets. An exception is when the variables are all binary, in which case splits can be made using just one variable at a time. This monothetic divisive method takes individual variables in sequence rather than amalgamating them into an average and divides a cluster so that all elements in the two subclusters have a common value of a



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particular variable, i.e. if the split is made on the alphabet variable then all elements in one subcluster will have value 1 for Latin script and in the other subcluster they will have value 0 of that variable, or Cyrillic script. Choice of which variable to choose has to be made on some optimality criterion, the discussion of which is beyond the scope of this chapter.

2.3.3 K-means clustering An alternative divisive (but non-hierarchical) approach is to specify the desired number of clusters, k say, and search for a division of the n objects into k groups which is “best” in some defined sense. Such methods are usually referred to as k-means procedures and are within the class of optimization methods. A common measure of “best” is to require the average distance between objects in a cluster and their cluster centroid to be minimised in comparison to the average distance of cluster centroids from the centroid of all objects. Here “centroid” usually indicates the mean value of the cluster, but could be some more general measure of the “center” of the cluster. The measure used may be based on squared Euclidean distances rather than actual Euclidean distances to penalise allocations where one or two objects are far away from the centroid. This ensures more compact clusters which is often a goal of the analysis. In theory one might try to examine all possible arrangements of the n objects into k clusters and see which is “best” but the number of possible allocations explodes rapidly with increasing n and k. For ten objects and three clusters, the number of allocations is a little less than ten thousand. Consequently, all available computer techniques rely on iterative procedures. For example, the first step is to divide the objects arbitrarily into k groups, calculate the group centroids and then reallocate an object to a different group if it is closer to that group’s centroid than to its own, re-calculating group centroids after each re-allocation. Generally, such a technique will eventually converge (meaning that no more re-allocations are required) and the final result will be optimal or close to optimal. There is no mathematical reason for the procedure to converge on the absolute optimal solution, so most computer packages allow the procedure to be tried several times with different randomly selected allocations. This description begs the question of how to choose k, the desired number of groups. In the absence of some value being determined a priori by the objectives of the research, essentially the answer is to try several values and see which produces the most “sensible answers”. One approach might be to try a more rapid technique such as single link agglomerative clustering to suggest a suitable number of clusters and then improve on the allocation. 2.3.4 Differently named methods There are several named techniques which appear to have special meanings or procedures, but are in reality merely particular computer implementations of the procedures described above. Many of these are contained in the widely used R library

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cluster and are actually functions that have been imaginatively given female first

names (see Kaufman and Rousseeuw 1990 for details). The basic function for agglomerative clustering in the library cluster is agnes(.) [from AGglomerative NESting]. This function can take (optional) arguments to determine the particular type of algorithm to be used (i.e. method = “single”, “average”, “complete” or “ward”). Within this package there are also functions available for other single non-agglomerative techniques, (i) diana(.) [from DIvisive ANAlysis Clustering] performs divisive hierarchical clustering, (ii) mona(.) [from MONothetic Analysis clustering of binary variables] is the form of divisive clustering appropriate when the values of all the variables are 0 or 1, while (iii) pam(.) [from Partitioning Around Medoids] and (iv) clara(.) [Clustering Large Applications] are both particular forms of K-means clustering; the latter is useful when the number of objects is very large (more than several thousand) while in other cases pam(.) is preferred. Finally, (v) fanny(.) [from Fuzzy ANalYsis clustering] implements a rarely used method which allows objects to belong partially to each of several different clusters. In fuzzy clustering, each point has a degree of belonging to clusters rather than belonging completely to just one cluster. Thus, points on the edge of a cluster may be in the cluster to a lesser degree than points in the centre of cluster.

Now, back to our example. What happens when we make the task a bit more difficult? We can add in more languages from one family, for example, languages that we know relate in a non-straightforward way to the core languages. As Figure 6 shows, cluster analysis can deal with such cases, keeping the newly added Celtic languages

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Figure 6.╇ Agnes clustering of Germanic (extended) cardinal numerals using a Single Linkage amalgamation algorithm

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Estonian

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Figure 7.╇ Agnes clustering of Slavic area cardinal numerals using a Single linkage amalgamation algorithm

distinct from the Germanic core that remains unchanged, while discovering similarities between the Celtic languages. In other cases, we might not want to limit our sample to a group of languages that are known to relate to each other but, for example, to all languages spoken in a particular area. Using areal data rather than family data shows how clustering deals with expected outliers. As an example, we include Baltic, Finnic and Ugric languages in the Slavic mix and obtain the dendrogram presented in Figure 7. Clearly, Latvian and Lithuanian share most similarities with the Slavic languages, as does, to some extent, Albanian. The further we move to the borders of the Slavic lands, towards Hungary in the South East and Estonian and Finnish in the North, the starker the differences become. We can also add in languages from two different families and ask whether different families can reliably be retrieved? This is done in Figure 8, which clearly shows a division between Germanic and Slavic families. The more information we include in the cluster analysis, the more complex the outputted dendrograms become. At the same time, as the number of clusters increases, the more urgently the question poses itself of how to decide on the optimal numbers of clusters.

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English Fresian Norwegian Swedish Icelandic Danish German Dutch Ukranian Russian Bulgarian Macedonian Serbo–Croat Bosnian Czech Polish Slovene Slovak

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Figure 8.╇ Agnes clustering of Germanic and Slavic cardinal numerals using a Single linkage amalgamation algorithm

2.4

Deciding on the “optimal” number of clusters

Cluster analysis presents the problem of how many factors, dimensions, or clusters to keep. Although “look for cluster groupings that agree with existing or expected structures” and “pick the one solution you like best” is not a frivolous comment in the context of cluster analysis, the utility of clusters must be assessed regardless of the method used to form the clusters. One rule of thumb for this is, as we mentioned before, to look at the height bar and to choose a place where the cluster structure remains stable for a long distance, i.e. no new clusters are added, such as, for example, between the Germanic and the Slavic group in Figure 8. Below we list three further criteria: 1. Size. All clusters should have enough cases to be meaningful. In the case of K-means clustering, where the researcher sets the number of clusters to be formed, one or more very small clusters indicates that the researcher has requested too many clusters. Analysis resulting in a very large, dominant cluster may indicate too few clusters have been requested. 2. Meaningfulness. Ideally, the meaning of each cluster should be readily intuited from the constituent variables used to create the clusters. Variable importance plots are one method of making this assessment. 3. Criterion validity. The cross-tabulation of the cluster identification names or numbers by variables that are known (from theory or prior research) to correlate with the concept which clustering is supposed to reflect should reveal the expected level of association.

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If these criteria are not met, care should be taken when interpreting the results of the cluster analysis. It may be the case that an inappropriate distance measure has been selected or that the hypothesized conceptual basis for clustering does not exist, resulting in arbitrary clusters. One way to assess the confidence one may have on the obtained cluster solution more objectively includes replicating the analysis on a different dataset or on subsets of the data to see if the structures emerge consistently. This is one of two relatively straightforward ways of validating a cluster analysis that are explained in the following section.

2.5

Calculating the “fit” of/validating a cluster solution

Let us consider another example, this one based on the pronunciation of Slavic numerals, listed in Table 3. The similarity matrix between languages was calculated by counting the number of matches of first letters as pronounced. This was converted to a distance matrix by subtracting each similarity from 10, as described in Section 2.2. The (resulting) dataset was subjected to a cluster analysis with Ward’s clustering algorithm, using the hclust package.6 The output dendrogram is presented in Figure 9.

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Figure 9.╇ hclust clustering of Slavic cardinal numerals as pronounced using Ward’s amalgamation algorithm 6. We switch to hclust here to maintain consistency with Section 2.5 where we illustrate pvclust that relies internally on hclust.

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In the next two sections we will examine the robustness of our clustering result in two ways, i.e. by means of examining silhouette widths (Section 2.5.1), as well as by running analyses on random subsamples of the dataset (Section 2.5.2).7

2.5.1 The Silhouette validation technique (Rousseeuw 1987) Silhouettes are a graphical aid to the interpretation and validation of cluster analysis. Each cluster is represented by a so-called silhouette, which is based on the comparison of its tightness and separation. This silhouette shows which objects lie well within their cluster, and which ones are merely somewhere in between clusters. The silhouette value measures the degree of confidence in the clustering assignment of a particular observation, with well-clustered observations having values near 1 and poorly clustered observations having values near −1. If the silhouette value is close to 1, the sample is “well-clustered”, i.e. it was assigned to a very appropriate cluster. If the silhouette value is around zero, that sample could be assigned to another cluster as well, and the sample lies equally far away from either option. If the silhouette value is close to –1, the sample is “misclassified” and is somewhere in between the clusters. The entire clustering is displayed by combining the silhouettes into a single plot, allowing an appreciation of the relative quality of the clusters and an overview of the data configuration. The overall average silhouette width for the entire plot is the average of the S(i) for all objects in the whole dataset. The largest overall average silhouette indicates the best clustering. Since the average silhouette width provides an evaluation of clustering validity, it might be used to select an “appropriate” number of clusters. For our dataset, we see that we can be reasonably sure that Ukrainian, Russian, Bulgarian and Macedonian form a coherent group, with the silhouette width for that cluster of four languages being 0.43 (Figure 10). We are less sure that Serbo-Â�Croat, Bosnian, Czech, Slovak and Slovene, if combined into one cluster, indeed belong together, their silhouette width being 0.20. Polish, finally, is kept separate, and the silhouette value for that separate cluster is 0, indicating that Polish could well have been assigned to a different cluster. The overall average silhouette width remains at a low 0.27, indicating that the proposed clustering as a whole may not be too sensible; this is very likely due to the way in which the pronunciation data was coded. Maybe a 7. The function cluster.stats() in the fpc package (Hennig 2010) provides a mechanism for comparing the similarity of two cluster solutions using a variety of validation criteria, including the average silhouette widths treated below. To be precise, cluster.stats() computes a number of distance based statistics which can be used for cluster validation, comparison between clusterings and decision about the number of clusters: cluster sizes, cluster diameters, average distances within and between clusters, cluster separation, average silhouette widths, the Calinski and Harabasz index, the best distance based statistics to decide about the number of clusters in a study of Milligan and Cooper (1985), Hubert’s gamma coefficient, the Dunn index and two indexes to assess the similarity of two clusterings, namely the corrected Rand index and Meila’s VI. Another package of interest in this respect is clValid (Brosk et al. 2011).

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Silhouette plot of (x = cutree (slavicpronunciation.clust.ward, k = 3), dist = slavicpronunciation 3 cluster C j j : n l ave

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2-cluster solution would fit the data better? In the next section we will introduce a technique that can assess this (un)certainty in terms of the more familiar p-values.

2.5.2 pvclust The uncertainty in hierarchical cluster analyses can be assessed, even if no independent test-sample is available, by means of p-values or values between 0 and 1 that indicate how strongly the clusters are supported by the data. pvclust is an R package that performs hierarchical cluster analysis on a numeric data matrix or data frame via the function hclust and automatically computes p-values for all clusters contained in the clustering of the original data.8 It also provides graphical tools such as the plot

8. The function pvclust, used for assessing uncertainty in clustering and illustrated below, is written so that it will only accept data entered as values of numerical variables (unlike agnes used so far which offers the choice of entering a distance matrix directly). Further, a method of calculating the distance matrix from the values of the numerical variables must be selected from a limited set of choices of Euclidean, Manhattan or binary. For the purposes of being able to illustrate pvclust we have fudged raw data by first calculating approximate Euclidean coordinates from the distance matrix using the R function cmdscale and then use these to calculate an approximate distance matrix. The result corresponds closely with that obtained based on actual numbers of matches and non-matches, no entry differing by more than 1.5 on a scale of distances between 0 and 10. This is not a technique we would usually recommend and we present it here only so that we can illustrate the use of pvclust for assessing uncertainty in clustering.

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function or the pvrect function which highlights clusters with relatively high/low p-values. For each cluster in hierarchical clustering, p-values are calculated via multiscale bootstrap resampling, a computer-based way of simulating similar datasets. pvclust provides two types of p-values: the AU (Approximately Unbiased) p-value (on the left, normally in red) and BP (Bootstrap Probability) value (on the right, normally in green). The AU p-value, which is computed by multiscale bootstrap resampling, is a better approximation to unbiased p-value than the BP value computed by normal bootstrap resampling. Going into details about bootstrap resampling methods is beyond the scope of this chapter. Clusters that are highly supported by the data will have large p-values. pvclust, by and large, confirms the assessment based on silhouette widths:9 we should not be too sure that the larger clusters exist outside of this dataset. When using a different dataset that likewise assesses the languages on the basis of the pronunciation of Slavic numerals between 1 and 10, we can be 100% sure, however, that Bulgarian and Ma� cedonian would be grouped together and 97% certain that Bulgarian, Macedonian, Ukrainian and Russian would be clustered together, while being 95% sure that Bosnian, Serbo-Croat and Czech would end up in the same group. Cluster dendrogram with AU/BP values (%)

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3. By way of conclusion This brief account could do little more than introduce Cluster Analysis as an intuitive tool for describing and categorizing linguistic data in a systematic and reproducible way that displays the outcome of the analysis visually in one dendrogram. We have emphasized that this does not give a totally “objective” method. On the contrary, there are many steps where subjective choices have to be made. We have highlighted these and discussed the impact that these may have on the ensuing results. The attentive reader will also have noticed that, different from its direct competitors PCA and MDS, Cluster Analysis does not provide information on the relative importance of variables or underlying factors; it is up to the analyst to extract these from the data (see Divjak and Gries 2006 for the implementation of some suggestions by Backhaus et al. 1996:â•›310–312). We did not feel it was appropriate here to go into the theoretical statistical background underpinning the methods. For these the reader is referred to Everitt et al. (2011) for the statistical side and to Johnson (2008), Baayen (2006) or Gries (2009) for an account in a linguistic setting. Neither have we done more than give the minimum of details of the R code and R language needed to implement them. For these the reader is referred to the textbooks and to the R system itself. Readers who invest some time trying the R system for themselves will quickly discover the power of its internal Help system. We have listed the names of the primary functions used for the various types clustering and these are sufficient to find details of how they are used and worked examples giving illustrations from the Help system. The reader is encouraged to work through these in detail and be assured that the initial effort will be quickly repaid.

References Alviar, J. J. (2008). Recent advances in computational linguistics and their application to biblical studies. New Testament Studies, 54(1),139–159 DOI: 10.1017/S0028688508000088 Baayen, R. H. (2008). Analyzing linguistic data: A practical introduction to statistics using R. Cambridge: Cambridge University Press. DOI: 10.1017/CBO9780511801686 Backhaus, K., Erichson, B., Plinke, W., & Weiber, R. (1996). Multivariate Analysemethoden: Eine anwendungsorientierte Einführung. 8th edition. Berlin; Heidelberg; New York: Springer. Brock, G., Pihur, V., Datta, S., & Datta, S. (2011). clValid: Validation of clustering results. Journal of Statistical Software, 25(4), March 2008. R package version 0.6-2. . Divjak, D., & Gries, St. Th. (2006). Ways of trying in Russian: Clustering behavioral profiles. Journal of Corpus Linguistics and Linguistic Theory, 2(1), 23–60. Everitt, B. S., Landau, S., Leese, M., & Stahl, D. (2011). Cluster analysis. 5th edition. Oxford: Wiley. DOI: 10.1002/9780470977811

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Gower, J., & Legendre, P. (1986). Metric and Euclidean properties of dissimilarity coefficients. Journal of Classification, 3(1), 5–48. DOI: 10.1007/BF01896809 Gries, St. Th. (2009). Statistics for linguistics with R: A practical introduction. Berlin: Mouton de Gruyter. DOI: 10.1515/9783110216042 Harnad, S. (2005). To cognize is to categorize: Cognition is categorization. In C. Lefebvre & H. Cohen (Eds.), Handbook on categorization (pp. 19–43). Oxford & London: Elsevier. DOI: 10.1016/B978-008044612-7/50056-1 Hennig, C. (2010). fpc: Flexible procedures for clustering. R package version 2.0-3. . Johnson, K. (2008). Quantitative methods in linguistics. New York: Wiley-Blackwell. Kaufman, L., & Rousseeuw, P. J. (1990). Finding groups in data: An introduction to cluster analysis (Series in Applied Probability and Statistics). New York: Wiley-Blackwell. Milligan, G. W., & Cooper, M. C. (1985). An examination of procedures for determining the number of clusters in a data set. Psychometrika, 50, 159–179. R Development Core Team (2008). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. . Rousseeuw, P. J. (1987). Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. Journal of Computational and Applied Mathematics, 20(1), 53–65. DOI: 10.1016/0377-0427(87)90125-7 Shaw, D. (1974). Statistical analysis of dialectal boundaries. Computers and the Humanities, 8, 173–177. DOI: 10.1007/BF02402137 Suzuki, R., & Shimodaira, H. An R package for hierarchical clustering with p-values. Retrieved from [Accessed 25 May 2012]. Tryon, R. C. (1939). Cluster analysis. New York: McGraw-Hill. Wichern, D. W., & Johnson, R. A. (2007). Applied multivariate statistical analysis. Englewood Cliffs: Prentice-Hall.

Appendix R code to create the distance matrices (tables) and dendrograms (figures) shown in this chapter In this final section we provide the code necessary to carry out the operations illustrated in this chapter. Those with little familiarity with R can run the code by copying it, bit by bit, into the R console, although it may be helpful to consult a basic introduction for R first. The data and R sessions can be downloaded from http://dx.doi.org/10.1075/hcp.43.16div.additional. We first provide the R code for calculating the tables of distances using the various measures we described above in Tables 5 through 14. The easiest function to use is dist(.) which is in the stats library and so is automatically loaded for every R session. The dist(.) function allows computation of distances based on the simple matching and Jacard coefficients for binary data and Euclidean and Manhattan distances for continuous data. Which distance is calculated is determined by specifying



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it the argument method. It should be noted that if method is given as binary then distances are calculated as the complement of the Jacard coefficient. To obtain distances based on the complement of a simple matching coefficient (i.e. giving equal weight to positive and negative matches) then the Manhattan method should be chosen. This is not mentioned in the R documentation. A more flexible function is daisy(.) which is in the cluster library and must be loaded separately. This allows all of the previously mentioned coefficients plus the Gower coefficient. The distance measures for binary variables are handled by specifying gower as the metric and then choosing symmetric or asymmetric for the simple or Jacard coefficients. Care must be taken when using the daisy(.) function that the classes of variables are declared correctly as factor or numerical. The R help system gives full details of this. Neither of these functions allows calculation of the Mahalanobis distances and although there is a mahalanobis function in the stats library it is not designed to calculate the complete set of pairwise distances between points. We give some code to produce the complete pairwise distances and experienced R users may recognise that the key idea is to standardise the data matrix before calculating the Euclidean distances. # load the library needed for accessing the function daisy(.) library(cluster) options(digits=3) # # # #

the following code assumes that all data files are in the current R working directory; if that is not the case, replace file=“filename.txt” with choose.files() that will let you browse your computer to select the file of interest

# read in the data from Table 6 from a comma separated file # with first line as header and first column as row names excategoric<-read.csv(file=“excategoric.csv”,header=T,row.names=1) # calculate distances dist(excategoric,method=“manhattan”)/2 dist(excategoric,method=“binary”) # read in data in Table 10 from a comma separated file with # first line as header and first column as row names exnumerical<-read.csv(file=“exnumerical.csv”, header=T, row.names=1) # calculate Euclidean distances dist(exnumerical,method=“euclidean”) # calculate Manhattan distances dist(exnumerical,method=“manhattan”) # calculate Mahalanobis distances v=var(exnumerical) x<-svd(v) vroot<-x$u%*%diag(sqrt(x$d))%*%t(x$v) dist(as.matrix(exnumerical)%*%solve(vroot))

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# read in complete data of mixed categorical and numerical # variables from a comma separated file with first line as # header and first column as row names exmixed<-read.csv(file=“exmixed.csv”,header=T,row.names=1) # calculate the Gower distances daisy(exmixed,metric=“gower”) # Repeat calculations of distances after converting data # to billions of speakers, then repeat calculations above exnumerical[,2]<-exnumerical[,2]/1000 # now have numbers of speakers in billions # calculate Euclidean distances dist(exnumerical) # calculate Manhattan distances dist(exnumerical,method=“manhattan”) # calculate Mahalanobis distances v=var(exnumerical) x<-svd(v) vroot<-x$u%*%diag(sqrt(x$d))%*%t(x$v) dist(as.matrix(exnumerical)%*%solve(vroot),method=“euclidean”)

Next, we provide the R code for running the cluster analyses we described above in Figures 3 through 11. # # # # # #

reads in .txt files, recognizes them as dissimilarity matrices and converts them to Rdata files this code assumes that all data files are in the current R working directory; if that is not the case, replace file=“filename.txt” with choose.files() that will let you browse your computer to select the file of interest

x<-read.table(file=“Germanic.txt”,header=T,row.names=1) # reads in .txt file germanic<-as.dist(x) # coerces the object x to be of class “distance”, # i.e. makes sure that the dissimilarity matrix is read # in as a ready dissimilarity matrix save(germanic, file=“germanic.Rdata”) # saves it as Rdata file x<-read.table(file=“Germanic_extended.txt”,header=T,row.names=1) germanicextended<-as.dist(x) save(germanicextended, file=“germanicextended.Rdata”) x<-read.table(file=“Slavic area.txt”,header=T,row.names=1) slavicarea<-as.dist(x) save(slavicarea, file=“slavicarea.Rdata”)



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x<-read.table(file=“Germanic_Slavic.txt”,header=T,row.names=1) germanicslavic<-as.dist(x) save(germanicslavic, file=“germanicslavic.Rdata”) x<-read.table(file=“Slavic pronunciation.txt”,header=T,row.names=1) # turns a similarity matrix into a distance matrix slavicpronunciation<-10-as.dist(x) save(slavicpronunciation, file=“slavicpronunciation.Rdata”) # loads the libraries needed to run the cluster analyses # runs the cluster analyses described and outputs # the dendrograms library(cluster) library(amap) #figure 3 load(“germanic.Rdata”) # loads the dataset germanic.clust.single<-agnes(germanic,method=“single”) # clusters the data using single linkage; no distance # metric needs to be specified since the data are entered # as dissimilarities plot(germanic.clust.single) # outputs the dendrogram #figure 4 load(“germanic.Rdata”) germanic.clust.compl<-agnes(germanic,method=“complete”) plot(germanic.clust.compl) #figure 5 load(“germanic.Rdata”) germanic.clust.average<-agnes(germanic,method=“average”) plot(germanic.clust.average) #figure 6 load(“germanicextended.Rdata”) germanicextended.clust.single<-agnes(germanicextended,method=“single”) plot(germanicextended.clust.single) #figure 7 load(“slavicarea.Rdata”) slavicarea.clust.single<-agnes(slavicarea,method=“single”) plot(slavicarea.clust.single)

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#figure 8 load(“germanicslavic.Rdata”) germanicslavic.clust.single<-agnes(germanicslavic,method=“single”) plot(germanicslavic.clust.single) #figures 9, 10 & 11 # loads the library library(pvclust) # loads the dataset load(“slavicpronunciation.Rdata”) # runs a multidimensional scaling to obtain # approximate Euclidean coordinates slavMDS<-cmdscale(slavicpronunciation,k=9,eig=TRUE,x.ret=TRUE) slavcoords<-slavMDS$points[,1:6] slavDIST<-dist(slavcoords,method=“euclidean”) # runs cluster analysis with hclust using # Ward’s amalgamation strategy slavicpronunciation.clust.ward<-hclust(slavDIST, method=“ward”) #plots the dendrogram plot(slavicpronunciation.clust.ward) # cuts the dendrogram into 3 clusters sil<-silhouette(cutree(slavicpronunciation.clust.ward,k=3), slavicpronunciation) # plots the silhouette widths plot(sil, nmax=80, cex.names = 0.5) # clusters the data using ward’s amalagamation algorithm # while taking 1000 random samples pron.slavic.pvclust<-pvclust(t(slavcoords), method.dist=“euclidean”, method.hclust=“ward”, nboot=1000) # plots the results plot(pron.slavic.pvclust) # draws rectangles around the highest cluster(s) that are # distinguished at the .05 level pvrect(pron.slavic.pvclust, alpha=0.95)

A simple way of creating dissimilarities from similarities for the numerals dataset is subtracting the difference value from the maximum similarity of 10, for example, as was done for the Slavic pronunciation dataset above slavicpronunciation.dis<-10-slavicpronunciation



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It may be necessary to transpose the rows and columns since pvclust clusters what is in the rows. This is done as follows: pron.slavic<-t(pron.slavic)

If a dataset contains large numbers of items to be clustered, the interactive function identify. hclust can be used to list the members of a cluster by pointing with the mouse and clicking (with the right button) on the vertical bars (a.k.a. ancestor lines).

Correspondence analysis Exploring data and identifying patterns Dylan Glynn

University of Paris VIII

Correspondence analysis is an exploratory technique for complex categorical data, typical of corpus-driven research. It identifies patterns of association and disassociation in those data. For instance, it can map the correlations between different uses of a linguistic form and its various social and/or morpho-syntactic contexts. The technique presents its results in the form of a two-dimensional plot, which visualises these relationships in an intuitive manner. These plots offer rich representations of the relations between different facets of complex data. Using R, this chapter explains how the technique works and offers a step-bystep explanation of its application and the interpretation of its results. The technique is also compared to the better-known and comparable cluster analysis. Keywords: categorical data, cluster analysis, exploratory statistics, R

1. A technique for visualising correlations in categorical data Correspondence analysis is a multivariate exploratory space reduction technique for categorical data analysis.1 Although true, such a description tells the linguist little. Equally true, but perhaps more helpful, is to describe correspondence analysis as an exploratory technique that reveals frequency-based associations in complex corpus data. Most importantly, perhaps, the technique visualises these associations to facilitate their identification. Linguists often wish to find relations between given linguistic forms, between their meanings and in what situations those forms and meanings are used. Correspondence analysis is especially designed for identifying such usage patterning. The visualisation of the relations takes the form of configuration biplots, or maps, which depict degrees of correlation and variation through the relative proximity

1. I would like to thank Koen Plevoets who first taught me this technique and Joost van de Weijer for his help polishing this paper. All shortcomings are my own.

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of data points (which represent linguistic usage features and/or the actual examples of use). This chapter describes how to perform correspondence analysis in R. It explains the R code needed to execute the analyses and shows how to interpret the results.

1.1

Use – What does correspondence analysis do?

In their quotidian research, linguists, from all kinds of theoretical orientations, analyse various usage-features of naturally occurring utterances. By way of example, imagine that one obtains 600 examples of a given word, a grammatical case, or a syntactic pattern. These examples can then be analysed, using traditional intuition-based analysis for a range of usage-features, such as tense, aspect, argument structure, agent type, the ground or path type, and the register or genre from which the example is taken. The results of analysing the examples of these usage-features can be summarised as counts of how often each of the features occurs. Significance tests can then be used to show that the occurrence of certain features is substantially more common than could be expected by chance. This statistically significant variation can then, in turn, be interpreted as representing a distinct pattern of usage. However, with more than a couple of different dimensions of analysis or large numbers of features at play, interpreting the numbers of occurrences becomes increasingly difficult, if not impossible. Quite simply, correspondence analysis is an exploratory tool that helps one find which usage-features co-occur with other usage-features, giving a map of their overall patterning. Assuming that one is adopting a cognitive or functional approach to language, these usage-patterns can be interpreted as grammatical description, operationalised in terms of relative frequency. It must be stressed that this technique is designed solely for exploratory purposes. In other words, it is a tool for finding things, not for establishing their significance or discerning their relevance. Therefore, it offers you no assurance that patterns found are anything more than a chance result, specific to the sample under observation. Moreover, this tool does not tell you where to look. Although exploratory, one must avoid ‘fishing’ for results by randomly combining factors in the hope of finding correlations that could be interpretable. Even if one finds correlations that ‘make sense’, such an approach increases the chance of finding co-incidental correlations or chance patterns in the sample.2 A metaphor that might be helpful is that of the shovel for the archaeologist: if one digs randomly, everywhere, it increases the chances of finding 2. Weller and Romney (1990:â•›57) suggest performing tests for independence, such as those presented in Chapter 1, to ascertain if there exists statistically significant variation before one performs correspondence analysis. Although this is optional, it may be a good guideline to avoid falling into the trap of thinking the correlations identified are significant. It must be remembered, however, that obtaining statistical significance is dependant upon the size of the sample. With a large enough sample, very small variations will be significant, and with small

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things, but exponentially increases the chance of finding irrelevant things. Correspondence analysis is a tool for digging in the data to look for patterns and correlations, but it certainly helps if one knows where to dig. This metaphor can serve us further: when an archaeologist finds an artefact, it is still up to the archaeologist to interpret the finding as well as to verify its authenticity. Correspondence analysis, assuming you have a reasonable hypothesis about where to look, is a basic and useful tool for unearthing patterns in the data, but it is no more than that.

1.2

Concept – How does correspondence analysis work?

Basically, correspondence analysis takes the frequency of co-occurring features and converts them to distances, which are then plotted, revealing how things are related by how close to or far from each other they are in a two- or three-dimensional visualisation. In the detail, there is much more to the technique, but this is the principle. Explaining a few key concepts will allow us to better understand the functioning of the technique as well as to interpret its results.

Distance matrix

The distance matrix is sometimes also called a proximity matrix and even a dissimilarity matrix. The concept is simple: the frequencies of co-occurrence are converted to distances. The resulting distance matrix can then be visualised in a two- or three-dimensional Euclidean space (‘normal’ perceptual space). In fact, more precisely, it is the differences between the rows and columns of frequencies that are converted to distances. Correspondence analysis uses the Chi-squared distance measure to produce the distance matrix. This measure is designed to compensate for different ‘amounts’ of a given category. If one has only a few examples of a given feature, let us say the ‘future tense’, it is highly likely that they will all, or mostly, co-occur with some other feature, such as a given verb. However, due to the low numbers involved, this is much more likely to be chance than other correlations identified. The Chi-squared distance measure attempts to compensate for this kind of bias. Nevertheless, despite the use of the Chi-squared measure, with experience, one will still observe (in the plots) correlations that are likely to be due to small numbers of a given feature. It is always necessary to go back to both the data, that is, the actual language examples, and to the raw frequencies, to see what the plots have ‘revealed’. Greenacre (2007:â•›Ch. 4) offers a lucid explanation of the Chi-squared distance measure.

samples (typical of semantic research), significance is much less commonly obtained. This is, of course, how it should be – it stops analysts making bold claims based on small samples.

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Euclidean cloud

The distance matrix takes the form of a Euclidean cloud. In other words, it is a spread of points in a given space, like rice thrown onto a board or the holes made by darts on a dartboard. In more technical parlance, correspondence analysis computes the ‘Eigenvectors’ (explained below) of a correlation matrix and produces this Euclidean ‘map’, in one or two dimensions of that correlation. This can be thought of as reducing a set of Chi-squared scores to Euclidean distances (natural perceptual distances), suitable for two- or three-dimension visualisations. For the reader familiar with exploratory statistics, it is essentially the same as principal components analysis, but modified for categorical data.

Profiles and mass

A profile is the behavioural characteristics of a given category in the analysis, determined by the set of relative co-occurrence frequencies of that category. In a frequency (contingency) table, it is a column or a row containing all the relative frequencies of those co-occurrences. It is these profiles that the correspondence analysis plots. To calculate the profile, you add the number of occurrences for each feature in a row. You then divide each of those occurrences by the sum of them. This gives you a profile figure for each cell. The same procedure is undertaken for the columns, giving you the column profiles. However, as mentioned above, not all the co-occurrences are of equal importance. Infrequent features would have a disproportionate effect if all were taken equally. Correspondence analysis uses the weighted averages of the profiles to compensate for this. In correspondence analysis, the term ‘mass’ is used to mean ‘weight’. Weighting an average modifies the calculation to bias certain scores. It is widely used in basic statistics, from calculating the average score in a class test to the average monthly profit of a franchised shop. Although the idea of adding bias to any calculation may raise concern, in this case it is conventional and entirely accepted within the statistics community.

Inertia and variation

The higher the inertia one obtains, the better. Inertia is the term used in correspondence analysis to talk about the degree of variation. The inertia is calculated on observed and expected frequencies of co-occurrence. Inertia is high when column and row profiles have large deviations from their averages. In multiple correspondence analysis (as opposed to binary correspondence analysis), these scores are not normally interpretable, which is a major drawback for this form of the technique. They are not interpretable because the scores calculated seriously underestimate the amount of accurately described variation, giving unnecessarily ‘bad’ results. Two corrections to this have been proposed, firstly by the original author of the technique, Benzécri (1979 [reported in Greenacre 2006:â•›68]), and secondly by one of the current main



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proponents of the technique, Greenacre (2006:â•›68). Greenacre argues that Benzécri’s original correction was biased towards an overly optimistic result, that is, explaining more variation than was actually the case. The {ca} package, described in Section 2.3.2, includes an option to apply Greenacre’s inertia adjustment.

Biplots

The concept behind the visualisation in a biplot is quite simple to understand. The correspondence analysis has calculated proximity values for the combination of the cells across the rows and columns of a contingency table. These can be plotted. Each dimension of the plot (there are two dimensions in a biplot) will represent a certain percentage of the structuring of the data variation, or ‘inertia’. Plotting a single dimension, a simple line (the x-axis), will place the data points on this line at varying distances from each other. However, in most situations, this will poorly represent the relations between those features. If we add a second dimension, the y-axis, we obtain a two-dimensional biplot, typical of correspondence analysis and a range of other space reduction techniques. This will, hopefully, accurately represent a great deal of the structure in the variation in the data. Mathematically, the number of possible dimensions is equal to the number of rows or columns (whichever is smaller) minus one. So, to visualise a table with five rows and eight columns, one would need four dimensions. The scores of the inertia (or explained variation) are typically given for these first two dimensions; the x and y axes of the biplot. Although it is possible to take any two of the mathematically possible dimensions and plot these. Normally, a combination of the first two dimensions captures a large percentage of the variation. Adding a third dimension, the z-axis, produces a three-dimensional plot that will even more accurately represent the behaviour of the data. Three-dimensional plots are also possible in R, but are not considered in this chapter. Sometimes, it is useful to examine combinations of dimensions one and three or even two and three in biplots, especially when the explained inertia is low. For most data sets, though, a combination of the first two dimensions offers the most accurate and interpretable visualisation of the variation and association in the data. The numerical summary of a correspondence analysis will list all the dimensions, but above the third or fourth dimension, it is rare that further dimensions represent anything more than a small fraction of the variation. In order to completely represent a contingency table, one would need all the mathematically possible dimensions. Unfortunately, there is a range of terminology that varies from one book to another and even from one R package to the next. A few terms that may arise, especially in the numerical summaries of the analysis include: ‘Eigenvalues’, which indicates the inertia; the ‘percentages of explained variance’, or simply the percentage of inertia; and ‘communalities’, which are the percentages of explained inertia for individual rows or columns. If one wishes to work with the technique, there are three excellent books that explain its functioning in a clear manner, accessible even to readers with

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no statistical training. These books are Greenacre (2007) Correspondence analysis in practice, Le Roux and Rouanet (2010) Multiple correspondence analysis, and Husson et al. (2011) Exploratory multivariate analysis by example using R.

1.3

Choice: Binary and multiple correspondence analysis

Correspondence analysis is, in fact, a family of techniques. There exist at least three kinds of binary correspondence analysis and three kinds of multiple correspondence analysis. Binary correspondence analysis can be understood as the basis for the multiple correspondence analysis. It has two advantages over the latter. Firstly, it indicates the percentage of explained variation for each axis. This tells you how well your analysis fits the data (how much of the variation/structure the analysis captures). It is even possible to add confidence ellipses that estimate statistical significance (see Section 2.4.1). Secondly, the contribution of each data point to the structuring of the data can be directly discerned by considering its position relative to the two axes, making the plots simpler to interpret. On the other hand, the advantage of multiple correspondence analysis is that you can add more than two factors. The ability to capture the interaction of more than two different factors should not be underrated. In linguistics, lexical structure, syntactic structure, prosodic structure, argument structure, as well as region, gender, register and so on, are all potentially and interdependently relevant in language structure and its description. Although it is possible to combine and/or concatenate (stack) factors as one normally does for cluster analysis and binary correspondence analysis, doing so can lead to overlooking important interactions in the data. This last point is important and warrants explanation. If we are looking at, for instance, the interaction of tense, aspect, mood and a range of near-synonymous verbs, we may propose the hypothesis that the grammatical semantics will indirectly reveal lexical semantic structure. In other words, the grammatical semantic profile of each verb will be indicative of the lexical semantic structure. To these ends, it is perfectly possible to combine the different grammatical factors, giving us usage features such as: feature 1 ‘present tense + indicative + perfective’, feature 2: ‘present tense + indicative + imperfective’, feature 3: ‘present tense + conditional + perfective’, feature 4: ‘present tense + conditional + imperfective’ and so forth. However, if we then want to add further semantic or sociolinguistic features, we may miss potentially important correlations. Although combining factors in this manner will permit us to perform cluster analysis and binary correspondence analysis, we will not know if there are interactions between the different factors. We may find that, for example, the conditional mood has an important correlation with the imperfective aspect in a certain register. This may be interesting in itself, but it may also severely bias the results if not accounted for separately. For example, for this given register, is the lexical-grammatical correlation observed due to the conditional



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or the imperfect or a combination? An answer to such a question is more difficult to discern in binary analysis. Therefore, there is always a trade-off – binary correspondence analysis gives more ‘reliable’ results and numerical indicators of explained variation, but it can struggle to represent the interaction of more than two factors simultaneously. Other than simple binary correspondence analysis, detrended correspondence analysis and canonical correspondence analysis have been developed. Detrended correspondence analysis includes a bias added to the distance matrix calculation. It is designed to counter a well-known effect with ‘long’ gradients, called the ‘horseshoe’ effect, whereby the data points tend to form an arch. The effect is occasionally visible in plots, but any experience with correspondence analysis should avoid misinterpreting results because of it.3 It should be noted that Greenacre (1984:â•›232) is sceptical about detrended correspondence analysis and it does not enjoy wide currency. It is, nevertheless, straightforward to perform in R.4 Canonical correspondence analysis, also termed constrained correspondence analysis, is popular in the life sciences, but is also directly relevant to linguistics. In a given study, it is perfectly common to be dealing with two different kinds of variables. Some categories interact with each other, but all relative to a different kind of category. For example, aspectual structure interacts with Aktionsart and tense in complicated and close ways. The role of, for example, register, in their interaction is of a different nature. We may not want to have the correspondence analysis treating the register features of conversation, news press and literature equally ‘mixed’ in with aspectual and temporal features. We can, therefore, treat the register dimension as an ‘external’ factor and the grammatical semantics as the ‘internal’ factors. The correspondence analysis then knows that we are actually interested in the internal factors and it accordingly attempts to map that space relative to the structure of the other. This results in less explained inertia overall, but (hopefully) more explained inertia for the factor that is the object of study.5 Multiple correspondence analysis techniques are an extension of binary correspondence analysis for the treatment of multi-way tables (binary correspondence analysis is restricted to ‘normal’ two-way tables). In the R sessions below, we consider three kinds – indicator matrix multiple correspondence analysis, Burt matrix multiple correspondence analysis, and joint multiple correspondence analysis. 3. See Greenacre (2007:â•›127–128) for an explanation of the horseshoe effect. 4. The package needed is {vegan} and the function is decorana. Oksanen (2006) has written a clear tutorial for the {vegan} package that explains the needed R command and offers examples. 5. With the package {vegan} and the function cca, it is straightforward to perform. Again, Oksanen (2006) offers an R tutorial on the possibilities. Canonical correspondence analysis is also performed by the {anacor} package, explained in De Leeuw and Mair (2008).

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Indicator multiple correspondence analysis is sometimes called homogeneity analysis (Gifi 1990; De Leeuw and Mair 2009a). Essentially, this technique ‘combines’ a binary correspondence analyses using what is called a ‘matrix of indicators’. Despite mathematical differences, its results are very similar to Burt matrix multiple correspondence analysis. Indeed, Greenacre (2007:â•›141) compares the two and concludes that there is no difference in the visualisation of the results, but does note that the Burt matrix produces more ‘optimistic’ percentages of inertia. However, for multiple correspondence analysis, it must be remembered that the percentages of explained inertia cannot be interpreted because they severely underestimate the representative quality of the biplot map. The Burt matrix multiple correspondence analysis is the most commonly implemented in R. A third type of multiple correspondence analysis is based on the Burt matrix method and has been termed joint correspondence analysis. Greenacre (2006:â•›68; 2007:â•›145) argues that it is superior both in terms of the explained inertia and in the accuracy of the visualisation. It works by restricting the analysis to the cross-tabulations that typically contain the correlations of interest, those that explain the inertia. Greenacre (2007:â•›Ch. 19) explains the technique in terms accessible to non-specialists.

2. Performing and interpreting correspondence analysis in R Before we begin with the application per se, we must cover a few general questions that are relevant to every correspondence analysis. The first important question is – what to look for. There are four issues: ‘fishing’, over-simplicity, over-complexity, and data sparseness. Let us briefly consider each in turn. By fishing, we mean the arbitrary (or near-arbitrary) selection of factors in the hope that one will find correlations. Correspondence analysis is a tool for identifying correlations, a tool that needs to be used in a reasoned fashion. There is no point in establishing correlations between the use of language features that bear no interpretable correlation in reality, or worse, bear an interpretable correlation, but are just a result of a few chance occurrences. In Section 1.1, the metaphor of an archaeologist digging was used to explain this point: by digging everywhere, it is sure that something will be found, but the chances of finding irrelevant things increase exponentially. Over-simplicity is less serious a problem, but still must be borne in mind. There is no use in using correspondence analysis to identify a correlation that a simple pie chart or histogram, combined with a test for significance, would do even better. Similarly, obvious correlations can dominate results at the expense of less obvious, and therefore, more interesting results. For example, since parenthetical uses of verbs are typically in the first person, including grammatical person and parentheticality in a correspondence analysis will primarily reveal an obvious, or trivial, association. The



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problem is, if these two factors are amongst a more complex range of factors, the obvious association could ‘override’, or ‘hide’, other associations. Although it is sometimes necessary to include such obvious correlations in an analysis (because one is seeking structures in other parts of the data), if it is possible to avoid doing so, then it should be avoided. Simply put, obvious correlations run the risk of ‘hiding’ the more interesting results. In other words, the plot will identify what is most strongly correlated instead of the subtler, yet analytically more important, correlations. Over-complexity occurs in binary correspondence analysis when using concatenated tables (see Section 2.2.3 below) and in a multiple correspondence analysis when too many factors are examined simultaneously. For example, there is obviously no point analysing, simultaneously, 22 factors, each with 16 features, even if one has thousands of examples. Without even considering the impossibility of accounting for the variation (inertia), in such a dataset, the results would not be interpretable for the simple reason that the visualisation of so many factors becomes impossible to decipher. Moreover, the chance of ‘false’ associations increases dramatically with the more variables and features that are considered simultaneously. There is no steadfast rule, but thinking about how the analysis works and being realistic about its limitations are the safest ways to avoid the problem of over-complexity. One way to avoid such over-complexity is to work with subsets. Subsets may be logical divisions within the data: for example, examining two dialects independently from one another or examining two lexemes or grammatical constructions separately. Similarly, certain features or factors can be combined. As long as the choice is reasoned and reported, it can help to simplify the interactions that the analysis is trying to explain. This principle extends to data sparseness and ‘small cells’. As a rule of thumb, one aims to have at least ten examples in each cell (the count of co-occurring features) of the cross-tabulated matrix (see below, this section). Obviously, this is not always possible, but cells of less than eight tend to cause distortions in the analysis. One may find that the analysis is ‘trying so hard’ to account for some relatively infrequent use that the important associations are not represented. A response to this problem is to leave out the examples (the rows in a flat data-frame, see below, this section) that contribute features only occurring a few times. First performing the correspondence analysis on the full set of data and then gradually taking out these small cells (rows of infrequent examples) is a good heuristic. Not only will it result in a better final analysis, the exploratory nature of correspondence analysis will help you to better understand the data and the correlations within them. The numerical output of binary correspondence analysis can be very helpful in identifying such problems. Using the numerical output, one can quickly see which data points are being poorly represented. This is explained in Section 2.3.1.

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Let us now turn to the computation and interpretation of correspondence analysis in R. Some common packages for correspondence analysis include: {MASS}, {ca}, {languageR}, {anacor}, {homals}, {FactoMineR}, {vegan}, {ade4} and {pamctdp}. Unfortunately, for reasons of brevity, we restrict the demonstration to a small selection of functionalities in the first four of these packages. However, references to further information and tutorials on each are offered. Each package is a suite of commands for performing correspondence analysis. They have different options and possibilities. The program R, works with functions, such as the function to read a table, to plot results of an analysis and, of course, to perform a statistical analysis. In simple terms, the functions are the commands that tell R what to do. Each function also has a set of ‘arguments’. These arguments are the ‘options’ that R should take into account in executing the command. Moreover, keeping a record of what you have done is vital in learning to use the program. There are many additions in R for keeping your working history and also for storing the functions you use often. However, when just beginning, it is perhaps simplest to use a text file and to simply ‘copy’ and ‘paste’ to and from R. Also, at the end of an R session, it is wise to save the history (what you have done) either within R or in a separate text file. This will help you to remember the steps you took the next time you perform an analysis. Further explanation on how to use R can be found in van de Weijer and Glynn (this volume, 343–364). In the R sessions below, after each line of command, another short line is added, following the # sign. This sign indicates that the program R should ignore what follows it and not try to interpret it as arguments belonging to the function. It is standard practice to explain command lines after such hash (#) signs. For the purposes of explaining how to perform and interpret the analyses in R, we will use artificial data. Let us take a set of near-synonymous verbs in an imaginary language. In this language, let us say, there are three mental predicates think, believe, and suppose, and three communication predicates, say, speak, and talk, which can be used figuratively to also indicate epistemic stance, just like the mental predicates. We take 575 occurrences of the verbs, more or less equally distributed. Correspondence analysis does not require equal distribution in such a situation, but we want to have as many examples as possible of each form, so making a balanced selection is the best way of achieving this. The imaginary language possesses a three-way distinction in the aspect-mood system, distinguishing between ‘Perfective’, ‘Imperfective’ and ‘Modal’ forms. Each of the examples is analysed for this grammatical category. The examples are also analysed for the grammatical person of the verb and the semantic type of the indirect object. Table 1 illustrates the kind of results one expects from such an analysis. Before we start the R session, an important aside must be made. There are two different data formats that the R functions use. It is crucial that the data is in the correct format. Details on loading the data can be found in van de Weijer and Glynn

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Table 1.╇ Example of flat data-frame Example

Verb

Gram. category

Person

Ind. obj. semantics

example1 example2 example3 example4 example5 example6 example7 example8 to 575 examples

think suppose suppose believe say talk suppose speak …

Perfective Modal Perfective Imperfective Imperfective Modal Imperfective Perfective …

1st 3rd 3rd 1st 3rd 1st 1st 1st …

Human Concrete_Thing Abstract_State_of_Affairs Concrete_Activity Abstract_State_of_Affairs Concrete_Thing Concrete_Activity Human …

Table 2.╇ Example of a numerical cross-tabulation contingency table Perfective Imperfective Modal

believe

think

suppose

say

speak

talk

32 24 44

28 24 52

22 34 48

16 42 29

20 49 26

14 44 27

(this volume, 343–364), but this fact is essential enough that it is worth repeating. We can call one format the flat ‘data-frame’ and the other the numerical ‘cross-tabulation’ (or contingency table). The data-frame is typically what one obtains after annotating (coding) linguistic examples in Excel, Filemaker or some database application. The cross-tabulation is a result of calculating, or numerically summarising, the data-frame. This can be done in Excel with the ‘pivot table’ option or by using a command in R, described in van de Weijer and Glynn (this volume). The easiest way to understand the two different formats is by way of example. Table 1 is an example of a data-frame; typically it would be in a spreadsheet or in a text file with tab delimited columns. Table 2 is typical of a cross-tabulation. Note that Table 2 only cross-tabulates columns two and three: “Gram. Category” by “Verb”. Again, van de Weijer and Glynn (this volume) offer more information on the different formats and how to convert data from one format to another. Once we have our data and we have the two relevant formats of the data, we can begin the correspondence analysis. Finally, note also that the data, R sessions and commands (with more detailed explanations) can be downloaded from http://dx.doi.org/10.1075/hcp.43.17gly.additional.

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2.1

R package {MASS}

The package {MASS} (Venables and Ripley 2002) comes pre-installed and so it only needs to be loaded. It has simple, but effective, functions for both binary correspondence analysis and multiple correspondence analysis. The first step is to load the package: > library(MASS)

2.1.1 Binary correspondence analysis in MASS Data must first be loaded in the numerical cross-tabulated format. We take the cross-tabulation in Table 2. The first command line below loads data from a text file containing a cross-tabulation. There are three ways of loading such data into R; we will use the choose.file() function. > data.xtab <- read.table(file.choose(), header= TRUE, sep=“\t”, row.names= 1) # Loads data from text file containing cross-tabulation # e.g.: table2.txt, downloadable from http://dx.doi.org/10.1075/hcp.43.17gly.additional # Specifies that the columns have labels, or ‘headers’.

This command line loads the data into R, calls it ‘data.xtab’ and specifies that the first row in the table is the column labels, or headers (header= TRUE). It also assumes that any blank space, tab or otherwise, is the sign of a new field. You can use function sep= “ ” to specify how the columns are separated. This is necessary if you have labels with blank spaces in them. If you are exporting data from a spreadsheet or database, then the columns are most likely to be tab delimited, in which case add the argument sep= “\t”. When first beginning, it is perhaps easiest to make sure there are no blank spaces in your labels and let R guess the structure of the table. The argument row.names= 1 specifies that the first column is the labels for the rows. This last argument is needed when loading a numerical cross-tabulation, but not for the flat data-frame. The function for performing a binary correspondence analysis in the package {MASS} is corresp. > ca_analysis <- corresp(data.xtab, nf= 2) # performs correspondence analysis on ‘data.xtab’ > plot(ca_analysis) # plots results of ‘ca_analysis’

Although the graphic options in R are excellent, the {MASS} package offers only a simple set of possibilities. To the last line of code above (plot(ca_analysis)), we



Correspondence analysis 455

can add the graphical ‘arguments’ which determine the appearance of the plot.6 For example, the argument cex changes the size of the font, the argument col specifies the colours, and xlim and ylim ‘zoom’ the plot by delimiting the x and y axes. These arguments should be added ‘inside’ the plot command, as shown in the example below: > plot(ca_analysis, col= 1, cex= 1, xlim= c(-.225,.375), ylim= c(-.4,.4)) # plots results of ca_analysis, in black, at font size 1, # ‘zoomed’ in on x and y-axes. See Figure 1.

The col argument can specify a range of colours by name “red”, black”, “blue” or by numbers, “1”, “2”, “3” etc. The argument cex takes a number that indicates the type size (1 = is default, 1.2 is larger, 1.3 larger still, and 0.8 smaller, and so forth). Zooming can be tricky at first, but becomes simpler with practice. The plots present numbers on the x and y axes. These numbers show the distance from the centre of the plot. The x and y axes can be ‘limited’ both in the negative and in the positive range with the following arguments xlim= c(-.05,.05), ylim= c(-.05,.05). Adding this string to the plot function will make the cut-off points for the plot -0.05 and +0.05 on the x-axis and –0.05 and +0.05 on the y-axis. Change those numbers to delimit, and therefore ‘zoom’, the plot. Experimenting with the zoom function will allow you to get a more legible plot. In Figure 1, the data points were positioned to make maximum use of the space, that is, to make sure that the entire box was used to display the ordination of the data points. The data submitted to this analysis are simple, but the result will allow us to understand the principles in interpreting correspondence biplots. The dispersion of the data points represents the variation of the co-occurrence of the different usage features – here, six verbs (columns) and three grammatical categories (rows). Proximity and distance represent degrees of association between the different features. The centre of the plot, indicated by the numbers on the x and y axes and by the cross in the centre, divides the plot into quadrants. This helps identify association. The corresp function in {MASS} does not produce the most attractive plots, but since it is the simplest to perform and comes pre-installed in R, we will explain the

6. Saving plots is an important, yet often side-lined, element to using R. In Mac OSX, plots are saved in the vector format .pdf. This means one has perfect resolution magnified to infinity. Under Mac OSX, in current versions of MSWord, importing with the Insert menu (not ‘cut and paste’) will maintain this perfect resolution in an MSWord document. Under Windows, depending on the version, MSWord does not accept .pdf or automatically converts it with poor quality output. Under Windows, plots should be saved as .png. Although the quality is not comparable to .pdf, it is acceptable.

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0.0

0.2

0.4

Modal think

suppose say

talk

Imperfective

0.0

0.0

0.2

0.2

0.4

0.4

0.6

–0.2

speak

–0.2

believe

–0.6

–0.4

–0.4

–0.2

Perfective

–0.2

–0.1

0.0

0.1

0.2

0.3

Figure 1.╇ Binary correspondence analysis, function corresp, package {MASS}

principles of interpretation with it. In the following sections, you will see how more sophisticated, yet still simple to use, packages produce superior biplots. In Figure 1, we see two distinct groupings of the verbs, distinguishing the mental predicates and the communication predicates. The verb suppose lies between the two groups, though clearly still on the same side of the plot as the other mental predicates. From this, we know that although it behaves like a mental predicate, its use is closer to the communication predicates. We also see that although the mental predicates form a distinct group, they are also distinguished along the vertical axis. The items believe and think are distinguished by the grammatical categories of Modal and Perfective. Although the distance between think and believe is relatively small, they are in different quadrants of the plot, and most importantly, the grammatical categories are on the ‘far side’ of the lexeme data points relative to each other. This shows the association to be distinctive. If the data points Modal and think were interchanged, then believe would be distinctly associated with Perfective, but think would only be associated with Modal, not distinctly so. It is for this same reason that we know there is a distinct association between the communication predicates and the Imperfective. The data point for the Imperfective lies on the ‘other side’ of the communication predicates data points relative to the mental predicates. This shows the distinctiveness of the Imperfective use with this group. A note should be made about the scales printed on the axes. They are not informative on their own, but help one to gauge relative distance. This is especially important when plots are not square, but are elongated or stretched to permit the representation of all the data points. In Figure 1, we have a slightly unusual situation where the plot is skewed. In this instance, it is not interfering with the results, but if the cloud of data



Correspondence analysis 457

points were more dense or the array more complex, this would have to be taken into account. We can summarise the interpretation of the plot as follows: For the mental predicates – Distinct usage in the aspect-mood system, relative to the communication predicates – Within the mental predicate group: believe is distinctly associated with the Perfective; think is distinctly associated with Modal; suppose is associated with the Modal, but its use is also relatively close to that of the communication predicates. For the communication predicates – Distinct in usage from the mental predicates due to their Imperfective profiling The numerical output for the {MASS} package is not helpful at this stage. We will examine the numerical output below in Section 2.3.1.

2.1.2 Multiple correspondence analysis in MASS This function is delightfully simple and powerful, but therein lies its danger. It is simple because one uses the data from a flat data-frame (such as the ‘raw’ data in an Excel file) which does not need to be converted to a contingency table, and also because two simple commands perform the analysis and plotting. It is powerful because (theoretically) one can add many variables to the analysis and perform complex multivariate analysis. Although this technique and these functions are excellent, care must be taken. It becomes increasingly difficult to interpret the results of the analysis as one increases the number of variables being treated. What is more, it becomes increasingly difficult to obtain reliable results. For demonstration purposes, let us add some more fictitious data. Column 5, in Table 1, shows the semantic type of the indirect object of the utterances. We can add this factor and perform a multiple correspondence analysis. It will show the interaction of three variables, the grammatical category of aspect – mood, the lexemes, and the semantic type of the indirect object. The function mca performs a multiple correspondence analysis. As mentioned above, for this function, there is no need to produce a numerical contingency table; the function accepts the flat data-frame as the input format of its data: > data.frm <- read.table(file.choose(), sep=“\t”, header= TRUE) #loads data from text file containing data-frame > mca_analysis <- mca(data.frm, abbrev= T) # performs the multiple correspondence analysis > plot(mca_analysis, rows= F, col= 1) # plots results of mca_analysis, see Figure 2

Abstr_SoA believe

0.01

0.02

0.03

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Perfect

–0.01

0.00

Abstr_thing suppose Modal think

Imperfective

Cncrt_activty

–0.02 –0.03

Cncrt_thing talk speak

Human say

–0.02

0.00

0.02

0.04

Figure 2.╇ Multiple correspondence analysis, function mca, package {MASS}

We add abbrev= T (T for ‘true’) to the mca function. This tells the function not to include the factor labels. Also, note row= F (F for ‘false’); this tells the plot function not to add the row numbers (that is, example numbers in linguistic analysis) to the plot. It is sometimes interesting to plot the row numbers in order to determine which actual examples are causing the interactions visualised in the plot. As for the factor labels, if one has features whose labels are the same for different factors, then one needs to add the factor labels to distinguish them on the plot. To activate these options, exchange F and T in the command line. Figure 2 presents the results of the multiple correspondence analysis of the three factors. Firstly, you will notice that some of the data points overlap, which can cause problems for interpretation. This is a natural result of visualising association through the proximity of data points, yet it means that often one must enlarge plots (after having saved them as image files) or zoom in on them in R in order to discern what data points are overlapping. These, in turn, must be explained and described in further detail when reporting results. There exists a package, {FactoMineR}, which has an option for so-called dynamic graphing that allows one to displace the labels (as opposed to small data points) interactively so that they do not overlap. Details are given in Section 2.5. It is this package that was used to make the plots in descriptive studies presented in the first section of this book. Interpreting the plot of a multiple correspondence analysis can be complex. In this plot, we have a multidimensional space that has been conflated to two dimensions. This means that data points may appear close to each other but, in fact, are



Correspondence analysis 459

placed far apart on the oblique dimension, back ‘into the page’, as it were. Caution, and a little experience, makes interpreting such plots reasonably straightforward. However, as one increases the numbers of factors to four or five, the plots can only be used as a rough guide and one must return to the data to check every association identified. In Figure 2, imagine the plot divided diagonally, horizontally and vertically. Locating the centre at the intersection of 0.00 and 0.00, we move out to see the three grammatical features, Imperfective, Perfective, and Modal, dividing up the dispersion of the plot. Once again, the Imperfective dominates the right side, where two of the communication predicates are located, talk and speak. With them is the indirect object semantic feature of Concrete Thing (Cncrt_thing). The position of the Imperfective data point, between the centre and the two communication predicates, suggests that having added the semantic features makes this less distinctly associated with the communication predicates. This interpretation would still see the Imperfective as a characteristic feature of the communication predicates, being located in the right half of the plot, but would see its distinctiveness being lessened. Although at first sight, this may seem reasonable, herein lies the trick of interpreting multiple correspondence analysis. Another interpretation, and one more likely to be accurate, is that the Imperfective is still highly distinctive of the communication predicates, but it is being drawn to the centre by the third communication verb, say, which is now on the bottom left side of the plot. It is probable that there is a multiple interaction here along this dimension of use. Adding the indirect object semantics has separated say from the group of communication predicates. Seeing that its position on the plot almost overlaps with the indirect object semantic feature of Human, but also that these two features cluster together a long way from the centre of the plot, we can safely suppose that say is highly associated with a Human indirect object. We also know, from the previous analysis, that the Imperfective is highly associated with say. In this situation, a likely interpretation would be that both the Imperfective and the Human indirect object are associated with say, but that the Human Indirect object is ‘pulling’ the lexeme away from its Imperfective – communication verb cluster, leaving the Imperfective data point stretched between say and the two other lexemes, speak and talk. This happens because the Human indirect object must be highly associated with some other feature and/or highly disassociated with the other communication predicates. If this were not the case, it too would group with the Imperfective on the right of the plot. This interpretation is complex, but rich. It is also reasonably clear, if one has some experience in interpreting correspondence biplots. We will return to some of these complex associations below and reconsider these relations using different packages and different ways of handling the data. Other findings include the distinct association of believe and the indirect object semantics of Abstract State of Affairs (Abstr_SoA). Also, the position of Concrete

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Activity (Cncrt_activity) as object semantics, lying between say and think/suppose, shows that these three lexemes share this feature, yet otherwise they are distinct. Despite this complexity, if we step back and return to our research question – the near-synonymy of the lexemes – we have a clear and coherent picture. The two sets of verbs, communication and mental, are still distinct. For the mental predicates, believe is distinct relative to the communication predicates. For the communication predicates, say is less so, relative to the mental predicates. This gives us an uneven continuum from talk and speak to say, which bridges the use with the mental verbs think and suppose. At the very end of this continuum, believe is distinctly distant from the communication predicates in its use. Importantly, we know what characterises this continuum. At one end, the communication predicates, speak and talk, are associated with Concrete Things as indirect objects and with the Imperfective aspect. Although still associated with Imperfectivity, midway on the continuum, say is more associated with the indirect objects of Concrete Activity and Human. At this point, we meet the mental predicates with suppose and think sharing an association with say of the object type of Concrete Activity. These lexemes, think and suppose, are central to the mental predicate cluster determined by Abstract Things as indirect objects and the Perfective aspect. Finally, believe, also relatively close to the other mental predicates, is quite distinct due to its association with Abstract States of Affairs as object semantics. In this fictitious description of near-synonymy, we have shown which verbs are similar and which verbs are distinct. Most importantly, we have shown why this is the case; what usage features are responsible for the similarities and differences. With some experience, such an interpretation of the results is reasonably clear. Of course, how these results inform the interpretation of language structure remains open to debate.

2.2

R package {languageR}

The {languageR} package, developed by Baayen (2011), has an impressive range of statistical options. However, for correspondence analysis, it is restricted to binary analysis. To these ends, it is simple to use and has an agreeable graphical output. The application is explained in Baayen (2008:â•›128–136). The package firstly needs to be installed and then loaded separately when used: > library(languageR)

Depending on your version of R and the operating system, it may require a range of other packages to be installed and loaded before it can be loaded. The R terminal will give you instructions to follow in case this happens.

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2.2.1 Binary correspondence analysis in languageR The function for binary correspondence analysis is corres.fnc. It expects the data to be inputted as a numerical cross-tabulation.

> data.xtab <- read.table(file.choose(), header= TRUE, sep=“\t”, row.names= 1) > data.t <- t(data.xtab) # transposes data. # Optional step, added here to improve plot legibility > ca_analysis <- corres.fnc(data.t) > plot(ca_analysis, ccex= 1.2, rcex= .85) # plots ca_analysis results with different font sizes # for the two axes. See Figure 3. > title(“Lexical Variation of Grammatical Categories”, cex.main= .95, sub= “package - languageR, function corres.fnc”, cex.sub= 0.85) # Adds titles to the plot, specifies font size

Firstly, note that the cross-tabulation was transposed, or inverted (data.t
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0.15

Lexical variation of grammatical categories

0.00

Imperfective

–0.05

0.05

speak

talk

say think Modal

–0.10

Factor 2 (7.4%)

0.10

Perfective believe

suppose

–0.4

–0.2

0.0

0.2

0.4

Factor 1 (92.6%) Package – languageR, function – corres.fnc

Figure 3.╇ Binary correspondence analysis, function corres.fnc, package {languageR}

2.2.2 Chi-squared test for significant variation Let us make a brief aside. In Gries (this volume, 365–390), the Chi-squared test was explained. We can apply it here to make sure that there is, indeed, significant variation between the different lexemes. The function is chisq.test and it expects the data to be a numerical cross-tabulation.

> x2.test <- chisq.test(data.xtab, correct= F) > x2.test data: data X-squared = 40.6513, df = 10, p-value = 1.301e-05

This shows there is significant variation between the lexemes. We can then call the Pearson residuals to see which categories are causing the most variation. Again, this is explained in Gries (this volume, 365–390). > x2.test$res believe think suppose say speak talk Perfect 1.887480 0.844261 -0.383690 -0.888823 -0.387302 -1.24804 Imperfect -2.236471 -2.433997 -0.837797 1.599814 2.195817 2.104913 Modal 0.748989 1.739817 1.114179 -0.888356 -1.855656 -1.108766

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We see from the Pearson residuals that the Imperfective uses of speak and talk and the lack of Imperfective uses of think and believe are the most important. We can bear this in mind when interpreting the plots. Looking at Figure 3, we see this fact represented visually and clearly so.

2.2.3 Concatenating tables and combining categories We have, until now, worked with very simple data. Although correspondence analysis can help us find correlations in such data, its true strength is revealed when applied to more complicated and multidimensional data. In Table 1, we presented the imaginary feature analysis: there were four columns after the examples – lexeme, grammatical category, grammatical person, and indirect object semantics. We saw, in Section 2.1.2, that a multiple correspondence analysis can help examine more than two factors simultaneously, but we also saw the complexity in interpretation that arises in some data sets. Although multiple correspondence analysis is necessary for finding correlations between the factors, there are two other ways of handling data that permit some exploration of different dimensions of use. First of all, using the pivot command in Excel, one can concatenate, or ‘stack’ tables. One literally generates two-dimensional tables and puts them together in a row, creating one long table. For instance, we can take the data for verb and grammatical category and, using the so-called ‘pivot’ function, produce a cross-tabulation. Then we repeat the operation for the verb and indirect object semantics. This gives us two tables we can join and submit to a binary correspondence analysis. However, it is much simpler to stack tables in R. A function is given in van de Weijer and Glynn (this volume, 343–364) which automatically generates stacked contingency tables in R. Table 3 is an example of such stacked, or concatenated, results. It is perfectly acceptable to tabulate data in this manner. However, it must be remembered that when used in multivariate statistics, stacking like this can conflate conceptually different dimensions of language structure. In the instance here, the indirect object semantics and the grammatical categories of aspect and mood have been combined in such a way that any relations between these different linguistic dimensions are lost. This Table 3.╇ Example of concatenated cross-tabulation Verb

Imperfect Modal

Perfect

Abstr. SoA

Abstr. thing

Cncrt activity

Cncrt thing

Human

believe say speak suppose talk think

24 42 49 34 44 24

32 16 20 22 14 28

41 â•⁄5 â•⁄5 â•⁄5 â•⁄1 15

37 25 22 62 â•⁄9 37

â•⁄8 17 â•⁄8 15 â•⁄4 16

â•⁄5 â•⁄8 51 16 68 13

â•⁄9 32 â•⁄9 â•⁄6 â•⁄3 23

44 29 26 48 27 52

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Table 4.╇ Example of concatenated cross-tabulation with combined factors Verb + Person

Imperf. Modal

Perfect Abstr. SoA

Abstr. thing

Cncrt Cncrt activity thing

Human

believe 1st Prs believe 3rd Prs say 1st Prs say 3rd Prs speak 1st Prs speak 3rd Prs suppose 1st Prs suppose 3rd Prs talk 1st Prs talk 3rd Prs think 1st Prs think 3rd Prs

18 â•⁄6 42 â•⁄0 44 â•⁄5 28 â•⁄6 37 â•⁄7 21 â•⁄3

12 20 â•⁄4 12 â•⁄9 11 â•⁄0 22 â•⁄8 â•⁄6 â•⁄8 20

23 14 16 â•⁄9 16 â•⁄6 22 40 â•⁄7 â•⁄2 20 17

â•⁄4 â•⁄4 10 â•⁄7 â•⁄5 â•⁄3 â•⁄5 10 â•⁄4 â•⁄0 â•⁄3 13

â•⁄3 â•⁄6 24 â•⁄8 â•⁄5 â•⁄4 â•⁄2 â•⁄4 â•⁄1 â•⁄2 â•⁄8 15

31 13 15 14 13 13 10 38 10 17 11 41

28 13 â•⁄3 â•⁄2 â•⁄4 â•⁄1 â•⁄0 â•⁄5 â•⁄1 â•⁄0 â•⁄3 12

â•⁄3 â•⁄2 â•⁄8 â•⁄0 36 15 â•⁄9 â•⁄7 42 26 â•⁄6 â•⁄7

combination means we will only be able to see the interaction of these categories relative to the different verbs, not the interaction between them. If we are only interested in the verbs and know there are no important interactions between indirect object semantics and mood-aspect, then this poses no problems. Table 4 shows another way of adding more information to a two-way table. Here we have combined two different factors. In Table 1, grammatical person and verb were listed as separate columns. However, semantically, it is perfectly reasonable to combine these two factors into one, a verb-person category. To obtain the new combined factor, ‘sort’ the two columns in Excel and add a new empty column, and create the new combined factor using the ‘copy-paste’ and ‘change all’ functions in Excel. Table 4 shows this combined factor of verb and person added to the cross-tabulation. A point of warning should be made about data sparseness. As we add more complexity to the tables, we obtain smaller cells. The more different things we consider simultaneously, the ‘thinner’ the data becomes. As a rule, cells below a count of 10 should be avoided. In practice, at least when dealing with manually coded data, this rule is broken. As long as care is taken when considering the plots and it is remembered that this is only an exploratory technique, some leeway on this front can be tolerated. However, small cells should always be reported. The numerical output, which we consider below in Section 2.3.1, also helps one gauge the reliability or ‘accuracy’ of a data point on a biplot. Let us now consider these tables submitted to binary correspondence analysis. Applying the same command line as that used to produce Figure 3 to the data presented in Table 3, produces the plot in Figure 4. Although the plot is inverted, the dispersion of the data points has shifted little, and the graphical representation in this package is superior; the results are the same. Indeed, the fact that the Imperfect is

Correspondence analysis 465

0.6



Human

Imperfect

THINK SUPPOSE Abstr_thing Modal

SPEAK

Perfect

–0.2

0.0

0.2

Cncrt_activity

TALK Cncrt_thing

BELIEVE

–0.6

–0.4

Factor 2 (22.4%)

0.4

SAY

–0.5

0.0

0.5

1.0

Factor 1 (63%)

Figure 4.╇ Binary correspondence analysis, data from Table 3, function corres.fnc, package {languageR}

being ‘stretched’ between two quadrants of the plot is clearer. Note also that the data point for Abstract States of Affairs lies just off the plot, distinctly and highly associated with believe, just as in Figure 2. It is also noteworthy that the explained inertia of the first two dimensions is 85% (dim 1: 63% + dim 2: 22.4%). This shows that the analysis is stable and we can interpret the plot with some confidence. Figure 5 visualises yet a more complex data set, presented in Table 4. In these data, we have added the grammatical person to the verbs as well as having concatenated the grammatical categories and the indirect object semantics. The added complexity reduces the amount of explained variation, which is now just over 72% for the first two dimensions. This is still a relatively high figure and assures us that the plot remains stable, despite the added complexity. We see that speak and talk behave in a similar manner to what we saw above in Figure 4. It seems that the addition of the variation in grammatical person does not affect their interaction with the aspect-mood and object semantics to any great extent. However, the behaviour of say, which we saw was distinct in Figure 4, has been explained. The 1st person say is found on the Imperfective/communication verb side of the plot, but the 3rd person usage of say, although somewhat hidden beneath another label, is found right in the centre of a mental predicate cluster, along with the Modal and Perfective profilings. We now know that it was a simplification to understand say as being between the communication predicates and the mental predicates.

1.0

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Cncrt_thing

SPEAK_3rdPrs Perfect

0.0

Factor 2 (21%)

0.5

TALK_3rdPrs

Modal THINK_3rdPrs SUPPOSE_3rdPrs BELIEVE_3rdPrs Abstr_SoA SAY_3rdPrs BELIEVE_1stPrs

TALK_1stPrs

SPEAK_1stPrs

Cncrt_activity Abstr_thing THINK_1stPrs

Imperfect SUPPOSE_1stPrs

–0.5

Human

SAY_1stPrs

–0.5

0.0

0.5

1.0

Factor 1 (51.5%)

Figure 5.╇ Binary correspondence analysis, data from Table 4, function corres.fnc, package {languageR}

It is, in fact, only the 3rd person uses that behave similarly to the mental predicates. Moreover, we see now that believe has joined the mental predicate cluster, which suggests that it was never so distinct from the mental predicate cluster as a whole. Instead, we see that it was just distinct from the 1st person uses of say, from which it was being pushed away in the visualisation. Finally, suppose in the 1st person has shifted right across to the Imperfective, completing the picture of a continuum between the two groups of verbs, where suppose in the 1st person behaves like a communication verb and say in the 3rd person like a mental predicate. Adding the extra dimensions of use has clarified the interaction of the verbs. It is precisely this kind of multivariate complexity that correspondence analysis is designed to capture. If the reader wishes to perform these analyses, the command line presented in Section 2.2.1 will produce the plots.

2.3

R package {ca}

The package {ca}, developed by Nenadić and Greenacre (2007) and Greenacre and Nenadić (2010), is another commonly-used package for performing binary and multiple correspondence analysis. The package does not come with the R installation and

Correspondence analysis 467



must be downloaded separately using the package installer. It is described in detail in Greenacre (2007:â•›232–240). Before we begin, load the package: > library(ca)

This package offers a wealth of possibilities, most of which go beyond our discussion. We will focus on its numerical output and the various options for multiple correspondence analysis that it includes.

2.3.1 Binary correspondence analysis in ca As before, the data must be loaded in a cross-tabulated matrix. > data.xtab <- read.table(file.choose(), header= T, sep=“\t”, row.names= 1) > ca_analysis <- ca(data.xtab) > plot(ca_analysis, col= 1)

Due to the limitations of space, the plot of this analysis is not included. It presents the same information as above. However, the numerical output in {ca} is comprehensive and informative and so we will focus on this. Although most of the output does not need reporting, as one becomes more experienced with correspondence analysis, the mass and explained inertia for the individual rows and columns can help one interpret unusual patterns, especially with data sets more complex than those we are using here. There are two sets of numerical output. The first is obtained by simply typing the object of the ca function. We called this object ca_analysis. This output is not presented here because it is quite voluminous. The second numerical output is obtained by asking for a summary of the results of the analysis. The summary below is of the analysis presented in Figure 5. > summary(ca_analysis) Principal inertias (eigenvalues): dim 1 2 3 4 5 6 7

value % cum% 0.252400 51.5 51.5 0.103030 21.0 72.5 0.069058 14.1 86.6 0.043973 9.0 95.6 0.016743 3.4 99.0 0.004762 1.0 100.0 00000000 0.0 100.0 -------- ----Total: 0.489967 100.0

scree plot ************************* ********** ******* **** **

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Rows: 1 2 3 4 5 6 7 8 9 10 11 12

| | | | | | | | | | | |

name BELIEVE_1 BELIEVE_3 SAY_1 SAY_3 SPEAK_1 SPEAK_3 SUPPOSE_1 SUPPOSE_3 TALK_1 TALK_3 THINK_1 THINK_3

| | | | | | | | | | | |

mass 106 68 106 45 115 50 66 115 96 52 70 111

qlt 383 659 737 604 953 760 651 524 971 910 698 775

inr 133 71 111 62 84 27 66 88 152 99 21 85

| | | | | | | | | | | |

k=1 -484 -575 170 -636 583 106 353 -428 843 574 21 -517

cor 382 642 56 601 953 42 254 485 914 354 3 717

ctr 98 89 12 72 155 2 33 83 269 68 0 118

k=2 cor ctr | -19 1 0 | | 94 17 6 | | -592 681 361 | | 42 3 1 | | -17 1 0 | | 438 718 94 | | -442 397 125 | | 121 39 16 | | 211 57 41 | | 719 556 262 | | -322 695 70 | | 147 58 23 |

| | | | | | | |

mass 189 197 115 63 167 59 140 71

qlt 958 764 740 427 408 373 998 326

inr 199 73 85 165 77 33 271 97

| | | | | | | |

k=1 574 -311 -410 -740 -237 -279 845 -223

cor 638 534 462 425 248 289 753 74

ctr 246 76 77 136 37 18 396 14

| | | | | | | |

Columns: 1 2 3 4 5 6 7 8

| | | | | | | |

name Impf Modl Prfc A_SA Abs_ Cncrt_c Cncrt_t Humn

k=2 -407 204 318 43 -191 -151 481 -411

cor 320 230 278 1 160 84 244 252

ctr 303 80 113 1 59 13 315 117

| | | | | | | |

The summary call begins with what it labels a ‘scree plot’. Scree plots are used to help decide how many dimensions are needed to explain the variation in the data. In principal components analysis, factor analysis and also in multidimensional scaling, such ‘plots’ are common. They offer a factor-by-factor breakdown of how much variation the analysis has explained. One looks for an ‘elbow’ in the plot, that is, a dimension where there is a marked drop in the amount of variation explained. There are no mathematical rules to decide this point, but typically it is clear – ‘most’ of the variation in the dispersion of data is explained by only a few of the dimensions. The more gradual the ‘descent’ of the scree plot, the more trouble the analysis is having in explaining the dispersion of the data. We see here that the analysis actually lacks a clear elbow and that adding dimensions beyond the first two (the visualised dimensions) actually continues to improve the explained inertia considerably, the 3rd and 4th dimensions adding 10% explanation respectively. The table in the summary call, ‘Principal inertias’, contains the vital information for understanding the structure of a correspondence analysis. It begins with the dimensions (dim), then lists the Eigenvalues (value), converts these to percentages of explained variation (%), and then calculates the cumulative explained variation with the addition of each dimension (cum%). Since biplot visualisations of the results of



Correspondence analysis 469

a correspondence analysis typically depict the first two dimensions, the numerical output here tells us that the first two dimensions explain 72.5% of the inertia. This means the plot that we interpret does not account for just over one quarter of the variation in the data. This information is a guide to how confident we can be about the accuracy of the depiction. At 72.5%, less variation is explained than in the previous (simpler) analyses, but this figure is still sufficiently high to interpret the plot, though with some caution. The scree plot shows us that it might be informative to also visualise the third-dimension, either in a three-dimensional plot or by producing two more biplots, with dimension 1 by dimension 3 and dimension 2 by dimension 3. Many of the R packages offer these possibilities, but we do not consider them here. Unlike {languageR}, the {ca} package does not automatically label the plots with the amount of explained inertia. If one wishes to label the x and y axes with the percentages of explained inertia, one simply uses the title function as above, for example: title(xlab= “Dim 1 (51.5%)”, ylab= “Dim 2 (21%)”). In the second half of the summary, we have two tables of information, one for the rows and one for the columns of the contingency table that is the basis of the analysis. Coordinates are only given for the first two dimensions (k=1 and k=2), the dimensions visualised in a biplot (note the plots produced in languageR call these factors 1 and 2). Normally, in correspondence analysis, interpretation is restricted to these first two dimensions. This table breaks down the analysis for you. For each row and each column in the table, the weight assigned to that column or row is indicated (mass). This was explained in Section 1.2. It is essentially a bias added to the calculation to stop small numbers having a disproportionate effect. The next score listed is the quality (qlt) and, as the name would suggest, this is a measure of the accuracy of the visualisation. This is a very useful score to consider. A low quality score for any given ‘feature’, that is, row or column, means the interpretation of its position on the plot should be treated with extra care. The numbers are given in thousandths, so a figure of 375 would be 37.5% and it indicates the explained inertia for a given row or column (that is, the labels on the plot). So, in the table above, the representation in the plot of TALK_1 would be 97.1% accurate, where BELIEVE_1 would be only 38.3% accurate. A quality score of less than 500 (50%) would suggest that the position of the data point in question does not necessarily accurately represent the relation of that feature to the others. This is often because a given feature is common to a wide range of different situations; that it correlates with distinct phenomena. For example, it may be equally used in the past tense and in the future tense, two tenses which are otherwise distinct in the analysis. In such situations, the data point will lie close to the centre of the plot, the intersection of the two axes. The other situation is mathematically similar, but analytically different. In situations where there are only few occurrences of a given feature, and those few occurrences behave in different ways, the same effect is obtained. In the latter situation, if it possible to do so without losing too much data, these examples can be omitted.

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To understand why this is the case, we need to think about how the biplots work. The plot is a representation of a complex n-dimensional set of associations in just two dimensions. Therefore, the points of the labels are not in their original, or mathematically true, positions, having been moved to enable a two-dimensional representation. By default, the biplots present the first two dimensions, but recall that the actual number of dimensions is the number or rows or columns (whichever is less), minus one. So in the table above, we have seven dimensions (the columns, minus one). Greenacre (2007:â•›87) explains this in greater detail, but the principle is that the quality score here is like the inertia score, explained above, broken down for each row and column (or plot label/data point). The inertia value (inr), to the right, is used to calculate the quality. But it can also be directly interpreted. The figure listed is the contribution of that row or column (feature) to explaining the total inertia. It is expressed in thousandths, so that in the output above, BELIEVE_1 explains 13.3% of the inertia in the analysis. So, given that the plot captures 72.5% of the inertia (distribution/variation in the data), this particular feature accounts for nearly 20% of the structure of the plot (13.3 / 72.5 x 100). The next two sections of the table, to the right, give the correlation (cor) and the contribution (ctr) for each of the two dimensions. These scores are, perhaps, less useful in most circumstances, but warrant explanation. The ctr is the contribution that a given row or column has made to explaining the inertia along a single principal axis, that is, one of the first two dimensions. For instance, the horizontal axis (k-1) in Figure 5 is largely determined by three features, TALK_1, SPEAK_1, and THINK_3. The correlation scores indicate the correlation between a principal axis and the row or column in question.

2.3.2 Multiple correspondence analysis in ca The {ca} package is one of the richest for multiple correspondence analysis. Its main strength lies in the fact that one can choose which of the three kinds of multiple correspondence analysis one wishes to perform. Moreover, one can choose to automatically adjust the inertias (using Greenacre’s (2006) calculation for adjustment). This option is only available for the Burt matrix multiple correspondence analysis. The function for multiple correspondence analysis is mjca. To this, one can ‘add’ the argument lambda where one specifies the kind of multiple correspondence analysis to perform: the indicator or homogeneity analysis with lambda= “indicator”; the Burt matrix analysis with lambda= “Burt”; the joint analysis with lambda= “JCA”; and the Burt analysis with Greenacre adjusted inertia values with lambda= “adjusted”. To perform and compare the different techniques, we use the data from the previous analyses, but we do not use the concatenated table. Multiple correspondence analysis may find important interactions between the aspect-mood grammatical semantics and the indirect object semantics, and so we must keep these two dimensions



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separate. We will, however, keep the combined categories of verb and grammatical person. For practical reasons, we cannot consider the plots of all four possibilities. The joint multiple correspondence and the adjusted inertia Burt multiple correspondence analysis produce the best results, both in terms of graphical output and explained inertia. This is to be expected since, as mentioned above, one cannot normally interpret the explained inertia scores in multiple correspondence analysis, unless they are obtained using the Greenacre ‘adjusted’ Burt matrix or the so-called joint method, explained below. > data.frm <- read.table(file.choose(), sep=”\t”, header= T) > mca_indicator_analysis <- mjca(data.frm, lambda= “indicator”) > summary (mca_indicator_analysis) Principal inertias (eigenvalues): dim value % cum% scree plot 1 0.587336 10.4 10.4 ************************* 2 0.479181 8.5 18.8 ******************* 3 0.457792 8.1 26.9 ****************** 4 0.442143 7.8 34.7 ***************** 5 0.397579 7.0 41.7 *************** 6 0.358378 6.3 48.0 ************* 7 0.333333 5.9 53.9 ************ 8 0.333333 5.9 59.8 ************ …

The output here has been abbreviated. Importantly, we see that only 18.8% of the inertia is explained. As mentioned above, inertia scores are not normally interpretable in multiple correspondence analysis and this low score is to be expected. In such analyses the inertia scores can be safely ignored. In order to obtain such scores, adjusted Burt or joint multiple correspondence analysis should be employed. These techniques are described below. We will not consider the results of the Burt multiple correspondence analysis. It suffices to point out that the explained inertia using the Burt matrix is slightly better at 27.1%, but again this is unrealistically pessimistic. The command for the Burt multiple correspondence analysis is: > mca_Burt_analysis <- mjca(data.frm, lambda= “Burt”)

The two most promising advances in multiple correspondence analysis are certainly the joint analysis and the adjustment to inertias in the Burt matrix analysis. Let us consider these. We begin with the joint correspondence analysis (Figure 7). By not including the diagonals, which offer little information to the analysis, we greatly improve the explained inertia and also the projection onto the two-dimensional plane, the biplot. The command for the joint multiple correspondence analysis is:

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> mca_joint_analysis <- mjca(data.frm, lambda= “JCA”) > plot(mca_joint_analysis, labels= c(0, 2), col= c(“white”, “black”)) # plots analysis with only data point labels, # see Fig. 6.

The plot function includes two arguments that we have not seen before. The command labels= c(0,2) hides the row numbers (which correspond to the number of one’s actual language example in the raw data set). Obviously, upon occasion, it is important to see which examples are causing the dispersion in a plot, especially when looking for exemplary occurrences in linguistic discussion and result reporting. The second argument, col= c(“white”, “black”), hides the co-occurrence points. This can be used at times to show how the co-occurrence of features is projected across the plot. For instance, sometimes there is a single kind of co-occurrence that causes a given feature to be pushed away from a group. Being able to add these points can help in plot description. Finally, the function psch= changes the symbol representing the point on the plot. A wide range of symbols exist and can be modified by changing the number. We cannot consider the full extent of the graphic options here, but the reader is encouraged to experiment with the plot function.

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The call for the numeric summary is as above:

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> summary(mca_joint_analysis) … Diagonal inertia discounted from eigenvalues: 0.2324778 Percentage explained by JCA in 2 dimensions: 70.4% …

We only consider two lines of the numerical summary of the joint correspondence analysis. As mentioned, joint analysis functions by removing the diagonals of the analysis. These ‘intersections’ of the tables contribute little to the explanatory power of the analysis. The first line shows us that we improved our explanation of inertia by 23% through their removal. The second line tells us that the explained inertia for the first two dimensions is 70.4%. Such a score should be reported, given the necessary caveat that estimating the explained inertia in a multiple correspondence analysis is normally unrealistically pessimistic and that this score is produced through a joint analysis. Plot interpretation is no different to the example interpretations presented above. We will not, therefore, interpret Figure 6, but will move onto the adjusted Burt analysis. The command line follows what we saw above. We begin with a numerical summary of the analysis: > mca_adjusted_analysis <- mjca(data.frm, lambda= “adjusted”) > summary(mca_adjusted_analysis) Principal inertias (eigenvalues): dim 1 2 3 4 5 6

value 0.145165 0.047861 0.034852 0.026639 0.009287 0.001411

% cum% 42.0 42.0 13.8 55.8 10.1 65.9 7.7 73.6 2.7 76.2 0.4 76.6

scree plot ************************* ******** ****** ***** **

The above numerical summary is truncated. We see that the inertia score in the first two dimensions is 55.8%. This is relatively low, but for a multiple correspondence analysis, we can still confidently interpret the biplot. For the plotting, once again, we hide the example numbers. The command for plotting Figure 8 follows: > plot(mca_adjusted_analysis, labels= c(0, 2), col= c(“white”, “black”)) # Figure 7.

The plots in Figure 6 and Figure 7 show the same results. However, if one compares the dispersion of the data points carefully, the spread is a little clearer in Figure 7, confirming Greenacre’s (2006) results in comparing the two methods. Moreover, the results here mirror those of the binary correspondence analysis presented in Figure 5.

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This shows that there are no important interactions between the factors aspect-mood and indirect object semantics. If there existed interactions between these parameters of usage, this extra complexity would be seen here. The plot offers a coherent picture of the clustering of the mental predicates with perfective aspect and modal uses. The exceptions are the first person uses of think and suppose, which are similar to the communication predicates due to their association with the Imperfective. Relative to the mental predicates, the communication predicates talk and speak also form a cluster in the top right quadrant. This cluster is less homogenous, being based vaguely upon Concrete Things as object semantics and the Imperfect. The position of the Imperfect between the top and the bottom of the right side of the plot shows how it is drawn between the 3rd person say and the rest of the communication verb cluster.

2.4

R package {anacor}

De Leeuw and Mair (2009a) developed an excellent package for simple binary and binary canonical correspondence analysis. Although canonical analysis is a useful type of correspondence analysis, described in Section 1.3, we cannot cover the technique here. Beyond its ability to perform canonical analysis, the package offers a rich variety

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of scaling and plotting options. We will consider one of these. The package must be first downloaded and at the beginning of the R session it must also be loaded: > library(anacor)

2.4.1 Binary correspondence analysis with confidence intervals in anacor The package {anacor} offers a range of scaling techniques and plot types – two invaluable additions to correspondence analysis. The different scaling methods can be applied to the rows and columns independently. This can be useful for revealing or highlighting different associations that are hidden in the blur of the plot. The centroid and standard scalings are typically the most useful in this regard. For some data sets, using a combination of the two dramatically increases the legibility of the results by setting one of the dimensions in the centre and ‘surrounding’ it with the other dimension. Unfortunately, we cannot cover this option, but the reader is strongly encouraged to experiment with combining different scaling methods with different data sets. Moreover, the package offers no fewer than seven two-dimensional plotting options. We will consider one plot type, termed the ‘joint plot’. Both the plotting and scaling options are explained in detail in De Leeuw and Mair (2009a). The data are loaded as a numerical cross-tabulation: > data.xtab <- read.table(file.choose(), header= T, sep=“\t”, row.names= 1) > ca_analysis <- anacor(data.xtab, scaling= c(“standard”, “standard”)) > plot(ca_analysis, plot.type= “jointplot”) # see Figure 8

The anacor function takes the argument scaling=, which specifies the scaling method for the x and y-axis. The plotting command takes the argument plot. type=, which specifies the type of plot desired. We have used the joint plot, which includes confidence ellipsoids. These ellipsoids are not based on a test for statistical significance, but estimate it using what the authors call the delta method (De Leeuw and Patrick 2009a). The ellipsoids are set at a ‘significance’ level of 95%, matching the alpha level of p < 0.05, standard in the social sciences. The plot reveals the same associations as the binary plots above, but the addition of the confidence ellipsoids is a welcome advance and will prove extremely useful for some data sets. For example, it here reveals that the associations between suppose in the 1st person and say in the 1st person and the Imperfect are almost surely significant. Of course, we must return to the data for specific tests of association and/ or move to configural frequency analysis and loglinear analysis for confirmatory results. The confidence ellipsoids are merely further guides to help understand relations visualised in a biplot.

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Figure 8.╇ Binary correspondence analysis, scaling “standard” vs. “standard”, function res, package {anacor}, plot type jointplot

The numerical output in anacor is basic but clear. The percentage of explained inertia for the first two dimensions, using the standard scaling, comes out at 82% (D1 50% + D2 32%) – a stable result: > summary(ca_analysis) z-test for singular values: Singular Values Asymptotical SE p-value D1 0.5024 0.0237 0 D2 0.3210 0.0282 0

2.5

Other R packages for correspondence analysis

We have only treated some of the functionalities of the packages presented. However, hopefully, enough detail on both the workings of R and the application and interpretation of correspondence analysis has been covered to allow the reader to delve further into the method and the packages presented. We have omitted five packages that need to be mentioned. Armed with the explanations above, these other packages should be approachable even for people new to R.

R package {homals}

De Leeuw and Mair (2009b), the developers of the {anacor} package, presented above, also author {homals}. This package has even more powerful graphic options than {anacor}. Not only does it offer joint plots and star plots, but there is also the



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option of static and interactive three-dimensional plotting. The interactive plotting allows one to turn the plot as an object in space, in order to obtain the optimal viewing point or to see how the data points are related when they are hidden behind each other. The R code is surprisingly simple, though there are large numbers of dependent packages, so make sure ‘install dependencies’ is selected when downloading/installing {homals}.

R package {vegan}

The {vegan} package, Oksanen (2006) and Oksanen et al. (2011), permits the detrended correspondence analysis described in Section 1.3. It also has excellent ordination graphics. It offers the option to ‘build’ correspondence plots, using a text function, to add labels for categories, rows, or columns, one at a time. This option is excellent for complex data sets with large numbers of categories. The analysis is performed on the entire set, but only certain data points are labelled, facilitating interpretation and reporting.

R package {ade4}

The R package {ade4} (Dray and Dufour 2007) is, in fact, an impressive suite of functions developed (and being developed) for the environmental sciences. Many of the techniques available in the package are useful for linguists. The suite includes a range of options for performing different kinds of correspondence analysis as well as for plotting not only the ordinate results (as above) but also the numerical output.

R package {FactoMineR}

A rich and powerful package, {FactoMineR} (Lê et al. 2008) performs principal components analysis (similar to correspondence analysis but for continuous data), binary correspondence analysis, and multiple correspondence analysis. One of its main advantages is an argument in the plot function invisible= which allows one to hide certain rows or columns. Although it is possible in vegan to build up a plot by adding rows and columns iteratively, this simple tool makes it easy to quickly see data points that are hidden, but also to remove complexity to aid in reporting. It also possesses interactive possibilities, enabling the user to move the labels on the plots (to improve legibility), to hide certain clusters of data points, and even to select certain clusters and zoom in on them. For some of these functionalities, one needs to download third party (yet free) software called DynGraph. The correspondence analyses presented in the first section of this book use this package. The use of the package is not covered in this discussion since, currently, DynGraph only runs on the MacOSX platform.

R package {pamctdp}

The package {pamctdp} (Pardo 2010) offers a range of tools for dealing with contingency tables and for controlling the rows and columns in correspondence analysis. One function that has wide application is the ability to produce barplots of the profiles

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of the rows or the columns of a correspondence analysis. This simple visualisation technique can help with reporting complex data sets. Producing such plots ‘manually’ in R is straightforward, but time consuming.

3. Choice – correspondence or cluster There are many statistical techniques and their number is growing. One of the most confounding hurdles for anyone beginning to use quantitative methods is knowing which techniques are possible for a given data type and which are most suitable for a given research question. This section outlines, briefly, a technique comparable to correspondence analysis and offers information on how to choose between them.

3.1

Hierarchical cluster analysis

As an exploratory technique for categorical data, correspondence analysis shares a great deal with cluster analysis (presented in the preceding chapter) in that it visualises data that are interpretable in an intuitive way by ‘categorising’ features relative to their occurrence with other features. Both techniques are obviously the kind of tools useful to linguists, and indeed, all social scientists. Despite their similarities, there are important differences. The most obvious difference lies in the visual representation of the results. The graphical representation of a correspondence analysis can be more difficult to interpret than the dendrograms typical of cluster analysis, but offers important advantages over the latter. This visual representation and interpretation is at once the strength and weakness of correspondence analysis. Firstly, the correspondence configuration biplots do not give the false impression that any observed ‘clustering’ is discrete, which is an unfortunate side effect of a poorly interpreted dendrogram. Of course, the discrete visualisation in a dendrogram means that the algorithm performs the ‘grouping’, not the interpreter (arguably more reliable). But correspondence is not about groupings; it is about associations in the data. Its representation of results is both more complex and more ‘analogue’, and therefore, arguably, a more socio-conceptually realistic representation of how different linguistic structures interact. This brings us to the second, more important, advantage – the configuration biplot shows the interaction of the different features of the different factors, rather than merely sorting the features of a single factor. Correspondence analysis reveals what is associated with what, in other words, which features of which variables are co-occurring with others. This is in contrast to cluster analysis, where one only sees how the features of one factor are grouped, not what features are responsible for that grouping. In other words, the cluster analysis shows what is similar and different, but not what causes that similarity and difference.

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It should be obvious that added complexity/detail as well as an analogue/subjective interpretation can pose serious problems in correspondence analysis. The plots can be extremely difficult to read and interpret accurately. If the goal of a study is to determine which features of a given dimension are similar and which are different, cluster analysis is a simple and powerful technique. However, if the goal is to understand the interactions of different dimensions of language use and structure, then correspondence analysis is worth the extra effort. Let us move to a comparison of the visual outputs. Figures 9–14, set out, side by side, the graphical representations resulting from the same data in the two techniques. Figure 9 is a dendrogram of a hierarchical agglomerative cluster analysis of the data

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presented in Figure 3, which is duplicated here as Figure 10 to aid in comparison. The cluster analysis in Figure 11 was performed using the package {MASS} and the function hclust. The distance matrix used is Euclidean and the agglomeration method for clustering “average”. The functions expect the data to be in a numerical cross-tabulation (contingency table) format. The command line is:

> data.xtab <- read.table(file.choose(), header= T, sep= “\t”, row.names= 1) > data.dist <- dist(data.xtab, method= “euclidean”) # converts frequency table to distance matrix > HCA <- hclust(data.dist, method= “average”) # performs the cluster analysis > plot(HCA, frame.plot= T) # Plots results and adds frame to plot, see Figure 10.

The comparison between Figure 9 and Figure 10 is self-explanatory. The biplot and the dendrogram present similar information differently. The main difference is that in the biplot, we see which features cause the ‘clustering’. The dendrogram in Figure 11 is produced in the package {pvclust} with the function pvclust. It also uses the Euclidean distance matrix, but this time the agglomerating method is Ward. See Divjak and Fieller (this volume, 405–442) for an explanation of these concepts. Importantly, this function for cluster analysis includes a set of bootstrapped p-values to offer confidence estimates for the clusters.7 The

7. Bootstrapping is a general statistical technique for obtaining an estimation of significance. It is not a test for significance per se, but is rather a method that generates a large set of samples (from the sample under investigation) with which to compare the results.

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confidence scores are labelled faintly next to the branches in the clusters. The R-code for this technique follows. Again, the functions expect the data to be in a cross-tabulation format.

> library(pvclust) > data.xtab <- read.table(file.choose(), header= T, sep= “\t”, row.names= 1) > data.t <- t(data.xtab) # inverts the data > PVClust <- pvclust(data.t, method.hclust= “ward”, method.dist= “euclidean”) # produces distance matrix, # performs cluster analysis and bootstraps the results. # Can take some time to process > plot(PVClust, frame= T) # Plots results, see Figure 12

The addition of the bootstrapped p-values is an important contribution to the analysis. Compare the results with Figure 12, a binary correspondence analysis with a similar estimation of significance included. The confidence ellipsoids representing significant p-values are designed to capture similar information. Both visualisations seem reasonably successful. The third cluster analysis, presented in Figure 13, is not in the form of a dendrogram but of an unrooted cluster or ‘phylogenetic’ tree. This representation has been used by Schmidtke-Bode (2009) and Divjak (2010). This form functions poorly for only six features. Though it distinguishes them well, the sparseness of the graphics leaves a lot to be desired. Therefore, the data from Table 4 are used. The function for this kind of plot is nj and it is found in the {ape} package.

> library(ape) > data.xtab <- read.table(file.choose(), header= T, sep= “\t”, row.names= 1) > data.dist <- dist(data.xtab) # converts frequency table to distance matrix > PhyloClust <- nj(data.dist) # performs the cluster analysis > plot(PhyloClust, type = “u”, frame= T, cex= .9) # Plots results, see Figure 14

The phylogenetic tree in Figure 13 is compared with a multiple correspondence analysis in Figure 14. With this more complex data, we see clearly how the two methods differ in their abilities to represent data structure. The phylogenetic tree is simple and intuitive in contrast to the correspondence analysis, which needs detailed explanation.

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However, we know from the discussion above that the correspondence analysis includes more information, information missing in the cluster analysis.

4. Further reading There is a growing range of packages for performing correspondence analysis as well as new and improved tools in R generally. Moreover, new lines of statistical research are sure to bring interesting options for the technique in the near future. Within statistics, there is work on implementing permutation, or resampling, tests for correspondence analysis, as well as developing and applying mathematical algorithms that better capture certain kinds of correlations in the data – the development of grade correspondence analysis (Kowalczyk et al. 2004) and so-called profile-based approaches (Speelman et al. 2003; Delaere et al. submitted) are examples at hand. Within Cognitive Linguistics, broadly speaking, the method of correspondence analysis has been applied by Arppe (2006), Plevoets et al. (2008), Szelid and Geeraerts (2008), Glynn (2009, 2010, 2014a, 2014b, in press), Glynn and Sjölin (2011), Krawczak and Glynn (2011), Krawczak (2014a, 2014b), and Krawczak and Kokorniak (2012), as well as several studies in this volume. There exists a good range of resources for learning more. J.  P.  Benzécri originally developed the technique in the late 1960s. In English, his work of reference is Benzécri (1992). More recently, Agresti (2002:â•›382–384) and Greenacre (1984) have championed the method. These works are difficult to approach for linguists, being concerned with the mathematics behind the technique, rather than its application and interpretation. In recent years, a range of volumes has appeared that can be used as manuals for performing the analysis. As mentioned above, Greenacre (2007) and Husson et al. (2011) are excellent manuals for both understanding the technique and performing it in R. Along these lines, Baayen (2008:â•›128–136) also offers a brief description. Le Roux and Rouanet (2010) is an excellent book: essentially it constitutes a detailed tutorial for the function-rich package {FactoMineR}, though it offers no R commands. Lastly, although older, Weller and Romney (1990) is another thorough and approachable alternative, but it also offers no R code. More advanced, yet still reasonably practical publications include Rencher (2002: Ch. 15), Le Roux and Rouanet (2005), and Murtagh (2005). Also consider Greenacre and Blasius (2006), which is a collection of articles that seek to advance different facets of the method. Greenacre (2007: Appendix C) offers an annotated bibliography. For specific information on the plotting options, see Gower et al. (2010) and Greenacre (2010). Correspondence analysis and the current range of packages for performing it in R offer a powerful and simple tool for identifying patterns in multifactorial data. The options for visualisation of its results can be difficult to explain, but are extremely rich in the information that they display. As an exploratory method, it is an excellent heuristic for getting into complex data and digging out what relates to what.



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References Agresti, A. (2002). Categorical data analysis (2nd ed.). Hoboken: John Wiley. DOI: 10.1002/ 0471249688 Arppe, A. 2006. Frequency considerations in morphology. Finnish verbs differ, too. SKY Journal of Linguistics, 19, 175–189. Baayen, R. H. (2008). Analyzing linguistic data: A practical introduction to statistics using R. Cambridge: Cambridge University Press. DOI: 10.1017/CBO9780511801686 Baayen, R. H. (2011). languageR: Data sets and functions with “Analyzing Linguistic Data: A practical introduction to statistics”. R package version 1.1. Retrieved from . Benzécri, J. P. (1992). Correspondence analysis handbook. New York: Marcel Dekker. De Leeuw, J., & Mair, P. (2009a). Simple and canonical correspondence analysis using the R package anacor. Journal of Statistical Software, 31, 1–18. Retrieved from . De Leeuw, J., & Mair, P. (2009b). Gifi methods for optimal scaling in R: The package homals. Journal of Statistical Software, 31, 1–20. Retrieved from . Delaere, I., Plevoets, K., & De Sutter, G. (Submitted). Measuring text type variation through profile-based correspondence analysis: How far apart are translated and non-translated Dutch? Target. International Journal of Translation Studies. Divjak, D. (2010). Structuring the lexicon: A clustered model for near-synonymy. Berlin & New York: Mouton de Gruyter. Dray, S., & Dufour, A.-B. (2007). The ade4 package: Implementing the duality diagram for ecologists. Journal of Statistical Software, 22, 1–20. Gifi, A. (1990). Nonlinear multivariate analysis. Chichester: Wiley. Glynn, D., & Sjölin, M. (2011). Cognitive Linguistic methods for literature: A usage-based approach to metanarrative and metalepsis. In A. Kwiatkowska (Ed.), Texts and minds: Papers in cognitive poetics and rhetoric (pp. 85–102). Frankfurt/Main: Peter Lang. Glynn, D. (2009). Polysemy, syntax, and variation: A usage-based method for Cognitive Semantics. In V. Evans, & S. Pourcel (Eds.), New directions in Cognitive Linguistics (pp. 77– 106). Amsterdam & Philadelphia: John Benjamins. Glynn, D. (2010). Synonymy, lexical fields, and grammatical constructions: A study in usage-based Cognitive Semantics. In H.-J. Schmid, & S. Handl (Eds.), Cognitive foundations of linguistic usage-patterns: Empirical studies (pp. 89–118). Berlin & New York: Mouton de Gruyter. Glynn, D. (2014a). The conceptual profile of the lexeme home: A multifactorial diachronic analysis. In J. E. Díaz-Vera (Ed.), Metaphor and metonymy across time and cultures (pp. 265–293). Berlin & New York: Mouton de Gruyter. Glynn, D. (2014b). The social nature of anger: Multivariate corpus evidence for context effects upon conceptual structure. In I. Novakova, P. Blumenthal, & D. Siepmann (Eds.), Emotions in discourse (pp. 69–82). Frankfurt/Main: Peter Lang. Glynn, D. (In press). Cognitive socio-semantics: The theoretical and analytical role of context in meaning. Review of Cognitive Linguistics. Gower, J., Gardner-Lubbe, S., & le Roux, N. (2010). Understanding biplots. Chichester: Wiley. Greenacre, M., & Blasius, J. (Eds.). (2006). Multiple correspondence analysis and related methods. London: Chapman & Hall. DOI: 10.1201/9781420011319

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Greenacre, M., & Nenadić, O. (2010). ca: Simple, multiple and joint correspondence analysis. R package version 0.33. Retrieved from . Greenacre, M. (1984). Theory and applications of correspondence analysis. London: Academic Press. Greenacre, M. (2006). From simple to multiple correspondence analysis. In M. Greenacre, & J. Blasius (Eds.), Multiple correspondence analysis and related methods (pp. 41–76). London: Chapman & Hall. DOI: 10.1201/9781420011319.ch2 Greenacre, M. (2007). Correspondence analysis in practice. London: Chapman & Hall. DOI: 10.1201/9781420011234 Greenacre, M. (2010). Biplots in practice. Bilbao: Fundación BBVA. Husson, F., Lê, S., & Pagès, J. (2011). Exploratory multivariate analysis by example using R. London: Chapman & Hall. Kowalczyk, T., Pleszczynska, E., & Ruland, F. (Eds.). (2004). Grade models and methods for data analysis. München: Springer. DOI: 10.1007/978-3-540-39928-5 Krawczak, K. (2014a). Shame and its near-synonyms in English: A multivariate corpus-driven approach to social emotions. In I. Novakova, P. Blumenthal, & D. Siepmann (Eds.), Emotions in discourse (pp. 84–94). Frankfurt/Main: Peter Lang. Krawczak, K. (2014b). Epistemic stance predicates in English: A quantitative corpus-driven study of subjectivity. In D. Glynn, & M. Sjölin (Eds.), Subjectivity and epistemicity: Corpus, discourse, and literary approaches to stance (pp. 355–386). Lund: Lund University Press. Krawczak, K., & Glynn, D. (2011). Context and cognition: A corpus-driven approach to parenthetical uses of mental predicates. In K. Kosecki, & J. Badio (Eds.), Cognitive processes in language (pp. 87–99). Frankfurt/Main: Peter Lang. Krawczak, K., & Kokorniak, I. (2012). Subjective construal of think in Polish. Poznań Studies in Contemporary Linguistics, 48, 439–472. DOI: 10.1515/psicl-2012-0021 Le Roux, B., & Rouanet, H. (2005). Geometric data analysis: From correspondence analysis to structured data analysis. London: Kluwer. Le Roux, B., & Rouanet, H. (2010). Multiple correspondence analysis. London: Sage. Lê, S., & Husson, F. (2008). FactoMineR: An R package for multivariate analysis. Journal of Statistical Software, 25, 1–18. Murtagh, F. (2005). Correspondence analysis and data coding with R and Java. London: Chapman & Hall. DOI: 10.1201/9781420034943 Nenadić, O., & Greenacre, M. (2007). Correspondence analysis in R, with two- and three-dimensional graphics: The ca package. Journal of Statistical Software, 20. Retrieved from . Oksanen, J., Blanchet, G., Kindt, R., Legendre, P., O’Hara, R. B., Simpson, G. L., Solymos, P., Henry, M., Stevens, H., & Wagner, H. (2011). vegan: Community ecology package. R package version 1.17-11. Retrieved from . Oksanen, J. (2006). Multivariate analysis of ecological communities in R: vegan tutorial. Retrieved from . Pardo, C. (2010). ‘pamctdp’. Retrieved from . Plevoets, K., Speelman, D., & Geeraerts, D. (2008). The distribution of T/V pronouns in Netherlandic and Belgian Dutch. In K. Schneider, & A. Baron (Eds.), Variational pragmatics: Regional varieties in pluricentric languages (pp. 181–209). Amsterdam & Philadelphia: John Benjamins.



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Rencher, A. (2002). Methods of multivariate analysis (2nd ed.). Chichester: Wiley. DOI: 10.1002/ 0471271357 Schmidtke-Bode, K. (2009). Going-to-V and gonna-V in child language: A quantitative approach to constructional development. Cognitive Linguistics, 20, 509–53. DOI: 10.1515/COGL.2009.023 Speelman, D., Grondelaers, S., & Geeraerts, D. (2003). Profile-based linguistic uniformity as a generic method for comparing language varieties. Computers and the Humanities, 37, 317–337. DOI: 10.1023/A:1025019216574 Szelid, V., & Geeraerts, D. (2008). Usage-based dialectology: Emotion concepts in the Southern Csango dialect. Review of Cognitive Linguistics, 6, 23–49. DOI: 10.1075/arcl.6.03sze Venables, W., & Ripley, B. (2002). Modern applied statistics with S (4th ed.). London: Springer. DOI: 10.1007/978-0-387-21706-2 Weller, S., & Romney, K. (1990). Metric scaling correspondence analysis. London: Sage.

Logistic regression A confirmatory technique for comparisons in corpus linguistics Dirk Speelman

University of Leuven

This text offers an introduction to binary logistic regression, a confirmatory technique for statistically modelling the effect of one or several predictors on a binary response variable. It is explained why logistic regression is exceptionally well suited for the comparison of near-synonyms in corpus data; the technique allows the researcher to identify the different factors that have an impact on the choice between near synonyms, and to tease apart their respective effects. Moreover, the technique is well suited to deal with the type of unbalanced data sets that are typical of Corpus Linguistics. First, we describe in which contexts logistic regression is applicable and we give examples of the types of research questions for which it is an appropriate tool. Next, we explain why and how logistic regression analysis is different from linear regression analysis and we illustrate how the output of logistic regression analysis can be interpreted, using the study of an alternation pattern in Dutch as our example. The R code used in the case study is explained in detail and an URL is given from which R code and data sets can be downloaded. Finally, suggestions for further reading are given. Keywords: confirmatory statistics, outcome prediction, statistical modelling

1. Introduction Although its roots date back to research in the biological sciences in the first half of the twentieth century (Berkson 1944; Wilson and Worcester 1943), logistic regression did not mature and gain acceptance until the 1960s and 1970s (e.g. Cox 1969; Nelder and Wedderburn 1972). After its initial acceptance in epidemiology, it rapidly spread to other fields. It is now widely accepted as a (or even the) dominant method for studies in which the response variable has two possible outcomes. It is commonly employed in biology, criminology, ecology, economics, engineering, health policy,

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medical sciences, and many other fields, and is supported by all major statistical software packages. Linguistics, more specifically, variationist linguistics, was an early adopter of logistic regression. The VARBRUL tool (Cedergren and Sankoff 1974; Sankoff 1988) was an early implementation of logistic regression implemented specifically in support of the analysis of linguistic variation. By consequence, many sociolinguists were using the technique even before it was implemented in the major statistical software packages. Goldvarb X (Sankoff, Tagliamonte, and Smith 2005), the latest incarnation of the VARBRUL program, is still widely used in variationist linguistics, even though nowadays major statistical software packages typically offer many more options than those in VARBRUL/Goldvarb (see e.g. Johnson 2008 for a discussion of this issue). By contrast, apart from the specific tradition of VARBRUL/Goldvarb use in sociolinguistics, logistic regression has only rather recently become more generally widespread in linguistics (some early examples are Williams 1994; Arnold et al. 2000; Grondelaers, Speelman, and Geeraerts 2002; and Keune et al. 2005). However, in recent years the number of linguistic studies that use logistic regression has been rapidly increasing. Logistic regression is a broad topic for several reasons. First, there are a great deal of technicalities involved in what happens ‘under the hood’ when a logistic regression analysis is run, just as there are a lot of different tools available that also sometimes differ in their technical details. Second, the technique can be applied to many different types of (linguistic) research questions, phenomena and data sets, including data obtained from psycholinguistic experiments and surveys, as well as data obtained from corpora. Third, since its first introduction, the technique has evolved in many ways and several extensions or variations of the technique now cover situations that were originally not covered by logistic regression (e.g. polytomous response variables; random factors). Since this paper cannot aspire to be exhaustive in its coverage, some choices were made. With respect to the first point, this description is intended as a non-technical introduction to logistic regression that does not discuss the underlying mathematics and instead zooms in on the basic rationale of the technique and on issues and pitfalls relating to the practical use of the technique. Second, examples in the paper will primarily be drawn from Corpus Linguistics. Third, we restrict ourselves to the basic technique and do not cover extensions such as polytomous response variables and random factors. References to literature that does cover these items are given in Section 7, at the end of the chapter.

2. Simple logistic regression analysis Just like other types of regression analysis, logistic regression is a technique that allows one to examine the relation between one or several predictor variables and a



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response variable. The most important variable in any regression analysis is the response variable (also called dependent variable or simply response). This is the variable that captures the linguistic behaviour in which you are primarily interested. Typically, it measures some aspect of the linguistic phenomenon of your interest, in the form of either some characteristic of the actual utterances that instantiate the phenomenon or some characteristic of their production, perception or evaluation. In traditional linear regression analysis, the response variable must be a numerical variable, such as reaction time in a lexical decision task (or some derived value thereof, such as log-transformed reaction time) or formant one position (F1 frequency) in the pronunciation of a particular vowel in a phonetic study, etc. Logistic regression, on the other hand, is designed for studies in which the response variable is a categorical variable with two possible values (this is often called a binary variable or a dichotomous variable; the ‘classical’ type of logistic regression that is the topic of this text, therefore, is sometimes called binary logistic regression or dichotomous logistic regression). Possible examples are the realisation or non-realisation of word-final r in spoken English, the choice between two (near)-synonyms such as bike versus bicycle, word order choice in particle placement (e.g. he picked up the book versus he picked the book up), the choice between s-genitive or of-genitive (e.g. John’s house versus the house of John), dative alternation (e.g. he gave me money versus he gave money to me), etc. The other variable or variables involved in a regression analysis are called predictor variables (or predictors or independent variables). These are the variables that you hypothesize may have an effect on the response variable (note that in this text the term ‘effect’ simply refers to a correlation pattern; it does not necessarily refer to a causal relation). In logistic regression, as is also the case in linear regression analysis, the predictor variables can be either numerical or categorical. Therefore, they can easily represent very different types of information, ranging from morpho-syntactic and semantic characteristics of the utterance under scrutiny over pragmatic characteristics of the utterance and its broader linguistic context, to characteristics of the speakers and hearers (or the writers and intended audience) and of the situation in which the utterance takes place or took place. Logistic regression, then, is suited for all investigations in which the variation in the response variable is essentially probabilistic in all situations under scrutiny. This means that, for all possible configurations of predictor values that can occur in a single observation, it holds true that both outcomes of the response variable are essentially possible, even if one outcome is far more probable than the other. Furthermore, the method assumes that, in all situations under scrutiny, the two possible outcomes of the response variable are two mutually exclusive alternatives that together exhaust the options the language user has at his disposal with respect to the phenomenon under scrutiny. In other words, the alternatives must perform (more or less) the same (linguistic) function and they must do so in a tertium excluditur type of way; it must

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not be the case that there exist other alternatives that perform the same function and that are not covered by the two outcomes of the response variable. The way we try to establish the effect of predictor variables on the response variable in logistic regression can best be explained by starting from linear regression, the ‘prototypical case’ of regression analysis, and then comparing logistic regression to this prototypical case. We start by comparing simple linear regression, which is linear regression with one predictor, with its logistic counterpart, simple logistic regression, which is logistic regression with one predictor. In Figure 1, we see three fictitious examples of relations between a predictor (on the x-axis) and a response (on the y-axis). In our first exploration of Figure 1, we only look at the points (the small circles) that are plotted, and for the moment we ignore the grey lines and the +-symbols. The scatterplot in the left panel represents all correct decisions in some lexical decision task in which stimuli are spoken with a regional accent; the points are instances of hearers reacting to a stimulus produced by some speaker; the x-axis represents the distance in kilometers between the hearer’s place of residence and the speaker’s place of residence. The y-axis represents log-transformed reaction times in the lexical decision task. The scatterplot illustrates that as the distances grow larger, on average the log-transformed reaction times also tend to be larger (i.e. the reactions tend to be slower). The middle panel and the right panel represent two different apparent-time studies in which the use, by speakers with ages varying from ten years to ninety years, of two alternative pronunciations of а phoneme are recorded; the alternative pronunciations are the presence and absence of some specific innovative feature (which we will not specify since the data are fictitious anyhow). For a logistic regression to be possible, the categorical response variable is (typically automatically) converted to a so-called dummy variable. Technically, this dummy variable is a numerical variable with only two possible values, namely 0 and 1.



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Value 1 is often called the success outcome (which is just a naming convention; it does not imply that this outcome is more desirable). The points in the middle plot and the right plot in Figure 1 are instances of a speaker using either one of two pronunciation variants. The x-axis represents the age of the speaker and the y-axis represents the pronunciation variant that was used (1 meaning ‘presence of the innovative feature’ and 0 meaning ‘absence of the innovative feature’). The middle and right plot are scatterplots like the left plot, but they look unusual because the response variable on the y-axis can have only two possible values. What we see, in the middle plot more clearly than in the right plot, is that in both plots, older people tend to use the innovative feature less often than younger people. You see this because the horizontal lines of points with y = 1 grow thinner as the age increases and the horizontal lines of points with y = 0 grow thicker as the age increases. Simple regression analysis tries to capture tendencies such as the ones we see in these scatterplots. In the case of the left panel, the most basic form of simple linear regression can be used. Conceptually what we do is we use simple linear regression to try and capture the relation between the predictor distance and response logRT (log-transformed reaction time) by trying to find a straight line that connects the logRT averages for each specific distance-value (or that at least deviates from these distance-specific logRT averages as little as possible). Technically, what the technique does is choose a straight line that is such that the sum of the squares of all residuals is as small as possible, the residuals being the vertical distances between the points in the scatterplot and the straight line that is chosen by the technique. This is called the ordinary least squares procedure for fitting a line. The fitted line is depicted in grey in the left panel of Figure 1. Technically, it is defined by two numbers. The first number is the intercept, which gives the y-value for x being zero. Here the fitted intercept is 6.8, meaning that according to the fitted line the mean logRT for distance zero is 6.8. The second number is the slope, which gives the fitted increase (or decrease) of y for each unit change in x. Here the fitted slope is 0.004, meaning that according to the fitted line the mean logRT increases by 0.004 for each kilometer that is added to the distance. Linear regression subsequently allows us to test whether the slope of this fitted line is significantly different from zero.1 This statistical test comes with an assumption: it is an acceptable simplification to think of the actual relation between distance and logRT as a straight line connecting all distance-specific mean logRTs from which the individual cases deviate in such a way that their vertical distances from this line are essentially ‘unstructured noise that behaves similarly across all ages’. The technical formulation of the latter assumption is that the actual vertical distances, the so-called errors, are normally distributed with mean zero and with a variance that is the same 1. Sometimes we also want to test whether the intercept is significantly different from zero, but most of the time we are more interested in the slope.

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for all distances.2 In the example in the left panel of Figure 1, we do not have enough separate cases for distance=0, distance=1, distance=2, etc. for us to verify, at that level of granularity, whether the data are in agreement with the above assumption. What we could do, however, to have at least a rough idea of whether the data are in agreement with this assumption, is split up the distances into the ranges zero to twenty kilometers, twenty to forty kilometers, forty to sixty, etc., and then for each range check whether at the midpoint of that range the line fitted by the regression is indeed close to the average logRT of that range. In Figure 1, we have plotted the average logRT for each range as a grey +-symbol, using the range midpoint as the x-coordinate. We see the +-symbols are reasonably close to the fitted line. Additionally, we can check whether, in each range, the observations are symmetrically scattered above and below the fitted line (thus rendering the residuals close to normal in this range) and whether they do so in a comparable way in all ranges (i.e. in such a way that the residuals are not markedly bigger in one range than in another). The data seem to be roughly in agreement with the assumption, so we can perform the statistical test. Incidentally, the result of the test for these data is that the slope, which is estimated to be 0.004, is clearly statistically significant at the usual 95% confidence level (p < 0.001, so we are far more than 95% confident that the actual slope, i.e. the slope in the population from which the sample was drawn, differs from zero). We can also build a 95% confidence interval for the slope, which turns out to range from 0.0036 to 0.0052. So the simple linear regression estimates that, for every additional kilometer, a value of 0.004 is added to the (distance-specific) average logRT, and the confidence interval states that we are 95% confident that the actual slope is between 0.0036 and 0.0052. In the middle panel and right panel of Figure 1, we see fitted lines that result from logistic regression analyses. The purpose of logistic regression is very similar to that of linear regression. Here too a line is fitted by the algorithm in such a way that it passes through all local (i.e. age-specific) average y-values (or at least gets as close as possible to this). But what does such a local average mean here? We can think of individual y-values as well as average y-values as ‘proportions of cases that have the innovative feature’. In the trivial case of individual observations, this proportion is always either 100% (if y = 1) or 0% (if y = 0), but if we look at several cases taken together (e.g. 10 cases taken together, three of which have y = 1 and seven have y = 0), the average y gives us the proportion of ‘successes’ in these cases (e.g. 3/10 = 0.3 = 2. The errors are the discrepancies between actual values of the response and the line that connects the actual local averages of the response in the whole ‘population’ that our data set is a sample from (which is a line that we assume exists, but that we cannot know exactly on the basis of our data set alone). The residuals are the discrepancies between values of the response in our data set and the line that we fit with our regression technique. The assumption underlying linear regression is that the errors are normal (and that, by consequence, the residuals also can be expected to be almost normal).



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30%). In a way that is very similar to what we did for the left panel of Figure 1, in the other panels we also split up the x-values in ranges (here using the ranges ten to twenty-six years, twenty-seven to forty-two, forty-three to fifty-eight, etc.) and plotted the average y-values for the ranges as +-symbols using the range midpoints 18, 34, 50, … as x-coordinates. You see the fitted lines are close to the +-symbols. In logistic regression, just like in linear regression, a fitted line either goes up all of the time or it goes down all of the time, or it is a flat horizontal line, and what we are essentially interested in is whether the line goes up or down in a way that is significantly different from the no-effect case of a flat horizontal line. Obviously there is an important difference between logistic and linear regression, which is that apart from the no-effect case (which is represented as a horizontal straight line in both logistic and linear regression), all other lines that can be fitted in logistic regression are not straight lines: they are logistic curves. In the (trivial) no-effect case, a logistic curve is a horizontal straight line, but all other logistic curves that can be fitted are a type of curve that approximates a straight line wherever the proportion of success is not too close to 0% or 100%, but in which the slope decreases (but never completely disappears) as the proportions of success approximate 0% or 100%. If, for the range of x-values that we study, proportions of success approach either 0% or 100%, we clearly see this change of slope (and if there are proportions that are close to both 0% and 100% we see ‘the full shape’ of the logistic curve, which is an S-shaped curve such as the one in the middle panel of Figure 1). Often, however, such extreme proportions do not occur among the x-values we study, and then, the visible part of the logistic curve often is hardly distinguishable from a straight line (as is the case in the right panel of Figure 1). The way the logistic curve is fitted is rather complicated: fitting a logistic relation between a predictor x and a proportion of success y is done by fitting a linear relation between predictor x and the logit of y. The logit of a proportion is a doubly transformed version of the proportion; it is the log-transformation of the odds that correspond to the proportion. We will illustrate, on the basis of Figure 2, that a linear relation between x and the logit of success proportion y implies a logistic relation between x and success proportion y. The top left panel in Figure 2 illustrates the first step in the two-step conversion of proportions into logits, which is the transition from proportions to odds. Odds are calculated as ‘number of successes divided by number of failures’, which is the same as ‘proportion of success divided by proportion of failure’. For instance, a success proportion of 80% corresponds to four successes for each failure (odds = 4/1 = 0.8/0.2 = 4) and a success proportion of 20% corresponds to one success for every four failures (odds = 1/4 = 0.2/0.8 = 0.25). As can be seen in the figure, the plot that maps proportions onto odds looks a bit strange in the sense that the result is asymmetrical; odds for proportions in which success outweighs failure span the range from one all the way to plus infinity. Odds for proportions in which failure outweighs success, on the other hand, are all between one and zero. The top right

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panel shows the second step in the two-step conversion of proportions into logits, which goes from odds to log-transformed odds (i.e. to logits), and which corrects the asymmetry. On the logit scale that we reach after the second transformation, zero is the point where success and failure are in balance; negative values (which can span the range from zero to minus infinity) indicate that failure outweighs success and positive values (which can span the range from zero to plus infinity) indicate that success outweighs failure. The bottom left panel illustrates the transition from proportions to log odds (i.e. to logits) in one step. We clearly see that for proportions that are sufficiently far removed from 0% and 100%, there is a ‘not too far from linear’ relation between proportions and logits, which means that a constant increase or decrease in proportions corresponds to a constant increase or decrease in logits, but as proportions get close to 0% and 100%, a constant increase or decrease in proportions corresponds to an increase or decrease in logits that gets bigger the closer we are to 0% and 100%. In the fourth panel, we flip the relation around and show the inverse transition from logits to proportions. We recognise the logistic curve we also saw in Figure 1: for proportions that are not too close to 0% and 100%, logits map almost linearly to proportions, but as proportions get close to 0% logits can keep on becoming smaller at a constant rate but with an ever-diminishing (but never completely vanishing) effect on the further decrease of the corresponding proportion. As proportions get close to 100%, logits can keep on becoming bigger at a constant rate but with an ever-diminishing (but never completely vanishing) effect on the further increase of the corresponding proportion. This fourth panel brings us to the most crucial observation regarding Figure 2; since logits have a logistic relation to proportions of success, anything that relates linearly to logits (most notably the predictors in our logistic regression models) will automatically also have a logistic relation to the proportions of success. Or still more explicitly, the absence of a linear effect of the predictor on the logit (flat horizontal line) implies the absence of a logistic effect of the predictor on the proportion of success (flat horizontal line); a positive linear effect of the predictor on the logit (straight line going up) implies a positive ‘logistic effect’ of the predictor on the proportion of success (S-curve going up); a negative linear effect of the predictor on the logit (straight line going down) implies a negative ‘logistic effect’ of the predictor on the proportion of success (S-curve going down). There are conceptual as well as technical reasons why we use logistic regression and fit logistic curves to model the ‘proportion of success’ in the case of a binary response variable (as opposed to trying to apply linear regression and fit straight lines to model these proportions of success). Conceptually, if you have a response variable, the outcomes of which are inherently probabilistic in all situations under investigation, and you have a predictor that has an effect on the probability of success in your response variable, it often makes sense to expect the effect of the predictor on the probability of success to become smaller as probabilities approach zero or a hundred

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–4

–2

0 Logit

2

4

Figure 2.╇ The relation between proportions, odds and logits

per cent. By way of a ‘thought exercise’, let us take a non-linguistic and a linguistic example to reason about this. First, consider the probability of some skilled basketball player succeeding in throwing the ball in the basket, with, as predictor variable, his distance from the basket (with distances ranging from say 1 meter to 28 meters) and as response variable a categorical variable with two possible outcomes; the ball either goes in (y = 1) or it does not (y = 0). It seems reasonable to expect there to be some distance where the probability of success is about 50%. I am not a basketball player, and to be fair I have no idea what this distance would be, but for the sake of the argument let us say it is about nine meters. It is reasonable then to expect that in the range of distances close to nine meters (say starting from six meters up to twelve meters) the probability of success clearly goes down for each extra meter that is added to the distance. However, as soon as you are in a distance range where the probability of success is really low (let us assume this starts from fourteen meters), it is reasonable to expect the probability of success to further drop with each additional meter one gets further from the basket, but no longer at the same rate as in the ‘middle area of distances’ (because otherwise

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one would rapidly end up with probabilities below 0%, which is impossible). Likewise, as soon as you are in a distance range where the probability of success is really high (let us assume this starts from five meters), it is reasonable to expect the probability of success to further rise with every additional meter one gets closer to the basket, but no longer at the same rate as in the ‘middle area’ (because otherwise one would rapidly end up with probabilities above 100%, which is impossible). In other words, the idea is that going still further when one is already far away from the basket very likely still makes the task more difficult, but this added difficulty only modestly affects proportions of success (because these already are really low). Likewise, coming still closer when one is already close to the basket very likely still makes the task easier, but this reduction of difficulty only modestly affects proportions of success (because these already are really high). A ‘thought exercise’, from linguistics, would be the situation of a person moving to another country and then taking classes to learn the language spoken in that country. In our (admittedly extremely simplistic) ‘thought exercise’, we use ‘number of language classes taken’ as a predictor and the response is the ‘success’ of sentences produced by the person in everyday conversations in this new language (each sentence being a separate case); let us say that for each sentence, y = 1 if the sentence is error-free and y = 0 if the sentence contains at least one error. It makes sense to assume that initially almost all sentences will contain errors and that it will take a while for the classes to pay off so much that the person will start producing completely error-free sentences. It further makes sense that subsequently the person gets to a stage where on the one hand lessons begin to pay off more clearly but on the other hand still a lot of further progress can be made, so further lessons can clearly improve the probability of producing completely successful sentences. Finally, however, when the person reaches a level in which most sentences will be produced correctly, more classes will still allow for progress but the pace of progress will drop, at least if progress is measured as ‘increase of the proportion of successful sentences’. It is likely that one will keep on making progress, but this additional progress will show less and less in the proportions of success since the person already is very successful with respect to the criterion of success that is used.3 Let us only briefly consider the technical reasons why attempts to apply linear regression to fit straight lines to model proportions of success can run into problems. The first technical reason boils down to the same thing as the conceptual reason 3. The purpose of the ‘thought exercise’ is to illustrate how it is reasonable to expect the slope to become less outspoken in the vicinity of 0% or 100% probability. The ‘thought exercise’ is not intended to illustrate that the slope must be constant (and therefore the line must be linear or almost linear) for all other probabilities (say for the area between 20% and 80% probability). Whether that is the case or not (and therefore), whether a straightforward application of logistic regression to the data is appropriate is an empirical question that must be examined when inspecting the statistical model that results from the analysis.



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mentioned above; when trying to fit a straight line, one may end up assigning impossible average proportions of success to some values of the predictor. When this only occurs for predictor values outside the range of our research interest (as would be the case in the right panel of Figure 1), this is not a serious problem. If, however, this occurs for predictor values inside the range of our research interest (as would be the case in the middle panel of Figure 1), that would very much affect the quality, interpretability and attractiveness of the analysis. Other technical problems that can arise are related to the assumption underlying inferential tests in linear regression (the assumption of the actual errors being normally distributed with mean zero and with a variance that is the same for all values of the predictor). Since the actual values of individual observations can only be zero and one, it is technically impossible for them to meet this assumption (with two possible values, a normal distribution is impossible; moreover, equal variance across very different proportions of success also becomes impossible). Therefore, the technique of logistic regression is built on a different assumption. Like in the case of linear regression, the assumption is that the ‘errors are just structureless random noise’, but the assumption is more adapted to the context of proportions of success. It can be restated, more technically, as: a logistic curve connects all x-value specific proportions of success, and the number of successes that can be expected for any specific x-value has a binomial distribution with sample size the number of observations for that x-value, and with underlying probability of success the actual average proportion of success for that x-value. Incidentally, because of this assumption, binary logistic regression is also sometimes called binomial logistic regression. Due to these differences, fitting the logistic regression is not done with the aforementioned ordinary least squares procedure but with a more complicated maximum likelihood estimation based iterative procedure (maximum likelihood estimation simply means that the procedure tries to pick, from all candidate lines/curves, the one that maximizes the theoretical probability of us encountering a data set like the one we actually did encounter).4, 5 For the middle panel of Figure 1, the logistic regression analysis estimates the logit of y to decrease by 0.09 each year and, moreover, the decrease turns out to be 4. In general, maximum likelihood estimation does not refer to one specific calculation procedure but rather to a generic strategy for parameter estimation. In fact, under the assumptions that underlie linear regression, the simple procedure of ordinary least squares renders maximum likelihood estimates and therefore can be regarded as equivalent to likelihood estimation in that context. 5. The reader may wonder whether linear regression and ordinary least squares estimation can still not be used if one switches to the logit scale and therefore models the relationship between predictor x and the logit of y (which, after all, is assumed to be a linear relation). This is not (generally) possible, because the logits of y for individual observations have the possible value minus infinity (if y = 0) and plus infinity (if y = 1), and, therefore, ordinary least squares and the assumptions underlying inferential tests in linear regression do not apply.

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significant at the usual 95% confidence level (p < 0.001, so we are far more than 95% confident that the actual slope differs from zero).6 The interpretation of the estimate –0.09 (decrease by 0.09) is that, according to this regression model, the logit of y at age n + 1 is the logit of y at age n minus 0.09 (some specific examples for the model at hand: according to the model, the logit is 3.07 at age 20 and at age 21 it is 2.98; at age 58, the logit is –0.19 and at age 59, it is –0.28). Just like in linear regression, the slope that characterises the relation between predictor x and the logit of y can be expressed in a single number. Unfortunately, the logit scale is not a very ‘natural’ scale, in the sense that most people have trouble imagining what the units on this scale represent. Therefore, some people prefer not to look at the estimate itself but to look at ‘e to the power of the estimate’ (in our case that would be e–0.09, which is 0.91). Its interpretation in the statistical model is straightforward: a decrease by 0.09 on the logit scale corresponds to a ratio of e–0.09 on the odds scale. In other words, the logit of y decreases by 0.09 each year and the odds of y are multiplied by e–0.09 each year. Or, still differently, for each unit that is added to the predictor, the odds of y are 91% of what they were before. Since it can be interpreted in this manner, the quantity ‘e to the power of the estimate’ is called the odds ratio for the predictor (meaning the ratio between, on the one hand, the odds of y for some predictor value x, and on the other hand, the odds of y for predictor value x + 1).7 The odds scale is a little simpler to interpret than the logit scale (after all, odds are sometimes used in non-technical contexts; think of horse races etc.), but of course the most ‘natural’ scale is that of the proportions of success. At that scale, however, the effect of the predictor can no longer be summarized with one number (or rather two, namely, intercept and slope). Instead, we need to calculate and list the fitted proportions of success for all different values of x. It is because of this that fitted proportions of success will typically not be reported. However, people interested in these values can easily derive them from the estimates that are reported in a logistic regression analysis.8

6. This significance test applies to the logit level as well as the proportion of success level. If, at the logit level, there is a significant linear effect, then it follows that at the proportion of success level there is a significant logistic effect. If at the logit level there is no significant linear effect, then it follows that at the proportion of success level, there is no significant logistic effect. 7. The following equations illustrate why an increase or decrease on the logit scale corresponds to a ratio on the odds scale: logitage=n = logitage=n–1 + estimateage e(logitage=n) = e(logitage=n–1 + estimateage) e(logitage=n) = e(logitage=n–1) × e(estimateage) oddsage=n = oddsage=n–1 × e(estimateage) 8. The following equations illustrate how to convert between logits, odds and proportions of success:

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3. Multiple logistic regression analysis

Proportion of success Age

ude Attit

Distance

ude Attit

Diffic

ulty Log of reaction time

Proportion of success

In multiple regression, the effect of two or more predictors on the response variable is studied simultaneously. Figure 3, below, illustrates the case of two predictors on the basis of three fictitious data sets. The left panel elaborates on the example in the left panel of Figure 1. We again look at the effect of distance on logRT, but now we add a second predictor, which is the difficulty of the word to be recognized (where we assume difficulty is some continuous scale that captures the degree to which the word has characteristics that make it harder to recognize; e.g. it captures the degree to which the word is rare or specialized). In this model, which is an example of multiple linear regression, the relation between predictors and response is captured by fitting a plane. The plane is fitted in such a way that the sum of the squares of the vertical distances between the plane and the actual observations is minimized, and it is described by means of three estimates. The intercept captures the fitted mean logRT at the point where distance and difficulty are both zero. The slope for distance captures the increase/decrease of the mean logRT with each additional kilometer and the slope for difficulty captures the increase/decrease of the mean logRT for each additional difficulty unit. The representation in Figure 3 is a little schematic; actual observations (which would float above and below the fitted plane) are not shown and neither are the actual values on the axes given. The key thing to observe is how a plane is produced by the combined effect of (an intercept and) two slopes. In this case, we have two positive slopes, but, of course, that does not have to be the case in general.

Figure 3.╇ Multiple linear regression (left) and multiple logistic regression (middle and right) prop = odds / (1 + odds) = elogit / (1 + elogit) prop / (1 – prop) = odds = elogit ln(prop / (1 – prop)) = ln(odds) = logit

Age

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In the middle and right panel of Figure 3, we see the type of surface that is fitted by means of multiple logistic regression. The examples elaborate on the examples from the middle and right panel of Figure 1. Once more, we display the effect of age on variant choice. One difference from Figure 1 is that this time we happen to call the traditional variant the success variant and therefore, we plot the probability of using the traditional variant. The result is that this time the proportion of success increases as age increases. We now add a second predictor, attitude, which captures the reported speaker’s attitude towards the local dialect. We see on the plots that not only age has an effect on variant choice, but that, additionally, a more positive attitude (i.e. a higher value for attitude) correlates with a higher proportion of success. The middle and the right panel show that logistic regression with two predictors fits a curved surface that sometimes is rather close to a plane (right panel) and sometimes is clearly S-shaped (middle panel). Although it is not clear from Figure 3, we can add that just like in simple logistic regression, the clear S-shape only shows up whenever proportions of success are close to 0% or 100%. Although it is no longer possible to come up with simple visualisations, multiple regression can easily accommodate more than two predictors. In general, the regression model will fit one overall intercept and a separate slope for each of the predictors that are added. The technique allows us to establish significance for the intercept and for each of the predictor slopes. Multiple regression with k predictors is not meant to be a convenient ‘shortcut’ alternative to conducting k separate simple regression analyses; it is different from that and at the same time is much more than that. Firstly, multiple regression can tell us how good we can model the behaviour of the response variable by means of the combined information of all k predictors (which is something the separate simple analyses cannot tell you). Secondly, if you want to establish the effect of predictor x1 on your response and you know there are other predictors that also have an effect on the response, then there are good reasons to also have those other predictors in the model. We call the slope of x1 fitted in a simple regression the marginal effect of x1 on y, and we call the slope of x1 fitted in a multiple regression the partial effect of x1 on y, when controlling for the other predictors. Let us further discuss the distinction between marginal effect and partial effect by means of the middle panel in Figure 3 where the predictors are age and attitude. Let us assume that, as is the case in Figure 3, both age and attitude have a positive effect on the proportion of use of the success response variant (which here is the traditional variant). Higher age boosts the use of the traditional variant and so does a positive attitude towards the local dialect. When simple regression establishes the marginal effect of age on variant choice, the speaker’s attitude is simply ignored. When multiple regression establishes the partial effect of age on variant choice, controlling for attitude, what happens basically boils down to the following: first, the technique zooms in on all speakers with a very negative attitude and it establishes the effect of age within



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that group. Next, it zooms in on the speakers with a moderately negative attitude and it once again establishes the effect of age within that group. Then it establishes the effect of age among the neutral attitude people; then for the mildly positive ones and then for the very positive ones. Finally, it estimates the partial effect of age as a sort of average of the effects that were measured for the different groups. Actually, in reality the data are not considered in the order that is suggested here, but, conceptually, this description helps us understand the principle. Moreover, multiple regression analysis, with the predictors age and attitude, will not only estimate the partial effect of age, controlling for attitude, but it will simultaneously calculate the partial effect of attitude, controlling for age. The first reason why a partial effect typically is more informative than a marginal effect is that when one calculates a marginal effect in a simple regression, the hidden effect of any important predictors that are left out of the model will increase the amount of variability that the simple regression model cannot account for, thus making the simple regression model less precise. For instance, when we model variant choice in function of the predictor age in a simple regression model, ignoring attitude differences, then there will be a lot of variability within each age group that is due to attitude differences, and obviously there is no way the simple regression model can account for that additional variability. In linear regression, such additional variability would manifest itself as larger residuals in the simple regression, but this, as such, would not necessarily affect the quality of the fitted slope. It would lead to wider confidence intervals in the simple regression model. In logistic regression, however, the mere presence of this additional variability can easily affect the slope that is estimated in the simple regression. Very often the presence of such additional variability will lead to the simple regression underestimating the effect of the predictor. If the data set we work with is not balanced with respect to the possible combinations of values of the predictors, i.e. if there happen to be correlation patterns between the predictors (which is often the case in corpus linguistic studies), then there is a second reason why marginal effects are to be distrusted. Suppose, for instance, that indeed older age and a more positive attitude both lead to more use of the traditional variant, but that in our data set there happens to be an over-representation of young positive attitude people and old negative attitude people (our corpora cannot be balanced for everything, so these things happen). What would happen then if we ran a simple logistic regression on these data to establish the effect of age on variant choice? The answer is obvious; the simple regression will underestimate the effect of age. Likewise, in a data set in which young negative attitude people and old positive attitude people happen to be over-represented, a simple regression model will overestimate the effect of age on variant choice. In general, such damaging effects of hidden variables in unbalanced data can be very severe. They may even lead to the direction of the slope of the marginal effect differing from the direction of the slope of the partial effect. In short, marginal effects can be very misleading.

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A multiple regression with all relevant predictors included, on the other hand, is very good at teasing apart the effects of all relevant predictors (e.g. age and attitude), even in unbalanced data sets. This makes multiple regression an extremely valuable tool for Corpus Linguistics.9 Especially when we move to studies with four, five or sometimes even more predictors, which is far beyond the point where we ourselves can tease apart the effects of all predictors by eyeballing the data (let alone oversee correlation patterns among predictors and the potential effect of these correlations on the marginal effects), multiple regression becomes indispensable.

3.1

Categorical predictors

We started our discussion of logistic regression with the case of numerical predictors. We did this because the rationale of regression (the idea of fitting lines and planes, or curves and surfaces) is easiest to grasp and visualize in these cases. In corpus linguistic studies, however, most of our predictors will be categorical. Fortunately, it is easy to encode categorical predictors in such a way that they can be used as predictors in regression analysis. This encoding (which happens automatically in R) is basically a process of translating categorical data into one or several so-called dummy variables (which are a type of numerical data with a very limited number of possible values). A categorical predictor with only two categories is typically encoded as a dummy variable with the possible values 0 and 1. For instance, the predictor sex (i.e. sex of the speaker as a predictor for variant choice), with possible values F and M, can be encoded as a single dummy variable sexM, with value 0 meaning ‘not male’ and value 1 meaning ‘male’ (this is an arbitrary choice; we could just as well have chosen for an encoding sexF, in which 0 means ‘not female’ and value 1 means ‘female’). In general, a categorical variable with k levels, i.e. k categories, can be encoded as a set of k-1 dummy variables. For instance, let us assume we have a predictor region, with possible values A, B and C, which represents the speaker’s region of birth. This predictor can be encoded by the combination of a first dummy variable regionB (with value 0 meaning ‘not region B’ and value 1 meaning ‘region B’), and a second dummy variable regionC (with value 0 meaning ‘not region C’ and value 1 meaning ‘region C’). If both these dummy variables have value 0, this means that the speaker is from region A. We call the latter value of the categorical variable, the one that is implied if all dummy variables have value 0, the base value (or reference value) of the variable. So in the case of sex the reference level is F, and in the case of region the reference level is A. Figure 4 illustrates how regression (in this case logistic regression) deals with these dummy variables. The plots in Figure 4 are schematic representations, like the 9. There are limits to the amount of correlation between predictors that multiple regression can handle, as we will discuss in the section on model diagnostics, but still multiple regression can take quite a lot of correlation among the predictors.

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Categorical predictor with three levels

nC Proportion of success

0.8 0.6 0.4

Regio

0.2 0.0

Proportion of success

1.0

Categorical predictor with two levels

0.0

0.2

0.4 0.6 sexM

0.8

1.0

RegionB

Figure 4.╇ Categorical predictors in logistic regression

ones in Figure 3; we only show the fitted curves. We do not show the individual observations in the data sets. The left panel shows a logistic relation that is fitted between the predictor sex and the proportion of success of some response variable. For the sake of simplicity, we look at a model in which only the predictor sex is included. As mentioned, and as we will see in detail when we look at actual R code, the conversion of sex to the dummy variable sexM is something that is done automatically, so we do not have to worry about that. Technically speaking, the model fits a complete logistic curve (depicted in grey) between the (in a trivial sense) ‘numerical’ dummy variable sexM and proportion of success, but since for sexM only the values 0 and 1 actually occur, the only relevant points on the fitted curve are the proportion of success for the case of sexM being zero and the proportion of success for the case of sexM being one (represented as two thick points in the plot). The output of the logistic regression analysis, which as always relates to the logit scale, consists of an intercept and a slope for sexM. It turns out that, in this fictitious case, the fitted intercept is –1.8 and the fitted slope for sexM is 2.57 (and consequently the corresponding fitted odds ratio is e2.57, which is about 13). The interpretation of all this is that, according to the model, the average logit for women (sexM = 0) is –1.8 and the average logit for men (sexM = 1) is –1.8 + 2.57, which is 0.77. When we translate these logit values to proportions of success (using the formulae in footnote 8), we find that the average proportion of success for women is about 14% and the average proportion of success for men is about 68%. In the right panel of Figure 4, we see a logistic relation that is fit between the predictor region and the proportion of success of some response variable. For the sake of simplicity, we look at a model in which only the predictor region is included. The model fits a complete surface (depicted in grey) that captures the relation between

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the (in a trivial sense) ‘numerical’ dummy variables regionB and regionC and the proportion of success, although only three combinations of values for regionB and regionC actually occur and, therefore, only three locations on the fitted surface are important (represented as three thick points in the plot). We see that, although there is only one predictor (region), the technique actually uses the multiple regression machinery that is needed for fitting a surface instead of a curve, and indeed a separate slope is fitted for regionB and for regionC. Due to this discrepancy between the number of predictors that are involved (only one in this case) and the number of slopes that are fitted (two in this case), some statisticians make a terminological distinction between, on the one hand, predictors and, on the other hand, regressors. We will follow that distinction. The term ‘predictor’ is more conceptual and relates to the original variables; the term ‘regressor’ is more technical and relates to the things for which slopes are being fitted. In this case there is one predictor, but there are two regressors. As it turns out, in the logistic regression analysis at hand, the fitted overall intercept is –0.59, the fitted slope for regionB is 0.85 and the fitted slope for regionC is 1.64 (all on the logit scale). The interpretation of this is that, according to the model, the average logit for region A is –0.59, the average logit for region B is –0.59 + 0.85 (which is 0.26) and the average logit for region C is –0.59 + 1.64 (which is 1.05). If we convert these numbers to the proportion of success scale, we see that the model estimates the average probability of success to be a bit under 35% in region A, a bit over 56% in region B and about 74% in region C.

3.2

Polynomials, transformed predictors and interactions

The machinery introduced up to this point covers the main needs for the most basic types of logistic regression modelling. Sometimes, however, we run into situations that need a more advanced approach. For instance, it may happen that the actual relation between some numerical predictor and the logit of the response is clearly non-linear and instead follows a more complicated curve. In these cases, one may need to transform the predictors or introduce polynomials as predictors in order to be able to adequately model this relation. Another possible complication that can occur with categorical as well as numerical predictors relates to the combined effect of two predictors, x1 and x2, on the logit not approximating a plane but instead forming a more complicated surface. When this happens, we say there is an interaction between the two predictors (meaning that the effect of x1 on the logit sometimes differs, depending on the value of x2, and conversely that the effect of x2 on the logit sometimes differs, depending on the value of x1). If this happens, we need to add a so-called interaction term as an additional predictor in order to be able to adequately model the combined effect of x1 and x2 on the logit of the response. The most commonly used type of interaction term is a so-called product term.

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In this introductory text, we will not dig into polynomials and transformed predictors. Since most predictors in Corpus Linguistics are categorical, they are often not needed in Corpus Linguistics. Of course, sometimes they are needed and for these cases we refer to the Further Reading section at the end of the chapter. Interaction terms will not be addressed in depth, but we will touch upon them in Section 3, on example R code and output for logistic regression.

4. Example R code 4.1

Output for simple logistic regression

There are several R commands that support logistic regression. We consider two popular ones. The first is the glm() command which comes pre-installed in the base system of R. It can be used for a wide range of generalized linear models, including binomial logistic regression (Nelder and Wedderburn 1972). The second is the lrm() command, a command that is dedicated to the logistic regression model and that is implemented in the rms package (Harrell 2001). Until recently, the package was called Design, which means older descriptions will refer to the package in this way. The basic functionalities have not changed and so older descriptions will still be applicable (although some details have changed). Our choice to illustrate both commands inevitably leads to some redundancy in the discussion, but there are good reasons to do so: firstly, because both approaches are popular and, secondly, because both approaches have their pros and cons. Before we start, we load the package we will use, which is the rms package.10 We assume this package is available for the remainder of this text. The R code snippets in this text should be seen as one continuing R session. R code and data files can be downloaded from http://dx.doi.org/10.1075/hcp.43.18spe.additional. > library(rms)

Next, we run our first logistic regression analysis using the fictitious data set that was introduced in the middle panel of Figure 1. We assume this data set, which contains 70 cases, is in the R data frame fig1Mid. When we look at the first cases in the data set, using the command head(), we see that for each case we have the age of the speaker and the variant that is used by the speaker (the data set contains only one utterance for each speaker). The age is stored in the numerical variable age and the variant that is used is stored in the categorical variable variant, with possible values old and young, referring to the traditional and the innovative variant, respectively. Additionally, the ages, which range from ten to ninety, are also summarized in age groups. This information 10. I assume the rms package has already been installed.

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is in the categorical variable age.group, with possible values a (ages ten to twenty-six years), b (twenty-seven to forty-two), c (forty-three to fifty-eight), d (fifty-nine to seventy-four) and e (seventy-five to ninety). > head(fig1Mid) age age.group variant 1 67 d old 2 74 d old 3 50 c young 4 53 c young 5 33 b old 6 66 d old

Before we run the logistic regression analysis, we test what is the order of the levels in the variable variant. > levels(fig1Mid$variant) [1] “old” “young”

It is important to know this. It is always the second level (in our case young) that will be treated as the success level in the logistic regression analysis. In our study, we do indeed want the innovative variant to be treated as the success level, but should the order have been different we could have used the command relevel(), explained in van der Weijer and Glynn (this volume) to change the order of the levels in variant. We first illustrate the use of glm() to run the logistic regression analysis. The first argument specifies the model we want to fit. In this case, we want to model the response variant in the function of the predictor age, which is expressed as variant ~ age. The symbol ~ in the formula is used to separate the response from the predictor(s). Notice how we can simply use the categorical variable variant as the response. Its translation into a dummy variable with values 0 and 1 is automatically done. The second argument specifies the data frame in which the data can be found. This argument is not strictly needed, but we use it to avoid having to write the first argument as fig1Mid$variant ~ fig1Mid$age. Since glm() supports more than just logistic regression, a third argument is needed to specify that we want a logistic regression analysis; the argument binomial stands for binomial logistic regression. We store the outcome of the analysis in an object fig1Mid.glm and then we ask for a summary representation of that object. > fig1Mid.glm <- glm(variant ~ age, data=fig1Mid, + family=binomial) > summary(fig1Mid.glm)

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Call: glm (formula = variant ~ age, family = binomial, + data = fig1Mid) Deviance Residuals: Min 1Q Median -2.5606 -0.6328 0.2292

3Q 0.6726

Max 2.1716

Coefficients:

Estimate Std. Error z value Pr(>|z|) (Intercept) 4.78652 1.12685 4.248 2.16e-05 *** age -0.08591 0.01950 -4.406 1.06e-05 *** --Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ‘ 1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 96.526 Residual deviance: 61.126 AIC: 65.126

on 69 on 68

degrees of freedom degrees of freedom

Number of Fisher Scoring iterations: 5

The Call: section in this summary representation simply repeats which model has been fitted. The Deviance residuals: section gives information on the distribution of the so-called deviance residuals. These deviance residuals are a bit more complicated than the regular residuals (vertical distances from the fitted line/curve) we discussed above, but their function is comparable; they measure the contribution of each item in our data to the overall deviance in the model, and, as we will see below, this overall deviance is a measure for the mismatch between the fitted model and the observed data. The Coefficients: section contains the estimates for the intercept and for the slope for age, which are about 4.79 and about –0.09, respectively. These estimates specify that the fitted linear relation between age and the logit of the response is such that the mean logit for age x is taken to be 4.79 plus x times –0.09. For instance, the logit is taken to be (4.79 + 0 × –0.09) = 4.79 at age zero, (4.79 + 10 × –0.09) = 3.89 at age ten, (4.79 + 20 × –0.09) = 2.99 at age twenty, etc. The columns Std. Error and z value are calculations in support of the inferential tests of the p-values, which can be found in the column Pr(>|z|).11 The significance codes to the right of the p-values are meant to enable you to quickly ‘classify’ the p-values into the categories 0 ≤ p€< 0.001 (‘***’), 0.001 ≤ p < 0.01 (‘**’), 0.01 ≤ p < 0.05 (‘*’),

11. These tests are the so-called Wald tests.

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0.05 ≤ p < 0.01 (‘.’) and 0.01 ≤ p ≤ 1.0 (‘ ’). The intercept test determines whether the intercept differs significantly from zero. The slope test determines whether the slope differs significantly from zero. At a 95% confidence level, we conclude that intercept or slope differ significantly from zero if p < 0.05, which, in the above output, clearly is the case for both intercept and slope. The output line (Dispersion parameter for binomial family taken to be 1) will not vary throughout this text. The so-called dispersion parameter is always taken to be one in traditional binomial logistic regression and is not important here.12 The section with Null deviance:, Residual deviance: and AIC: contains information on how much better the current model, the so-called fitted model, performs than a so-called intercept only model. An intercept only model is a model without predictor(s) that can only fit one overall average proportion of success, irrespective of the value(s) of the predictor(s), and which, therefore, must assume that the average proportion of success is the same for all contexts.13 In order to explain the concepts null deviance and deviance, we go back to the rationale of Maximum Likelihood Estimation (MLE). MLE tries to find estimates that maximize the likelihood of encountering our data set. For instance, in the context of fitting an intercept only model, what happens conceptually is that the algorithm takes into consideration all possible values for the intercept (each time asking: what if this were the ‘correct’ model?) and picks the one according to which the likelihood of encountering our data set is highest. Let us use Lint as a notation for the likelihood of encountering our data set according to the specific intercept only model that was actually picked by the algorithm. Likewise, in the context of fitting a fitted model, what happens conceptually is that the algorithm takes into consideration all possible combinations of values for intercept and slope(s) (each time asking: what if this combination were the ‘correct’ model?) and picks the combination according to which the likelihood of encountering our data set is highest. Let us use Lfit as a notation for the likelihood of encountering our data set according to the specific fitted model that was

12. In several other types of regression analysis, within the general framework of generalized linear models, this dispersion parameter (which expresses the amount of variability we assume exists in the errors) is estimated on the basis of our sample. For instance, in so-called quasibinomial logistic regression, the dispersion parameter is not taken to be one but is estimated from the data. However, quasibinomial logistic regression, which is a technique that can be useful if our binomial regression models suffer from overdispersion (to be explained later in this text), is beyond the scope of this text. 13. The estimate for the intercept fitted by the intercept only model must not be, and typically is not, equal to the estimate for the intercept fitted by the fitted model. The intercept in the intercept only model will correspond to the overall proportion of success in the data set. The intercept in the fitted model typically will differ from that.

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actually picked by the algorithm.14 The null deviance is then simply –2 × log(Lint) and the deviance is –2 × log(Lfit). As we see in Figure 5, transformation –2 × log(p), with p being some proportion grows from zero to plus infinity as p drops from one to zero. Substituting some likelihood L for p in the formula –2 × log(p), as we obtain a smaller L, the higher the corresponding deviance –2 × log(L) will be. Therefore, deviances are measures of the discrepancy between some model and a data set. More specifically, the null deviance measures the discrepancy between the intercept only model and the data, and the deviance measures the discrepancy between the fitted model and the data. In other words, the smaller the deviance is, the better the model fits the data. The degrees of freedom of the null deviance (sample size minus one) and the degrees of freedom of the deviance (sample size minus one minus number of regressors) are additional pieces of information that will be used in a log likelihood ratio test (to be explained later in the text) that tests whether the reduction of deviance when moving from the intercept only model to the fitted model 14. Although finding the best estimates efficiently with MLE is not trivial, determining Lint and Lfit given a specific model (i.e. given a specific intercept or intercept plus slope) is actually very intuitive and straightforward, as I hope to show with the following set of instructions. The probability of encountering a data set given some model is simply the product, over all items, of the probability of encountering that item given the model. You see below that even for a good model, Lfit is actually a very small probability. This should not surprise us: Lfit does not simply express the probability of encountering k successes in a sample of size n, it expresses the probability of encountering the exact sequence of successes and failures that we find in the data set. Note that some of the commands listed below will not be explained until later in the text and in Footnote 15. If you are not yet familiar with some of the commands or expressions, you may want to continue reading the main text first and come back to this footnote later. > fig1Mid.glm.int <- glm(variant ~ 1, data=fig1Mid, family=binomial) +

# intercept only

> obs <- as.numeric(fig1Mid$variant) - 1 # observed response (0 or 1) > pred.int <- predict(fig1Mid.glm.int, type=“response”) +

# predict for intercept only

> pred <- predict(fig1Mid.glm, type=“response”) # predict for fitted

> lik.int <- ifelse(obs, pred.int, 1 - pred.int) # item lik for int only > lik <- ifelse(obs, pred, 1 - pred) # item lik for fitted > prod(lik.int)

[1] 1.095754e-21

# global lik given intercept only model correct

> -2 * log(prod(lik.int))# deviance of intercept only model [1] 96.52569

> prod(d$lik)

# global lik given fitted only model correct

> -2 * log(prod(d$lik))

# deviance of fitted model

[1] 5.329571e-14 [1] 61.12584

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Relation between p and –2 * log(p)

–2 * log(p)

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Figure 5.╇ The relation between proportion p and –2 × log(p)

is significant or not (in other words, whether the difference between null deviance and deviance is significant). The AIC: value is a corrected version of the deviance that has the additional benefit that it can be compared across models (for the same data set and response variable) with different numbers of predictors. The Number of Fisher Scoring iterations: section finally tells us how many iterations were needed to converge upon the reported estimates for intercept and slope (remember that logistic regression uses an iterative Maximum Likelihood Estimation procedure). Next we run the same model using lrm(). The two lines of code before the call to lrm() as well as the arguments x=T and y=T in the actual call are merely instructions to keep track of certain pieces of information about our data, either stored in a general setting in R (in the case of the datadist object, which basically stores information related to the distribution of the variables in the data frame fig1Mid) or stored in the result of the regression analysis (in the case of x=T and y=T, which basically instructs lrm() to store more intermediate results in its result object than it does by default). We will routinely make use of the datadist option whenever we run lrm() on a newly introduced data set, and of the x=T and y=T arguments whenever we run lrm(). Apart from x=T and y=T, the actual call to lrm() looks similar to the call to glm(), the only difference being that the binomial argument is not needed (since lrm() is dedicated to the logistic regression model). > > > >

fig1Mid.dd <- datadist(fig1Mid) options(datadist=“fig1Mid.dd”) fig1Mid.lrm <- lrm(variant ~ age, data=fig1Mid, x=T, y=T) fig1Mid.lrm

Logistic Regression Model lrm(formula = variant ~ age, data = fig1Mid, x = T, y = T)

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Obs 70 Old 32 Young 38

Model Likelihood Ratio Test LR chi2 35.40 d.f. 1 Pr(> chi2) <0.0001

max |deriv| 2e-08 Coef Intercept 4.7865 age -0.0859

S.E. 1.1269 0.0195

Discrimination Indexes R2 0.531 g 2.290 gr 9.872 gp 0.381 Brier 0.135

Rank Discrim. Indexes C 0.878 Dxy 0.757 gamma 0.757 tau-a 0.381

Wald Z Pr(>|Z|) 4.25 <0.0001 -4.41 <0.0001

The output, which, in the case of lrm(), is not shown with summary(), but is shown by simply printing the result object, contains parts that look either familiar or self-explanatory. At the top, the call information is shown, and below that, at the left, the distribution of the response variable is shown (here too the last level is the response level). At the bottom, the coefficients and their corresponding p-values are shown. These results are identical to those in glm() (except perhaps that here very small p-values are indicated as <0.0001). The only really new part is the middle part of the output where a whole range of statistics is shown. We will not discuss all of them, but will introduce the ones I believe to be most important. Firstly, the items LR chi2, d.f. and Pr (>chi2) summarize an inferential test that tests whether the deviance in the fitted model is significantly smaller than the null deviance (i.e. than the deviance in the intercept only model). The statistic LR chi2 stands for the model likelihood ratio chi-square, sometimes also simply called model chi-square. It is equal to the null deviance minus the deviance and at the same time is also equal to –2 × log(Lint/Lfit). The smaller the likelihood ratio Lint/Lfit is, and therefore the larger –2 × log(Lint/Lfit) is (cf. Figure 5), the more evidence there is that the fitted model is a better fit that the intercept only model. The inferential test to test whether the difference between the fit of both models is statistically significant is a chi-squared test with one degree of freedom (cf. d.f.), the value of which is the degrees of freedom in the intercept only model (69) minus the degrees of freedom in the fitted model (68). The corresponding p-value (Pr (>chi2)), indicated as <0.0001 in the output and therefore clearly smaller that 0.05, shows that the difference in fit between the models is statistically significant at the usual 95% confidence level.15 15. Another way to conduct the same test is by explicitly building an intercept only model and performing a log likelihood ratio test for nested binomial glm models with the command anova(SMALLERMODEL, LARGERMODEL, test=“Chisq”). Such a test can be conducted to compare any couple of nested models SMALLERMODEL and LARGERMODEL, where nested means that LARGERMODEL contains all predictors in SMALLERMODEL plus one or several additional predictors. The test tests whether the reduction of deviance (which here is called residual deviance) when going from SMALLERMODEL to LARGERMODEL is significant. With p = 2.685e-09

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Some often-used measures of the quality of the model are C, Dxy, and R2. The measures C and Dxy quantify the classificatory quality of the model. In order to explain these measures, we first illustrate the simple concept of a classification table in the following code. We start by displaying, once again, the first rows of the data set (because they are instrumental in seeing what happens in the other instructions). Then we store the values of variant, recoded as 0 for old and 1 for young, in the vector obs. If we look at the first items in obs (which correspond to the first items in fig1Mid), we see that the ‘old variant’ cases have received value 0 (failure) in obs and the ‘young variant’ cases have received value 1 (success) in obs. Next we use the command predict() to calculate for all items in our data set the corresponding fitted probability of success according to the model fig1Mid.glm and we store those probabilities in the vector pred. The first argument for predict() is the model (or more precisely, the output object fig1Mid.glm of the regression analysis). Its second argument (type= “response”) specifies that we want the fitted values to be on the probability of success scale (and not on the logit scale). If we look at the first items in pred (which correspond to the first items in fig1Mid), we see how for each item we obtain the average probability of success for the age in that item (for instance, in the first item the average probability of success is 27% because this person has an age of 67; recall that according to the model, the fitted logit for age 67 is (4.786 + 67 × –0.086) = –0.97, which indeed corresponds to a fitted proportion of success of 0.27. A classification table now is a cross tabulation of the observed outcomes by the predicted outcomes. A simple procedure to determine which outcomes the model predicts is to interpret predicted proportions of 50% or higher as a prediction of success (1) and to interpret predicted proportions of less than 50% as a prediction of failure (0). So we build the table class.table according to this procedure and display it. Observed values are in the rows and predicted values are in the columns. The correct predictions are the ones in the diagonal going from the top left to the bottom right. We can, thus, the reduction is definitely significant at the usual 95% confidence level. Note that the formula variant ~ 1 means ‘model the response variant in function of nothing but an intercept’. > fig1Mid.glm.int <- glm(variant ~ 1, data=fig1Mid, family=binomial) + # intercept only > anova(fig1Mid.glm.int, fig1Mid.glm, test=”Chisq”) Analysis of Deviance Table Model 1: variant ~ 1 Model 2: variant ~ age Resid. Df Resid. Dev Df Deviance P(>|Chi|) 1 69 96.526 2 68 61.126 1 35.4 2.685e-09 *** --Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1



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calculate the classificatory success as the proportion of items in these cells, which turns out to be 84%. > head(fig1Mid) age age.group variant 1 67 d old 2 74 d old 3 50 c young 4 53 c young 5 33 b old 6 66 d old > obs <- as.numeric(fig1Mid$variant) - 1 > head(obs) [1] 0 0 1 1 0 0 > pred <- predict(fig1Mid.glm, type=“response”) > head(pred) 1 2 3 4 5 6 0.2749295 0.1720517 0.6202930 0.5579999 0.8755925 0.2923827 > class.table <- table(obs, as.numeric(pred>=0.5), + dnn=c(“obs”, “pred”)) > class.table pred obs 0 1 0 27 5 1 6 32 > sum(diag(class.table)) / sum(class.table) [1] 0.8428571 > max(apply(class.table,1,sum)) / sum(class.table) [1] 0.5428571

However, this simple measure has to be put in perspective. Firstly, it must always be compared to the classificatory success for the intercept only model, which then serves as a baseline to which we compare our measure (and which we calculate in the last instruction above). The calculation of this baseline is simple: our intercept only model simply predicts all cases to have a probability of success of 38/70 = 54% (which is the overall proportion of success in the data set). Since 54% is more that 50%, the intercept only model would therefore (according to our simple classification rule) always predict success, which would be a correct prediction in 54% of the cases. Knowing this, we can now state that simple classificatory success for our data goes up from the baseline of 54% for the intercept only model to 84% for the fitted model. Explicitly mentioning the baseline is especially important if the response variable has an

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outspoken overall bias in the data set (because then even the intercept only model can have impressive-looking classificatory success). A second caveat is that this simple measure may fail to see some of the classificatory quality of the model by imposing the crude 50% cut-off value. As it turns out, in the current example cut-offs that are a bit higher than 50% (in the range of 52% up to 55%) produce slightly better classification results. The measures C and Dxy can be seen as more refined versions of the classification table idea that gets rid of the need for an arbitrary cut-off value. Although the rationale of the measures can be explained in several ways, I find the following perspective the simplest. We start from the set of all pairs of observations in our data in which the first has an observed failure and the second has an observed success. For the first six items in the data set [see head(fig1Mid)], these would be the pairs (1, 3), (1, 4), (2, 3), (2, 4), (5, 3), (5, 4), (6, 3) and (6, 4), but of course for the complete data set there are many more. These pairs represent all ‘occurrences of variability’ in the response variable that the model either could or could not be sensitive to. For each of these pairs we ask ourselves: does the model capture the observed pattern (but this time without using cutoff values)? We do this by classifying the pair as either concordant, discordant or tie. A concordant pair is a pair such as (1, 3), where the item with observed success (item 3) has the highest predicted probability of success (62% > 27%). Note that since we no longer use a cut-off value, pairs can also be concordant if both predicted probabilities are higher than 50% or if both have predicted probabilities that are lower than 50%, as long as the correct one has the highest value. In a concordant pair, the predicted direction of the difference is in line with the observed direction of the difference, and therefore the predictions can be said to ‘capture’ the observed pattern. A discordant pair is a pair such as (5, 3), where the item with the observed success (item 3) has the lowest predicted probability of success (62% < 88%). Note that even if both probabilities are above 50% in the example, we still call this a discordant pair. In a discordant pair, the predicted direction of the difference is at odds with the observed direction of the difference; the predictions not only fail to capture the observed pattern, but they completely go against it. A ‘tie’, finally, would be a pair with an observed difference but with identical predictions. We do not have such an example among the eight pairs we introduced above, but it is easy to imagine what they look like: examples would be pairs of people with the same age that use different variants. In a tie, the lack of predicted difference causes the predictions to miss out on the observed pattern. If CP then is the number of concordant pairs in a data set, DP the number of discordant pairs and TP the number of ties, the measure Dxy (the full name of which is Somer’s Dxy) is (CP-DP) divided by (CP+DP+TP). It is a measure of the rank correlation between the values in pred and the binary values in obs. In general, the rank correlation measure Dxy can take values ranging from minus one to plus one, but in the regression analysis context in which we use the measure here, they will range from zero to one (since in any decent model CP will be at least as large as DP). The measure



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C is a rescaled version of Dxy calculated as (1 + Dxy)/2. It is also known as the ROC area (i.e. the area under the ROC curve).16 If values of Dxy range from zero to one, then the corresponding values of C will range from 0.5 to 1. We speak of decent classificatory quality if C is 0.8 or more (and if Dxy is 0.6 or more). One final remark is that for intercept only models, Dxy will always be zero (and consequently C will always be 0.5), since the intercept only model only contains ties. Therefore, for Dxy and C, there is no need to explicitly mention the baseline Dxy and C, as we had to do for simple classification success on the basis of class.table. Finally, the measure R2, which is more specifically Nagelkerke’s pseudo R2, is a measure that is designed to be the logistic regression counterpart of the R2 index in linear regression analysis, but the interpretation of which I find far less straightforward than that of R2 in linear regression. The index is often used and is definitely useful, but one must keep in mind that it cannot be interpreted as a proportion of explained variation (or proportional reduction of unexplained variation) in the way R2 is interpreted in linear regression (the concept of proportional reduction of unexplained variation, as we understand it in linear regression, only makes sense if residuals/errors have equal variance across different values of the response variable and we can expect the proportional reduction to be equal across different predicted values of the response variable).17 Up to this point, we have covered information that is readily available via either summary(fig1Mid.glm) or fig1Mid.lrm or both. If we ignore the footnotes for a moment, the only point where I have needed additional R code was for the generation and interpretation of the classification table class.table and even that

16. The ROC curve is created as follows: we repeat the procedure of making a classification table for cut-off values ranging from 100% to 0%. For each classification table, we add a point to a scatterplot with as its x-value the false positive rate in the table (i.e. the proportion, among the observed failure responses, of items for which success is predicted) and as its y-value the true positive rate in the table (the proportion, among the observed success responses, of items for which success is predicted). The ROC curve then is the line that connects all points. The x-values of the points in the curve will range from 0.0 (for the highest threshold) to 1.0 (for the lowest threshold). The y-values will be lowest for the highest thresholds and will grow larger for lower thresholds. A good model then is a model for which the ROC curve goes up rapidly, which indicates that the model can combine a high true positive rate with a relatively low false positive rate. 17. Nagelkerke’s pseudo R2 is an adjusted version of Cox and Snell’s pseudo R2. The formula for the latter is 1 – (Lint/Lfit)2/n, with n the number of observations in the data set. The smaller the ratio Lint/Lfit, and therefore the smaller the transformed ratio (Lint/Lfit)2/n, and hence the larger 1 – (Lint/Lfit)2/n, the more outspoken the superiority of the fitted model over the intercept only model will be. A downside to this measure is that it can never reach the value of 1.0. Therefore, Nagelkerke’s adjustment to Cox and Snell’s measure is to divide it by 1 – (Lint)2/n, so that possible values can cover the whole range from 0.0 to 1.0.

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endeavour mainly led to the conclusion that simple classification success as derived from class.table is a less sophisticated measure than the measures Dxy and C that are in fig1Mid.lrm. Of course, sometimes, we do want more than the direct output of summary (fig1Mid.glm) and fig1Mid.lrm. Firstly, we may want to further explore the estimates, which are once again displayed below. In the code below, suppressed parts of the R output are indicated by […]. > summary(fig1Mid.glm) […] Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) 4.78652 1.12685 4.248 2.16e-05 *** age -0.08591 0.01950 -4.406 1.06e-05 *** […]

The estimate for the intercept is 4.79, and appears to indicate that a person of age zero has an average logit of 4.79 (corresponds to odds of 120 to 1 and a proportion of 99%), which, according to the significance test, is significantly different from a logit of zero (i.e. from odds of 1 to 1 and a proportion of 50%). Of course, this is not what it means because an age of zero is outside the range of ages under investigation and we do not want to extrapolate the trend we observe outside the range of ages we study (firstly because such extrapolations are always dangerous, and secondly because in this case we know for a fact that the extrapolation cannot be correct, because people of age zero produce neither of the two variants under scrutiny). So, in this model, the intercept is simply a tool to know where to draw the fitted line, but has no meaning in its own right. If we wanted, we could modify the model in order to obtain a more meaningful intercept. Instead of using the actual age as predictor, we could use centred age as predictor (i.e. age centred around its mean 51.6; or in other words, age expressed as the difference from the mean age). For example, someone with an age of 30 has a centred age of –21.6 and someone with an age of 60 has a centred age of 8.4. We run this analysis below. > fig1Mid$ageC <- fig1Mid$age - mean(fig1Mid$age) > summary(glm(variant ~ ageC, data=fig1Mid, family=binomial)) […] Coefficients:

Estimate Std. Error z value Pr(>|z|) (Intercept) 0.35333 0.32786 1.078 0.281 ageC -0.08591 0.01950 -4.406 1.06e-05 *** […]



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This analysis is identical to the previous one in every detail except (a) that the name of the age predictor has changed and (b) that the intercept now refers to the fitted logit for a person with a centred age of zero (i.e. with an age of 51.6). We see that according to the model, a person of an age of 51.6 has an average logit of 0.35 (which corresponds to odds of 1.4 to 1 and a proportion of about 59%), which, according to the significance test, is not significantly different from a logit of zero (i.e. from odds of 1 to 1 and a proportion of 50%). Going back to the model with regular age as predictor and moving to the far more important estimate which is the slope age, we see that according to the model for each year that is added to the age, 0.09 is subtracted from the average logit (and conversely for each year that is subtracted from the age, 0.09 is added to the average logit). The odds are requested as follows: > exp(coef(fig1Mid.glm)) (Intercept) age 119.8829912 0.9176727

At age zero, the odds are 120 (i.e. 120 to 1) and with each additional year these odds are multiplied by 0.91. The 95% confidence intervals for the estimates are requested as follows: > confint(fig1Mid.glm) Waiting for profiling to be done… 2.5 % 97.5 % (Intercept) 2.8377877 7.32063059 age -0.1296267 -0.05201228

Therefore, we are 95% confident that the correct slope for age, on the logit scale, is between –0.13 and –0.05. The 95% confidence intervals for the odds are requested as follows: > exp(confint(fig1Mid.glm)) Waiting for profiling to be done… 2.5 % 97.5 % (Intercept) 17.0779426 1511.1565962 age 0.8784232 0.9493172

We see now very clearly that there is quite a lot of uncertainty regarding the intercept (the confidence interval for the intercept covers probabilities from 94% up to 99.9%) but that does not concern us here, since we zoom in on the effect of age. We see that we are 95% confident that the odds ratio between consecutive years is between 88% and 95%.

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# figure 6 cdplot(variant ~ age, data=fig1Mid, ylevel=2:1) rug(jitter(fig1Mid$age), col=“white”) # figure 7 plot(Predict(fig1Mid.lrm, age, fun=plogis))

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Figures 6 and 7.╇ Observed (left) and fitted (right) effect of age on variant choice

Figures 6 and 7, which were generated with the code above, enables us to see what all this means on the proportions of success scale. The left plot has nothing to do with the regression model. It is a conditional density plot of our data. A conditional density plot is related to a spinogram [spineplot()] in the way a density plot relates to a histogram. A conditional density plot depicts the observed relative proportion of the two variants for different age groups, but instead of selecting a discrete set of age groups, it applies a smoothing technique that enables us to see the gradual transition of this proportion along the age axis. At the bottom of the plot, we have also added the individual items (with their correct ages, but with some horizontal jitter added so that the items do not hide each other too much) so that we can see how much information is behind the different parts of the conditional density plot. The right plot is generated with plot(Predict(fig1Mid.lrm, age, fun=plogis)). This instruction plots the effect of age on the proportions of success scale and also plots 95% confidence margins around the fitted averages (the argument fun=plogis causes the plot to be on the proportions scale instead of on the logit scale). We see that the model rather nicely mirrors the pattern that is observed in the conditional density plot.

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4.2

Output for multiple logistic regression

For the discussion of multiple logistic regression in R, we introduce a new non-fictitious data set. The object noemen contains 446 instances of the noemen/heten alternation pattern that were found in the spontaneous speech section of the Belgian part of the Spoken Dutch Corpus (Oostdijk 2000). In informal Belgian Dutch, the verb noemen is sometimes used with the meaning ‘to be called’, as in (1) and (2). The other variant, heten, as in (3) and (4), is the variant that most speakers in Belgium would call ‘the correct variant’ (and is the only one that is used in The Netherlands; the verb noemen is very well known in The Netherlands, but is only used with the meaning ‘to call’, as in (5), which, in Belgium too, is the most dominant use of noemen). The analysis we discuss here only contains cases such as (1) to (4). Cases such as (5), in which noemen has a very different meaning, were excluded from the analysis. 1. Ik noem Dirk. (I’m called Dirk.) 2. Dat noemt heteroscedasticiteit. (That’s called heteroscedasticity.) 3. Ik heet Dirk. (I’m called Dirk.) 4. Dat heet heteroscedasticiteit. (That’s called heteroscedasticity.) 5. Ik noem dat onzin. (I call this nonsense.) We use head() to show the structure of the data. > head(noemen) variant conver.type generation region occup.type 1 heten face.to.face from.1980 LI neutral 2 heten face.to.face from.1980 AB higher.edu 3 heten face.to.face from.1980 AB higher.edu 4 heten face.to.face from.1980 AB higher.edu 5 heten face.to.face before.1980 OV higher.edu 6 heten face.to.face before.1980 LI higher.edu

The variable variant is the response variable, with levels heten and noemen (noemen will be the success level in the analyses). The predictor conver.type (conversation type) has levels face.to.face and telephone (face.to.face will be the reference level in the analyses). The predictor generation is a rough classification of the speakers in two age groups: the reference level is before.1980 (born before 1980) and the other level is from.1980 (born in 1980 or later). All recordings in the corpus are roughly from the same period (around 2000), so what we try to find with the predictor generation is an apparent time effect. Ideally, we would have liked to have used age as a numerical predictor, but we restrict our analysis to a simpler categorical predictor.18 The predictor region represents the region of birth 18. Although in general it is better to use the ‘richer information’ in a numerical variable age, rather than the ‘simplified information’ in a categorical variable generation, we refrained

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of the speakers. Values are AB (the central provinces Antwerp and Brabant), LI (the province Limburg in the east of the country), WV (the province West-Flanders in the west of the country), and OV (the province East-Flanders in between Antwerp and West-Flanders). The reference value is OV. Finally, the variable occ.type (occupation type) is a coarse-grained classification of the occupation types of the speakers into the categories higher.edu (profession requires higher education), no.higher.edu (profession does not require higher education), and neutral (professions for which the link to higher education is either variable or unknown; obviously this is a ‘rest category’). The level higher.edu is the reference value. We start by running a model with all predictors (but without interactions), and we call the resulting model noemen.glm.1 (glm output) and noemen.lrm.1 (lrm output). The less important or redundant parts in the output have been suppressed. > noemen.glm.1 <- glm(variant ~ conver.type + generation + + region + occup.type, + data=noemen, family=binomial) > summary(noemen.glm.1) […] Null deviance: 618.06 on 445 degrees of freedom Residual deviance: 506.24 on 438 degrees of freedom AIC: 522.24 […] > noemen.dd <- datadist(noemen) > options(datadist=“noemen.dd”) > noemen.lrm.1 <- lrm(variant ~ conver.type + generation + + region + occup.type, + data=noemen, x=T, y=T) > noemen.lrm.1 […]

Obs 446 heten 228 noemen 218

Model Likelihood Ratio Test LR chi2 111.82 d.f. 7 Pr(> chi2) <0.0001

max |deriv| 2e-07

Discrimination Indexes R2 0.296 g 1.338 gr 3.811 gp 0.275 Brier 0.191

Rank Discrim. Indexes C 0.778 Dxy 0.555 gamma 0.571 tau-a 0.278

from using a numerical predictor in this analysis because we wanted to present a typical corpus linguistics case study [most (but not all) predictors in corpus linguistics case studies are categorical]. As it turns out, in this dataset using age instead of generation would have led to a model that is perhaps somewhat more refined (and superior), but that is otherwise essentially the same as the model discussed in this chapter.

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Intercept conver.type=telephone generation=from.1980 region=WV region=AB region=LI occup.type=neutral occup.type=no.higher.edu

Coef -0.8543 1.0898 1.5300 -0.2991 -0.6125 -1.6589 0.5473 0.9652

S.E. 0.2832 0.2418 0.2931 0.3047 0.3074 0.3648 0.3171 0.2724

Wald Z -3.02 4.51 5.22 -0.98 -1.99 -4.55 1.73 3.54

Pr(>|Z|) 0.0026 <0.0001 <0.0001 0.3264 0.0463 <0.0001 0.0844 0.0004

The overall log likelihood ratio test in noemen.lrm.1 shows that the deviance of the model with the four predictors (= 7 regressors) is significantly smaller than that of the intercept only model (Pr chi2 <0.0001), which is good because otherwise there would be no point in further inspecting this model. This test tells us that at least one of the predictors, or at least some combination of the predictors, makes the model outperform the intercept only model. It does not tell us that all predictors make a relevant contribution to this difference in quality. Next, we look at the estimates and their significance (also in noemen.lrm.1). The intercept (logit = –0.9; prop = 48%) gives us the fitted average success for the case of all predictors having the value zero (meaning: conver.type=face.to.face, generation=before.1980, region=OV, occup.type=higher.edu). I have not chosen the reference values in such a way that they are expected to all favour noemen, in which case they would jointly represent the category I expect to be most noemen-friendly, nor have I chosen the reference values to jointly refer to a category that is more ‘normal’ or ‘typical’ than other categories. Therefore, the intercept as such is not important to me. Let us pick out some predictors to discuss the interpretation of the estimates and their significance tests. Notice first of all how, in the output, all categorical predictors have automatically been translated into dummy variable regressors (whereby lrm() gives long names such as e.g. conver.type=telephone for the dummy variable that is 1 for telephone conversations and 0 for face-to-face conversation).19 For instance, for the predictor conver.type the significance test for the regressor conver. type=telephone indicates there to be a significant difference in logit between the situation conver.type=telephone and the reference situation conver.type= face.to.face. Moreover, the estimate for this difference (logit = 1.09; odds ≈ 3/1) tells us that the logit of noemen is estimated to be 1.09 higher for telephone conversations than for face-to-face conversations (and the odds are estimated to be about 19. The format of the regressor names in lrm() actually renders the notation conver. type=telephone ambiguous in this text. In this text, that notation can either refer to the regressor conver.type=telephone or to the situation where the predictor conver.type has the value telephone. Often the difference is irrelevant but in some cases, e.g. conver. type=face.to.face, only one of the two interpretations applies (since there is no regressor conver.type=face.to.face).

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three times as high). For the predictor region, we see in the test for the regressor region=WV that no significant difference between region=WV and the reference value region=OV was found. On the other hand, we see for the regressor region=LI that a significant difference between region=WV and the reference value region=OV was found (and is estimated to be –1.66 on the logit scale and about 1/5 on the odds scale; so the logit for region=LI is estimated to be 1.66 less than that for region=OV and the odds are estimated to be five times as small). Note that it would take some time, but it is, in principle, straightforward to calculate the predicted proportion of success for every possible category in the data (i.e. for every possible configuration of values of predictors) by simply taking the sum of all estimates that apply to the category, including the intercept, and then turning the result into a proportion. The output gives no information on the comparison of two non-reference levels in a predictor, such as, for instance, the comparison of region=LI and region=WV. We would need to change the reference level of region and re-run the model if we wanted that information. Another piece of information that is not readily available for predictors with more than two levels is the significance of the predictors taken as a whole. A handy R command for this is drop1(…, test=“Chisq”). For each predictor, it performs a log likelihood ratio test for nested models, comparing the complete model to the model with that predictor dropped, each time testing whether dropping that predictor makes the deviance significantly larger or not. > drop1(noemen.glm.1, test=“Chisq”) Single term deletions Model: variant ~ conver.type + generation + region + occup.type Df Deviance AIC LRT Pr(Chi) <none> 506.24 522.24 conver.type 1 527.12 541.12 20.878 4.894e-06 *** generation 1 535.11 549.11 28.869 7.743e-08 *** region 3 531.26 541.26 25.018 1.530e-05 *** occup.type 2 519.37 531.37 13.132 0.001407 ** --Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

We see that for every predictor, removal makes the deviance significantly larger, so we conclude that all predictors are significant in our model. As we did with the simple regression model, we now use plot(Predict (noemen.lrm.1, fun=plogis)) to visualize the partial effects of the predictors on a proportions of success scale. This function call generates as many plots as there are predictors (Figure 8). > plot(Predict(noemen.lrm.1, fun=plogis))

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Region

Occup.type

0.6

0.4

0.2

Hghr.d

Neutrl

N.hgh.

AB

LI

Conver.type

OV

WV

Generation

0.6

0.4

0.2

Face.to.face

Telephone

Before.1980

From.1980

Figure 8.╇ Partial effect of the predictors in the model noemen.lrm.1

Since, on the scale of proportions, the effect of the predictors is (often very similar, but) not identical in all situations, the plotting algorithm has to pick a specific situation in order to be able to plot proportions and proportion differences. The specific situation that is chosen by this plotting algorithm is determined by the reference levels of the other predictors. For instance, the partial effect of conversation type is plotted for the specific situation of generation=before.1980, region=AB, and occup.type=higher.edu. The plotting algorithm also plots 95% confidence margins around the fitted averages. We now run a second model (noemen.glm.2 and noemen.lrm.2), in which we add an interaction term for region by generation, which allows for the effect of region to be different in the two generations. The specific reason why we test this is because we suspect that the noemen-variant has recently gained wider acceptance, or at least wider usage, as one of the characteristics of a newly emerging nationwide variety of colloquial Belgian Dutch. The interaction term, represented in the formula as generation:region, is a so-called product term. So what values do the items in the data set have for generation:region? In general, the value of an item for the interaction x1:x2 between the predictors x1 and x2 is literally the product of its values for x1 and x2. In the case of predictors x1 and x2 that are themselves encoded as several

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regressors, the interaction term will consist of new regressors that represent the products of the regressors of x1 and x2. In our case, the interaction is represented as three regressors. For instance, the regressor generation=from.1980 * region=WV represented the product of generation=from.1980 and region=WV. The value of generation=from.1980 * region=WV is 1 if both generation=from.1980 and region=WV are 1 and is 0 otherwise. > noemen.glm.2 <- glm(variant ~ conver.type + generation + + region + occup.type + + generation:region, + data=noemen, family=binomial) > summary(noemen.glm.2) […] Null deviance: 618.06 on 445 degrees of freedom Residual deviance: 482.34 on 435 degrees of freedom AIC: 504.34 […] > noemen.lrm.2 <- lrm(variant ~ conver.type + generation + + region + occup.type + + generation:region, + data=noemen, x=T, y=T) > noemen.lrm.2 […] Model Likelihood Ratio Test Obs 446 LR chi2 135.73 heten 228 d.f. 10 noemen 218 Pr <0.0001 max |deriv| 7e-07

Discrimination Indexes R2 0.350 g 1.586 gr 4.885 gp 0.298 Brier 0.181

Rank Discrim. Indexes C 0.800 Dxy 0.599 gamma 0.617 tau-a 0.300

Coef S.E. Wald Z Pr(>|Z|) Intercept -0.8518 0.2018 -4.22 <0.0001 conver.type=telephone 1.0057 0.2521 3.99 <0.0001 generation=from.1980 -0.8356 0.1580 -5.29 <0.0001 region=WV 0.5184 0.2120 2.45 0.0145 region=AB 0.4123 0.2028 2.03 0.0420 region=LI 0.2742 0.2057 1.33 0.1826 occup.type=neutral 0.5408 0.3180 1.70 0.0890 occup.type=no.higher.edu 1.0873 0.2895 3.76 0.0002 generation=from.1980 * region=WV 0.9268 0.2100 4.41 <0.0001 generation=from.1980 * region=AB 0.1612 0.2023 0.80 0.4256 generation=from.1980 * region=LI -0.3157 0.2060 -1.53 0.1255



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> drop1(noemen.glm.2, test=“Chisq”) […] Df Deviance AIC LRT Pr(Chi) <none> 482.34 504.34 conver.type 1 498.68 518.68 16.343 5.284e-05 *** occup.type 2 497.06 515.06 14.719 0.0006366 *** generation:region 3 506.24 522.24 23.902 2.618e-05 *** […]

To give an example of what this interaction allows for: if in a model without interaction the effect of region=WV would be –0.10606 if generation=before.1980 (=reference generation), and the effect of generation=from.1980 would be –0.09124 if region=OV (=reference region), then it would have to be the case that the effect of region=WV combined with generation=from.1980 would have to be the sum of –0.10606 and –0.09124. In the model with interaction, however, it is possible to ‘correct’ that latter sum, making it the sum of –0.10606 and –0.09124 and 0.76557 (the figures are taken from the above output). By consequence, this model allows for the effect of region (on the logit scale) to be different in different generations. The drop1() command shows that the addition of the interaction term has significantly reduced the deviance of the model. We, therefore, decide to keep it in the model. But what does the interaction tell us exactly? We combine two tools for exploring this. Both have their limitations, but in combination they are quite informative. First, we use a mosaic plot to check if we see traces of an interaction in the observed data. A correct picture could only come from a mosaic plot with all variables from the model included, but we choose to simplify matters and just look at variant by generation and region (even though we know that not controlling for the other variables may distort the picture). The result is shown in Figure 9. > plot(table(noemen$generation, noemen$region, + noemen$variant), + col=T, main=“variant ~ generation + region”)

We see that within the old generation, there is a clear region effect (noemen is most popular in OV, less so in its neighbouring regions and is least popular in the region that is furthest away from OV). However, this effect has disappeared in the young generation. Second, we look at the predicted values to get a picture of what the model makes of this (once again, our picture is a bit unclear because we do not control for the other variables).20 For each combination of values for generation and region, we 20. There are other, more sophisticated methods to explore the combined effect of two interacting terms in a model. One package that we want to mention in particular is the effects package (Fox 2003), which supports many techniques for visualizing the effects of predictors

526 Dirk Speelman

Variant ~ generation + region Before.1980 Noemen

From.1980 Heten Noemen

LI

AB

WV

OV

Heten

Figure 9.╇ Mosaic plot of variant by generation and region

calculate the mean predicted probability (x.mean), its standard deviation (x.sd), and the number of cases (x.n). The mean predicted probabilities confirm the pattern from the mosaic plot. So the interaction confirms the hypothesis of noemen originally being a somewhat more local phenomenon that has recently spread over the whole country. > + + + + + > + +

predict.info <- function(x) { # assumes x is numeric vector of predictions result <- c(mean(x), sd(x), length(x)) names(result) <- c(“mean”, “sd”, “n”) return(result) } aggregate(predict(noemen.glm.2, type=“response”), list(noemen$region, noemen$generation), predict.info)

(with 95% confidence margins). For instance, the combined effect of the interacting terms in the model noemen.glm.2 could be visualised with the instructions: > library(effects)

> plot(effect(“generation*region”,noemen.glm.2))

All effects in the model could be visualised at once with: > plot(allEffects(noemen.glm.2))

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1 2 3 4 5 6 7 8

Group.1 OV WV AB LI OV WV AB LI

Group.2 before.1980 before.1980 before.1980 before.1980 from.1980 from.1980 from.1980 from.1980

x.mean 0.66666667 0.45833333 0.31395349 0.06250000 0.59459459 0.67647059 0.77777778 0.59459459

x.sd 0.18788276 0.18866238 0.19044277 0.04043570 0.16932037 0.09336409 0.09800288 0.10651400

x.n 63.00000000 96.00000000 86.00000000 48.00000000 37.00000000 34.00000000 45.00000000 37.00000000

Incidentally, the code we just used can easily be modified to generate the list of predicted probabilities for all categories in the data (i.e. all possible combinations of values of the predictors that occur in the data). We do this below, but we suppress most of the output. There are 43 lines in the output because 5 of the 48 theoretically possible combinations do not occur in the data. > aggregate(predict(noemen.glm.2, type=“response”), + list(noemen$region, noemen$generation, + noemen$conver.type, noemen$occup.type), + predict.info) Grp.1 Group.2 Group.3 Group.4 x.mean x.sd x.n 1 OV before.1980 face2face higher.edu 0.43974421 0.00 23.00 2 WV before.1980 face2face higher.edu 0.24715753 0.00 35.00 3 AB before.1980 face2face higher.edu 0.15073898 0.00 45.00 4 LI before.1980 face2face higher.edu 0.02497667 0.00 18.00 […] 42 AB from.1980 telephone neutral 0.89284457 0.00 8.00 43 LI from.1980 telephone neutral 0.74984350 0.00 6.00

5. Model diagnostics In linear regression, which relies heavily on the assumption of normal errors, a lot of model diagnostics exist that involve inspecting the residuals in the model and looking for indications that the model assumptions are violated. Compared to that, the model assumptions in logistic regression are much less demanding, but still there is a clear need to test if nothing is wrong in the way the model fits the data. The assumption of a binomial distribution of the response implies certain expectations about the amount of variability we can expect in the data given a specific model. If we detect an amount of variability that is not in line with these expectations – a phenomenon which is called underdispersion when we detect less variation than expected, and overdispersion if we detect more variation than we expect (overdispersion is, obviously, the more common problem) – then this undermines the assumption. A first quick check we can do to test for this is to compare the residual deviance in the

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model to the residual degrees of freedom in the model; should the residual deviance be much larger than the residual degrees of freedom, then that would be an indication of overdispersion. In noemen.lrm.2, this comparison gives no indication of overdispersion (Residual deviance: 482.34 on 435 degrees of freedom). Second, we can perform the so-called Hosmer-Lemeshow-Cessie goodness of fit test. A significant result in that test would indicate a significant lack of fit. We do not obtain a significant lack of fit here (p = 0.0755884), but the rather low p-value does indicate that the fit is far from good. > residuals(noemen.lrm.2, type=”gof”) Sum of squared errors Expected value|H0 80.6027138 81.3454554 Z P -1.7768775 0.0755884

SD 0.4180039

If any of the above techniques signals a problem, the most likely reason is that important predictors are missing from the model (or that the model is for some other reason too simplistic to provide an acceptable fit). Another thing that should be tested routinely is whether there are any correlation patterns among the predictors that are so outspoken that this makes the model less reliable (this is the so-called problem of multicollinearity). We can test this with the command vif() which we run on the lrm model without interactions. Values higher than four should be considered problematic. If they occur, one of the problematic variables should be removed from the model and the model should be rerun and tested again.21 > vif(noemen.lrm.1) conver.type=telephone 1.178568 region=AB 1.689968 occup.type=no.higher.edu 1.386220

generation=from.1980 1.674683 region=LI 1.626993 occup.type=neutral 1.654916

region=WV 1.724891

Finally, it can also happen that individual items in your data set have too big an influence on your model. Candidate problematic cases can be detected as shown below, together with the estimate they could affect the most (the numbers are row numbers in the data set). Inspection of these cases involves manual inspection as well as running a model with these cases removed and testing whether indeed the models differ

21. An alternative solution would be to use a dimension reduction technique to remove the redundancy from the predictors.



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substantially. The decision to permanently remove certain items from the analysis should only be a last resort (and obviously should be well documented). > which.influence(noemen.lrm.2) $Intercept [1] “265” “267” “268” “270” “271” $generation [1] “151” $region [1] “238” “239” “450” $`generation * region` [1] “188” “238” “239” “450”

6. Variable selection Logistic regression is a powerful and versatile tool, but it is not a very easy technique to use. One of the more difficult aspects of its use is variable selection. Variable selection, sometimes also called model selection, is the process of deciding which of the candidate predictors or interactions between predictors to include in the (final) model. From a ‘mechanical hypothesis testing perspective’, it might seem that this is not a process, but simply is a ‘one step procedure’ that boils down to including all candidate predictors to the model and running the model. However, in just about any non-trivial study, the task is more complicated than that and issues of the fit, interpretability and replicability of the model arise. On the one hand, the comparison of models often helps us acquire a deeper understanding of the relation between the model(s) and the data. On the other hand, we must be careful that the very process of multiple model comparison does not trick us into ‘data fishing’. In sum, variable selection is the sometimes-tricky task of striking a balance between on the one hand misreading or oversimplifying the patterns in the data and on the other hand overfitting to the ‘noise’ in the data. An interesting reference regarding this topic is Harell (2001).

7. Which conditions should my data set meet? It has been mentioned before that logistic regression analysis can handle data from corpus studies as well as from experimental designs. In the case of corpus studies, most of the time the best approach to collecting your data is to retrieve all occurrences of the phenomenon under scrutiny from your corpus and include all these occurrences in your data set (of course, you do exclude all spurious hits and all cases with contexts in which variation is not possible). In general, you do not have to try to balance your data set. Firstly, logistic regression can handle a lot of correlation patterns among the

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predictors. Secondly, in logistic regression, variable levels within one variable do not have to be balanced, neither for the response variable nor for the predictors. The only downside of unbalanced data is that unbalanced data often require larger data sets. This brings us to the following point. How many data points do I need for my study? This crucially depends on the number of regressors you consider for inclusion in the model. Several rules of thumb exist. Here I only mention one general rule of thumb, which is the one I believe is most important. The rule starts from the overall number of occurrences in the data set for the least frequent response level. For instance, in the noemen data set this would be 218, the overall frequency of the variant noemen (the other variant, heten, has a frequency of 228). The rule of thumb then says that the maximum number of regressors one should consider for inclusion in the model must not be more than this frequency divided by 20. So, in the noemen data set, the maximum number of regressors must not be more than 10 or 11 (see Harrell (2001:â•›60–61) and the studies that are cited there, for a more detailed and nuanced discussion of sample size issues). The biggest risk related to the inclusion of too many regressors is overfitting. Overfitting is fitting a model that follows the patterns in the data so closely that it picks up idiosyncratic as well as generalizable patterns. An overfitted model will not be reproducible in replication studies. On the one hand, it will typically exaggerate the size of effect that does exist, and on the other hand, it will also detect pseudo-effects that are actually no more than accidental idiosyncratic irregularities in the data set. Next to rules of thumb such as the one just mentioned, there are other, more advanced, techniques that help reduce the risk of overfitting (see e.g. Harell 2001 on cross-validation and shrinkage).

8. Beyond the limits of traditional binomial logistic regression In a sense, it is inappropriate to include a section called ‘Beyond the limits of traditional binomial logistic regression’ in an introductory text that has barely scratched the surface of what can be done within traditional binomial logistic regression. Moreover, just like any other popular modern technique in statistics, logistic regression is constantly being enhanced, and therefore the boundaries of what is ‘traditional binomial logistic regression’ are unclear ones and they are probably shifting. Still, there is a need to position what is discussed in this text in a wider context and point to some techniques that extend binomial logistic regression or can be seen as alternatives to it. The first thing that springs to mind is multinomial logistic regression, which is a further elaboration of logistic regression that supports categorical response variables with more than two levels, and proportional odds models (also called ordinal logistic regression), which support ordinal response variables.



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A second extension is the incorporation into generalized linear models (and therefore also in logistic regression models) of mixed model analysis. In mixed model terminology, all predictors that were discussed in this text are so-called fixed effect predictors. Mixed models allow for the combination in one model of both fixed effect predictors and so-called random effects (also called random factors), which are identifiable sources of random variation. Random effects are useful for many contexts, but let me give just one example. Suppose that in the data set for some Corpus Linguistics study you have 1000 items that were produced by 200 different speakers. In other words, many of these speakers have produced several items in your data. Obviously this fact can introduce certain patterns in the data (a type of interdependence between certain observations) because behaviour by the same speaker is likely to be more similar than behaviour by different speakers. Ignoring this fact when analysing the data may lead to biased results and incorrect conclusions. On the other hand, one does not want to treat speaker as a fixed effect because (a) it would have 200 levels which would make it both a terribly ‘dominant’ and a terribly uninterpretable predictor, and (b) fitting fixed effect slopes for individual speakers would not be interesting and would not lead to replicable studies or general, reproducible results (in other words, the model would overfit to irrelevant idiosyncratic patterns in the data). This is an example where ‘speaker’ would be a good candidate for a random factor. Contrary to the levels of a fixed effect predictor, the levels of a random factor that occur in a data set are assumed to be a random selection from a typically much larger set of levels in the population. In other words, if we replicate a study, the levels of the fixed effect will be the same as in the original study. The levels of a random factor, however, will typically be another random sample from the large set of levels in the population. In the case we just discussed, it will typically be other speakers. Mixed models then are designed to account for the variation caused by random factors without giving them the status of fixed effects. Yet another avenue is the exploration of non-linear relations between numerical or ordinal predictors and logits. The assumption of linearity is hardly ever obvious. Often it is an acceptable simplification of reality, often it is not. Within traditional binomial regression, we can use polynomials and transformed predictors. Beyond it, we can explore splines for logistic models and generalized additive logistic models. Finally, it should be mentioned that beyond generalized linear models (either with or without random effects) there are many other statistical tools that can be used for classification (i.e. for predicting class membership of items on the basis of the properties of the items) and that the types of analyses discussed in this text can be seen as classification tasks with the classes being the levels of the response variable. Examples of such techniques are classification trees and forests (a.o. conditional inference trees and random forests), support vector machines, memory based learning, Bayesian networks, and many others.

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9. Further reading A gentle, yet broader introduction to logistic regression can be found in Pampel (2000). Some more advanced textbooks on logistic regression are Hosmer and Lemeshow (2000), and Hilbe (2009). More information on the VARBRUL tradition of logistic regression in Sociolinguistics can be found in Paolillo (2002) and Tagliamonte (2006), amongst others.

References Arnold, J., Wasow, Th., Losongco, A., & Ginstrom, R. (2000). Heaviness vs. newness: The effects of complexity and information structure on constituent ordering. Language, 76, 28–55. Berkson, J. (1944). Application of the logistic function to bio-assay. Journal of the American Statistical Association, 39, 357–365. Cedergren, H., & Sankoff, D. (1974). Variable rules: Performance as a statistical reflection of competence. Language, 50, 33–56. DOI: 10.2307/412441 Cox, D. R. (1969). The analysis of binary data. London: Chapman and Hall. Fox, J. (2003). Effect displays in R for generalised linear models. Journal of Statistical Software, 8(15), 1–27. Retrieved from . Grondelaers, S., Speelman, D., & Geeraerts, D. (2002). Regressing on er. Statistical analysis of texts and language variation. In A. Morin, & P. Sébillot (Eds.), 6èmes journées internationales d’analyse statistique des données textuelles (pp. 335–346). Rennes: Institut National de Recherche en Informatique et en Automatique. Harrell, F. E. (2001). Regression modeling strategies: With applications to linear models, logistic regression, and survival analysis. Berlin: Springer. Hilbe, J. M. (2009). Logistic regression models. London: Chapman & Hall/CRC Press. Hosmer, D., & Lemeshow, S. (2000). Applied logistic regression (2nd ed.). New York: Wiley. DOI: 10.1002/0471722146 Johnson, D. E. (2008). Getting off the GoldVarb standard: Introducing Rbrul for mixed-effects variable rule analysis. Language and Linguistics Compass, 3, 359–83. DOI: 10.1111/j.1749-818X.2008.00108.x Keune, K., Ernestus, M., van Hout, R., & Baayen, H. (2005). Social, geographical, and register variation in Dutch: From written mogelijk to spoken mok. Corpus Linguistics and Linguistic Theory, 1, 183–223. DOI: 10.1515/cllt.2005.1.2.183 Nelder, J., & Wedderburn, R. (1972). Generalized linear models. Journal of the Royal Statistical Society: Series A, 135, 370–384. DOI: 10.2307/2344614 Oostdijk, N. (2000). The spoken Dutch corpus: Overview and first evaluation. In S. Markantontou, S. Piperidis, & G. Stainhauoer (Eds.), Proceedings of the second international conference on language resources and evaluation (pp. 887–893). Athens: Institute for Language and Speech Processing. Pampel, F. C. (2000). Logistic regression: A primer. Thousand Oaks, CA: Sage.



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Paolillo, J. (2002). Analyzing linguistic variation: Statistical models and methods. Stanford: CSLI. Sankoff, D. (1988). Variable rules. In U. Ammon, N. Dittmar, & K. J. Mathheier (Eds.), Berlin sociolinguistics: An international handbook of the science of language and society, Vol. 2. (pp. 984–997). Berlin & New York: Walter de Gruyter. Sankoff, D., Tagliamonte, S., & Smith, E. (2005). Goldvarb X: A variable rule application for Macintosh and Windows. Department of Linguistics, University of Toronto. Tagliamonte, S. A. (2006). Analysing sociolinguistic variation. Cambridge: Cambridge University Press. DOI: 10.1017/CBO9780511801624 Williams, R. S. (1994). A statistical analysis of English double object alternation. Issues in Applied Linguistics, 5, 37–58. Wilson, E. B., & Worcester, J. (1943). The determination of L. D. 50 and its sampling error in bio-assay. Proceedings of the National Academy of Sciences, 29, 257–262. DOI: 10.1073/pnas.29.8.257

Name index

A Adler, Jeffreyâ•… 315, 317, 318, 319, 322, 362 Afifi, Abdelmonemâ•… 316, 318, 322 Agresti, Alanâ•… 320, 321, 322, 323, 482 Aijmer, Karinâ•… 184, 185, 281 Albert, Jamesâ•… 323 Aldenderfer, Markâ•… 99 Allan, Keithâ•… 88 Allerton, Davidâ•… 147, 148, 149, 150, 174 Altenberg, Bengtâ•… 149 Alviar, Joséâ•… 406 Amberber, Mengistuâ•… 224 Andrén, Matsâ•… 310 Apresjan, Juriâ•… 10 Arnold, Jenniferâ•… 259, 488 Arppe, Anttiâ•… 14, 122, 187, 310, 317, 318, 322, 325, 327, 482 Athanasiadou, Angelikiâ•… 147, 149, 152, 174 Atkins, Berylâ•… 22, 310 Azen, Raziaâ•… 321, 322 B Baayen, Haraldâ•… 136, 137, 218, 272, 315, 316, 317, 318, 319, 321, 323, 324, 325, 326, 327, 362, 382, 405, 407, 435, 460, 482 Backhaus, Klausâ•… 435 Baguley, Thomâ•… 326 Balahur, Alexandraâ•… 310 Barðal, Jóhannaâ•… 41 Barnabé, Aurélieâ•… 310, 317 Barrio, Gregarioâ•… 106 Bartens, Raijaâ•… 254, 265, 266 Barthélemy, Jean-Pierreâ•… 18 Bartmiński, Jerzyâ•… 12 Bartning Ingeâ•… 180 Bates, Douglasâ•… 327

Bates, Elizabethâ•… 187, 188 Beitel, Dinaraâ•… 95 Bellavia, Elenaâ•… 17 Benki, Joséâ•… 101 Benzécri, Jean-Paulâ•… 148, 158, 317, 446, 447, 482 Beretta, Alanâ•… 87 Berkson, Josephâ•… 487 Berthele, Raphaelâ•… 318, 325 Biber, Douglasâ•… 155, 281, 282, 283, 292, 325 Blank, Andreasâ•… 87 Blashfield, Rogerâ•… 99 Boas, Hansâ•… 83 Boers, Frankâ•… 22 Bolinger, Dwightâ•… 148, 281 Bondarko, Aleksandrâ•… 12, 13 Borg, Ingwerâ•… 317, 318 Bortz, Jürgenâ•… 376 Boscarino, Josephâ•… 106 Bouma, Gerlofâ•… 208 Brace, Nicolaâ•… 102 Braun, Johnâ•… 136, 317, 318, 319, 321, 322, 324, 325, 326, 327, 362 Breckenridge, Jamesâ•… 95 Bresnan, Joanâ•… 101, 206, 218, 254, 259, 264, 266, 267, 280, 310, 324 Broccias, Cristianoâ•… 63, 64, 69 Brooks, Patriciaâ•… 366 Brugman, Claudiaâ•… 19, 20, 88 Bucholtz, Maryâ•… 88 Bybee, Joanâ•… 15, 190, 206, 318, 367, 397 Byloo, Pieterâ•… 182, 191 C Cadoret, Marineâ•… 317 Cappelle, Bertâ•… 255, 260, 262 Carlson, Lauraâ•… 265 Carretero, Martaâ•… 310 Carroll, Johnâ•… 310

Casad, Eugeneâ•… 22 Cedergren, Henriettaâ•… 488 Ceulemans, Evaâ•… 216 Chaffin, Rogerâ•… 25, 316 Chambers, Jackâ•… 88 Chatterjee, Sampritâ•… 136, 137, 321 Chaturvedi, Anilâ•… 106 Chessel, Danielâ•… 326 Chomsky, Noamâ•… 123 Christensen, Runeâ•… 322, 327 Church, Kennethâ•… 147 Cienki, Alanâ•… 21 Clancy, Stevenâ•… 318 Clatworthy, Janeâ•… 99 Coates, Jenniferâ•… 181, 182, 190, 191 Coleman, Lindaâ•… 20 Colleman, Timothyâ•… 40, 41, 42, 48, 49, 309, 316 Collins, Peterâ•… 181, 183, 184, 185, 191, 201 Combs-Orme, Terriâ•… 322, 323, 325 Comrie, Bernardâ•… 226, 254, 256, 265, 266 Cooper, Marthaâ•… 93, 432 Cooper, Williamâ•… 259 Coșeriu, Eugenioâ•… 10 Coulmas, Florianâ•… 88 Coventry, Kennyâ•… 265 Cox, Davidâ•… 487 Cox, Michaelâ•… 318 Cox, Trevorâ•… 318 Crawley, Michaelâ•… 316, 318, 319, 321, 323, 326, 327, 362, 382, 383 Croft, Williamâ•… 19, 21, 62, 70, 71, 83, 318, 325 Croissant, Yvesâ•… 327 Cruse, Alanâ•… 10, 145, 153 Culioli, Antoineâ•… 12 Cuyckens, Hubertâ•… 17, 19, 20, 21, 88, 118

536 Corpus Methods for Semantics

D D’Andrade, Royâ•… 225 Dąbrowska, Ewaâ•… 20, 22, 89, 228 Daille, Béatriceâ•… 310 Dalgaard, Peterâ•… 315, 316, 321, 322, 324, 325, 362 Danielewiczowa, Magdalenaâ•… 225 Davies, Markâ•… 146, 154, 393 De Clerck, Bernardâ•… 40, 41, 46, 49, 52 De Cock, Barbaraâ•… 310 De Haan, Ferdinandâ•… 182 De Leeuw, Janâ•… 326, 349, 350, 474, 475, 476 De Schutter, Gertâ•… 48 de Stadler, Leonâ•… 22 De Sutter, Gertâ•… 206 de Vega, Manuelâ•… 266, 268 Deane, Paulâ•… 17, 19, 20 Degand, Liesbethâ•… 207 Deignan, Aliceâ•… 309 Delaere, Isabelleâ•… 482 Delbeque, Nicoleâ•… 22 Delorge, Martineâ•… 44, 46, 51, 309 DeMaris, Alfredâ•… 136 Depraetere, Ilseâ•… 190 Desagulier, Guillaumeâ•… 317 Deshors, Sandraâ•… 190, 201, 310, 321 Dewell, Robertâ•… 17, 229 Dickey, Stephanâ•… 227, 228, 229, 230, 232, 233, 234 Diehl, Hanneleâ•… 310 Divjak, Dagmarâ•… 27, 89, 95, 128, 131, 157, 163, 174, 180, 186, 188, 192, 195, 226, 235, 236, 307, 308, 310, 321, 324, 325, 435, 481 Dixon, Robertâ•… 64 Dodge, Yadolahâ•… 136, 244 Downing, Angelaâ•… 171 Drenan, Robertâ•… 316, 317 Dubois, Danièleâ•… 19, 23 Duda, Richardâ•… 99 Dufour, Anne-Béatriceâ•… 326, 477 Dunbar, Georgeâ•… 19, 87 Duyck, Wouterâ•… 42 Dziwirek, Katarzynaâ•… 307, 308

E Eckert, Penelopeâ•… 88 Eddington, Davidâ•… 206, 318 Edmonds, Philipâ•… 153 Edwards, Davidâ•… 323 Einspruch, Ericâ•… 100 Elsness, Johanâ•… 281, 282, 288, 294 Erades, Pieterâ•… 278 Erelt, Matiâ•… 255, 256, 257 Evans, Vyvyanâ•… 17, 19, 120 Everitt, Brianâ•… 93, 94, 99, 162, 315, 316, 317, 318, 319, 321, 325, 327, 328, 362, 435 Evert, Stefanâ•… 147, 316, 325 Eyrich, Christophâ•… 22 F Fabiszak, Małgorzataâ•… 126, 247 Faraway, Julianâ•… 136, 137, 320, 321, 322, 327, 382 Fauconnier, Gillesâ•… 13 Feist, Micheleâ•… 265, 266 Fellbaum, Christianeâ•… 73 Fidell, Lindaâ•… 101, 318, 322, 324, 325 Field, Andyâ•… 105, 321, 322, 327 Fillmore, Charlesâ•… 18, 19, 20, 21, 22, 25, 27, 83 Firth, Johnâ•… 146, 308 Fischer, Kerstinâ•… 205, 236, 307, 310 Fleischman, Suzanneâ•… 190 Flores Salgado, Elizabethâ•… 310 Fontaine, Johnnyâ•… 310 Ford, Marilyn â•… 254, 259, 264, 266, 267 Fortescue, Michaelâ•… 223, 224 Fought, Carmenâ•… 88 Fox, Johnâ•… 525 Freese, Jeremyâ•… 322, 323, 325 Fuchs, Catherineâ•… 26 Funke, Stefanâ•… 326 G Gabrielatos, Costasâ•… 182, 184, 185 Garrod, Simonâ•… 265 Gass, Susanâ•… 188 Geeraerts, Dirkâ•… 10, 15, 16, 17, 18, 19, 20, 21, 22, 23, 26, 27, 40,

87, 88, 118, 119, 120, 121, 122, 124, 206, 207, 208, 209, 215, 217, 219, 280, 307, 310, 311, 317, 321, 325, 488 Geiger, Richardâ•… 22 Gelman, Andrewâ•… 321 Gentner, Dedreâ•… 265, 266 Gifi, Albertâ•… 450 Gilbert, Ericâ•… 174 Gilquin, Gaëtanelleâ•… 17, 122, 157, 165, 308, 309, 316, 324, 325 Givón, Talmyâ•… 12, 13 Glynn, Dylanâ•… 16, 18, 21, 27, 46, 61, 72, 73, 74, 83, 117, 119, 120, 132, 134, 135, 136, 205, 223, 224, 226, 234, 236, 238, 253, 254, 272, 273, 274, 280, 288, 307, 208, 310, 311, 316, 317, 321, 322, 324, 325, 482, 506 Goddard, Cliffâ•… 224, 225 Goldberg, Adeleâ•… 12, 20, 42, 49, 61, 63, 66, 67, 83, 151, 152, 156, 173, 174, 367, 392 Gower, Johnâ•… 414, 418, 420, 421, 422, 437, 438, 482 Green, Paulâ•… 106 Greenacre, Michaelâ•… 46, 134, 148, 158, 239, 317, 326, 445, 446, 447, 448, 449, 450, 466, 467, 467, 470, 471, 473, 482 Greenberg, Josephâ•… 267 Gries, Stefanâ•… 18, 22, 25, 26, 27, 62, 66, 67, 68, 70, 81, 87, 94, 95, 117–128, 130, 131, 135, 137, 141, 156, 157, 160, 162, 163, 165, 174, 180, 186, 192, 193, 194, 195, 201, 206, 216, 217, 226, 236, 254, 288, 289, 307, 308, 309, 310, 315, 316, 318, 319, 231, 322, 324, 325, 326, 327, 372, 378, 382, 387, 391, 392, 393, 395, 397, 405, 407, 435 Grochowska, Alinaâ•… 230 Groenen, Patrickâ•… 318 Grondelaers, Stefanâ•… 10, 206, 236, 280, 310, 321, 488 H Hadfield, Jarrodâ•… 327 Hadi, Aliâ•… 136, 137, 321 Hagège, Claudeâ•… 254, 256, 265, 266

Name index 537



Halliday, Michaelâ•… 12 Hanauer, Davidâ•… 316 Hanks, Patrickâ•… 87, 147 Härdle, Wolfgangâ•… 316, 317, 318 Harnad, Stevanâ•… 405 Harrell, Frankâ•… 211, 321, 327, 505, 530 Haspelmath, Martinâ•… 40 Hawkins, Barbaraâ•… 19 Hawkins, Johnâ•… 259 Hebda, Annaâ•… 224, 247 Hennig, Christianâ•… 326, 432 Hermerén, Larsâ•… 182, 185, 197 Herskovits, Annetteâ•… 20, 265, 268 Heylen, Krisâ•… 27, 106, 205, 206, 280, 310, 321, 324 Hidetoshi, Shimodairaâ•… 326 Hilbe, Josephâ•… 320, 321, 322, 323, 325, 532 Hill, Jenniferâ•… 321, 323 Hilpert, Martinâ•… 27, 61, 156, 157, 175, 308, 309, 316, 325, 403 Hirst, Graemeâ•… 153 Hoffmann, Thomasâ•… 308, 318, 325 Hommerberg, Charlotteâ•… 382, 283 Hopper, Paulâ•… 7, 281 Hosmer, Davidâ•… 101, 105, 212, 320, 528, 532 Hothorn, Torstenâ•… 214, 315, 316, 317, 319, 321, 325, 327, 328, 362 Hox, Joopâ•… 324 Huddleston, Rodneyâ•… 182, 190, 201 Husson, Francoisâ•… 317, 325, 326, 448, 482 Hyltenstam, Kennethâ•… 180 I Ito, Takehikoâ•… 187, 188 Izenman, Alanâ•… 316, 317, 318, 325 J Jackendoff, Rayâ•… 224 Janda, Lauraâ•… 19, 20, 21, 22, 27, 118, 230, 310 Janssen, Theoâ•… 40 Järvikivi, Juhaniâ•… 122 Johnson, Danielâ•… 488

Johnson, Keithâ•… 316, 321, 326, 327, 362, 382, 405, 407, 435 Johnson, Markâ•… 224 Johnson, Richardâ•… 408 Johnson, Valenâ•… 323 Jones, Jamesâ•… 325 Jones, Stevenâ•… 11 Jones, Valâ•… 99 Junker, Marie-Odileâ•… 224 K Kallel, Amelâ•… 101 Kaltenböck, Guntherâ•… 282, 288, 393, 402 Kastovsky, Dieterâ•… 10 Kaufman, Leonardâ•… 326, 428 Kay, Paulâ•… 20, 21, 83, 152 Kearns, Katherineâ•… 282, 288, 294 Keen, Kevinâ•… 328, 362 Kemmer, Suzanneâ•… 206, 207, 209, 210 Kennedy, Graemeâ•… 149, 155 Keune, Karenâ•… 488 Kilborn, Kerryâ•… 187, 188 Kilgarriff, Adamâ•… 16, 74, 119, 147, 156 Kittay, Evaâ•… 19, 21, 23 Klavan, Janeâ•… 26, 258, 275, 280, 310, 319, 324, 325 Kleiber, Georgeâ•… 19, 118 Klein, Deborahâ•… 87 Kleinbaum, Davidâ•… 101 Klinge, Alexâ•… 182, 185 Kokorniak, Iwonaâ•… 247, 310, 317, 482 Konat, Barbaraâ•… 224, 247 Kowalczyk, Teresaâ•… 482 Krawczak, Karolinaâ•… 27, 224, 247, 310, 317, 322, 324, 325, 482 Kreitzer, Anatolâ•… 17, 20 Krishnamurthy, Rameshâ•… 88 Kristiansen, Gitteâ•… 88 Kroonenberg, Pieterâ•… 322, 325 Kruisinga, Etskoâ•… 378 Kudrnáčová, Naděždaâ•… 124 Kustova, Galinyâ•… 225 L Labov, Williamâ•… 88 Lakoff, Georgeâ•… 10, 12, 14, 17, 18, 19, 20, 22, 25, 119, 120, 224

Lancelot, Renaudâ•… 326 Langacker, Ronaldâ•… 7, 25, 49, 145, 151, 219, 227, 234, 254, 268 Le Roux, Brigitteâ•… 317, 325, 448, 482 Lê, Sébastienâ•… 326, 477 Leacock, Claudiaâ•… 19, 88 Ledolter, Johannesâ•… 316, 322 Leech, Geoffreyâ•… 154, 181, 182, 201 Legendre, Pierreâ•… 414, 418 Lehrer, Adrienneâ•… 19, 21, 22, 23, 26, 88, 120 Lehrer, Keithâ•… 26 Lemeshow, Stanleyâ•… 101, 105, 212, 320, 528, 532 Lemmens, Maartenâ•… 21, 22 Lesnoff, Matthieuâ•… 326 Lestrade, Sanderâ•… 254, 256, 265, 266 Levin, Bethâ•… 63, 263 Levshina, Nataliaâ•… 26, 216, 217, 310, 317, 319, 321, 324, 325 Levy, Josephâ•… 132 Lewandowska-Tomaszczyk, Barbaraâ•… 22, 88, 307, 308 Liamkina, Olgaâ•… 17 Liaw, Andyâ•… 326 Lienert, Gustavâ•… 376 Lindner, Susanâ•… 19, 20, 232 Lipka, Leonardâ•… 10 Locke, Philipâ•… 171 Loewenthal, Judithâ•… 210 Lohmann, Arneâ•… 375 Long, Scottâ•… 323, 325 Lorenz, Gunterâ•… 149, 156 Louwerse, Maxâ•… 316 Luraghi, Silviaâ•… 254, 265, 266 Lutzeier, Peterâ•… 10 Lyons, Johnâ•… 10 M MacLaury, Robertâ•… 19, 23 MacWhinney, Brianâ•… 180, 187, 188 Maechler, M.â•… 326 Magidson, Jayâ•… 106 Maindonald, Johnâ•… 136, 317, 318, 319, 312, 323, 324, 325, 326, 327, 362 Mair, Patrickâ•… 326, 449, 450, 474, 475, 476

538 Corpus Methods for Semantics

Malchukov, Andrejâ•… 40 Manning, Chrisâ•… 147 Marden, Joaquimâ•… 147 Marques de Sá, Joaquimâ•… 136 Medin, Douglasâ•… 206 Meex, Birgittaâ•… 17 Mel’čuk, Igorâ•… 10 Melis, Ludoâ•… 20 Menard, Scottâ•… 212, 320, 321 Mervis, Carolynâ•… 206, 216 Milligan, Glennâ•… 93, 432 Milroy, Lesleyâ•… 88 Mittal, Hrishiâ•… 362 Moisl, Hermannâ•… 94, 99 Mojena, Richardâ•… 98 Mondorf, Brittaâ•… 254, 259, 260 Montoyo, Andrésâ•… 310 Morgan, Pamelaâ•… 20 Morgenstern, Aliyahâ•… 310 Moss, Marcâ•… 104 Mulac, Anthonyâ•… 280, 281, 282, 288, 294 Müller, Henrikâ•… 182, 185 Mun, Eun-Youngâ•… 322 Murphy, Gregoryâ•… 87 Murphy, Lynnâ•… 10, 11 Murtagh, Fionnâ•… 317, 482 Myers, Danâ•… 25, 316 N Neandić, Olegâ•… 326 Neff, Joanneâ•… 184, 185 Nelder, Johnâ•… 487, 505 Nerlich, Brigitteâ•… 19, 88 Nevalainen, Terttuâ•… 149, 174 Newman, Johnâ•… 20, 44, 309 Nicholls, Dianeâ•… 88 Nordmark, Henrikâ•… 317, 322 Norušis, Marijaâ•… 102 Norvig, Peterâ•… 19 Nuyts, Janâ•… 190, 191 O O’Connell, Annâ•… 323 Oakes, Michaelâ•… 322 Ojutkangas, Kristaâ•… 254, 265, 266, 268 Oksanen, Jariâ•… 449, 477 Oostdijk, Nellekeâ•… 519 Orme, Johnâ•… 322, 323, 325 Otani, Naokiâ•… 186, 193, 194, 195

P Pagès, Jérômeâ•… 146 Palander-Collin, Minnaâ•… 280, 281 Palmeos, Paulineâ•… 256, 257, 266 Palmer, Frankâ•… 182, 190, 191 Palmer, Garyâ•… 225 Pampel, Fredâ•… 532 Paolillo, Johnâ•… 532 Paprotté, Wolfâ•… 21, 23 Paradis, Caritaâ•… 147, 148, 149, 150, 152, 153, 162, 164, 173, 174 Pasich-Piasecka, Agnieszkaâ•… 230 Pawłowska, Reginaâ•… 225 Pedersen, Tedâ•… 156 Peng, Chao-Yingâ•… 104, 105 Pęzik, Piotrâ•… 309 Pichler, Heikeâ•… 309 Piernikarski, Cezaryâ•… 229 Pinker, Stevenâ•… 63, 64 Plevoets, Koenâ•… 317, 443, 482 Poole, Keithâ•… 318, 325 Przybylska, Renataâ•… 228, 230, 232 Pütz, Martinâ•… 19, 23, 88, 308 Q Quine, Willardâ•… 153 Quirk, Randolphâ•… 148, 150 R Radden, Günterâ•… 19, 182, 229 Rakova, Marinaâ•… 19, 88 Rannat, Rutaâ•… 254 Rao, Vithalaâ•… 106 Rastier, Françoisâ•… 10 Rauh, Gisaâ•… 23 Ravid, Doritâ•… 316 Ravin, Yaelâ•… 19, 88 Read, Jonathonâ•… 310 Reed, Susanâ•… 190 Reif, Monikaâ•… 88, 308 Rencher, Alvinâ•… 317, 482 Rice, Sallyâ•… 18, 20, 21, 26, 119, 309, 316 Ripley, Brianâ•… 318, 319, 325, 326, 454 Rissanen, Mattiâ•… 149, 174, 280, 281, 282, 283, 288, 292

Robinson, Justynaâ•… 88, 89, 90, 98, 106, 111, 310, 316, 319, 321, 325 Roever, Christianâ•… 326 Rohdenburg, Günterâ•… 281, 282, 288, 293 Romney, Kimballâ•… 444, 482 Rosch, Eleanorâ•… 119, 206, 216 Rosenbach, Anetteâ•… 255 Ross, Johnâ•… 259 Rouanet, Henryâ•… 317, 325, 448, 482 Rousseeuw, Peterâ•… 326, 428, 432 Rudzka-Ostyn, Brygidaâ•… 19, 20, 21, 22, 23, 118, 228, 310 Ruette, Tomâ•… 318 S Saffran, Jennyâ•… 367 Sagi, Eyalâ•… 309 Salkie, Raphaelâ•… 185, 193, 195 Salm, Siretâ•… 258 Saltini, Annaâ•… 106 Sanders, Joséâ•… 22 Sandra, Dominiekâ•… 20, 26, 119, 316 Sankoff, Davidâ•… 488 Sarmento, Simoneâ•… 182, 184, 185 Schaffer, Margueriteâ•… 206 Scheibman, Joanneâ•… 310, 367 Scherer, Klausâ•… 310 Schermer-Vermeer, Everdinaâ•… 51 Schmid, Hans-Jörgâ•… 15, 21, 22, 26, 106, 122, 173, 318, 366, 397, 481 Schmidtke-Bode, Karstenâ•… 318, 481 Schneider, Walterâ•… 13 Schulze, Rainerâ•… 20, 25, 316 SchuÌ‹tze, Hinrichâ•… 147 Schwarz, Monikaâ•… 19, 23 Sethuraman, Nityaâ•… 367 Shaw, Davidâ•… 406 Sheather, Simonâ•… 321, 323 Sheskin, Davidâ•… 382 Shiffrin, Richardâ•… 13 Simar, Léopoldâ•… 316, 317, 318 Simon-Vandenbergen, AnneMarieâ•…149 Sinclair, Johnâ•… 155

Name index 539



Śmiech, Witoldâ•… 227, 228, 232 Smith, Ericâ•… 488 Smith, Jenniferâ•… 281, 282, 288, 294 Smith, Robertâ•… 322, 325 Solovyev, Valeryâ•… 27, 310, 316 Speelman, Dirkâ•… 27, 101, 136, 206, 207, 208, 209, 215, 217, 219, 223, 236, 243, 280, 288, 289, 310, 321, 325, 355, 382, 482 Spooren, Wilbertâ•… 22 Steckel, Joelâ•… 106 Stefanowitsch, Anatolâ•… 13, 18, 26, 62, 66, 67, 68, 70, 81, 131, 147, 152, 156, 157, 160, 162, 165, 307, 309, 311, 315, 316, 316, 325, 391, 392, 393, 397 Stepanov, Juriâ•… 12 Stevens, Jamesâ•… 318 Stoffel, Cornelisâ•… 146, 150, 155 Storjohann, Petraâ•… 153 Storms, Gerritâ•… 216 Strobl, Carolinâ•… 319, 326 Stukker, Ninneâ•… 207, 209 Suzuki, Ryotaâ•… 326 Sweetser, Eveâ•… 87 Szelid, Veronikaâ•… 317, 325, 482 Szmrecsanyi, Benediktâ•… 136, 254, 255, 310, 317, 318, 321, 325 Szwedek, Aleksanderâ•… 224 T Tabachnick, Barbaraâ•… 101, 318, 322, 324, 325 Tabakowska, Elżbietaâ•… 228, 229, 233, 243 Taboada, Maiteâ•… 310 Tagliamonte, Saliâ•… 281, 282, 288, 294, 488, 532

Talmy, Leonardâ•… 12, 25, 265, 268 Tan, Pang-Ningâ•… 94, 99 Tarling, Rogerâ•… 322, 323, 325 Taylor, Johnâ•… 17, 19, 20, 22, 23, 88 Therneau, Terryâ•… 326 Thompson, Lauraâ•… 320, 322, 326, 327 Thompson, Susanâ•… 280, 281, 282, 288, 294 Tomasello, Michaelâ•… 15, 218, 366 Torres Cacoullos, Renaâ•… 281, 282, 283, 288, 293, 294, 295 Tottie, Gunnelâ•… 382, 383 Traugott, Elisabethâ•… 146, 281 Tribushinina, Elenaâ•… 122 Tryon, Robertâ•… 406 Tsohatzidis, Savasâ•… 19, 23 Tuggy, Davidâ•… 10, 19 Tummers, Joséâ•… 9, 101, 205, 324 Turner, Markâ•… 13 Tyler, Andreaâ•… 17, 19, 120 V Vainik, Eneâ•… 254 Van Belle, Williamâ•… 40, 48 Van Bogaert, Julieâ•… 309 Van der Leek, Frederikeâ•… 63, 64 Van der Zee, Emileâ•… 265 Van Langendonck, Willyâ•… 40, 48 Van Peer, Willieâ•… 316 Vandeloise, Claudeâ•… 17, 19, 20, 265, 268 Vanhove, Martineâ•… 88 Vanparys, Janâ•… 19 Venables, Williamâ•… 318, 319, 325, 326, 454 Vendler, Zenoâ•… 191, 225, 236

Verdonik, Darinkaâ•… 310 Verhagen, Arieâ•… 48, 205, 207, 209, 210, 215 Verschueren, Jefâ•… 10, 19 Victorri, Bernardâ•… 10, 26 von Eye, Alexanderâ•… 318, 322, 325, 326 Vorkachev, Sergeyâ•… 12 Vorlat, Emmaâ•… 22 W Walker, Cindyâ•… 321, 322 Walker, Jamesâ•… 281, 282, 288, 293, 294 Ward, Joeâ•… 163 Wasow, Thomasâ•… 259, 260, 262 Wedderburn, Robertâ•… 487, 505 Weller, Susanâ•… 444, 482 Wichern, Deanâ•… 408 Wiebe, Janyceâ•… 310 Wiechmann, Danielâ•… 147, 316 Wiener, Matthewâ•… 326 Wierzbicka, Annaâ•… 10, 12, 19, 224, 225 Williams, Robertâ•… 488 Wilson, Dianaâ•… 367 Wilson, Edwinâ•… 487 Wong, Mayâ•… 325 Worcester, Janeâ•… 487 Wulff, Stefanieâ•… 27, 201, 254, 259, 309, 310, 316, 318, 319, 403 Z Zawada, Brittaâ•… 19, 88, 325 Zelinsky-Wibbelt, Corneliaâ•… 19 Zeschel, Arneâ•… 309 Zhao, Yanchangâ•… 326 Zlatev, Jordanâ•… 16, 19, 119, 310

Subject index

A Access (software)â•… 345 ade4â•… 326, 452, 477 Adessive caseâ•… 253–275 adpositional constructionâ•… 253–275 agglomeration methodâ•… see linkage algorithm Agglomerative algorithmsâ•… see linkage algorithms agnesâ•… 326, 423, 425, 428–430, 433, 439, 440 AICâ•… see Akaike’s information criterion Akaike’s information criterionâ•… 136, 211, 212, 213, 218, 508, 510 amapâ•…439 anacorâ•… 326, 449, 452, 474– 476, 479 anovaâ•… 385–387, 511, 512 aodâ•…326 apeâ•… 480, 481 as.distâ•… 438, 439 as.numericâ•… 509, 513 average linkageâ•… see linkage algorithms B Base (software)â•… 345 behavioural-profile approachâ•… see multifactorial usagefeature analysis binary correspondence analysisâ•… see correspondence analysis binary logistic regressionâ•… see logistic regression binomial logistic regressionâ•… see binary logistic regression, under regression analysis binomial testâ•… 147, 165, 315 biplotâ•… 317, 318, 447, 448, 454, 455, 458–460, 464, 465, 472, 478, 479, 780

bootstrap resamplingâ•… 99, 138, 163, 164, 319, 434, 480, 481 bootstrap validationâ•… see bootstrap resampling BP approachâ•… see multifactorial usage-feature analysis Burt matrixâ•… 134, 239, 449, 450, 470, 471, 474 C c-score, goodness-of-fit, underâ•… see c-statistic caâ•… 326, 361, 362, 447, 452, 454, 466, 467, 470, 472, 474, 480 Calc (software)â•… 345 canonical correspondence analysisâ•… see correspondence analysis carâ•…387 categorical dataâ•… 94, 226, 314, 315, 319–321, 324, 326, 349, 352, 355, 358, 366, 367, 369, 371, 409–411, 413, 414, 416, 418, 421, 438, 443, 446, 478, 489, 490, 495, 502, 503, 505, 519, 520 categorical variablesâ•… see categorical data causative constructionâ•… 12, 21, 67, 165, 205–219 cbindâ•… 354, 357 cfaâ•…326 cfa2â•…326 cforestâ•…326 Chi-square automatic interaction detection (CHAID)â•… 105, 106 Chi-squared testâ•… 132, 138, 147, 151, 156, 169, 259, 266, 309, 315, 318, 325, 370–381, 445, 446, 462, 463, 511 chisq.testâ•… 370, 373, 374, 376, 378, 281, 462

city block distanceâ•… see Manhattan, under distance measures claraâ•… 326, 428 clmâ•…327 classification and regression tree analysis (CART) classification tree analysisâ•… 89, 99, 105–110, 213–218, 318–319, 325, 326, 531 random forest analysisâ•… 319, 324, 326, 531 regression tree analysisâ•… 213, 319 Clustan (software)â•… 93, 94 clusterâ•…437–440 cluster analysis fuzzy cluster analysisâ•… 428 hierarchical agglomerative cluster analysisâ•… 91–101, 126, 228, 129, 132, 148, 157–159, 162, 163, 164, 192–195, 201, 226, 227, 234, 238, 245–247, 316, 217, 325, 326, 405–441, 478–482 k-means cluster analysisâ•… 316, 326, 422, 427, 428, 430 k-medoid cluster analysisâ•… 428 cluster.statsâ•…432 clustering algorithmsâ•… see linkage algorithms cmdscaleâ•… 326, 433, 440 coefficients (logistic regression)â•… see estimated coefficients of predictors Cognitive Linguisticsâ•… 7–10, 13, 16 –18, 21, 22, 25, 26, 187, 206, 309, 310, 311, 405, 482 Cognitive Semanticsâ•… 7, 17, 18, 19, 21, 22, 24–26, 28, 117–120, 158, 173, 205

542 Corpus Methods for Semantics

collexeme analysisâ•… see collostructional analysis collinearityâ•… see multicollinearity collostructional analysis collexeme analysisâ•… 62–63, 65–67, 70, 72–73, 75–76, 82, 84, 147, 154, 156–164, 168, 393–397 covarying-collexeme analysisâ•… 315, 392, 400–403 distinctive collexeme analysisâ•… 147–148, 154, 157, 158, 162, 165–172, 201, 315, 392, 397–400 colnamesâ•… 351, 352, 353 complementationâ•… 229, 244, 247, 280–300, 382–387 complete linkageâ•… see linkage algorithms conative constructionâ•… 62–67, 81–84 confidence intervalsâ•… 99, 296, 298, 475, 501, 517 configural frequency analysisâ•… 135, 136, 138, 321, 324, 325, 236 Construction Grammarâ•… 42, 52, 63, 66, 151, 152, 173, 254, 392 contingency tableâ•… 66, 134, 148, 158, 345, 346, 350, 356–358, 446, 447, 453, 457, 463, 464, 469, 477, 481, 512 continuous dataâ•… 314, 318, 319, 324, 352, 358, 365, 366, 409, 411, 413, 416, 418–420, 433, 436, 477, 489, 490, 505, 519 correspondence analysis binary correspondence analysisâ•… 132–134, 240, 242, 326, 446, 448, 449, 451, 454–457, 461–467, 475–477, 479, 481 canonical correspondence analysisâ•… 449, 461, 474 detrended correspondence analysisâ•… 449, 477 multiple correspondence analysisâ•… 134, 226, 239, 317, 326, 382, 446, 448–450, 454, 457–460, 470–474, 477, 480, 481

corres.fncâ•… 461, 462, 465,

466, 469 correspâ•… 326, 454–456 count dataâ•… see categorical data covarying-collexeme analysisâ•… see collostructional analysis Cox and Snell’s pseudo R2 statisticâ•… see goodness-of-fit cross-tabulationâ•… see contingency table ctreeâ•…326 D

datadistâ•… 510, 520 dataframeâ•… 344–354, 356–358, 365, 453 decision tree analysisâ•… see classification tree analysis, under classification and regression tree analysis degree modifiersâ•… 146–164, 173–174 degrees of freedomâ•… 44, 49, 106–108, 137, 169, 195, 381, 509, 511, 528 dendrogramâ•… 92, 93, 95–99, 128–131, 148, 158, 163, 164, 193–195, 316, 422–427, 478–481 Designâ•…327 detrended correspondence analysisâ•… see correspondence analysis deviance residualsâ•… see residual deviance dianaâ•…428 dichotomous logistic regressionâ•… see binary logistic regression, under regression analysis discrete dataâ•… see categorical data dissimilarity matrixâ•… see distance measures distâ•… 423, 436–438, 440, 480, 481 distance measuresâ•… 92, 128, 130, 163, 193 Canberraâ•… 130, 131, 163, 192 Euclideanâ•… 128–130, 163, 417–420, 426, 427, 437, 438, 446, 480

Mahalanobisâ•… 417, 420, 421, 437, 438 Manhattan (City-block)â•… 131, 417–420, 433, 436–438 phi square (mean square)â•… 92, 94 distinctive collexeme analysisâ•… see collostructional analysis divisive algorithmsâ•… 426–428 drop1â•… 522, 525 Dunning’s log-likelihood ratioâ•… 161 Dxyâ•… see Somers’ Dxy under goodness-of-fit DynGraph (software)â•… 169, 477 E estimated coefficients (of predictors / log odds ratios)â•… 101–103, 136–139, 211–213, 215, 218, 244, 273, 274, 289, 292– 299, 384–387, 507, 519–527 estimates (logistic regression)â•… see estimated coefficients of predictors Euclidean distanceâ•… see distance measures Excel (software)â•… 345, 347, 453, 457, 463, 464 F

FactoMineRâ•… 169, 326, 452,

458, 477, 482

factorâ•… 352, 355 fannyâ•…428

FileMaker (software)â•… 345 Fisher-Yates exact testâ•… 54, 66, 68, 147, 156, 165, 244, 267, 309, 315, 325, 371, 395 fisher.testâ•…371 fpcâ•… 326, 432 frequency dataâ•… see categorical data frequency tableâ•… see contingency table Functional Linguisticsâ•… 8–13, 308, 310 furthest neighbour linkageâ•… see complete linkage, under linkage algorithms fuzzy cluster analysisâ•… see cluster anlaysis

Subject index 543



Fuzzy Set Theoryâ•… 26, 27, 119, 150, 153, 181, generalized linear modelsâ•… see regression analysis G

glmâ•… 326, 327, 383, 384, 505–507,

509, 510–513, 515–517, 520, 524

glmmPQLâ•…327

Goldvarb X (software)â•… 488 Goodman-Kruskal’s Gammaâ•… see goodness-of-fit goodness-of-fit c-statisticâ•… 104, 136, 137, 212, 243, 244, 273, 289, 515 Cox and Snell’s pseudo (generalised) R2 statisticâ•… 104, 105, 515 Goodman-Kruskal’s Gammaâ•… 212 Hosmer-Lemeshow-Cessie testâ•… 104, 105, 212, 528 log likelihood ratio test (–2 log likelihood)â•… 104, 105, 137, 212, 509, 511, 521, 522 McFadden’s pseudo (generalised) R2 statisticâ•… 138, 213 Nagelkerke’s pseudo (generalised) and adjusted R2 statisticâ•… 105, 137–140, 196, 243, 291, 511, 515 Somers’ Dxyâ•… 212, 273, 514 Gower universal similarity coefficientâ•… 418, 420–422, 437, 438 H

hcfaâ•…326 hclustâ•… 129, 130, 163, 326, 423,

431, 433, 440, 441, 479–481

headâ•… 348, 505, 506, 513, 514, 519

hierarchical agglomerative cluster analysis (HAC)â•… see cluster analysis hierarchical modellingâ•… see mixed-effects logistic regression, under regression analysis homalsâ•… 452, 476, 477

homogeneity analysisâ•… see indicator multiple correspondence analysis, under correspondence analysis Hosmer-Lemeshow-Cessie testâ•… see goodness-of-fit I indicator multiple correspondence analysisâ•… see correspondence analysis inertiaâ•… 46, 53, 133, 134, 170, 239, 240, 446, 447, 449–451, 461, 465, 467–474, 476 interceptâ•… 215, 218, 384, 491, 498–500, 503, 504, 507–509, 511, 521, 522 J Jacard coefficientâ•… 414, 416, 436, 437 joint multiple correspondence analysis (search for joint)â•… see correspondence analysis K k-means cluster analysisâ•… see cluster analysis klaRâ•…326 kmeansâ•…326 L

languageRâ•… 452, 460–462, 465,

466, 469, 479

ldaâ•…326 levelsâ•… 355, 506

linear discriminant analysisâ•… 216, 318, 319, 326 linear regressionâ•… see regression analysis linkage algorithms average linkageâ•… 94, 424–426, 439, 480 complete linkage (furthest neighbour)â•… 94, 424–426, 439 single linkage (nearest neighbour)â•… 94, 129, 194, 423, 424

Wardâ•… 92, 94, 130, 163, 246, 428, 431–434, 440, 480–481 listâ•… 369, 373–375, 378, 381, 526, 527 lme4â•…327 lmerâ•… 218, 327 log likelihood ratio testâ•… see goodness-of-fit log likelihood test (–2 log likelihood)â•… see log likelihood ratio test under goodness-of-fit log oddsâ•… 221, 215, 494 log odds ratiosâ•… see estimated coefficients of predictors logistic regressionâ•… see regression analysis logitsâ•… 493–495, 497, 498, 531 loglinear analysisâ•… 174, 321, 325, 326, 475 loglmâ•…326 lrmâ•… 327, 505, 510, 511, 515, 516, 518, 520, 521, 524, 528 M Mahalanobis distanceâ•… see distance measures Manhattan distanceâ•… see distance measures Marascuilo procedureâ•… 378, 379, 380 MASSâ•… 288, 326, 327, 454, 456– 458, 479, 480 matching coefficientâ•… 414–417, 437 MATLAB (software)â•… 323 matrixâ•… 369, 373–375 MCAâ•…326 mcaâ•… 326, 457, 458 McFadden’s pseudo R2 statisticâ•… see goodness-of-fit MCMCglmmâ•…327 MCMClogitâ•…327 MCMCpackâ•…327 McNemar’s Paired Chi-squared test mergeâ•…354 MI Scoreâ•… see mutual information score

544 Corpus Methods for Semantics

mixed effectsâ•… see mixed-effects logistic regression under regression analysis mixed modelâ•… see mixed-effects logistic regression under regression analysis mixed-effects logistic regressionâ•… see regression analysis mjcaâ•… 326, 470–474, 480 mlogitâ•…327 monaâ•…428 mosaic plotâ•… 525, 526 multicollinearityâ•… 136, 138, 139, 243, 272, 273, 289, 528 multidimensional scalingâ•… 317, 325, 326, 406, 440, 468 multifactorial usage-feature analysis (also behaviouralprofile approach)â•… 118–123, 124, 125, 135, 161, 180, 186, 192, 195, 200, 201, 224, 226, 236, 309–311 multilevel logistic regressionâ•… see mixed-effects logistic regression, under regression analysis multilevel modellingâ•… see mixed-effects logistic regression, under regression analysis multinomâ•…327 multinomial logistic regressionâ•… see regression analysis multiple correspondence analysisâ•… see correspondence analysis multiple logistic regressionâ•… see logistic regression, under regression analysis multiway frequency analysisâ•… see loglinear analysis mutual information scoreâ•… 147, 149, 151, 156, 309, 316, 325 N Nagelkerke’s adjusted pseudo R2â•… see R2 score Nagelkerke’s pseudo R2 statisticâ•… see goodness-of-fit nearest neighbour distanceâ•… see single linkage algorithm, under linkage algorithms

njâ•… 480, 481 nnetâ•…327

Nominal dataâ•… 226, 314, 322, 369, 410, 414 NotePad (software)â•… 345 Numbers (software)â•… 345 Numerical variablesâ•… see continuous data O odds ratiosâ•… 53, 54, 78, 82, 101–103, 211, 215, 267, 371, 372, 493–495, 498, 503, 514, 516, 517, 521, 522 operationalisationâ•… 9, 13–15, 22, 27, 73, 118, 119, 122, 123, 135, 139, 208, 215–217, 258, 259, 262, 282, 311, 407, 408, 444 ordered dataâ•… see ordinal data ordered multinomial logit regressionâ•… see ordinal logistic regression, under regression analysis ordinalâ•…327 ordinal dataâ•… 100, 314, 323, 409–412, 418, 530, 531 ordinal dataâ•… 100, 314, 323, 409, 410, 411, 418, 530, 531 ordinal logistic regressionâ•… see regression analysis overdispersionâ•… 508, 527, 528 P

pamâ•…428 pamctdpâ•… 452, 477, 478 pamkâ•…326 parâ•…358 partyâ•… 326, 477

Pearson residualsâ•… 44, 46, 52, 58, 59, 132, 138, 238, 239, 259, 263, 370, 373, 374, 377, 462, 463 periphrastic causativesâ•… 165, 207 PhyloClustâ•…481 phylogenetic tree plotâ•… 480, 481 plotâ•… 359, 439, 440, 454, 455, 457, 458, 461, 467, 473, 481, 518, 522, 525, 526 Poisson regressionâ•… see regression analysis polrâ•…327

polychotomous logistic regressionâ•… see multinomial logistic regression, under regression analysis polytomousâ•…327 polytomous logistic regressionâ•… see multinomial logistic regression, under regression analysis predictâ•… 509, 512, 513, 526, 527 predictor estimates / coefficients (logistic regression)â•… see estimated coefficients of predictors prettyâ•… 145, 6, 148, 149, 152, 157, 159–175 prop.tableâ•… 380, 381 proportional odds logistic regressionâ•… see ordinal logistic regression, under logistic regression proportional odds regressionâ•… see ordinal logistic regression, under regression analysis proportionsâ•… 376, 492, 493, 494, 495, 496, 497, 498, 500, 503, 512, 518, 522, 523 proportions testâ•… 315 prototype effectsâ•… 9, 13–16, 18, 25, 26, 62, 88, 117–128, 136, 138, 139, 141, 206, 216, 217, 219 Prototype Set Theoryâ•… see prototype effects pvclustâ•… 163, 164, 326, 431, 433, 434, 440, 441, 479–481 pvrectâ•… 434, 440 Q

quasipoisâ•…326

R R (software)â•… 312, 313, 324–328, 343–345, 362–364, 368–369, 395, 437, 444, 482, 505 radial network analysisâ•… 18, 24, 26, 27, 118–120, 123 randomForestâ•…326 rbindâ•…354 rdaâ•…326 read.tableâ•… 344, 347, 348 receiver operating characteristic curveâ•… see c-statistic

Subject index 545



regression analysis binary logistic regressionâ•… 136–141, 193, 195–200, 210–213, 321, 322, 325, 327, 243–245, 272–274, 289–299, 382, 488–530 generalized linear modelsâ•… 383, 505, 508, 531 linear regressionâ•… 314, 382, 383, 489–494, 496–499, 501, 515 mixed-effects logistic regressionâ•… 288, 323, 325 multinomial logistical regressionâ•… 135, 187, 322, 323, 325, 327, 382, 488, 530 ordinal logistic regressionâ•… 323, 325, 327, 530, 531 Poisson regressionâ•… 322, 382–387, regression tree analysisâ•… see classification and regression trees analysis relevelâ•… 355, 506 residual devianceâ•… 507, 508, 511, 520, 527, 528 residualsâ•… 491, 492, 501, 507, 515 see also residual deviance and Pearson residuals rmâ•…351 rmsâ•… 137, 327, 505 ROCâ•… see c-statistic under goodness-of-fit rpartâ•…214, 326

S SAS (software)â•… 313 scaleâ•…420 semantic classâ•… 62, 63, 66, 70, 73, 75, 147, 158, 161, 175, 209, 215, 218 sentiment analysisâ•… 310 silhouetteâ•…440 silhouette plotâ•… 433 silhouette validation techniqueâ•… 139, 194, 432, 433, 434 similarity measureâ•… see distance measures single linkageâ•… see linkage algorithms smacofâ•…326 smacofSymâ•…326 sociolinguisticsâ•… 117, 158, 321, 406, 488, 532 Somers’ Dxyâ•… see goodnessof-fit SPSS (software)â•… 93, 94, 100– 102, 105, 106, 111, 313, 322, 323 Stata (software)â•… 313, 322, 323 Statistica (software)â•… 313 statistical significanceâ•… 75, 78, 98, 104, 107, 127, 135, 138, 244, 273, 315, 321, 444, 448, 475 statsâ•… 326, 436, 437 strâ•…349 subsetâ•…354 summaryâ•… 348, 349, 355, 360

T tâ•… 350, 440, 441, 461, 481 t-scoreâ•… 147, 309, 316, 325 tableâ•… 356, 357, 513 tabular dataâ•… see categorical data TextEdit (software)â•… 345 TextWrangler (software)â•… 345 titleâ•… 461, 469 treeâ•…326 U underdispersionâ•… 387, 527 usage-feature analysisâ•… see multifactorial usagefeature analysis V VARBRUL (software)â•… 488, 532 variance inflation factorâ•… 136, 137, 244, 273, 289, 528 veganâ•… 449, 452, 477 vifâ•…528 vifâ•… see variance inflation factor ward algorithm, see linkage algorithms W WordGen (software)â•… 42 WordPad (software)â•… 345 Wordsmith (software)â•… 284 Z z-scoreâ•… 93, 309, 316, 325 X χ2 testâ•… see Chi-squared test