Time Series Analysis of Discourse: Method and Case Studies [1 ed.] 9781138584631, 9780429505881, 9780367732677

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Time Series Analysis of Discourse

This volume serves as a comprehensive introduction to time series analysis (TSA), used commonly in financial and engineering sciences, to demonstrate its potential to complement qualitative approaches in discourse analysis research. The book begins by discussing how time has previously been conceptualized in the literature, drawing on studies from variationist sociolinguistics, corpus linguistics and critical discourse analysis. The volume then segues into a discussion of how TSA is applied in other contexts in which observed values are expected to be dependent on earlier values, such as stock markets and sales figures, and introduces a range of discourse-specific contexts to show how the technique might be extended to analyze trends or shed further light on relevant themes in discourse over time. Each successive chapter features a different discourse context as a case study, from psychotherapy sessions to university lectures and news articles and looks at how studying different variables over time in each context – ­metaphors, involvement markers, and keywords, respectively – can contribute to a greater understanding of both present and future discourse activity in these settings. Taken together, this book highlights the value of TSA as a complementary approach to meaning-based analysis in discourse, making this ideal reading for graduate students and scholars in discourse analysis looking to employ quantitative methods in their research practice. Dennis Tay is an Associate Professor in the Department of English, The Hong Kong Polytechnic University. His research interests include cognitive linguistics, discourse analysis, mental healthcare communication and the statistical modeling of discourse.

Routledge Studies in Linguistics

12 Relational Semantics and the Anatomy of Abstraction Tamar Sovran 13 Language Contact and the Origins of the Germanic Languages Peter Schrijver 14 Metonymy and Language A New Theory of Linguistic Processing Charles Denroche 15 A Forensic Linguistic Approach to Legal Disclosures ERISA Cash Balance Conversion Cases and the Contextual Dynamics of Deception James F. Stratman 16 Conceptual Conflicts in Metaphors and Figurative Language Michele Prandi 17 The Language of Pop Culture Edited by Valentin Werner 18 Perspectives from Systemic Functional Linguistics Edited by Akila Sellami-Baklouti and Lise Fontaine 19 Time Series Analysis of Discourse Method and Case Studies Dennis Tay For more information about this series, please visit: https://www. routledge.com/Routledge-Studies-in-Linguistics/book-series/SE0719

Time Series Analysis of Discourse Method and Case Studies

Dennis Tay

First published 2019 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN and by Routledge 52 Vanderbilt Avenue, New York, NY 10017 Routledge is an imprint of the Taylor & Francis Group, an informa business © 2019 Taylor & Francis The right of Dennis Tay to be identified as author of this work has been asserted by him in accordance with sections 77 and 78 of the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. Library of Congress Cataloging-in-Publication Data A catalog record has been requested for this book ISBN: 978-1-138-58463-1 (hbk) ISBN: 978-0-429-50588-1 (ebk) Typeset in Times New Roman by codeMantra

Contents

1 Time in discourse analysis 1 2 The basic logic and process of TSA 18 3 Case study 1: metaphor in psychotherapy sessions 48 4 Case study 2: non-informational language in university lectures 70 5 Case study 3: thematic keywords in newspaper discourse 93 6 Summary, limitations and future directions 108 Index 121

1 Time in discourse analysis

What is discourse analysis? Language is often researched at two broad levels. The first level lies “within the sentence” and describes the more stable rules and properties of a language such as its speech sounds, word meanings and grammar. The second level is about how people use language to achieve various objectives in everyday life. The study of pragmatics, for example, considers how usage contexts contribute to meaning. Another closely ­related area is the study of discourse. In general, discourse research goes “beyond the sentence” to examine the dynamic ways in which language influences and gets influenced by various aspects of social life. There are many examples of basic linguistic “building tasks” (Gee, 2005) to create everyday social reality such as the ­enactment of activities, construction of identities and establishment of connections between people and objects. They are manifest in a diverse range of contemporary settings from newspaper articles to social media, and doctor–patient communication to university lectures. The forms and structures of discourse that enable and are shaped by these tasks are likewise diverse. A cursory list of widely studied examples includes anaphora, coherence, speech acts, turn-taking, topics, syntactic structures, politeness, metaphor, rhetoric and so on (Van Dijk, 2011). Some discourse analysts limit themselves to documenting and describing these phenomena and their functions, while others take a more critical approach to explore how language is linked to wider sociopolitical i­ssues like sexism, racism and environmentalism. The advent of new media technologies that enable multiple and often simultaneous modes of meaning making such as images, film and music has also significantly expanded the scope and complexity of discourse research (Bateman, 2014; O’Halloran, 2011). Painting an integrated picture of the multiple branching pathways of discourse research has itself proven to be a challenging endeavor (­Johnstone, 2008; Van Dijk, 2011; Wetherell, Taylor, & Yates, 2001).

2  Time in discourse analysis Nevertheless, we can venture to say with some risk of oversimplification that the basic objective of much of discourse research is to understand the relationship between two conceptually independent things. One of these things is the observed forms, structures and functions of discourse, and the other is the social context of their occurrence. An important aspect of this relationship is how discourse and society change with the passage of time. Consider how social processes evolve over different time scales. Attitudes toward a conversational partner can shift in a matter of seconds or less, while the formation and shaping of political ideologies often take decades and even centuries. The big question frequently asked by discourse analysts is how these changes are mirrored in corresponding shifts in language use, or how language and discourse change might itself be responsible for triggering social change. Therefore, there has always been at least a trace of a chronological or diachronic perspective across the numerous varieties of discourse analysis. I begin by giving a brief overview of this chronological perspective in three major discourse-related research approaches – variationist sociolinguistics, corpus-assisted discourse studies and critical discourse analysis (CDA). Research falling under these approaches overlaps in terms of foci and methodologies, and collectively illustrates the many advances that have been made in our attempt to understand discourse across time. Besides pointing out these advances, the more important present purpose is to highlight several limitations and issues with this body of work. The discussion eventually leads to the introduction of the subject matter of this book, the complementary methodology of time series analysis (TSA).

Time in variationist sociolinguistics The study of relationships between language, discourse, culture and society is known as sociolinguistics. One of its branches, “variationist sociolinguistics”, focuses on how language and discourse vary along social variables that characterize speakers such as age, gender, social class and time periods. The key idea is that language varies due to social conditioning and does so in surprisingly systematic ways. These patterns of variation are traditionally analyzed in terms of quantitative relationships between linguistic and social variables (Labov, 1963, 1969, 1972). The classic example is William Labov’s comprehensive description of how pronunciation varied with one’s social standing in New York City in the 1960s. In a series of pioneering studies, Labov demonstrated that the frequency of variable final or p ­ reconsonantal /r/ correlated positively with the level of social prestige implicitly asserted

Time in discourse analysis  3 by speakers. Gradually, qualitative analyses of related issues, such as attitudes and perceptions, and strategic management of these language and discourse differences also became significant (Eckert, 2000; ­Milroy, 1980). Penelope Eckert’s (2000) exemplary ethnographic study of “jocks” and “burnouts” in a high school setting showed that speakers actively make use of these differences to construct fluid social identities and manage relationships. Time becomes an explicit factor in sociolinguistics research when we consider things like the age of speakers, or significant historical events, as socially conditioned sources of language variation and change. The variation can sometimes be rather subtle and puzzling. For example, it seems difficult to offer a plausible explanation for why young ­Canadians are more likely to say it’s so cold today, while ­m iddle-aged speakers prefer it’s really cold (Tagliamonte, 2012). Likewise, for some reason, adolescents in Glasgow use significantly less “discourse lubricants” like you know and I mean than adults (­Macaulay, 2005). The causes and repercussions of language change are at other times far more ­drastic and spun into a web of complex sociopolitical developments. An example is the nationwide reform of the writing ­system in China in the mid-20th century, which is an inextricable part of broader political reform (Ping, 1999). The significance of time in variationist sociolinguistics is also ­underlined at the fundamental level of methodology. A clear example is the long-standing debate between the “real-time” and “apparenttime” approaches to studying language variation and change. Returning to the examples above, to confirm if certain language preferences have changed across generations in Canada and Glasgow, a plausible method would be to collect data across actual historical time periods and compare speakers of similar age groups. If we call this the “real-time” approach, variationist sociolinguists have proposed an intriguing alternative known as the “apparent-time” approach. This means to compare language patterns between different age groups at a common moment in time. The underlying assumption is that ­linguistic habits become stable after a certain age. Old people are still ­speaking in the same ways as when they were young, and thus differences with young people today suggest a genuine change across generations. The apparent-time approach enjoys advantages such as easier data collection and sampling control. However, although there is often a good match with real-time data, it has been criticized for underestimating “age-graded changes”, i.e. changes that happen across certain phases in life and are repeated in subsequent generations (Boberg, 2004; Sankoff & Blondeau, 2007). Our present concern is not with the

4  Time in discourse analysis relative merits of either approach (see Cukor-Avila & Bailey, 2013 for a comprehensive review), but rather to observe two points stemming from the discussion. The first is that time is of primary interest in sociolinguistic studies of language and discourse. The variable of time is often explicitly factored into research designs, even generating its own strand of methodological debate. However, this interest is noticeably inclined toward the gradual evolution of language and discourse over a long period, often a generation of speakers or more. Although relatively spontaneous contexts like face-to-face interaction are also a key focus for researchers who have come to identify themselves as “interactionist sociolinguists” (Gumperz, 1982), the question of how language and discourse features shift in such compressed time frames has not been asked to the same extent. In fact, if we were to compare gradual change patterns across generations with the more dynamic shifts characteristic of spontaneous interaction, the latter is likely to throw up intricacies that require a different method of analysis.

Time in corpus-assisted discourse studies Corpus linguistics has undergone rapid developments in recent decades to establish itself as a key approach to the study of language and discourse. Its main feature is the computer-aided processing and analysis of textual data on ever-growing scales (Wiedemann, 2013), which allows researchers to infer general patterns of language use (Gray & Biber, 2011) while not sacrificing attention to multiple specific instances. The particular r­ elevance of corpus linguistic techniques to discourse analysis is highlighted by researchers who refer to their work as “corpus-assisted discourse studies”. This is defined as “the investigation and comparison of features of particular discourse types, integrating into the analysis, where appropriate, techniques and tools within corpus linguistics” (­Partington, 2010:88). From this perspective, corpus linguistics can be seen as a methodological toolkit rather than a specific field of inquiry (Baker, 2006; McEnery & Hardie, 2012). The most common techniques that can s­ upport discourse research include keyword analysis, which ­uncovers relative over/underuse of specific words in a corpus, and concordance analysis, which highlights phenomena of interest as they are exactly used in context. Corpus techniques have been applied to descriptive and comparative studies of all kinds of things like grammar (Leech, Hundt, Mair, & Smith, 2009), ­humor (Holmes & Marra, 2002) and ­figurative ­language (­Stefanowitsch & Gries, 2006), and in domains ranging from education (Biber, 2006) to m ­ edia (Bednarek, 2006) and healthcare (Semino, D ­ emjén, Hardie, Payne, & Rayson, 2018), just to name a few.

Time in discourse analysis  5 The time factor is likewise a primary focus of what has come to be known as “diachronic corpus-based studies”. Many widely used corpora such as the Helsinki Diachronic Corpus of English Texts and ARCHER (A Representative Corpus of Historical English Registers) are in fact built specifically to study language and discourse change. Like-minded researchers working with smaller self-built corpora follow the similar approach of segmenting their datasets into sub-­c orpora each representing a particular time interval (Bamford, Cavalieri, & ­Diani, 2013). These intervals can range from months to years to decades depending on the context at hand. A common way to study change is to identify language and discourse features of interest, tabulate their frequencies within each sub-corpus and compare these frequencies between sub-corpora for evidence of significant differences. Partly due to the nature of most corpus software programs that allow quick identification and cross-corpora comparison of discrete lexical units, the most widely used procedure to determine change is the log-likelihood significance test (see Oakes, 1998). This essentially measures the degree of association between two categorical variables. In the case of diachronic corpus studies, one variable is the language or discourse feature X under investigation, which is defined by the two categories X and non-X. That is to say, every lexical unit in the corpus is either X or not. The other variable is time, arbitrarily defined by the time intervals underlying the sub-corpora, for example decade A and decade B. The resulting log-likelihood or LL score suggests whether the difference in occurrence of X versus non-X across the two time periods is more likely an outcome of chance (LL < 3.84) or genuine change (LL ≥ 3.84 at the standard significance level of 0.05). Although it is technically possible to extend both the language/discourse and time variable to more than two categories to study change over multiple periods, most diachronic corpus-based studies appear to be limited to investigating just two successive periods at once. Another noteworthy but seldom mentioned point is that since time is defined as a categorical variable, its constituting periods must fulfill the assumption of being independent categories. The assumption of independence is often explained in statistics textbooks as meaning that each data unit should only fall under one category per variable. In most cases, this is unproblematic because a language or discourse unit can neither be both X and non-X, nor occur at two time periods at once. However, strict independence also requires that “no case carries more than random information about any other case” (von Eye & Mun, 2013:9). This means that a certain unit should not exert more than random

6  Time in discourse analysis influence on how another unit is categorized, across either variable. If we consider the language/discourse variable, there is some doubt over whether this is a realistic assumption to make given the ecological or “intertextual” nature of many discourse contexts (Kilgarriff, 2001). Similarly, considering the time variable, we can think of cases where the frequency of occurrence at time A is likely to influence the corresponding frequency at time B in some way. The presence of internal relationships within temporally ordered observations is generally known as autocorrelation, a statistical phenomenon seldom discussed in language research (Koplenig, 2017). We shall discuss autocorrelation and its implications in much more detail, but for now it is adequate to acknowledge its importance when studying the time factor in discourse.

Time in critical discourse analysis The relationship between discourse phenomena and the social world is perhaps most explicitly theorized by exponents of the paradigm known as critical discourse analysis (CDA). This relationship is described as dialectical: on the one hand, (these) situational, institutional, and social contexts shape and affect discourse, on the other hand discourses influence social and political reality. In other words, discourse constitutes social practice and is at the same time constituted by it. (van Leeuwen & Wodak, 1999:92) At first glance, the above characterization sounds just like our general understanding of discourse and social processes as two things informing each other. What makes CDA unique and “critical” is its explicit focus on the notions of ideology and power – how they shape language, and how language in turn (re)produces dominant ideologies and power relations in everyday social life (Fairclough, 2013). Therefore, while a sociolinguist may simply be interested in describing gender differences in the use of discourse features, CDA practitioners go further to critically consider how these differences reveal or even perpetuate the social construction of gender. Gee (2005:26) succinctly describes this type of perspective as assuming that language use always comes with “other stuff”. CDA is thus best conceived as a general “approach, position, or stance” (Van Dijk, 1995:17) that makes use of different research methodologies including those in sociolinguistics and corpus lin­g uistics (Baker, Gabrielatos, Khosravinik,

Time in discourse analysis  7 Mcenery, & Wodak, 2008). Rather than outlining a general methodological approach, the strongest thread of consistency within CDA research is its emancipatory outlook and advocacy for social change. Despite the general clarity of this conceptual thrust, the precise correspondences between discourse and social phenomena are often painted with broad and varied strokes by different CDA practitioners. This is apparent from Wodak and Meyer’s (2009:22) conceptual summary of different ways of doing CDA. The authors situate various CDA approaches along two perpendicular clines called linguistic operationalization and level of social aggregation. The first cline spans from “broad” to “detailed”, while the second has “agency” and “structure” as its two ends. The socio-cognitive approach (Van Dijk, 2009), for instance, considers communicative elements in the broadest contextually defined sense and their relationship with individual cognitions of social reality. It is therefore placed at the “broad” and “agency” ends of the clines. In contrast, the discourse-historical approach (Reisigl & Wodak, 2001) examines specific linguistic realizations and their “decisive role on the genesis, production, and construction of certain social conditions” (van ­Leeuwen & Wodak, 1999:92). It therefore occupies a place at the “detailed” and “structure” ends. A pioneering study under this approach examined linguistic manifestations of racial prejudice in various genres of public discourse in the 1986 Austrian presidential campaign. However, the ­linguistic and discourse data were not only analyzed on their own terms, but also as ostensible evocations of Austria’s complex anti-Semitic political history (Wodak et al., 1990). Regardless of their positions on the conceptual clines, it is this avowed emphasis on evolving social situations, institutions and structures as backdrops of discourse that brings the temporal dimension into focus for different CDA approaches. Reisigl (2017:53) outlines three ways in which CDA practitioners can relate discourse to history. Two of these are characteristically broad and open to multiple interpretations – taking a “discourse fragment” as a starting point and reconstructing its prehistory by relating the present to the past, as was the case with the Austrian example, and comparing how different social actors semiotically represent the past “with respect to claims of truth, normative rightness and truthfulness”. The third way is of special present interest because it simultaneously alludes to issues with time-based CDA analyses, and the complementary approach to be introduced in this book. In full, it suggests that A diachronic series or sequence of thematically or/and functionally connected discourse fragments or utterances is taken as a starting point, and their historical interrelationships are reconstructed

8  Time in discourse analysis within a specified period. This way, specific discourse elements can be related to each within a particular period of the past, e.g. a period of some months, years, decades, etc. (Reisigl, 2017:53) The systematicity implied by this approach would indeed be exemplary for CDA practitioners. For all the critical insights it has provided, CDA has been less explicit in showing how discourse phenomena can be traced across well-demarcated historical periods in ways that are replicable and connect meaningfully with qualitative explication. It is unclear, for example, where the empirical basis lies in asserting links between contemporary electoral discourse and historical events many decades prior. Non-replicability and the associated issues of non-representativeness and analytic inconsistency are in fact major objections raised by CDA critics (Widdowson, 2005). However, while some critics are hostile toward the fundamental assumptions of CDA (Hammersley, 1997), others openly discuss potential ways of addressing its perceived shortcomings, especially the impressionistic character of its methodologies (Breeze, 2011).

The case for time series analysis The above discussion not only highlights different interrelated approaches to time-based discourse analysis, but it also paints a collective picture of limitations summarized below: 1 Approaches taken by some critical discourse analysts to interpret discourse with respect to complex sociohistorical factors may fail to define and connect temporal variables to discourse variables in systematic and replicable ways. 2 On the other hand, approaches that make this connection clear have two tendencies. First, in sociolinguistic inquiry, the focus tends to be on language and discourse behavior over extended time frames (e.g. generations), with less attention to spontaneous changes in interactive discourse contexts. These spontaneous changes may form more intricate change patterns that require different analytical methods. 3 Second, studies using corpus linguistic techniques tend to limit the analysis of language and discourse change to a very small number of arbitrarily defined time intervals. The analyses also assume independence rather than possible interdependence among temporally ordered observations. These imply that the presence of autocorrelation between observations is usually overlooked.

Time in discourse analysis  9 The main aim of this book is to present and demonstrate TSA as a complementary methodological approach that can address these limitations. As its name suggests, TSA is the analysis of a series of observations made across time using statistical techniques. The quintessential example of a time series is stock prices, with their daily fluctuations capturing the attention of economists and investors alike. TSA methods have long been used in research and applied fields including science, engineering, economics and finance to understand many different kinds of phenomena along time scales ranging from seconds to decades (Vandaele, 1983). As the methods themselves evolve, they continue to attract promising new applications in areas like the psychological sciences (Jebb, Tay, Wang, & Huang, 2015). However, TSA remains virtually unexplored for humanistic phenomena like discourse, even though naturally occurring text and talk can often behave in very similar ways to canonical examples of time series. We will see that TSA bears some conceptual resemblance to statistical modeling techniques more common in applied linguistics such as linear regression. The single most important difference is that TSA assumes the interdependence of consecutive values, while linear regression focuses on independent cross-sectional data. In other words, rather than treating observations as separate outcomes under different levels of the independent variable(s), TSA considers how these outcomes are internally related with one another. The exact nature and implications of this feature will be elaborated in the next chapter. For now, we can assert that TSA is better at handling finer details in temporal patterns that can be expected to arise in different real-life discourse scenarios due to this interdependence. Consider the example shown in ­Figure 1.1 which we will revisit in due course. The phenomenon of interest is the number of metaphors used by a therapist and his client, plotted against 30 consecutive psychotherapy session intervals. Defined as the act of describing and potentially thinking of something in terms of something else (Semino, 2008), metaphor is a discourse phenomenon of interest to therapists because it facilitates the expression of difficult-to-describe feelings and performs other therapeutic functions like relationship building (Lyddon, Clay, & Sparks, 2001; Tay, 2017). A typical example is the thematic metaphorical description of various kinds of life experiences as a journey (Lakoff, 1993; Lakoff & J­ ohnson, 1999), as seen in expressions like we have come a long way and this opportunity is my ticket to success. Journey metaphors are indeed commonly used by therapists and clients to talk about issues ranging from relationships to careers to the therapeutic experience itself (Tay, 2011). The fact that therapists are supposed to guide and interact with their

10  Time in discourse analysis

Figure 1.1  U  se of metaphors across psychotherapy sessions.

clients in a progressive manner over multiple sessions strongly implies that what was said in the past influences what will be said in the future, resulting in the interdependence across sessions described earlier. Researchers often visually inspect their data prior to quantitative analysis to gain a useful intuitive sense of what can be expected. We can tell from a glance that Figure 1.1 is quite complex. There are many rises and falls from one interval to the next as well as a few consecutive periods where the frequency of metaphors remains constant. The temporal pattern is erratic and cannot be adequately handled by basic regression techniques, which might be one of the reasons why researchers prefer not to spend too much time investigating such patterns explicitly. They choose instead to focus on the substantive qualities and implications of the metaphors, even though the notion of client change is relevant in this context and could benefit from some discussion of discourse across time (Levitt, Korman, & Angus, 2000; Rowat, De Stefano, & Drapeau, 2008). We will see that the pattern in Figure 1.1 can in fact be satisfactorily described by a single basic equation otherwise known as a time series model. This equation relates the frequency of metaphor use at any interval to other calculable

Time in discourse analysis  11 elements. In turn, the “modelability” of this series points toward an underexplored kind of regularity underpinning the seeming spontaneity of metaphor as a therapeutic resource. We will also see how such regularities exist in other discourse contexts and what this implies for researchers and relevant practitioners. Time series models are mathematical in nature. The equations that define them are made up of parts that describe and connect corresponding components in the series at hand. Another important objective of this book is to explore, albeit with a speculative tone, the qualitative inflections of these models – a point that is almost never raised in their usual domains of application like engineering and finance. The key idea is that time series models and their components are interpretable in ways similar to other discourse analytic constructs. They have the potential to directly offer a new type of structural insight into discourse behavior over time. We can think of these models as “discourse signatures” of sorts, each providing an interpretative schema to classify and explain how and why different discourse phenomena behave in the ways they do. Just like standard regression models, we will also see that time series models allow the possibility of forecasting future values. The relevance and usefulness of forecasting discourse will be critically discussed in their respective contexts.

Overview and structure of this book This book will present three case studies from Chapters 3 to 5. Each chapter focuses on a distinct context and a salient discourse phenomenon therein. The case studies collectively demonstrate the feasibility of applying TSA to investigate the development of discourse across time, in ways which address the limitations of the existing approaches highlighted above. Each chapter also stands alone in drawing attention to specific time-related questions within that case study context. The structure of each chapter is similar. They start with some background information and a concise review on the context and phenomenon at hand, followed by a step-by-step application of TSA to sample datasets, and then a discussion of the findings and implications. The case study chapters will be preceded by a formal introduction to TSA in Chapter 2. The aim is to provide a basic but adequate understanding of its logic and process to discourse researchers who may not have a mathematics or statistics background. Different from most TSA textbooks, the intention here is to avoid equations and computational details as much as possible and focus on ideas relatable to discourse analysis. This introduction will equip readers for the upcoming

12  Time in discourse analysis chapters and perhaps use TSA for their own work. There are many different TSA approaches, but the introduction will be limited to the widely used Box–Jenkins method (Box, Jenkins, Reinsel, & Ljung, 2015), and the simple univariate case of modeling just one variable at a time. I will advance the overarching “discourse as time series” argument and suggest that discourse phenomena are analogous to traditional TSA phenomena when viewed in terms of the major time series components of trends, seasons, cyclic movements and irregular fluctuations. With close reference to a hypothetical time series, I will then explain the key concepts of autocorrelations, the different types of time series models collectively known as ARIMA (autoregressive integrated moving average) models, fitting models to the data and using them to forecast future values. I will also briefly discuss different statistical software programs for TSA and provide some sample code for basic analysis. Chapter 3 presents the first case study on the use of metaphors in psychotherapy talk. We already saw from the brief example above how metaphor use is of interest to mental health practitioners and discourse analysts alike, with the existing research not paying enough attention to the temporal development of metaphor use. Besides showing how TSA sheds new light on the seemingly erratic distribution of metaphors in this highly spontaneous discourse activity, I suggest how it can be used for comparative purposes to study metaphor use between different therapy paradigms. In Chapter 4, the second case study, we switch gears from the interactive setting of psychotherapy to the use of non-informational language in weekly university lectures across different academic disciplines. There is a rich research tradition on how teachers use non-informational or “subjective” discourse elements to express attitudes and engage students, with most studies focusing on their forms, functions and other substantive aspects. Despite its obvious differences with psychotherapy, we can already see how TSA spotlights a commonality between these case study contexts – both unfold across natural time intervals where past sessions are expected to influence future ones, and the structural characteristics and implications of salient discourse phenomena are overlooked relative to their substantive qualities. This common thread continues to run through Chapter 5 where we examine the use of thematic keywords across considerably longer time frames in newspaper discourse. Over the past few decades, prominent keywords such as “terrorism” and “democracy” and the various topics and events they index have been extensively discussed in (critical) discourse research. The issue of diachronic change stands at the forefront and tends to be examined with respect to watershed

Time in discourse analysis  13 events like 9/11. Once more, the application of TSA demonstrates how the substantive impact of these watershed events on newspaper discourse could be reconsidered, by examining changes across a longer period within which they are situated. The case studies featured in this book have been selected to broadly reflect issues and phenomena of interest to contemporary discourse researchers. Let us first consider the general nature of the contexts – psychotherapy, the university classroom and newspapers – all of which perform important social roles. Besides representing a mix of spoken and written registers, they also range from the purely monologic to the purely dialogic, with hybrid cases in between. The contrasting nature of these contexts implies that the corresponding discourse phenomena to be examined also vary in interesting ways. One of these lies with their degree of contextualization. While thematic keywords in newspapers often refer to abstract sociopolitical entities, non-­informational language in classrooms and metaphorical expressions in therapy are more likely to index context-specific meanings and interrelationships. The implications arising from these different contexts and phenomena are also varied. How TSA may articulate clinical implications for therapy, pedagogical implications for classroom teaching and ideological implications for news discourse will be a key point of interest in this book. Another noteworthy point is the range of time scales represented by these case studies. Spontaneous interaction contexts like psychotherapy are characterized by rapidly shifting discourse behaviors that may form interesting patterns within the span of a single hourly session, while newspaper language often responds to real-world events that unfold over a much longer period. It is thus unsurprising that the analyses will feature a diverse range of different time series models offering various interpretative possibilities – from “autoregressive” to “moving average” and “random walk” models, all of which will be explained in turn. We can therefore say that each case study c­ hapter qualifies as an independent unit of inquiry, but their juxtaposition also conveys something meaningful about the nature of discourse in general. The concluding Chapter 6 offers a synthesized summary of the case studies, draws some generalizations about the nature of discourse as time series, outlines several limitations of the book and provides plausible future research directions to advance the TSA of discourse. Besides reviewing the time series models featured in the case studies, I will highlight a few major model types that are common elsewhere but unattested in the present data. The bird’s eye view of the results will enable us to reflect on the general modelability of discourse data vis-à-vis

14  Time in discourse analysis other common types of time series data. Much of this reflection will be related to the long-standing methodological tussle between qualitative and quantitative inquiry in humanities and social sciences, and the reconciliatory potential offered by an approach like TSA. A book of this nature, which aims to balance basic methodological instruction with analysis, will invariably be limited in its breadth and depth. I will therefore conclude the book by outlining some key limitations and offering plausible directions for researchers interested in taking TSA further than the present scope allows.

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Time in discourse analysis  15 Gumperz, J. J. (1982). Discourse Strategies. Cambridge: Cambridge University Press. Hammersley, M. (1997). On the foundations of critical discourse analysis. Language and Communication, 17(3), 237–248. doi:10.1016/S0271-5309(97)00013-X Holmes, J., & Marra, M. (2002). Having a laugh at work: How humour contributes to workplace culture. Journal of Pragmatics, 34, 1683–1710. Retrieved from http://www.sciencedirect.com/science/article/pii/S0378216602000322 Jebb, A. T., Tay, L., Wang, W., & Huang, Q. (2015, June). Time series analysis for psychological research: Examining and forecasting change. Frontiers in Psychology, 6, 1–24. doi:10.3389/fpsyg.2015.00727 Johnstone, B. (2008). Discourse Analysis (2nd ed.). Oxford: Blackwell. Kilgarriff, A. (2001). Comparing corpora. International Journal of Corpus Linguistics, 6(1), 97–133. Koplenig, A. (2017). Why the quantitative analysis of diachronic corpora that does not consider the temporal aspect of time-series can lead to wrong conclusions. Digital Scholarship in the Humanities, 32(1), 159–168. Retrieved from https://academic.oup.com/dsh/article-lookup/doi/10.1093/ llc/fqv011 Labov, W. (1963). The social motivation of a sound change. Word, 19, 273–309. Labov, W. (1969). Contraction, deletion, and inherent variability of the English copula. Language, 45(4), 715–762. Labov, W. (1972). The social stratification of (r) in New York City department stores. In Sociolinguistic Patterns (pp. 43–54). Philadelphia, PA: University of Pen. Lakoff, G. (1993). The contemporary theory of metaphor. In A. Ortony (Ed.), Metaphor and Thought (2nd ed., pp. 202–251). Cambridge: Cambridge University Press. Lakoff, G., & Johnson, M. (1999). Philosophy in the Flesh: The Embodied Mind and Its Challenges to Western Thought. New York: Basic Books. Leech, G., Hundt, M., Mair, C., & Smith, N. (2009). Change in Contemporary English. A Grammatical Study. Cambridge: Cambridge University Press. Levitt, H., Korman, Y., & Angus, L. (2000). A metaphor analysis in treatments of depression: Metaphor as a marker of change. Counselling Psychology Quarterly, 13(1), 23–35. Lyddon, W. J., Clay, A. L., & Sparks, C. L. (2001). Metaphor and change in counselling. Journal of Counseling & Development, 79(3), 269–274. Macaulay, R. (2005). Talk that Counts : Age, Gender, and Social Class Differences in Discourse. New York: Oxford University Press. McEnery, T., & Hardie, A. (2012). Corpus Linguistics. Method, Theory and Practice. New York: Cambridge University Press. Milroy, L. (1980). Language and Social Networks. Oxford: Blackwell. O’Halloran, K. (2011). Multimodal discourse analysis. In K. Hyland & B. ­Paltridge (Eds.), Continuum Companion to Discourse Analysis (pp. 120–137). London and New York: Bloomsbury. Oakes, M. P. (1998). Statistics for Corpus Linguistics. Edinburgh, England: Edinburgh University Press.

16  Time in discourse analysis Partington, A. (2010). Modern Diachronic Corpus-Assisted Discourse Studies (MD-CADS) on UK newspapers: An overview of the project. Corpora, 5(2), 83–108. Ping, C. (1999). Modern Chinese: History and Sociolinguistics. Cambridge: Cambridge University Press. Reisigl, M. (2017). The discourse-historical approach. In J. Flowerdew & John E. Richardson (Eds.), The Routledge Handbook of Critical Discourse Studies (pp. 44–59). New York: Routledge. doi:10.4324/9781315739342.ch3 Reisigl, M., & Wodak, R. (Eds.). (2001). Discourse and Discrimination: Rhetorics of Racism and Anti- semitism. London: Routledge. Rowat, R., De Stefano, J., & Drapeau, M. (2008). The role of patient-generated metaphors on in-session therapeutic processes. Archives of Psychiatry and Psychotherapy, 1, 21–27. Sankoff, G., & Blondeau, H. (2007). Language change across the lifespan: /r/ in Montreal French. Language, 83, 560–588. Semino, E. (2008). Metaphor in Discourse. Cambridge and New York: ­Cambridge University Press. Semino, E., Demjén, Z., Hardie, A., Payne, S., & Rayson, P. (2018). Metaphor, Cancer, and the End of Life: A Corpus-Based Study. New York: Routledge. Stefanowitsch, A., & Gries, S. T. (Eds.). (2006). Corpus-Based Approaches to Metaphor and Metonymy. Berlin and New York: Mouton de Gruyter. Tagliamonte, S. A. (2012). Variationist Sociolinguistics. Change, Observation, Interpretation. West Sussex, England: Wiley-Blackwell. Tay, D. (2011). THERAPY IS A JOURNEY as a discourse metaphor. Discourse Studies, 13(1). doi:10.1177/1461445610387736 ­ emino & Tay, D. (2017). Using metaphor in healthcare: Mental health. In E. S Z. Demjen (Eds.), Routledge Handbook of Metaphor and Language (pp. 371–385). London and New York: Routledge. Van Dijk, T. A. (1995). Aims of critical discourse analysis. Japanese Discourse, 1, 17–27. Van Dijk, T. A. (2009). Society and Discourse. How Social Contexts Influence Text and Talk. New York: Cambridge University Press. Van Dijk, T. A. (Ed.). (2011). Discourse Studies: A Multidisciplinary Introduction (2nd ed.). London: Sage. van Leeuwen, T., & Wodak, R. (1999). Legitimizing immigration control: A discoursehistorical analysis. Discourse Studies, 1(1), 83–118. doi:10.1177/ 1461445699001001005 Vandaele, W. (1983). Applied Time Series and Box-Jenkins Models. Orlando, FL: Academic Press. von Eye, A., & Mun, E.-Y. (2013). Log-linear Modeling: Concepts, Interpretation, and Application. Hoboken, NJ: John Wiley & Sons. Wetherell, M., Taylor, S., & Yates, S. J. (Eds.). (2001). Discourse Theory and Practice: A Reader. London: Sage. Widdowson, H. (2005). Text, Context, Pretext: Critical Issues in Discourse Analysis. Oxford: Blackwell.

Time in discourse analysis  17 Wiedemann, G. (2013). Opening up to dig data: Computer-assisted analysis of textual data in social sciences. Historical Social Research, 38(4), 332–357. Wodak, R., & Meyer, M. (2009). Critical discourse analysis: History, agenda, theory, and methodology. In R. Wodak & M. Meyer (Eds.), Methods for Critical Discourse Analysis (2nd ed., pp. 1–33). London: Sage. Wodak, R., Pelikan, J., Nowak, P., Gruber, H., de Cillia, R., & Mitten, R. (1990). “Wir sind alle unschuldige Täter!” Diskurshistorische Studien zum Nachkriegsantisemitismus. Frankfurt am Main: Suhrkamp.

2 The basic logic and process of TSA

The general nature of TSA A time series is a set of consecutive measurements of the same v­ ariable made at equally spaced intervals in time. Well-known examples of naturally occurring time series over different time frames include stock markets, sales figures, rainfall, and birth/death rates. The primary objective of time series analysis (TSA) is to mathematically describe the entire series as an equation, which then allows prediction or forecasting of its future values. In contexts like engineering and manufacturing, TSA is also a key component of what is known as “process control”, i.e. interventions to achieve safe, consistent and/or profitable performance levels based on historical data (Alwan & Roberts, 1988). I will follow most writers in using the terms “predict” and “forecast” interchangeably in this book. Some argue that there are nuanced differences between these terms, but the argument relates more to statistical theory and is of little consequence here. TSA conceptually resembles standard regression analysis. Time is the independent variable with the designated time intervals as its levels, and the phenomenon represented by the series observed at each interval constitutes the dependent variable. However, a crucial difference is that measurements are assumed to not influence one another in standard regression analysis, but consecutive observations of time series data are precisely expected to do so. The canonical example is the stock market, or any finance-related time series in general, where there is a long-held belief that present prices are shaped by the historical trends of past prices. We will see that it is in fact the mathematical nature of this interdependence, known as “autocorrelation”, which crucially informs the TSA process. The meaning of this term is quite transparent as the prefix auto means “self”, so autocorrelation refers to how the series is correlated within

The basic logic and process of TSA  19 itself. Significant autocorrelations also result in patterns like cycles and localized fluctuations that are seldom seen in typical examples of linear regression. As pointed out in Chapter 1, TSA could provide novel insights into temporal aspects of discourse structure invisible to conventional discourse analytic methods. The three case study contexts in this book (psychotherapy, university lectures and newspaper articles) broadly represent different discourse domains and collectively demonstrate the feasibility and value of TSA. This chapter prepares readers for the upcoming case studies by introducing the basic logic and process of TSA with as few equations and computations as possible. Some background knowledge of statistical concepts like mean, variance, correlations and modeling will be assumed. The introduction and case studies will be limited to the widely used Box–Jenkins method of TSA (Box, Jenkins, Reinsel, & Ljung, 2015), and the simple univariate analysis of only one variable at a time. I begin with an introductory caveat on why standard linear regression analysis, typical of many applied linguistic scenarios, may not be adequate in capturing finer details in natural time series data. Next, I outline the major components of a typical financial time series, from which the analogous nature of discourse contexts is suggested. Using a single hypothetical example, I then go through the major steps of the Box–Jenkins TSA method, and how the resultant mathematical models that describe the time series could be meaningfully interpreted in a humanistic context like discourse. I conclude with a brief introduction to popular software packages for conducting TSA, focusing on SAS that is used throughout the book. This chapter does not intend to and cannot replace standard TSA textbooks that emphasize computational details (e.g.  Bowerman  & O’Connell, 1987; Vandaele, 1983). I will not elaborate on alternative TSA approaches like the Holt–Winters method (Winters, 1960) or more advanced topics such as multivariate TSA. The multivariate analysis of time series involves modeling a group of variables and their interactions (Montgomery & Weatherby, 1980; Tsay, 2013), and performs a crucial role in the economics and finance context. Its potential applications to discourse analysis will be briefly discussed in the concluding chapter where I reflect on the limitations of this book and future research directions. Lastly, an important takeaway message from this chapter is that TSA is far from a matter of simply applying statistical procedures. It involves a combination of software-aided computation and manual judgment by the analyst. In the present context of discourse analysis, we will see that judicious interpretation of time series models plays an even greater role than usual.

20  The basic logic and process of TSA

A caveat on linear regression models In many applied linguistics contexts, standard linear regression models are used with the assumption that measurements are independent of one another. A simple example is the test scores of different subjects, or the number of hours spent by each of them studying. These models project an “averaged fit” of the available data, and assume that future observations will exhibit small but random deviations from this average fit. A discourse analyst attempting to model a discourse variable across time may also be inclined to use linear regression models especially if the data seems to suggest a strong linear trend by visual inspection. Consider a hypothetical variable yt, say, the number of hedges observed over 30 consecutive time intervals in a spontaneous conversation. Figure 2.1 shows the scatterplot of the two variables of yt and time, and the regression line resulting from fitting a simple linear regression model. A good fit is suggested at first glance as the observed values cluster closely around the regression line. In terms of the regression statistics, both the intercept and coefficient for t, estimated at 14.274 and 0.812, respectively, are statistically significant (p < 0.0001). The confidence intervals (not illustrated here) are reasonably short, and the R-squared coefficient of 0.857 can be considered high. The model yt = 0.812t + 14.274 could thus be confidently used to predict future use of hedges if so desired.

Figure 2.1  Scatterplot of linear regression for variable yt.

The basic logic and process of TSA  21 However, a procedure often overlooked by (applied) linguists when conducting regression analysis is residual diagnostics. Residuals refer to the difference between the observed and predicted values of each data point and thus reflect the error of the regression model. In a standard scatterplot like Figure 2.1, the size of each residual is indicated by the vertical distance between each observed value and the regression line. If a regression model has indeed accurately and exhaustively described the pattern in the data, there should be no further patterns across the series of residuals. Residual diagnostics are a set of procedures to verify if this is the case, and usually involve plotting the residual values against the independent and dependent variables. Figure 2.2 shows the (un)standardized residuals of yt plotted across the 30 time points. We see a roughly equal mix of positive and negative residuals. A positive residual means that the actual observed value is higher than the predicted value at that time interval (the circle is above the line), and vice versa. This reflects the aforementioned “averaged fit” where values randomly scatter above or below the regression line. However, a careful examination reveals that the errors tend to persist in the same direction over many consecutive intervals. The last ten intervals in particular have all been predicted to be lower than what they actually are, with some evidence of a worsening upward deviation. This suggests that the series is undergoing a “localized” recent upward trend which, while averaged out by previous movements in the opposite direction, deserves careful consideration if the primary objective is to predict

Figure 2.2  Plot of residuals for yt against observations.

22  The basic logic and process of TSA the immediate future. In other words, the model is good at capturing the overall distribution of hedges but less effective with local details and evolving trends. A prediction of the number of hedges at the 31st time interval using this model would therefore be based purely on the “averaged fit” and overlook the short-term rises and falls observable in the raw plot. These short-term fluctuations are in fact indicative of more complex interdependence within observations – something very typical in contexts like finance and engineering, and as this book hopes to show, characteristic in discourse contexts as well, when there are theoretically motivated reasons to suppose that past values leave their signature on future values.

Components of time series data Sales figures are prime examples of time series data. Figure 2.3 sketches a hypothetical company’s monthly sales performance over a period of 20 years. The raw figures are represented in the first panel, and then decomposed into the key additive components of time series data – trend, seasonality, cyclic changes and what is “left behind” as the remainder. The raw figures are simply a plot of sales (y-axis) along the monthly intervals (x-axis). It is easy to identify by visual inspection alone a gradual upward trend comprising local fluctuations that recur quite consistently over time. The trend and regular fluctuations are components that form patterns that are difficult to account for with the type of standard regression analysis discussed in the previous section. The TSA process deals with this by extracting or “filtering out” these individual components, each of which contributes toward the mathematical description of the series, until no more information can be extracted. There are several useful analogies to depict this process, like brewing coffee through a filter or passing sugar cane through a juicer until only the pulp remains. We will see that the latter analogy is more apt because TSA can involve iterative passes through the same procedure just like sending sugar cane multiple times through the juicer. We will also see that sometimes the raw data needs to undergo certain transformation procedures first to fulfill statistical assumptions. The extracted information eventually yields a final time series model which is presented in terms of an equation for yt, the value of the series at time t. This final model is a result of adding up or multiplying individual components, which are known, respectively, as additive and multiplicative modeling. Only the former will be discussed here.

The basic logic and process of TSA  23 Component

Graphical representation

Raw figures A plot of the observed variable against time

Trend Gradual long-term (>1 year) increase/decrease in the underlying level of the series. May be linear or non-linear, deterministic or stochastic

Seasonality Short-term (1.6 for lower lags (lags 1–3), and t-value >2 for higher lags. A spike in PACF is considered to exist at lag k if the magnitude of the t-value >2 at all lags. We are now ready to identify candidate models based on our knowledge of the relative behavior of ACF and PACF. Step 3: Identify candidate models We saw from our example that the ACF and PACF tend to exhibit two types of general signature behavior – cutting off or dying down. Cutting off means an abrupt transition from statistical significance to non-significance from one lag to the next, suggesting a certain time frame within which values are autocorrelated, while dying down means a gradual transition where the autocorrelation “lingers on” for some lags. In many cases, if either the ACF or PACF cuts off, the other will die down, but sometimes both can behave similarly. The analyst must now relate this behavior to the major model types in TSA and decide which one best describes it: an autoregressive (AR) model, a moving

34  The basic logic and process of TSA average (MA) model, a combination of both (ARMA) or other variants we will come across in the upcoming case studies. These ­major model types are collectively known as ARIMA models. ARIMA is the acronym for “autoregressive integrated moving average”. “Integrated” denotes the order of integration, which just means the number of differencing procedures required to achieve stationarity as described earlier. ARIMA suggests that AR and MA models are fundamental in TSA, so we will focus on them right now. Mathematically, AR models describe the current value of the time series as a function of its prior values, while MA models describe the current value as a function of irregular fluctuations in past intervals. What these imply or “mean” in a discourse context will be briefly discussed at the end of the chapter and illustrated in the following case studies. For now, Table 2.2 provides some guidelines adapted from Bowerman and O’Connell (1987) which match different basic (P)ACF behavior patterns to the candidate models most likely to be suitable. We just saw in Figure 2.8 that ACF has spikes up to lag 1 and cuts off after lag 1 while PACF dies down. This corresponds to the first behavior pattern in the guidelines. The most likely candidate is therefore an MA(1) model. As with all other statistical models, the MA(1) model contains parameters, which now have to be estimated based on the observed data and evaluated for its goodness of fit. Table 2.2  B  asic guidelines for model selection based on ACF and PACF behavior Behavior pattern

Candidate model

ACF has spikes up to lag k and cuts MA model of order k, i.e. MA(k) off after lag k. PACF dies down model ACF dies down. PACF has spikes up AR model of order k, i.e. AR(k) model to lag k and cuts off after lag k. Both ACF and PACF have spikes up If ACF cuts off more abruptly, use to lag k and cuts off after lag k MA(k) model If PACF cuts off more abruptly, use AR(k) model If both appear to cut off equally abruptly, try both models to see which fits better Both ACF and PACF die down ARMA model of order k, i.e. both MA(k) and AR(k) model Both ACF and PACF have no spikes No suitable model since at all lags autocorrelations are absent

The basic logic and process of TSA  35 Step 4: Estimate parameters and evaluate goodness of fit Parameters are numerical constants that, alongside variables, determine the value of an equation. There are different approaches to parameter estimation in general statistical analysis such as conditional least squares and maximum likelihood estimation. Opinions differ regarding their relative superiority (Broersen & De Waele, 2000; Genschel & Meeker, 2010), but various approaches can be easily tried and compared using software like SAS. In many practical cases, the outcomes will not be too divergent. Although parameter estimation is thus also an automated process, evaluating these parameters for goodness of fit involves manual comparative judgment in cases where more than one candidate model is identified. As mentioned, MA models describe the current value as a function of past irregular fluctuations. The schematic mathematical form of an MA(1) model is yt = μ − at − θ1at−1, where yt is the present value in the series, μ is the true or “population” mean of the whole series, at is the present value of the residual (i.e. observed – predicted value at time t), at−1 is the value of the residual at time t − 1, and θ1 is a coefficient also known as the MA(1) operator. The number of MA operators corresponds to the order of the model, i.e. k operators for an MA(k) model. The parameters to be estimated are thus μ and θ1. In contrast, AR models describe the current value of a time series as a function of its prior values. The form of an AR(1) model is thus yt = (1 − Φ1)μ + at + Φ1yt−1, the key difference being that the AR operator prefaces yt−1 (value of series at t − 1) instead. Figure 2.9 shows the estimated parameters and statistics of the MA(1) model for the present example series using the maximum likelihood estimation approach. Under “Parameter” MU represents μ and MA1, 1 represents θ1. On the left panel, we see that μ is estimated to be 0.0055284 and θ1 is −0.35195. These estimates are tested for whether they are significantly different from zero. The p-value for μ is 0.9658, which suggests that the null hypothesis of μ = 0 should not be rejected, i.e. μ should be treated as zero. The p-value for θ1 is