Composite-Based Structural Equation Modeling: Analyzing Latent and Emergent Variables [1 ed.] 1462545602, 9781462545605

Table of contents :
Series Editor’s Note
Preface
Contents
1 Introduction
2 Auxiliary Theories
3 Model Specification
4 Model Identification
5 Model Estimation
6 Global Model Assessment: Model Fit
7 Local Model Assessment
8 Confirmatory Composite Analysis
9 Mediation Analysis
10 Second-Order Constructs
11 Analyzing Interaction Effects
12 Importance-Performance Analysis
Acronyms
Glossary
References
Author Index
Subject Index
Disclosure
About the Author

Citation preview

Composite-Based Structural Equation Modeling

Methodology in the Social Sciences David A. Kenny, Founding Editor Todd D. Little, Series Editor www.guilford.com/MSS This series provides applied researchers and students with analysis and research design books that emphasize the use of methods to answer research questions. Rather than emphasizing statistical theory, each volume in the series illustrates when a technique should (and should not) be used and how the output from available software programs should (and should not) be interpreted. Common pitfalls as well as areas of further development are clearly articulated. R EC EN T V OLU MES PRINCIPLES AND PRACTICE OF STRUCTURAL EQUATION MODELING, FOURTH EDITION Rex B. Kline HYPOTHESIS TESTING AND MODEL SELECTION IN THE SOCIAL SCIENCES David L. Weakliem REGRESSION ANALYSIS AND LINEAR MODELS: CONCEPTS, APPLICATIONS, AND IMPLEMENTATION Richard B. Darlington and Andrew F. Hayes GROWTH MODELING: STRUCTURAL EQUATION AND MULTILEVEL MODELING APPROACHES Kevin J. Grimm, Nilam Ram, and Ryne Estabrook PSYCHOMETRIC METHODS: THEORY INTO PRACTICE Larry R. Price INTRODUCTION TO MEDIATION, MODERATION, AND CONDITIONAL PROCESS ANALYSIS: A REGRESSION-BASED APPROACH, SECOND EDITION Andrew F. Hayes MEASUREMENT THEORY AND APPLICATIONS FOR THE SOCIAL SCIENCES Deborah L. Bandalos CONDUCTING PERSONAL NETWORK RESEARCH: A PRACTICAL GUIDE Christopher McCarty, Miranda J. Lubbers, Raffaele Vacca, and José Luis Molina QUASI-EXPERIMENTATION: A GUIDE TO DESIGN AND ANALYSIS Charles S. Reichardt THEORY CONSTRUCTION AND MODEL-BUILDING SKILLS: A PRACTICAL GUIDE FOR SOCIAL SCIENTISTS, SECOND EDITION James Jaccard and Jacob Jacoby LONGITUDINAL STRUCTURAL EQUATION MODELING WITH Mplus: A LATENT STATE–TRAIT PERSPECTIVE Christian Geiser COMPOSITE-BASED STRUCTURAL EQUATION MODELING: ANALYZING LATENT AND EMERGENT VARIABLES Jörg Henseler

Composite-Based Structural Equation Modeling Analyzing Latent and Emergent Variables ..........................................................................

Jörg Henseler Series Editor’s Note by Todd D. Little

THE GUILFORD PRESS New York London

© 2021 The Guilford Press A Division of Guilford Publications, Inc. 320 Seventh Avenue, Suite 1200, New York, NY 10001 www.guilford.com All rights reserved No part of this book may be reproduced, translated, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording, or otherwise, without written permission from the Publisher. Printed in the United States of America This book is printed on acid-free paper. Last digit is print number: 9 8 7 6 5 4 3 2 1

Library of Congress Cataloging-in-Publication Data Names: Henseler, Jörg, author. Title: Composite-based structural equation modeling : analyzing latent and emergent variables / Jörg Henseler. Description: New York, NY : The Guilford Press, [2021] | Series: Methodology in the social sciences | Includes bibliographical references and index. Identifiers: LCCN 2020033492 | ISBN 9781462545605 (cloth) Subjects: LCSH: Structural equation modeling. Classification: LCC QA278.3 .H464 2021 | DDC 519.5/3--dc23 LC record available at https://lccn.loc.gov/2020033492

Series Editor’s Note An analyst’s toolbox can’t be too broad. Bringing Jörg Henseler’s book on composite-based structural equation modeling (SEM) to Guilford’s Methodology in the Social Sciences series adds a critical tool to our incredible collection of analytic resources. I have been extremely pleased with each contribution to the series and Jörg’s is no exception. As someone who loves SEM in general, I was blown away with what composite-based SEM adds and broadens in terms of analytic dexterity. Jörg’s expertise is both broad and deep and, coupled with his incredible ability to make the new concepts accessible, is truly an extraordinary gift. The culmination of this gift is Composite-Based Structural Equation Modeling: Analyzing Latent and Emergent Variables. So, what does Jörg bring to our collective toolbox? As intimated in the title of his book, SEM is a factor-based modeling approach to identify latent variables from common variance among a set of indicators. Jörg’s coverage of this approach is both refreshing and quite useful to help contrast the benefits of the composite-based approach to SEM that focuses on variance-based decompositions using partial least squares estimation to identify emergent variables. Emergent variables are useful in a number of contexts where latent variables may not be optimal. Using synthesis theory (instead of measurement theory), Jörg demonstrates how emergent variables are a formidable tool to model formative concepts such as activities, capabilities, designs, indices, instruments, mixes, norms, orientations, policies, practices, quality, skills, solutions, strategies, systems, treatments, values, and the like. Consequently, this book is of particular value for researchers in disciplines in which composites are ubiquitous, such as in business (e.g., marketing), criminology, education, ecology, sociology, political science, information systems, and so on. Jörg provides detailed tutorials using his easy-to-use software program, ADANCO, and the R package, cSEM. There is also an excellent companion website (see the box at the end of the table of contents) that includes the data and syntax files for the diverse examples included in this book, along with

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Series Editor’s Note

presentation slides that are very handy for developing course content on composite-based modeling. One of the added values of Jörg’s integrative work is how he has solved the conundrum integrating multiple interrelated composites into structural equation models. His work is not just an introduction to composite-based modeling but includes many critical advanced concepts in the context of emergent variables, including mediation, moderation, higher-order variables, multiple-group modeling, and nonlinear effects, as well as confirmatory composite analysis (sets of interrelated composites, which is the analogue to confirmatory factor analysis). Jörg’s book is very refreshing to read and is extremely accessible for students and professionals alike. I personally learned a tremendous amount of wonderful information that I will integrate into my own research and teaching going forward. As an old dog, I enjoyed learning new tricks with the aid of Jörg, “the composite whisperer.” As always, enjoy! TODD D. LITTLE Isolating at my “Wit’s End” retreat Lakeside, Montana

Preface Structural equation modeling (SEM) has become an important element of the methodological toolbox of researchers in social and business science. Both its usefulness and its ease of use have led to its widespread adoption. While, for instance, SEM’s capability to test entire theories, to distinguish between substantial theory and auxiliary theory (i.e., construct operationalization), and to take into account and correct for measurement error largely explains its usefulness, an engaged community (in particular, SEMNET) as well as a rich body of literature have increased its ease of use. Why another book on SEM? Given the plethora of established SEM textbooks such as Acock (2013), Bollen (1989b), Brown (2014), Byrne (1998), Hancock and Mueller (2013), Hayduk (1987), Hoyle (2012), Kaplan (2008), Kline (2015), Loehlin and Beaujean (2017), Marcoulides and Moustaki (2002), Mulaik (2009), Raykov and Marcoulides (2006), or Schumacker and Lomax (2016), this question is obvious. The answer is simple, but also somewhat surprising: They miss a valuable capability of SEM, namely the possibility to model, estimate, and test composite models. Not that I’m the first one to notice. Already more than 10 years ago, Grace (2006, p. 143) noted, “Up to this present time, the emphasis in SEM has been on latent variables as the means of conveying theoretical concepts. It is my view that this is quite limiting.” Since then, nothing has changed. SEM is widely understood as “factor-based SEM” (Rigdon, 2012), and all extant introductory SEM texts promulgate that the auxiliary theory has to be expressed by common factor models. However, they neglect that while SEM can correct for measurement error, it does not imply that it has to do that. Alternatively, researchers can model constructs as composites, i.e., as linear combinations of observed variables. While researchers in ecology, business, design sciences, sensory science, and beyond have started to work with composites, methodologists have left the central questions around composites unanswered: Are composites really a model? How should one specify composite models? When are composite models identified? How can composite models be estimated? Do composite models require new

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Preface

tests of model fit? These are the questions that motivated the genesis of this book. The present book rethinks SEM with regard to the employed auxiliary theory and lays the focus on composites. To do so, it contains a couple of chapters and sections that are unique; i.e., they do not exist in this form in any other textbook on SEM: • Chapter 1 presents a typology of SEM techniques that differentiates between composite-based and factor-based SEM, as well as between variance-based and covariance-based SEM. • In Chapter 2, this book dives particularly deep into the nature of auxiliary theories. It develops synthesis theory as an auxiliary theory of emergent variables and contrasts it with the well-known measurement theory of latent variables. • Section 3.2 shows how to specify composite models by means of emergent and excrescent variables. • Chapter 4 covers the particular identification issues of composite models. • A landmark is certainly Chapter 8, which explains confirmatory composite analysis (CCA). CCA was recently introduced by Schuberth, Henseler, and Dijkstra (2018a) in analogy to its well-known counterpart, confirmatory factor analysis (CFA). • In most chapters, readers will find software tutorials explaining the use of ADANCO and the R package cSEM. On the one hand, this book provides a full-fledged introduction to SEM, and covers all basic steps: model specification, model identification, model estimation, and model testing and assessment. In this way, the book is much more similar to classical texts on SEM (in particular Kline, 2015) than to textbooks dedicated to particular composite-based SEM techniques such as partial least squares path modeling (e.g., Falk & Miller, 1992; Hair, Hult, Ringle, & Sarstedt, 2016; Sanchez, 2013; Wong, 2019) or generalized structured component analysis (Hwang & Takane, 2014), and it can formidably serve as a primer for novices in SEM. On the other hand, it is a valuable reference for readers who already have a background in using SEM for factor models and who would like to learn more about the use of SEM for composite models. Finally, the book covers advanced topics that are useful for all analysts, for instance, moderating effects, mediating effects, and higher-order constructs. Experienced users will find useful details, extensions, and clarifications. Readers will, for instance, learn

Preface

ix

• what composite-based SEM is and which steps it entails, • what types of research questions can be answered using compositebased SEM, • how structural equation models should be specified using ADANCO and cSEM, • how to report the results of composite-based SEM and where to find the relevant output in ADANCO and cSEM, and • how to interpret the findings. The book contains many visualizations, examples, and summary tables. Datasets are provided so that the reader can do the examples on his or her own computer. The book is written at a level such that beginning PhD students and advanced master’s students in management, marketing, information systems research, ecology, psychology, sociology, communication science, and most other fields will be able to understand it without problems. However, the audience for this monograph is by no means limited to researchers in the aforementioned disciplines. Rather, the book also opens composite-based SEM’s application spectrum toward more designoriented disciplines, such as psychotherapy, tourism technology, humanmedia interaction, and new technology research. In these disciplines, CCA as implemented in ADANCO and cSEM has the potential to play a similar role to the one CFA plays in the behavioral sciences. Thank you very much to the highly professional team of The Guilford Press, in particular C. Deborah Laughton, Laura Patchkofsky, Robert Sebastiano, Juliet Simon, and Dazzia Szczepaniak, for their guidance through the publishing process. Moreover, I would like to thank all the people who supported me in one way or the other in writing this book, be it by providing comments about the various chapters or by permitting me to use materials of theirs. In particular, I would like to express my gratitude to:

• Richard P. Bagozzi, University of Michigan, Ann Arbor, MI, USA • Jose Benitez, ESC Rennes School of Business, France • Kenneth A. Bollen, University of North Carolina, Chapel Hill, NC, USA • Ana Castillo, University of Granada, Spain • Gabriel Cepeda, University of Seville, Spain • Naveen Donthu, Georgia State University, Atlanta, GA, USA • Georg Fassott, University of Kaiserslautern, Germany • Todd Little, Texas Tech University, Lubbock, TX, USA • Caroline Lancelot Miltgen, Audencia Business School, Nantes, France

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Preface • • • • • • • • • • • •

Marion Laußegger, University of Twente, the Netherlands Manuel Rademaker, University of Wuerzburg, Germany Gautam Ray, University of Minnesota, Minneapolis, MN, USA Ellen Roemer, Ruhr West University of Applied Sciences, Mülheim an der Ruhr, Germany José Luis Roldán, University of Seville, Spain Laura Ruiz Santiago, ESC Rennes School of Business, France Tamara Schamberger, University of Wuerzburg, Germany Holger Schiele, University of Twente, the Netherlands Florian Schuberth, University of Twente, the Netherlands Michel Tenenhaus, HEC Paris, Jouy-en-Josas, France Chris Vermaas, University of Twente, the Netherlands Ibtissam Zaza, Middle Tennessee State University, Murfreesboro, TN, USA

A very special word of thanks goes to Theo K. Dijkstra (University of Groningen, the Netherlands), a great scholar, friend, and role model, for all his support over the years and in particular for sharing his memories of Herman O. A. Wold’s research group at the Wharton School, Philadelphia (see Figure 1), the breeding ground of partial least squares. Without Theo’s valuable scientific contributions, the advancement of composite-based SEM would be much more limited. This book is dedicated to him.

FIGURE 1. Herman O. A. Wold and his research group in 1977. From left to right: Theo K. Dijkstra, Heino Apel, Herman O. A. Wold, Baldwin S. Hui.

Contents

1

Introduction 1.1 The Nature of Structural Equation Modeling / 1 1.2 What Is Composite-Based SEM? / 8 1.3 For Which Purpose Should One Use Composite-Based SEM? / 13 1.3.1 1.3.2 1.3.3 1.3.4 1.3.5 1.3.6

1.4

Using Composite-Based SEM for Confirmatory Research / 13 Using Composite-Based SEM for Explanatory Research / 15 Using Composite-Based SEM for Exploratory Research / 15 Using Composite-Based SEM for Descriptive Research / 16 Using Composite-Based SEM for Predictive Research / 17 When to Use Composite-Based SEM? / 18

Software Tutorial: Getting Started / 19 1.4.1 1.4.2

2

First Steps in ADANCO / 19 First Steps in cSEM / 23

Auxiliary Theories with Florian Schuberth

2.1 2.2 2.3 2.4 3

1

Model Speci¿cation 3.1 What Is a Structural Equation Model? / 38 3.2 The Outer Model / 42 3.2.1 3.2.2 3.2.3 3.2.4 3.2.5

3.3 3.4

25

The Need for Auxiliary Theories / 25 Different Types of Science / 27 The Auxiliary Theory of Behavioral Science: Measurement Theory / 29 The Auxiliary Theory of Design Science: Synthesis Theory / 31 38

Composite Models / 44 Reflective Measurement Models / 51 Causal-Formative Measurement Models / 53 Single-Indicator Measurement Models / 54 Categorical Variables / 56

The Inner Model / 58 Software Tutorial: Model Specification / 63 3.4.1 3.4.2

Specifying Structural Equation Models in ADANCO / 65 Specifying Structural Equation Models in cSEM / 69

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Contents Model Identi¿cation 4.1 The Necessity of Identification / 73 4.2 Ensuring Model Identification in Composite-Based SEM / 75 4.3 Ensuring Empirical Identification in Composite-Based SEM / 77 4.4 “Chance Correlations” / 78 4.4.1 4.4.2

4.5 4.6 5

The Dominant Indicator Approach as a Solution to Sign Indeterminacy / 80 Identification Rules / 81

5.1.1 5.1.2 5.1.3

5.3 5.4

Consistent PLS / 102 Sum Scores with Correction for Attenuation / 105

Estimating Models Using ADANCO / 110 Estimating Models Using cSEM / 113

Global Model Assessment: Model Fit 6.1 The Motivation for Model Fit / 118 6.2 Model Fit Tests / 120 6.2.1 6.2.2

6.4 6.5

Non-Parametric Model Fit Tests / 120 Parametric Model Fit Tests / 123

Standardized Root Mean Squared Residual (SRMR) / 124 Root Mean Square Residual Covariance (RMSθ ) / 125 Fit Measures Provided by Covariance-Based SEM / 125

What If Model Fit Is Low? / 127 Beware of Alleged Goodness-of-Fit Indices / 129 6.5.1 6.5.2

6.6

118

Model Fit Indices / 124 6.3.1 6.3.2 6.3.3

Four “Goodness-of-Fit Indices” That Are Not Model Fit Indices / 129 The Different Meanings of Fit / 132

Tutorial: Model Testing / 133 6.6.1 6.6.2

7

Stand-Alone Constructions: Sum Scores, Preset Weights, and Principal Components / 86 The PLS Path Modeling Algorithm / 89 Generalized Structured Component Analysis / 96

Fitting Functions / 109 Tutorial: Model Estimation / 110 5.4.1 5.4.2

6.3

85

Composite-Based Estimators for Reflective Models / 101 5.2.1 5.2.2

6

The Problem with “Chance Correlations” / 78 Avoiding “Chance Correlations” / 79

Model Estimation 5.1 Composite-Based Estimators for Composite Models / 86

5.2

73

Using ADANCO for Model Testing / 134 Using cSEM for Model Testing / 138

Local Model Assessment 7.1 The Need for Reliability and Validity / 142 7.2 Assessing Composite Models of Emergent Variables / 144 7.2.1 7.2.2 7.2.3

Nomological Validity / 144 The Reliability of Composites / 145 Weights / 145

142

Contents 7.3

Assessing Reflective Measurement Models of Latent Variables / 146 7.3.1 7.3.2 7.3.3 7.3.4

7.4 7.5

R2 and Adjusted R2 / 155 Inter-Construct Correlations / 155 Path Coefficients / 156 Indirect Effects / 157 Total Effects / 157 Effect Size (Cohen’s f 2 ) / 157

Inferential Statistics and the Bootstrap / 158 Construct Scores / 160 What If There Is No Output? / 161 Tutorial: Model Assessment / 163 7.9.1 7.9.2

8

Construct Validity / 146 Unidimensionality / 147 Discriminant Validity / 147 Reliability of Construct Scores / 150

Assessing Causal-Formative Measurement Models / 153 Assessing Inner Models / 155 7.5.1 7.5.2 7.5.3 7.5.4 7.5.5 7.5.6

7.6 7.7 7.8 7.9

Model Assessment Using ADANCO / 163 Model Assessment Using cSEM / 171

Con¿rmatory Composite Analysis with Florian Schuberth

8.1 8.2 8.3 8.4 8.5 8.6

Confirmatory Composite Analysis Using ADANCO / 193 Confirmatory Composite Analysis Using cSEM / 195

Mediation Analysis 9.1 The Logic of Mediation / 202 9.2 Mediation Analysis Using Composite-Based SEM / 204 9.3 Tutorial: Mediation Analysis / 208 9.3.1 9.3.2

10

179

Motivation / 179 Confirmatory Composite Analysis: Model Specification / 182 Confirmatory Composite Analysis: Model Identification / 185 Confirmatory Composite Analysis: Model Estimation / 188 Confirmatory Composite Analysis: Model Testing / 190 Tutorial: Confirmatory Composite Analysis / 191 8.6.1 8.6.2

9

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202

Mediation Analysis Using ADANCO / 210 Mediation Analysis Using cSEM / 213

Second-Order Constructs 10.1 A Typology of Second-Order Constructs and Their Use / 220 10.2 Modeling Type-I Second-Order Constructs: Latent Variables Measured by Latent Variables / 224 10.3 Modeling Type-II Second-Order Constructs: Emergent Variables Made of Latent Variables / 225 10.4 Modeling Type-III Second-Order Constructs: Latent Variables Measured by Emergent Variables / 233 10.5 Modeling Type-IV Second-Order Constructs: Emergent Variables Made of Emergent Variables / 236

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Contents 10.6 Modeling Type-V Second-Order Constructs: Latent Variables Measured by Different Types of Variables / 240 10.7 Modeling Type-VI Second-Order Constructs: Emergent Variables Made of Different Types of Variables / 241 10.8 Tutorial: Second-Order Constructs / 242 10.8.1 Modeling Second-Order Constructs with ADANCO / 242 10.8.2 Modeling Second-Order Constructs with cSEM / 250

11

Analyzing Interaction Effects 11.1 The Logic of Interaction Effects / 255 11.2 Estimating Interaction Effects with Composite-Based SEM / 259

255

11.2.1 Multigroup Analysis / 260 11.2.2 The Two-Stage Approach for Analyzing Interaction Effects / 262 11.2.3 The Orthogonalizing Approach for Analyzing Interaction Effects / 264

11.3 Visualizing Interaction Effects / 266 11.3.1 Surface Analysis / 267 11.3.2 Spotlight Analysis / 268 11.3.3 Floodlight Analysis / 268

11.4 Three-Way Interactions / 270 11.5 Nonlinear Effects / 272 11.6 Tutorial: Interaction Effects / 274 11.6.1 Analyzing Interaction Effects Using ADANCO / 275 11.6.2 Analyzing Interaction Effects Using cSEM / 276

12

Importance-Performance Analysis 12.1 Nature and Fields of Application / 281 12.2 A Step-by-Step Guide to Conducting IPA Using Composite-Based SEM / 283 12.3 Tutorial: Importance-Performance Analysis / 290

281

12.3.1 Using ADANCO for Importance-Performance Analysis / 290 12.3.2 Using cSEM for Importance-Performance Analysis / 297

Acronyms

301

Glossary

304

References

315

Author Index

345

Subject Index

353

Disclosure

363

About the Author

364

The companion website, www.guilford.com/henseler-materials, includes data files and syntax for the book’s examples, along with presentation slides.

Composite-Based Structural Equation Modeling

1 Introduction This chapter provides a general introduction to structural equation modeling (SEM) and an overview of various SEM techniques. It introduces composite-based SEM as those SEM techniques that involve composites in the estimation phase. Composite-based SEM can help answer research questions of various nature: con¿rmatory research, explanatory research, exploratory research, predictive research, and descriptive research.

1.1

The Nature of Structural Equation Modeling

Structural equation modeling (SEM) is a collection of statistical analyses “that allow a set of relationships between one or more independent variables (IVs), either continuous or discrete, and one or more dependent variables (DVs), either continuous or discrete, to be examined” (Ullman & Bentler, 2003, p. 607). In particular, it encompasses covariance structure analysis (CSA; Jöreskog, 1973), confirmatory factor analysis (CFA; Jöreskog, 1969), confirmatory composite analysis (CCA; Schuberth, Henseler, & Dijkstra, 2018a), and latent (growth) curve analysis (Meredith & Tisak, 1990). Researchers mostly use SEM to explain a part of the world by means of a set of linear (and sometimes nonlinear) equations. According to Byrne (1998, p. 3), “[t]he term structural equation modeling conveys two important aspects of the procedure: (a) that the causal processes under study are represented by a series of structural (i.e., regression) equations, and (b) that these structural relations can be modeled pictorially to enable a clearer conceptualization of the theory under study.” This possibility to (graphically) model and estimate parameters for relationships between constructs and to test complete behavioral science theories is a major reason for SEM’s attractiveness (Bollen, 1989b). But there are more reasons why SEM has become very popular in business and social sciences. Its ability to model 1

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FIGURE 1.1. Family tree of SEM.

theoretical concepts by means of latent variables, to take into account various forms of measurement error, and to test entire theories makes it useful for a plethora of research questions. Fornell (1982) calls SEM a “second generation of multivariate analysis,” because it can be thought of as a combination of two simpler analyses: first, an analysis such as principal component analysis (PCA) or principal axis factoring (PAF) to generate numerical proxies that serve as stand-ins for theoretical concepts, and second, an analysis such as multiple linear regression analysis to estimate the relationships between those proxies. Whereas factor analytical techniques have mainly been developed in psychometrics, regression analysis has been a subject of investigation in econometrics. That means, SEM synthesizes procedures developed in psychometrics and econometrics (Bollen & Long, 1993) as well as statistics in general. Figure 1.1 illustrates this geneological perspective on SEM.

Introduction

3

It has become good scientific practice to distinguish between the (conceptual) plane of theory and the (empirical) plane of observation. The plane of theory contains the theoretical concepts and hypotheses on their interrelationships. Theoretical concepts (also called hypothetical variables) are products of abstract thinking that have been defined at some point; examples are attitudes, methods, traits, and solutions. Theoretical concepts are attributes of some object (Rossiter, 2002) and refer to an abstraction formed by generalizing from particulars (Billiet, 2016). They are typically visualized by means of triangles. In contrast, the plane of observation relates to sensory experience and consists of the observed variables and their covariation. Observed variables are characterized by rectangles or squares. They do not have to be literally observed by the researcher; rather, a variable is categorized as observed if it can be inferred with certainty from the data (Borsboom, 2008). Figure 1.2 depicts the presented view of a scientific theory as a structured network of interrelated variables. According to Hempel (1952, p. 36), [a] scientific theory might [. . . ] be likened to a complex spatial network: Its terms are represented by the knots, while the threads connecting the latter correspond, in parts, to the definitions and, in part, to the fundamental and derivative hypotheses included in the theory. The whole system floats, as it were, above the plane of observation and is anchored to it by rules of interpretation. These might be viewed as strings which are not part of the network but link certain points of the latter with specific places in the plane of observation. By virtue of those interpretive connections, the network can function as a scientific theory: From certain observational data, we may ascend, via an interpretive string, to some point in the theoretical network, thence proceed, via definitions and hypotheses, to other points, from which another interpretive string permits a descent to the plane of observation. The fact that theoretical concepts are not directly observable renders them inaccessible for empirical research. Researchers solve this problem by purposefully introducing abstract variables – the so-called constructs (Hox, 1997), which serve as statistical stand-ins for the theoretical concepts. Constructs are statistical variables that are not by themselves observable, but can be mathematically inferred from observable variables through a mathematical model. Generally speaking, most constructs “can only be measured through observable measures or indicators that vary in their degree of observational meaningfulness and validity. No single indicator can capture the full theoretical meaning of the underlying construct and hence, mul-

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Composite-Based Structural Equation Modeling

Plane of Theory

Observed Variable

Substantial Theory

Auxilia r y Th eory

Auxilia r y Th eory

Concept

Construct (Latent Variable)

Observed Variable

Observed Variable

Concept

Construct (Emergent Variable)

Observed Variable

Observed Variable

Observed Variable

Plane of Observation

FIGURE 1.2. The structure of theory.

tiple indicators are necessary” (Steenkamp & Baumgartner, 2000, p. 196). The dominant kinds of constructs are latent and emergent variables (Cohen, Cohen, Teresi, Marchi, & Velez, 1990). Latent variables are typically modeled as common factors underlying a set of observed variables. In graphical representations of structural equation models, they are represented by ovals. Emergent variables are usually modeled as composites of observed variables. They are graphically symbolized by hexagons. This

Introduction

5

book clearly distinguishes between concepts and constructs,1 because they differ in the opportunities they offer to researchers. Whereas the relationships between constructs can be empirically tested, this holds less so for the relationships between theoretical concepts. Testing relationships between concepts requires an additional, interpretative step, namely ensuring that the construct represents the concept well. The link between concepts and their observed variables is the subject of auxiliary theory (Costner, 1969). Auxiliary theory is of utmost importance, because “no main body of deductive theory can ever be tested without the use of auxiliary theory, whether explicitly formulated or not” (Blalock, 1968, p. 25). This is where SEM comes in: Not only is SEM able to test structural theories, it can simultaneously test auxiliary theories that make the concepts operational. Chapter 2 is entirely dedicated to auxiliary theories. The diversity of analyses subsumed under SEM makes it challenging to exactly define SEM. One way to do so is by eliciting their common steps. From this perspective, SEM is a multivariate statistical technique that consists of the following four steps: (1) model specification, (2) model identification, (3) model estimation, and (4) model assessment. Model specification is covered in Chapter 3, model identification in Chapter 4, model estimation in Chapter 5, and model assessment in Chapters 6 (global model assessment) and 7 (local model assessment). The presentation on model assessment is spread across two chapters in order to recognize the importance of the concept of model fit. Model specification is the topic of Chapter 3. Structural equation models can be specified in a graphical or a syntax-based fashion. Graphical model specification requires that a researcher draw a model, consisting of constructs, indicators, and the relationships between them. Syntax-based model specification requires that a researcher formulate the structural equation model as a set of equations. Figure 1.3 depicts a structural equation model specified with two different software programs for composite-based SEM: ADANCO (“ADvanced ANalysis of COmposites”) as a graphical solution, and the package cSEM (Rademaker & Schuberth, 2020) for R (R Core Team, 2020) as a syntax-based solution. The model is inspired by Bergami and Bagozzi (2000). In this model, the constructs organizational prestige and organizational identification explain the constructs affective commitment (love) and affective commitment (joy), controlling for gender. Not only must analysts specify the relationships between constructs, they also must specify each construct as a latent or an emergent variable and 1

Note that not all methodologists agree with this view; e.g., Edwards and Bagozzi (2000) define a construct as “a conceptual term used to describe a phenomenon of theoretical interest” (pp. 156-157), which means that they conflate the terms “concept” and “construct.”

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Composite-Based Structural Equation Modeling







  









  

 


  

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