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A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM) Third Edition To the Academy of Marketing Science (AMS) and its members Sara Miller McCune founded SAGE Publishing in 1965 to support the dissemination of usable knowledge and educate a global community SAGE publishes more than 1000 journals and over 600 new books each year, spanning a wide range of subject areas Our growing selection of library products includes archives, data, case studies and video SAGE remains majority owned by our founder and after her lifetime will become owned by a charitable trust that secures the company’s continued independence Los Angeles | London | New Delhi | Singapore | Washington DC | Melbourne A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM) Third Edition Joseph F Hair, Jr University of South Alabama G Tomas M Hult Michigan State University Christian M Ringle Hamburg University of Technology, Germany and University of Waikato, New Zealand Marko Sarstedt Ludwig-Maximilians-University Munich, Germany and Babeș-Bolyai University, Romania FOR INFORMATION: Copyright © 2022 by SAGE Publications, Inc SAGE Publications, Inc All rights reserved No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher 2455 Teller Road Thousand Oaks, California 91320 E-mail: order@sagepub.com SAGE Publications Ltd Oliver’s Yard 55 City Road London EC1Y 1SP United Kingdom SAGE Publications India Pvt Ltd B 1/I Mohan Cooperative Industrial Area All trademarks depicted within this book, including trademarks appearing as part of a screenshot, figure, or other image are included solely for the purpose of illustration and are the property of their respective holders The use of the trademarks in no way indicates any relationship with, or endorsement by, the holders of said trademarks Printed in the United States of America Mathura Road, New Delhi 110 044 India SAGE Publications Asia-Pacific Pte Ltd 18 Cross Street #10-10/11/12 China Square Central Singapore 048423 Library of Congress Cataloging-in-Publication Data Names: Hair, Joseph F., Jr., 1944- author | Hult, G Tomas M., author | Ringle, Christian M., author | Sarstedt, Marko author Title: A primer on partial least squares structural equation modeling (PLS-SEM) / Joe F Hair, Jr., G Tomas M Hult, Christian M Ringle, Marko Sarstedt Description: Third edition | Los Angeles : SAGE, [2022] | Includes bibliographical references and index | Identifiers: LCCN 2021004786 | ISBN 9781544396408 (paperback) | ISBN 9781544396415 (epub) | ISBN 9781544396422 (epub) | ISBN 9781544396330 (pdf) Subjects: LCSH: Least squares | Structural equation modeling Classification: LCC QA275 P88 2022 | DDC 511/.42— dc23 LC record available at https://lccn.loc.gov/2021004786 This book is printed on acid-free paper Acquisitions Editor: Leah Fargotstein Editorial Assistant: Kenzie Offley Production Editors: Natasha Tiwari, Gagan Mahindra Copy Editor: Terri Lee Paulsen Typesetter: C&M Digitals (P) Ltd Proofreader: Ellen Brink Indexer: Integra Cover Designer: Candice Harman Marketing Manager: Victoria Velasquez 21 22 23 24 25 10 BRIEF CONTENTS Prefacexi About the Authors xviii Chapter • An Introduction to Structural Equation Modeling Chapter • Specifying the Path Model and Examining Data 40 Chapter • Path Model Estimation 85 Chapter • Assessing PLS-SEM Results—Part I: Evaluation of the Reflective Measurement Models 109 • Assessing PLS-SEM Results—Part II: Evaluation of the Formative Measurement Models 140 • Assessing PLS-SEM Results—Part III: Evaluation of the Structural Model 186 Chapter • Mediator and Moderator Analysis 228 Chapter • Outlook on Advanced Methods 271 Chapter Chapter Glossary305 References327 Index352 DETAILED CONTENTS Prefacexi About the Authors Chapter 1 • An Introduction to Structural Equation Modeling xviii Chapter Preview What Is Structural Equation Modeling? Considerations in Using Structural Equation Modeling Composite Variables Measurement7 Measurement Scales Coding10 Data Distributions 10 Principles of Structural Equation Modeling Path Models With Latent Variables Testing Theoretical Relationships Measurement Theory Structural Theory PLS-SEM, CB-SEM, and Regressions Based on Sum Scores 12 12 13 14 14 15 Considerations When Applying PLS-SEM18 Key Characteristics of the PLS-SEM Method Data Characteristics Minimum Sample Size Requirement Missing Value Treatment Nonnormal Data Scales of Measurement Secondary Data Model Characteristics 18 24 24 27 28 28 28 30 Guidelines for Choosing Between PLS-SEM and CB-SEM31 Organization of Remaining Chapters 32 Summary34 Review Questions 36 Critical Thinking Questions 36 Key Terms 36 Suggested Readings 37 Chapter 2 • Specifying the Path Model and Examining Data 40 Chapter Preview 41 Stage 1: Specifying the Structural Model 41 Mediation44 Moderation45 Control Variables 47 Stage 2: Specifying the Measurement Models Reflective and Formative Measurement Models Single-Item Measures and Sum Scores Higher-Order Constructs Stage 3: Data Collection and Examination 50 51 57 59 61 Missing Data 62 Suspicious Response Patterns 64 Outliers64 Data Distribution 65 Case Study Illustration—Specifying the PLS-SEM Model Application of Stage 1: Structural Model Specification Application of Stage 2: Measurement Model Specification Application of Stage 3: Data Collection and Examination Path Model Creation Using the SmartPLS Software 67 67 69 71 72 Summary79 Review Questions 81 Critical Thinking Questions 82 Key Terms 82 Suggested Readings 83 Chapter 3 • Path Model Estimation 85 Chapter Preview 85 Stage 4: Model Estimation and the PLS-SEM Algorithm 86 How the Algorithm Works 86 Statistical Properties 92 Algorithmic Options and Parameter Settings to Run the Algorithm 94 Results96 Case Study Illustration—PLS Path Model Estimation (Stage 4) Model Estimation Estimation Results 97 97 99 Summary104 Review Questions 105 Critical Thinking Questions 106 Key Terms 106 Suggested Readings 106 Chapter 4 • Assessing PLS-SEM Results—Part I: Evaluation of the Reflective Measurement Models 109 Chapter Preview 109 Overview of Stage 5: Evaluation of Measurement Models 110 Stage 5a: Assessing Results of Reflective Measurement Models 116 Step 1: Indicator Reliability Step 2: Internal Consistency Reliability Step 3: Convergent Validity Step 4: Discriminant Validity Case Study Illustration—Evaluation of the Reflective Measurement Models (Stage 5a) Running the PLS-SEM Algorithm Reflective Measurement Model Evaluation 117 118 120 120 127 127 128 Summary136 Review Questions 137 Critical Thinking Questions 137 Key Terms 137 Suggested Readings 138 Chapter 5 • Assessing PLS-SEM Results—Part II: Evaluation of the Formative Measurement Models 140 Chapter Preview 140 Stage 5b: Assessing Results of Formative Measurement Models 141 Step 1: Assess Convergent Validity Step 2: Assess Formative Measurement Models for Collinearity Issues Step 3: Assess the Significance and Relevance of the Formative Indicators Bootstrapping Procedure Concept Bootstrap Confidence Intervals Case Study Illustration—Evaluation of the Formative Measurement Models (Stage 5b) Extending the Simple Path Model Reflective Measurement Model Evaluation (Recap) Formative Measurement Model Evaluation 143 145 148 152 152 156 159 159 169 171 Summary182 Review Questions 183 Critical Thinking Questions 183 Key Terms 184 Suggested Readings 184 Chapter 6 • Assessing PLS-SEM Results—Part III: Evaluation of the Structural Model 186 Chapter Preview 186 Stage 6: Structural Model Results Evaluation 187 Step 1: Assess the Structural Model for Collinearity Step 2: Assess the Significance and Relevance of the Structural Model Relationships Step 3: Assess the Model’s Explanatory Power Step 4: Assess the Model’s Predictive Power Number of Folds Number of Repetitions Prediction Statistic Results Interpretation Treating Predictive Power Issues Step 5: Model Comparisons Case Study Illustration—Evaluation of the Structural Model (Stage 6) 191 192 194 196 198 199 200 201 204 205 209 Summary223 Review Questions 225 Critical Thinking Questions 225 Key Terms 225 Suggested Readings 226 Chapter 7 • Mediator and Moderator Analysis Chapter Preview 228 228 Mediation229 Introduction229 Measurement and Structural Model Evaluation in Mediation Analysis 233 Types of Mediating Effects 233 Testing Mediating Effects 236 Multiple Mediation 238 Case Study Illustration—Mediation 240 Moderation243 Introduction243 Types of Moderator Variables 245 Modeling Moderating Effects 247 Creating the Interaction Term 249 Product Indicator Approach 249 Orthogonalizing Approach 250 Two-Stage Approach 251 Guidelines for Creating the Interaction Term 253 350 A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM) Temme, D., Kreis, H., & Hildebrandt, L (2010) A comparison of current PLS path modeling software: Features, ease-of-use, and 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Cheltenham: Edward Elgar Zhao, X., Lynch, J G., & Chen, Q (2010) Reconsidering Baron and Kenny: Myths and truths about mediation analysis Journal of Consumer Research, 37(2), 197–206 INDEX Absolute contribution, 151 Aguinis, H., 50, 254 Aguirre-Urreta, M I., 53, 158 Akaike weights, 206–208 Algorithmic options, 94–96 Alternating extreme pole data responses, 64 Anderson, R E., 50, 62, 66 Articles, 4–5 Artifacts, 53 Attractiveness (ATTR), 50–51, 51 (exhibit), 161 (exhibit) Average variance extracted (AVE), 117, 119, 141 Babin, B J., 50, 62, 66 Bandwidth-fidelity dilemma, 278 Baron, R M., 234 Bassellier, G., 150 Baumgartner, H., 29 Bayesian information criterion (BIC), 205 Beaty, J C., 254 Becker, J.-M., 17, 91, 280, 291, 293 Bentler, P M., 86, 297 Berneth, J B., 50 Bias-corrected and accelerated (BCa) bootstrap confidence intervals, 158 Binary coded data, 28 Binary (dummy) variables, 48–49 Binz Astrachan, C., 280 Black, W C., 50, 62, 66 Boik, R J., 254 Bollen, K A., 282 Bootstrap cases, 153 Bootstrapping, 123, 133 outer weights, results for, 179 (exhibit) p values in modeling window, 178 (exhibit) rules of, 159 (exhibit) 352 Bootstrapping confidence interval formative measurement models, 153–159, 155 (exhibit) reflective measurement models, 123–124 Bootstrap samples, 153 Bovaird, J A., 249 Cascaded moderator analysis, 248 Casewise deletion, 62 Categorical control variable, 48–49, 49 (exhibit) Categorical moderator variable, 245 Categorical scale, Causal indicators, 53–54, 92 Causal links, 43 Causal-predictive paradigm, 22, 43 CB-SEM See Covariance-based structural equation modeling (CB-SEM) Cenfetelli, R T., 150 Centroid weighting scheme, 90 Cepeda-Carrión, G., 232 Chatelin, Y.-M., 90 Chatla, S B., 188 Cheah, J.-H., 73, 90, 91, 144, 259 Chen, Q., 234 Chin, W W., 90, 251, 253 Ciavolino, E., 91 Cluster analysis, 290 Coding, 10 Coefficient of determination (R²), 195 Comma-separated value (.csv), 73 Common factor-based SEM, 15 Common factor model, 297 Communality, 117, 119 Index 353 Competence (COMP), 50–51, 51 (exhibit), 67–71 mediation, 240–243 model estimation, PLS-SEM, 100–103 moderation, 261–267 reflective measurement model assessment, 127–135 structural model assessment, 210–223 Competitive mediation, 234 Complementary mediation, 234 Composite-based SEM, 16, 23 PLS-SEM algorithm, 86 Composite indicators, 53–54 Composite reliability, 119 Composite score, Composite variables, 6, (exhibit), 16 Compositional invariance, 294, 295 (exhibit) Conditional indirect effect, 257 Conditional process models, 257 Configural invariance, 294, 295 (exhibit) Confirmatory composite analysis (CCA), 111, 114, 114–115 (exhibit) Confirmatory factor analysis, Confirmatory tetrad analysis in PLS-SEM (CTA-PLS), 56, 281–285 indicators, 282 (exhibit) model-implied nonredundant vanishing tetrads, 283 results, 285 (exhibit) steps, 282–283 vanishing tetrads, 282 Consistency at large, 93 Consistent PLS-SEM (PLSc-SEM), 296–297 Constructs, PLS-SEM algorithm, 86 Content validity, 117 Continuous moderator variable, 246 Convergence, 96 Convergent validity, 120 assessment, 143–145 Corporate reputation on customer satisfaction (CUSA), 67–71 mediation, 240–243 model estimation, PLS-SEM, 100–103 moderation, 261–267 reflective measurement model assessment, 127–135 structural model assessment, 210–223 Corporate social responsibility (CSOR), 50–51, 51 (exhibit), 145, 161 (exhibit) Correlation weights, 89 Covariance-based structural equation modeling (CB-SEM), common factor-based SEM, 15 common variance and, 18 guidelines for choosing, 31, 32 (exhibit) PLS-SEM and, 15 vs PLS-SEM selection, 31, 32 (exhibit) sum scores and, 15–18 Coverage error, 157 Critical t values, 154, 192 Cronbach’s alpha, 118–120, 129 Cross-loadings, 122 Cross-validated predictive ability test (CVPAT), 208 Customer loyalty (CUSL), 67–71, 210–223 mediation, 240–243 model estimation, PLS-SEM, 100–103 moderation, 261–267 reflective measurement model assessment, 127–135 Danks, N., 205, 221 Data characteristics, 29 (exhibit) metric scale, 28 minimum sample size requirements, 24–27 missing value treatment, 27 nonnormal data, 28 secondary data, 28–29 Data collection and examination, 61 case study, 71–72 distribution, 65–66 guidelines for examining, 66–67 (exhibit) 354 A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM) missing data, 61–63 outliers, 64–65 questionnaires and, 61–62 response patterns, 64 Data distributions, 10–11, 65–66 Data matrix, 86 (exhibit), 87 Dawson, J., 256 Degrees of freedom (df), 154 DeVellis, R F., 50 Diagonal lining, data response, 64 Diamantopoulos, A., 50, 57, 59 Dijkstra, T K., 86, 114, 119, 189 (exhibit), 190 (exhibit) Direct effect, 44, 194 Direct-only nonmediation, 234 Disattenuated correlation, 122 Discriminant validity, 120–126 bootstrap confidence interval, 123–124, 133 cross-loadings, 122 disattenuated correlation, 122 Fornell-Larcker criterion, 121–122, 121 (exhibit), 132 (exhibit) heterotrait-heteromethod correlations, 122 heterotrait-monotrait ratio (HTMT), 122–124, 123 (exhibit), 132 (exhibit) monotrait-heteromethod correlations, 122, 124 Disjoint two-stage approach, 280 Eberl, M., 67 Effect indicators See Reflective measurement Efron, B., 158 Embedded two-stage approach, 280 Empirical t value, 154 Endogeneity, 285–286 Endogenous latent variables, 13, 42 PLS-SEM algorithm, 88 EP-theoretic approach, 22 Equality of composite mean values and variances, 294, 295 (exhibit) Equidistance, Error terms, 13 Esposito Vinzi, V., 90 Evaluation criteria, 109–110 See also PLS-SEM results Exact fit test, 189 (exhibit) Exogenous latent variables, 13, 42 PLS-SEM algorithm, 88 Explaining and predicting (EP) theories, 22 Explanatory power, structural model, 194–196 Exploratory factor analysis, Extended repeated indicators approach, 280 Factor (score) indeterminacy, 17 Factor weighting scheme, 90 Falk, R F., 43 f2 effect size, 195 interpretation of, 196 (exhibit) Finite mixture partial least squares (FIMIX-PLS), 291 First-generation techniques, limitations of, 3–4 Fordellone, M., 293 Formative index, 52 Formative indicators absolute contribution, 151 decision-making process, 152 (exhibit) relative contribution, 149 rules, 153 (exhibit) Formative measurement, 14, 51–57 PLS-SEM algorithm, 88 PLS-SEM results, 113 vs reflective measurement, 52 (exhibit), 54–56 Formative measurement model assessment, 171–181 bootstrapping procedure, 152–159, 155 (exhibit) case study, 159–181 collinearity issues, 145–148, 148 (exhibit) content specification, 141 Index 355 convergent validity, 143–145 corporate reputation, theoretical model of, 159 correlation matrix, 146 global single item, 144 higher-order construct, 150 indicators of, 148–152, 160–161 (exhibit) PLS-SEM algorithm, 166 (exhibit), 167 procedure, 142 (exhibit) redundancy analysis, 143, 172 (exhibit) results, 141 rules of, 153–159 simple path model, 159 SmartPLS software, 156 tolerance (TOL), 146 variance inflation factor (VIF), 147, 148 (exhibit) VIF values, 173 (exhibit) Formative-reflective higher-order construct, 278 Fornell-Larcker criterion, 121–122 discriminant validity, 132 (exhibit) visual representation of, 121 (exhibit) Fuchs, C., 57 Full measurement invariance, 295 Full mediation, 234 Gaussian copula approach, 286 Genetic algorithm segmentation in PLS-SEM (PLS-GAS), 291 Geweke and Meese criterion (GM), 205 Global single item, validation of, 144, 144 (exhibit) Goodness-of-fit index (GoF), 189 (exhibit) Graphical interfaces, 91–92 Gregor, S., 22 Grimm, M S., 62–63 Gudergan, S P., 24, 56, 115, 158, 276, 280, 284 Gupta, S., 286 Hadaya, P., 25, 88 Haenlein, M., 25 Hair, J F., 15, 23, 24, 25, 31, 50, 54, 59, 62, 66, 111, 114, 115, 190 (exhibit), 276, 280, 293, 297 Hauff, S., 277 Hayes, A F., 237 (exhibit), 258, 259 Henseler, J., 25, 54, 114, 121, 122, 123, 124, 158, 189 (exhibit), 190 (exhibit), 253, 289, 290, 294, 295 Heterogeneity, 46, 229, 288 (exhibit) Heterotrait-heteromethod correlations, 122 Heterotrait-monotrait (HTMT) ratio, 117, 122–124, 123 (exhibit) confidence intervals, 134 (exhibit) Hierarchical component model, 277 See also Higher-order constructs Higher-order component, 60, 278 Higher-order constructs, 59–61, 277–281 example, 60 (exhibit) types of, 278, 279 (exhibit) Higher-order models See Higher-order constructs Hildebrandt, L., 91 Ho, J A., 259 Holdout sample, 197 Howard, M C., 111, 114 Huang, W., 86, 297 Hult, G T M., 25, 59, 286, 294 Hwang, H., 90 Hypothesis tests, 50 Hypothesized relationships, 192 Importance-performance map analysis (IPMA), 272, 273 direct, indirect, and total effects, 275 (exhibit) model, 273 (exhibit) rescaling, 274 Index of moderated mediation, 258 Indicators, 7–8 causal, 53–54 composite, 53–54 formative measurement models assessment, 148–152 path models and, 12 356 A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM) PLS-SEM algorithm, 87 for reflective measurement, 70 (exhibit) reliability, 117–118 Indirect effect, 44, 194 Indirect-only mediation, 234 Individual mediating effect, 239 Initial values, PLS-SEM algorithm, 95 Inner model See Structural model In-sample predictive power, 195 Interaction effect, 245 Interaction term, 248, 249 guidelines for creating, 253 model evaluation, 253–254 results interpretation, 254–257 Internal consistency reliability, 118–120 Interpretational confounding, 149 Interval scale, Inverse square root method, 25–27 Ismail, I R., 91 Item non-response, 62 Items/manifest variables, Iterative reweighted regressions segmentation (PLS-IRRS), 293 Jarvis, C B., 281 Joint mediating effect, 239 Kaiser, S., 57 Kamakura, W A., 57 Kenny, D A., 233–234 K-fold cross-validation, 198 Kim, K H., 43 Klein, K., 280 Klesel, M., 289 Kock, N., 25, 88 Kolmogorov-Smirnov test, 11 Kreis, H., 91 Kurtosis, 11, 66 Lance, C E., 294 Latent class techniques, 287 Latent variables, scores, 86 Lauro, C., 90 Leroi-Werelds, S., 153–154 Likeability (LIKE), 67–71 mediation, 240–243 model estimation, PLS-SEM, 100–103 moderation, 261–267 reflective measurement model assessment, 127–135 structural model assessment, 210–223 Likert scales, 10, 71, 95, 221 Lim, Q H., 259 Linear regression model (LM) benchmark, 201–202 Listwise deletion, 62 Little, T D., 249 Lohmöller, J.-B., 30, 86, 91 Lower-order components, 60, 278 Loyalty construct, 42, 42 (exhibit) mediating effect, 43–44, 43 (exhibit) Lynch, J G., 234 MacKenzie, S B., 50, 281 Management competence, 150 Manifest variables, Marakas, G M., 53 Marcolin, B L., 251 Maximum number of iterations, 96 Mean absolute error (MAE), 200–204 Mean value replacement, 62 Measurement, 7–8 composite score, concept of, error, indicators, 7–8 invariance, 294–295 items/manifest variables, of latent variables/constructs, process, single-item constructs, Measurement invariance of composite models (MICOM) procedure, 294, 295 (exhibit) Measurement model, 13, 41 case study, 69–71 confirmatory tetrad analysis in PLS-SEM (CTA-PLS), 56 Index 357 guidelines for choosing, 56 (exhibit) higher-order component, 60 higher-order constructs, 59–61 lower-order components, 60 nomological validity, 113 path model, 50, 61 (exhibit) PLS-SEM algorithm, 87 PLS-SEM results, 110 (exhibit), 113 reflective and formative measurement models, 51–57 reliability, measurement error, 111–113 second-order constructs, 60 single-item measures, 57–59 specification, 50–61 sum scores, 57–59 validation, 111–113 Measurement model misspecification, 281 Measurement scale, categorical, equidistance, interval, nominal, ordinal, ratio scale, Measurement theory, 13, 14 Mediated moderation, 259 Mediation, 44–45, 44 (exhibit), 228, 229 analysis procedure, 235 (exhibit) case study, 240–243 cause-effect relationship, 230 (exhibit), 231 (exhibit) evaluation in, 233 model, 230 (exhibit), 232 (exhibit) multiple, 238–240 PROCESS vs PLS-SEM, 237–238 (exhibit) rules, 240 (exhibit) testing, 236–238 types of, 233–236 Mediator construct, 228 Mena, J A., 15 Metric scale, 28 Metrological uncertainty, 17 Miller, N B., 43 Minimum sample size requirements, 24–27, 27 (exhibit) Missing data, 61–63 alternating extreme pole responses, 64 diagonal lining response, 64 kurtosis, 66 levels, 62 outlier response, 64–65 skewness, 66 straight lining response, 64 survey non-response, 62 surveys, 64 Missing values model estimation, PLS-SEM, 99, 99 (exhibit) treatment, 27, 62 Model characteristics, 19–20 (exhibit), 30–31, 31 (exhibit) Model comparisons, 43, 205–209, 222 (exhibit) Model complexity, 94 Model estimation, PLS-SEM, 97–99 missing values, 99, 99 (exhibit) path coefficients, 100–101, 100–101 (exhibit) PLS-SEM algorithm settings, 98 (exhibit) results, 99–103 singular data matrix, 99 Model overfit, 195 Model parsimony, 190 Moderated mediation, 257 Moderation, 45–47, 229 case study, 260–267 categorical moderator variable, 245 continuous moderator variable, 246 heterogeneity and, 46 interaction term, 249 modeling effects, 247–248 multigroup analysis, 46, 47 (exhibit), 245 (exhibit) orthogonalizing approach, 250–251 overview, 243–245 product indicator approach, 249–250 358 A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM) rules, 259–260 (exhibit) theoretical model, 46 (exhibit), 244 (exhibit) two-stage approach, 251–252 types of, 245–246 Moderator effect, 45, 247 Moderator variable, 243 Monotrait-heteromethod correlations, 122, 124 Mooi, E A., 63, 65, 72 Multicollinearity, 145 Multigroup analysis, 46, 47 (exhibit), 287–290 Multiple mediation, 238–240 analysis, 238 Multiple moderator model, 248 Multiple regression analysis, with sum scores, 16 Multivariate analysis, coding, 10 organization of, (exhibit) PLS regression, 18 See also Covariance-based structural equation modeling (CB-SEM); Partial least squares structural equation modeling (PLS-SEM) Necessary condition analysis (NCA), 276–277 Newsted, P R., 251 Ng, S I., 259 Niehaves, B., 289, 290 Nitzl, C., 111, 114, 232 No-effect nonmediation, 234 Nominal scale, Nomological validity, 113 Nonnormal data, 28 Non-response data, 62 Normal data distributions, 11 Observed heterogeneity, 286–294 Oliver, R L., 22 One-tailed test, 192 Ordinal scale, Orthogonalizing approach, 249–250 Outer loadings, 88 reflective measurement model assessment, 128 relevance test, 118 (exhibit) Outer model in PLS-SEM, 13 Outer weights, 88 Outliers, 64–65 Out-of-sample predictive power, 196 Pairwise deletion, missing data, 63 Parameter settings, 94–96 Parametric approach, 289 Park, S., 286 Parsimonious models, 205 Partial least squares k-means (PLS-SEM-KM), 293 Partial least squares structural equation modeling (PLS-SEM), algorithm, 22 case studies, 67–72 vs CB-SEM selection, 31, 32 (exhibit) characteristics of, 18–24, 19–21 (exhibit) common factor-based SEM and, 15–16 composite-based SEM and, 16, 23 data characteristics, 19 (exhibit), 24–29, 27 (exhibit) guidelines for choosing, 31, 32 (exhibit) limitations of, 22 metric scale, 28 minimum sample size requirements, 24–27 missing value treatment, 27 model characteristics, 19–20 (exhibit), 30–31, 31 (exhibit) model estimation, 20 (exhibit), 23 model evaluation, 20–21 (exhibit) model fit measures in, 189–190 (exhibit) nonnormal data, 28 procedure for applying, 33 (exhibit) R² values, 18 secondary data, 28–29 sum scores and, 15–18 variance-based SEM approach, 18 Index 359 Partial measurement invariance, 295 Partial mediation, 234 Path coefficients, 90 structural model assessment, 217 (exhibit) Path model, 12, 12 (exhibit) measurement, 13, 41 SmartPLS software and, 62, 63, 67, 72–79 structural, 13, 41 theoretical relationships, 13–15 Path weighting scheme, 90 Percentile method, 157 Performance (PERF), 159, 161 (exhibit) Permutation test, 289 Pierce, C A., 254 PLSpredict procedure, 188, 196, 199 (exhibit) guidelines, 203 (exhibit) PLS regression, 18 PLS-SEM algorithm, 86 composite-based SEM method, 86 constructs, 86 convergence, 96 data matrix for, 86 (exhibit), 87 exogenous constructs, 88 factors, 89 formative measurement models assessment, 166 (exhibit), 167 indicators, 87 initializing rules, 96 (exhibit) initial values, 95 latent variables, 86, 88 maximum number of iterations, 96 measurement model, 87 options and parameter, 94–96 path coefficients, 90 path model and data for, 87 (exhibit) prediction, 90 raw data, 86 results, 96–97 R² value, 90 secondary data, 87 statistical properties, 92–94 stop criterion, 96 structural model, 88 weighted, 90, 91 PLS-SEM bias, 23, 93 PLS-SEM results confirmatory composite analysis (CCA), 114, 114–115 (exhibit) evaluation criteria, 109–110 formative measurement model, 113 measurement error, 111 measurement models, 110 (exhibit) nomological validity, 113 outer loadings, 170 (exhibit) reflective measurement model, 112 reliability, 111–113 rules, 116 (exhibit) structural model, 110 (exhibit) validity, 111, 112 PLS typological path modeling (PLS-TPM), 291 Podsakoff, N P., 50 Podsakoff, P M., 50, 281 Preacher, K J., 238, 256 Prediction, 90 error, 201 Prediction-oriented segmentation in PLS-SEM (PLS-POS), 291 Predictive power model, 196–205 folds, number of, 198–199 interpretation, results, 200–204 issues, 204–205 linear regression model (LM) benchmark, 201–202 repetitions, 199–200 statistic, 200 Procedure for applying PLS-SEM, 33 (exhibit) PROCESS vs PLS-SEM, mediation analysis, 237–238 (exhibit) Product indicator approach, 249 Q2 statistic, 197 Quality (QUAL), 159, 160–161 (exhibit), 210–223 Questionnaires and data collection, 61–62 360 A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM) Ramayah, T., 91 Ratio scale, Ray, S., 188, 205 Redundancy analysis, 143–144 Reflective-formative higher-order construct, 278 Reflective measurement evaluation criteria, 112 vs formative measurement, 52 (exhibit), 54–56 indicators for, 70 (exhibit) model, 11, 51–57, 114 PLS-SEM algorithm, 88 Reflective measurement model assessment, 116–117, 169–170 case study, 127–135 composite reliability, 119 construct reliability and validity, 130 (exhibit) content validity, 117 convergent validity, 120 Cronbach’s alpha, 118–120, 129 discriminant validity, 120–126 Fornell-Larcker criterion, 121–122, 121 (exhibit) heterotrait-monotrait ratio (HTMT), 122–124, 123 (exhibit) indicator reliability, 117–118 internal consistency reliability, 118–120 outer loadings, 118 (exhibit), 128 PLS-SEM algorithm, 127–135 quality criteria, 129 reliability coefficient, 119 rules, 126 (exhibit) SmartPLS software, 127–135 Reflective-reflective higher-order construct, 278 Regression analysis, 3–4 Regression weights, 89 Reinartz, W., 25 Relative contribution, indicators, 149 Relevance of significant relationships, 193 Reliability coefficient, 119 Reliability, measurement error, 111–113 Repeated indicators approach, 279 Reputation construct, 42, 42 (exhibit) categorical variable, 49, 49 (exhibit) mediating effect, 43–44, 43 (exhibit) Rescaling, 274 Response-based procedure for detecting unit segments in PLS path modeling (REBUS-PLS), 291 Response-based segmentation techniques, 291 Response patterns, data collection, 64 Retrospective approach, 25–26 Review articles, (exhibit) Richter, N F., 277 Rigdon, E E., 17, 54, 276 Ringle, C M., 15, 24, 25, 31, 54, 56, 59, 90, 115, 121, 122, 123, 158, 190 (exhibit), 273, 276, 277, 280, 289, 291, 293, 294, 295, 297 Risher, J J., 31 Rockwood, N J., 259 Roldán, J L., 91, 232 Rönkkö, M., 53, 158 Root mean square error (RMSE), 200–204 Root mean square residual covariance (RMStheta), 189 (exhibit) R² values, 18, 195 PLS-SEM algorithm, 90 Sarstedt, M., 15, 17, 23, 24, 25, 31, 43, 54, 57, 59, 63, 65, 72, 73, 90, 115, 121, 122, 123, 158, 190 (exhibit), 205, 221, 273, 276, 277, 280, 291, 293, 294, 295 Satisfaction construct, 42, 42 (exhibit) categorical variable, 49, 49 (exhibit) mediating effect, 43–44, 43 (exhibit) Scales, 52 of measurement, 28–29 Schlittgen, R., 293 Schuberth, F., 114, 190 (exhibit), 289, 290 Schubring, S., 277 Schwaiger, M., 67, 69, 159 Secondary data, 28–29 PLS-SEM algorithm, 87 Index 361 Second-generation techniques, tools, Second-order constructs, 60, 278 SEM See Structural equation modeling (SEM) Serial mediating effect, 239 Shapiro-Wilk test, 11, 65 Sharma, P N., 43, 205, 221 Shmueli, G., 43, 188, 190 (exhibit), 196, 205 Simple corporate reputation model, 68 Single-item constructs, Single-item measures, 57–59 guidelines for, 58 sum scores and, 59 Single mediation analysis, 238 Singular data matrix, 99 Sinkovics, R R., 158, 289 Skewness, 11, 66 Slope plot, 256 SmartPLS software bootstrapping options in, 175 (exhibit) to create new project, 73–79 data view in, 74 (exhibit) extended model in, 163 (exhibit), 241 (exhibit) formative measurement models assessment, 156, 162, 163–165 (exhibit) initial model, 76 (exhibit) mediation, 240 model estimation, 97–103 path model and, 62, 63, 67, 72–79 reflective measurement model, assessment of, 127–135 simple model with names and data assigned, 78 (exhibit) Sobel, M E., 236 Sobel test, 236 “Soft modeling,” 28–29 Software packages, statistical, 92 Specific indirect effect, 238 Squillacciotti, S., 291 Standard error, 192 Standardized root mean square residual (SRMR), 189 (exhibit) Standardized values, 192 Statistical modeling technique, Statistical power, 22 Statistical properties, 92–94 Steenkamp, J B E M., 29 Stop criterion, PLS-SEM algorithm, 96 Straight lining, data response, 64 Streukens, S., 153–154 Structural equation modeling (SEM), coding, 10 common factor-based, 15 composite variables, 6, (exhibit) covariance-based structural equation modeling (CB-SEM), data distributions, 10–11 elements, measurement, 7–9 PLS path modeling, types of, Structural equation modeling, principles of measurement theory, 14 path model, 12–13 structural theory, 14–15 theoretical relationships, 13–14 Structural model, 13 case study, 67–69 causal links, 43 control variables, 47–50 endogenous latent variables, 42 exogenous latent variables, 42 guidelines for, 61 (exhibit) mediating effect, 44–45, 44 (exhibit) model comparisons, 43 moderation, 45–47 PLS-SEM algorithm, 88 PLS-SEM results, 110 (exhibit) specification, 41 theoretical model, 67–69 types of constructs, 42, 42 (exhibit) Structural model assessment BIC values, 223 bootstrapping results, 214–215 (exhibit) 362 A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM) bootstrapping samples, 216 (exhibit) case study, 209–223 for collinearity, 191 comparisons, 205–209 critical value, 192 direct, indirect, and total effects, 194 explanatory power, 194–196 f2 effect sizes, 219 (exhibit) hypothesized relationships, 192 modeling window, results in, 211 (exhibit) overview, 187 path coefficients, 217 (exhibit) PLSpredict results report, 220 (exhibit), 221 (exhibit) predictive power, 196–205 procedure, 188 (exhibit) relevance of significant relationships, 193 rules of, 208–209 (exhibit) significance and relevance of, 192–194 standard error, 192 standardized values, 192 total effects, 213 (exhibit) VIF values, 212 (exhibit) Structural theory, 13, 14–15 Studentized bootstrap method, 158 Sum scores, 16, 57–59 PLS-SEM algorithm, 94 Suppressor variable, 234 Survey non-response, 62 Surveys, missing data, 64 Techniques, advanced confirmatory tetrad analysis in PLS-SEM (CTA-PLS), 281–285 consistent PLS-SEM, 296–297 endogeneity, 285–286 higher-order construct, 277–281 measurement invariance, 294–295 observed heterogeneity, 286–294 unobserved heterogeneity, 286–294 Tee, K K., 259 Temme, D., 91 Tenenhaus, M., 90 10 times rule, 25 Tetrad, 281 Text (.txt) data sets, 73 Theoretical t values, 154 Theory, 13 Thiele, K O., 25, 43, 59, 205 Three-way interaction, 248 Ting, H., 91 Ting, K.-F., 282 Tolerance (TOL), 146 Total effects, 194 structural model assessment, 213 (exhibit) Total indirect effect, 238 Training sample, 197 Two-stage approach, 251, 280 Two-tailed test, 192 Two-way interaction, 248 Unit non-response See Survey non-response Unobserved heterogeneity, 286–287 cluster analysis, 290 finite mixture partial least squares (FIMIX-PLS), 291 genetic algorithm segmentation in PLS-SEM (PLS-GAS), 291 iterative reweighted regressions segmentation (PLS-IRRS), 292 partial least squares k-means (PLS-SEM-KM), 293 PLS typological path modeling (PLS-TPM), 291 prediction-oriented segmentation in PLS-SEM (PLS-POS), 291 response-based procedure for detecting unit segments in PLS path modeling (REBUS-PLS), 291 response-based segmentation techniques, 291 “Unwise deletion,” data, 63 Index 363 Validation, 111 measurement error, 111–113 Vandenberg, R J., 294 Vanishing tetrads, 282 Variance-based SEM, 18 Variance inflation factor (VIF), 147 collinearity assessment using, 148 (exhibit) Variate See Composite variables Velasquez Estrada, J M., 188 Vichi, M., 293 Völckner, F., 291 Wagner, R., 62–63 Weighted PLS-SEM (WPLS) algorithm, 91 Wende, S., 56, 158, 284 Wetzels, M., 280 Widaman, K F., 249 Wilczynski, P., 57 Will, A., 56, 158, 284 Winklhofer, H M., 50 Wold, H., 28, 30, 86 Zhao, X., 234