Table of Contents
Preface xiii
Authors xix
List of Figures xxi
List of Tables xxix
List of Algorithms xxxi
Abbreviations xxxiii
Greek Alphabet xxxvii
I Preliminaries and Basic Methods 1
1 Framing Structural Equation Modelling 3
1.1 What Is Structural Equation Modelling? 3
1.2 Two Approaches to Estimating SEM Models 6
1.2.1 Covariance-based SEM 6
1.2.2 Partial least squares SEM 8
1.2.3 Consistent partial least squares SEM 9
1.3 What Analyses Can PLS-SEM Do? 10
1.4 The Language of PLS-SEM 11
1.5 Summary 13
2 Multivariate Statistics Prerequisites 15
2.1 Bootstrapping 15
2.2 Principal Component Analysis 19
2.3 Segmentation Methods 28
2.3.1 Cluster analysis 28
2.3.1.1 Hierarchical clustering algorithms 30
2.3.1.2 Partitional clustering algorithms 39
2.3.2 Finite mixture models and model-based clustering 42
2.3.3 Latent class analysis 48
2.4 Path Analysis 49
2.5 Getting to Partial Least Squares Structural Equation Modelling 56
2.6 Summary 59
Appendix: R Commands 59
The bootstrap 60
Principal component analysis 62
Segmentation methods 65
Latent class analysis 74
Path analysis 74
Appendix: Technical Details 80
More insights on the bootstrap 80
The algebra of principal components analysis 82
Clustering stopping rules 84
Finite mixture models estimation and selection 86
Path analysis using matrices 87
3 PLS Structural Equation Modelling: Specification and Estimation 89
3.1 Introduction 89
3.2 Model Specification 92
3.2.1 Outer (measurement) model 93
3.2.2 Inner (structural) model 96
3.2.3 Application: Tourists satisfaction 97
3.3 Model Estimation 101
3.3.1 The PLS-SEM algorithm 102
3.3.2 Stage I: Iterative estimation of latent variable scores 103
3.3.3 Stage II: Estimation of measurement model parameters 107
3.3.4 Stage III: Estimation of structural model parameters 107
3.4 Bootstrap-based Inference 108
3.5 The plssem Stata Package 110
3.5.1 Syntax 111
3.5.2 Options 112
3.5.3 Stored results 113
3.5.4 Application: Tourists satisfaction (cont.) 113
3.6 Missing Data 118
3.6.1 Application: Tourists satisfaction (cont.) 121
3.7 Effect Decomposition 123
3.8 Sample Size Requirements 127
3.9 Consistent PLS-SEM 129
3.9.1 The plssemc command 130
3.10 Higher Order Constructs 134
3.11 Summary 139
Appendix: R Commands 140
The plspm package 141
The cSEM package 145
Appendix: Technical Details 151
A formal definition of PLS-SEM 151
More details on the consistent PLS-SEM approach 153
4 PLS Structural Equation Modelling: Assessment and Interpretation 155
4.1 Introduction 155
4.2 Assessing the Measurement Part 156
4.2.1 Reflective measurement models 156
4.2.1.1 Unidimensionality 156
4.2.1.2 Construct reliability 157
4.2.1.3 Construct validity 157
4.2.2 Higher order reflective measurement models 159
4.2.3 Formative measurement models 160
4.2.3.1 Content validity 161
4.2.3.2 Multicollinearity 161
4.2.3.3 Weights 163
4.3 Assessing the Structural Part 163
4.3.1 R-squared 164
4.3.2 Goodness-of-fit 165
4.3.3 Path coefficients 165
4.4 Assessing a PLS-SEM Model: A Full Example 167
4.4.1 Setting up the model using plssem 167
4.4.2 Estimation using plssem in Stata 170
4.4.3 Evaluation of the example study model 172
4.4.3.1 Measurement pan 172
4.4.3.2 Structural part 176
4.5 Summary 178
Appendix: R Commands 178
Appendix: Technical Details 183
Tools for assessing the measurement part of a PLS-SEM model 183
Tools for assessing the structural part of a PLS-SEM model 185
II Advanced Methods 187
5 Mediation Analysis With PLS-SEM 189
5.1 Introduction 189
5.2 Baron and Kenny's Approach to Mediation Analysis 189
5.2.1 Modifying the Baron-Kenny approach 191
5.2.2 Alternative to the Baron-Kenny approach 192
5.2.3 Effect size of the mediation 195
5.3 Examples in Stata 195
5.3.1 Example 1: A single observed mediator variable 196
5.3.2 Example 2: A single latent mediator variable 198
5.3.3 Example 3: Multiple latent mediator variables 203
5.4 Moderated Mediation 207
5.5 Summary 207
Appendix: R Commands 208
6 Moderating/Interaction Effects Using PLS-SEM 215
6.1 Introduction 215
6.2 Product-Indicator Approach 217
6.3 Two-Stage Approach 220
6.4 Multi-Sample Approach 223
6.4.1 Parametric test 224
6.4.2 Permutation test 225
6.5 Example Study: Interaction Effects 226
6.5.1 Application of the product-indicator approach 226
6.5.2 Application of the two-stage approach 229
6.5.2.1 Two-stage as an alternative to product-indicator 229
6.5.2.2 Two-stage with a categorical moderator 230
6.5.3 Application of the multi-sample approach 234
6.6 Measurement Model Invariance 235
6.7 Summary 237
Appendix: R Commands 238
Application of the product-indicator approach 238
Application of the two-stage approach 239
Application of the multi-sample approach 243
Measurement model invariance 247
7 Detecting Unobserved Heterogeneity in PLS-SEM 249
7.1 Introduction 249
7.2 Methods for the Identification and Estimation of Unobserved Heterogeneity in PLS-SEM 251
7.2.1 Response-based unit segmentation in PLS-SEM 251
7.2.2 Finite mixture PLS (FTMIX-PLS) 261
7.2.3 Other methods 266
7.2.3.1 Path modelling segmentation tree algorithm (Path-mox) 266
7.2.3.2 Partial least squares genetic algorithm segmentation (PLS-GAS) 267
7.3 Summary 268
Appendix: R Commands 268
Appendix: Technical Details 271
The math behind the REBUS-PLS algorithm 271
Permutation tests 274
III Conclusions 277
8 How to Write Up a PLS-SEM Study 279
8.1 Publication Types and Structure 279
8.2 Example of PLS-SEM Publication 280
8.3 Summary 285
IV Appendices 287
A Basic Statistics Prerequisites 289
A.1 Covariance and Correlation 289
A.2 Linear Regression Analysis 296
A.2.1 The simple linear regression model 296
A.2.2 Goodness-of-fit 299
A.2.3 The multiple linear regression model 300
A.2.4 Inference for the linear regression model 302
A.2.4.1 Normal-based inference 303
A.2.5 Categorical predictors 305
A.2.6 Multicollinearity 309
A.2.7 Example 311
A.3 Summary 320
Appendix: R Commands 321
Covariance and correlation 321
Bibliography 325
Index 341
