Table Of ContentStructural Equation
Modelling with Partial
Least Squares Using
Stata and R
Structural Equation
Modelling with Partial
Least Squares Using
Stata and R
Mehmet Mehmetoglu
Department of Psychology,
Norwegian University of Science and Technology
Sergio Venturini
Department of Management,
Università degli Studi di Torino
First edition published 2021
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ISBN: 9781482227819 (hbk)
ISBN: 9780429170362 (ebk)
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To Rannvei Sæther [M]
A Deborah,
il mio tesoro più prezioso,
per quello che fai,
per quello che sei [S]
Contents
Preface xiii
Authors xix
ListofFigures xxi
ListofTables xxix
ListofAlgorithms xxxi
Abbreviations xxxiii
GreekAlphabet xxxvii
I PreliminariesandBasicMethods 1
1 FramingStructuralEquationModelling 3
1.1 WhatIsStructuralEquationModelling? . . . . . . . . . . . . . . . 3
1.2 TwoApproachestoEstimatingSEMModels . . . . . . . . . . . . 6
1.2.1 Covariance-basedSEM . . . . . . . . . . . . . . . . . . . . 6
1.2.2 PartialleastsquaresSEM. . . . . . . . . . . . . . . . . . . 8
1.2.3 ConsistentpartialleastsquaresSEM . . . . . . . . . . . . . 9
1.3 WhatAnalysesCanPLS-SEMDo? . . . . . . . . . . . . . . . . . 10
1.4 TheLanguageofPLS-SEM . . . . . . . . . . . . . . . . . . . . . 11
1.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2 MultivariateStatisticsPrerequisites 15
2.1 Bootstrapping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 PrincipalComponentAnalysis . . . . . . . . . . . . . . . . . . . . 19
2.3 SegmentationMethods . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3.1 Clusteranalysis . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3.1.1 Hierarchicalclusteringalgorithms . . . . . . . . 30
2.3.1.2 Partitionalclusteringalgorithms. . . . . . . . . . 39
2.3.2 Finitemixturemodelsandmodel-basedclustering . . . . . 42
2.3.3 Latentclassanalysis . . . . . . . . . . . . . . . . . . . . . 48
2.4 PathAnalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
2.5 GettingtoPartialLeastSquaresStructuralEquationModelling . . . 56
vii
viii Contents
2.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Appendix:RCommands . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Thebootstrap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Principalcomponentanalysis . . . . . . . . . . . . . . . . . . . . . 62
Segmentationmethods . . . . . . . . . . . . . . . . . . . . . . . . 65
Latentclassanalysis . . . . . . . . . . . . . . . . . . . . . . . . . 74
Pathanalysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Appendix:TechnicalDetails . . . . . . . . . . . . . . . . . . . . . . . . 80
Moreinsightsonthebootstrap . . . . . . . . . . . . . . . . . . . . 80
Thealgebraofprincipalcomponentsanalysis . . . . . . . . . . . . 82
Clusteringstoppingrules . . . . . . . . . . . . . . . . . . . . . . . 84
Finitemixturemodelsestimationandselection . . . . . . . . . . . 86
Pathanalysisusingmatrices . . . . . . . . . . . . . . . . . . . . . 87
3 PLSStructuralEquationModelling:SpecificationandEstimation 89
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
3.2 ModelSpecification . . . . . . . . . . . . . . . . . . . . . . . . . 92
3.2.1 Outer(measurement)model . . . . . . . . . . . . . . . . . 93
3.2.2 Inner(structural)model . . . . . . . . . . . . . . . . . . . 96
3.2.3 Application:Touristssatisfaction. . . . . . . . . . . . . . . 97
3.3 ModelEstimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
3.3.1 ThePLS-SEMalgorithm . . . . . . . . . . . . . . . . . . . 102
3.3.2 StageI:Iterativeestimationoflatentvariablescores . . . . 103
3.3.3 StageII:Estimationofmeasurementmodelparameters . . . 107
3.3.4 StageIII:Estimationofstructuralmodelparameters . . . . 107
3.4 Bootstrap-basedInference . . . . . . . . . . . . . . . . . . . . . . 108
3.5 TheplssemStataPackage . . . . . . . . . . . . . . . . . . . . . 110
3.5.1 Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
3.5.2 Options . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
3.5.3 Storedresults . . . . . . . . . . . . . . . . . . . . . . . . . 113
3.5.4 Application:Touristssatisfaction(cont.) . . . . . . . . . . . 113
3.6 MissingData . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
3.6.1 Application:Touristssatisfaction(cont.) . . . . . . . . . . . 121
3.7 EffectDecomposition . . . . . . . . . . . . . . . . . . . . . . . . 123
3.8 SampleSizeRequirements . . . . . . . . . . . . . . . . . . . . . . 127
3.9 ConsistentPLS-SEM . . . . . . . . . . . . . . . . . . . . . . . . . 129
3.9.1 Theplssemccommand. . . . . . . . . . . . . . . . . . . 130
3.10 HigherOrderConstructs . . . . . . . . . . . . . . . . . . . . . . . 134
3.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
Appendix:RCommands . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Theplspmpackage . . . . . . . . . . . . . . . . . . . . . . . . . 141
ThecSEMpackage . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Appendix:TechnicalDetails . . . . . . . . . . . . . . . . . . . . . . . . 151
AformaldefinitionofPLS-SEM . . . . . . . . . . . . . . . . . . . 151
MoredetailsontheconsistentPLS-SEMapproach . . . . . . . . . 153
Contents ix
4 PLSStructuralEquationModelling:AssessmentandInterpretation 155
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
4.2 AssessingtheMeasurementPart . . . . . . . . . . . . . . . . . . . 156
4.2.1 Reflectivemeasurementmodels . . . . . . . . . . . . . . . 156
4.2.1.1 Unidimensionality . . . . . . . . . . . . . . . . . 156
4.2.1.2 Constructreliability . . . . . . . . . . . . . . . . 157
4.2.1.3 Constructvalidity . . . . . . . . . . . . . . . . . 157
4.2.2 Higherorderreflectivemeasurementmodels . . . . . . . . 159
4.2.3 Formativemeasurementmodels . . . . . . . . . . . . . . . 160
4.2.3.1 Contentvalidity . . . . . . . . . . . . . . . . . . 161
4.2.3.2 Multicollinearity . . . . . . . . . . . . . . . . . . 161
4.2.3.3 Weights . . . . . . . . . . . . . . . . . . . . . . 163
4.3 AssessingtheStructuralPart . . . . . . . . . . . . . . . . . . . . . 163
4.3.1 R-squared . . . . . . . . . . . . . . . . . . . . . . . . . . . 164
4.3.2 Goodness-of-fit . . . . . . . . . . . . . . . . . . . . . . . . 165
4.3.3 Pathcoefficients . . . . . . . . . . . . . . . . . . . . . . . 165
4.4 AssessingaPLS-SEMModel:AFullExample . . . . . . . . . . . 167
4.4.1 Settingupthemodelusingplssem . . . . . . . . . . . . . 167
4.4.2 EstimationusingplsseminStata . . . . . . . . . . . . . . 170
4.4.3 Evaluationoftheexamplestudymodel . . . . . . . . . . . 172
4.4.3.1 Measurementpart . . . . . . . . . . . . . . . . . 172
4.4.3.2 Structuralpart . . . . . . . . . . . . . . . . . . . 176
4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
Appendix:RCommands . . . . . . . . . . . . . . . . . . . . . . . . . . 178
Appendix:TechnicalDetails . . . . . . . . . . . . . . . . . . . . . . . . 183
ToolsforassessingthemeasurementpartofaPLS-SEMmodel . . . 183
ToolsforassessingthestructuralpartofaPLS-SEMmodel . . . . . 185
II AdvancedMethods 187
5 MediationAnalysisWithPLS-SEM 189
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 189
5.2 BaronandKenny’sApproachtoMediationAnalysis . . . . . . . . 189
5.2.1 ModifyingtheBaron-Kennyapproach . . . . . . . . . . . . 191
5.2.2 AlternativetotheBaron-Kennyapproach . . . . . . . . . . 192
5.2.3 Effectsizeofthemediation . . . . . . . . . . . . . . . . . 195
5.3 ExamplesinStata . . . . . . . . . . . . . . . . . . . . . . . . . . 195
5.3.1 Example1:Asingleobservedmediatorvariable . . . . . . 196
5.3.2 Example2:Asinglelatentmediatorvariable . . . . . . . . 198
5.3.3 Example3:Multiplelatentmediatorvariables . . . . . . . . 203
5.4 ModeratedMediation . . . . . . . . . . . . . . . . . . . . . . . . . 207
5.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
Appendix:RCommands . . . . . . . . . . . . . . . . . . . . . . . . . . 208
