Structural equation modeling applications using Mplus

537 Pages·10.643 MB·English

by  Wang, Jichuan;Wang, Xiaoqian(Contributor)

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Structural Equation
Modeling
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Structural Equation
Modeling
Applications Using Mplus
Second Edition
Jichuan Wang
GeorgeWashingtonUniversity,UnitedStates
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Xiaoqian Wang
MobleyGroupPacificLtd.
P.R.China
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Thiseditionfirstpublished2020
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Contents
Preface ix
1 Introductiontostructuralequationmodeling 1
1.1 Introduction 1
1.2 Modelformulation 3
1.2.1 Measurementmodels 4
1.2.2 Structuralmodels 6
1.2.3 Modelformulationinequations 7
1.3 Modelidentification 11
1.4 Modelestimation 14
1.4.1 Bayesestimator 17
(cid:2) 1.5 Modelfitevaluation 19 (cid:2)
1.5.1 Themodel𝜒2statistic 20
1.5.2 Comparativefitindex(CFI) 20
1.5.3 TuckerLewisindex(TLI)ornon-normedfitindex(NNFI) 21
1.5.4 Rootmeansquareerrorofapproximation(RMSEA) 22
1.5.5 Rootmean-squareresidual(RMR),standardizedRMR
(SRMR),andweightedRMR(WRMR) 22
1.5.6 Informationcriteriaindices 24
1.5.7 ModelfitevaluationwithBayesestimator 25
1.5.8 Modelcomparison 26
1.6 Modelmodification 27
1.7 ComputerprogramsforSEM 28
Appendix1.A Expressingvariancesandcovariancesamongobserved
variablesasfunctionsofmodelparameters 30
Appendix1.B MaximumlikelihoodfunctionforSEM 32
2 Confirmatoryfactoranalysis 33
2.1 Introduction 33
2.2 BasicsofCFAmodels 34
2.2.1 Latentvariables/factors 39
2.2.2 Indicatorvariables 39
2.2.3 Itemparceling 40
2.2.4 Factorloadings 42
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vi CONTENTS
2.2.5 Measurementerrors 42
2.2.6 Itemreliability 44
2.2.7 Scalereliability 44
2.3 CFAmodelswithcontinuousindicators 45
2.3.1 Alternativemethodsforfactorscaling 52
2.3.2 Modelestimateditemreliability 57
2.3.3 Modelmodificationbasedonmodificationindices 57
2.3.4 Modelestimatedscalereliability 58
2.3.5 Itemparceling 60
2.4 CFAmodelswithnon-normalandcensoredcontinuousindicators 61
2.4.1 Testingnon-normality 61
2.4.2 CFAmodelswithnon-normalindicators 62
2.4.3 CFAmodelswithcensoreddata 67
2.5 CFAmodelswithcategoricalindicators 70
2.5.1 CFAmodelswithbinaryindicators 72
2.5.2 CFAmodelswithordinalcategoricalindicators 76
2.6 Theitemresponsetheory(IRT)modelandthegradedresponse
model(GRM) 77
2.6.1 Theitemresponsetheory(IRT)model 77
2.6.2 Thegradedresponsemodel(GRM) 86
2.7 Higher-orderCFAmodels 91
(cid:2) 2.8 Bifactormodels 96 (cid:2)
2.9 BayesianCFAmodels 102
2.10 Plausiblevaluesoflatentvariables 110
Appendix2.A BSI-18instrument 113
Appendix2.B Itemreliability 114
Appendix2.C Cronbach’salphacoefficient 116
Appendix2.D Calculatingprobabilitiesusingprobitregression
coefficients 117
3 Structuralequationmodels 119
3.1 Introduction 119
3.2 Multipleindicators,multiplecauses(MIMIC)model 120
3.2.1 Interactioneffectsbetweencovariates 126
3.2.2 Differentialitemfunctioning(DIF) 127
3.3 Generalstructuralequationmodels 137
3.3.1 Testingindirecteffects 141
3.4 Correctingformeasurementerrorinsingleindicatorvariables 144
3.5 Testinginteractionsinvolvinglatentvariables 150
3.6 Moderatedmediatingeffectmodels 153
3.6.1 Bootstrapconfidenceintervals 159
3.6.2 Estimatingcounterfactual-basedcausaleffectsinMplus 160
3.7 Usingplausiblevaluesoflatentvariablesinsecondaryanalysis 164
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CONTENTS vii
3.8 Bayesianstructuralequationmodeling(BSEM) 167
Appendix3.A Influenceofmeasurementerrors 173
Appendix3.B Fractionofmissinginformation(FMI) 175
4 Latentgrowthmodeling(LGM)forlongitudinaldataanalysis 177
4.1 Introduction 177
4.2 LinearLGM 178
4.2.1 UnconditionallinearLGM 178
4.2.2 LGMwithtime-invariantcovariates 184
4.2.3 LGMwithtime-invariantandtime-varyingcovariates 189
4.3 NonlinearLGM 192
4.3.1 LGMwithpolynomialtimefunctions 192
4.3.2 PiecewiseLGM 203
4.3.3 Freetimescores 210
4.3.4 LGMwithdistaloutcomes 211
4.4 MultiprocessLGM 216
4.5 Two-partLGM 221
4.6 LGMwithcategoricaloutcomes 229
4.7 LGMwithindividuallyvaryingtimesofobservation 238
4.8 Dynamicstructuralequationmodeling(DSEM) 241
(cid:2) 4.8.1 DSEMusingobservedcenteringforcovariates 241 (cid:2)
4.8.2 ResidualDSEM(RDSEM)usingobservedcenteringfor
covariates 245
4.8.3 ResidualDSEM(RDSEM)usinglatentvariablecentering
forcovariates 248
5 Multigroupmodeling 253
5.1 Introduction 253
5.2 MultigroupCFAmodels 254
5.2.1 Multigroupfirst-orderCFA 258
5.2.2 Multigroupsecond-orderCFA 289
5.2.3 MultigroupCFAwithcategoricalindicators 306
5.3 MultigroupSEM 316
5.3.1 Testinginvarianceofstructuralpathcoefficientsacross
groups 322
5.3.2 Testinginvarianceofindirecteffectsacrossgroups 326
5.4 Multigrouplatentgrowthmodeling(LGM) 327
5.4.1 Testinginvarianceofthegrowthfunction 332
5.4.2 Testinginvarianceoflatentgrowthfactormeans 335
6 Mixturemodeling 339
6.1 Introduction 339
6.2 Latentclassanalysis(LCA)modeling 340
6.2.1 DescriptionofLCAmodels 341
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viii CONTENTS
6.2.2 Definingthelatentclasses 347
6.2.3 Predictingclassmembership 347
6.2.4 UnconditionalLCA 348
6.2.5 DirectlyincludingcovariatesintoLCAmodels 360
6.2.6 ApproachesforauxiliaryvariablesinLCAmodels 363
6.2.7 ImplementingthePC,three-step,Lanza’s,andBCH
methods 365
6.2.8 LCAwithresidualcovariances 370
6.3 ExtendingLCAtolongitudinaldataanalysis 373
6.3.1 Longitudinallatentclassanalysis(LLCA) 373
6.3.2 Latenttransitionanalysis(LTA)models 375
6.4 Growthmixturemodeling(GMM) 392
6.4.1 Unconditionalgrowthmixturemodeling(GMM) 394
6.4.2 GMMwithcovariatesandadistaloutcome 402
6.5 Factormixturemodeling(FMM) 411
6.5.1 LCFAmodels 417
Appendix6.A IncludingcovariatesinLTAmodel 418
Appendix6.B Manuallyimplementingthree-stepmixturemodeling 434
7 Samplesizeforstructuralequationmodeling 443
(cid:2) 7.1 Introduction 443 (cid:2)
7.2 TherulesofthumbforsamplesizeinSEM 444
7.3 TheSatorra-Sarismethodforestimatingsamplesize 445
7.3.1 ApplicationofTheSatorra-SarismethodtoCFAmodels 446
7.3.2 ApplicationoftheSatorra-Saris’smethodtolatentgrowth
models 454
7.4 MonteCarlosimulationforestimatingsamplesizes 458
7.4.1 ApplicationofaMonteCarlosimulationtoCFAmodels 459
7.4.2 ApplicationofaMonteCarlosimulationtolatentgrowth
models 463
7.4.3 ApplicationofaMonteCarlosimulationtolatentgrowth
modelswithcovariates 467
7.4.4 ApplicationofaMonteCarlosimulationtolatentgrowth
modelswithmissingvalues 469
7.5 EstimatesamplesizeforSEMbasedonmodelfitindexes 473
7.5.1 ApplicationoftheMacCallum–Browne–Sugawara’s
method 474
7.5.2 ApplicationofKim’smethod 477
7.6 Estimatesamplesizesforlatentclassanalysis(LCA)model 479
References 483
Index 507
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