Structural equation modeling: applications using Mplus
Introduction 1
1.1 Model formulation 2
1.1.1 Measurement model 4
1.1.2 Structural model 6
1.1.3 Model formulation in equations 7
1.2 Model identification 11
1.3 Model estimation 14
1.4 Model evaluation 17
1.5 Model modification 23
1.6 Computer programs for SEM 24
Appendix 1.A Expressing variances and covariances among observed
variables as functions of model parameters 25
Appendix 1.B Maximum likelihood function for SEM 27
2 Confirmatory factor analysis 29
2.1 Basics of CFA model 30
2.2 CFA model with continuous indicators 42
2.3 CFA model with non-normal and censored
continuous indicators 58
2.3.1 Testing non-normality 58
2.3.2 CFA model with non-normal indicators 59
2.3.3 CFA model with censored data 65
2.4 CFA model with categorical indicators 68
2.4.1 CFA model with binary indicators 69
2.4.2 CFA model with ordered categorical indicators 77
2.5 Higher order CFA model 78
Appendix 2.A BSI-18 instrument 86
Appendix 2.B Item reliability 86
Appendix 2.C Cronbach’s alpha coefficient 88
Appendix 2.D Calculating probabilities using PROBIT regression
coefficients 88
Structural equations with latent variables 90
3.1 MIMIC model 90
3.2 Structural equation model 119
3.3 Correcting for measurement errors in single
indicator variables 130
3.4 Testing interactions involving latent variables 134
Appendix 3.A Influence of measurement errors 139