Description
Presents a useful guide for applications of SEM whilst systematically demonstrating various SEM models using Mplus
Focusing on the conceptual and practical aspects of Structural Equation Modeling (SEM), this book demonstrates basic concepts and examples of various SEM models, along with updates on many advanced methods, including confirmatory factor analysis (CFA) with categorical items, bifactor model, Bayesian CFA model, item response theory (IRT) model, graded response model (GRM), multiple imputation (MI) of missing values, plausible values of latent variables, moderated mediation model, Bayesian SEM, latent growth modeling (LGM) with individually varying times of observations, dynamic structural equation modeling (DSEM), residual dynamic structural equation modeling (RDSEM), testing measurement invariance of instrument with categorical variables, longitudinal latent class analysis (LLCA), latent transition analysis (LTA), growth mixture modeling (GMM) with covariates and distal outcome, manual implementation of the BCH method and the three-step method for mixture modeling, Monte Carlo simulation power analysis for various SEM models, and estimate sample size for latent class analysis (LCA) model.
The statistical modeling program Mplus Version 8.2 is featured with all models updated. It provides researchers with a flexible tool that allows them to analyze data with an easy-to-use interface and graphical displays of data and analysis results.
Intended as both a teaching resource and a reference guide, and written in non-mathematical terms, Structural Equation Modeling: Applications Using Mplus, 2nd edition provides step-by-step instructions of model specification, estimation, evaluation, and modification. Chapters cover: Confirmatory Factor Analysis (CFA); Structural Equation Models (SEM); SEM for Longitudinal Data; Multi-Group Models; Mixture Models; and Power Analysis and Sample Size Estimate for SEM.
- Presents a useful reference guide for applications of SEM while systematically demonstrating various advanced SEM models
- Discusses and demonstrates various SEM models using both cross-sectional and longitudinal data with both continuous and categorical outcomes
- Provides step-by-step instructions of model specification and estimation, as well as detailed interpretation of Mplus results using real data sets
- Introduces different methods for sample size estimate and statistical power analysis for SEM
Structural Equation Modeling is an excellent book for researchers and graduate students of SEM who want to understand the theory and learn how to build their own SEM models using Mplus.
Table of Contents
Preface ix
1 Introduction to structural equation modeling 1
1.1 Introduction 1
1.2 Model formulation 3
1.3 Model identification 11
1.4 Model estimation 14
1.5 Model fit evaluation 19
1.6 Model modification 27
1.7 Computer programs for SEM 28
Appendix 1.A Expressing variances and covariances among observed variables as functions of model parameters 30
Appendix 1.B Maximum likelihood function for SEM 32
2 Confirmatory factor analysis 33
2.1 Introduction 33
2.2 Basics of CFA models 34
2.3 CFA models with continuous indicators 45
2.4 CFA models with non-normal and censored continuous indicators 61
2.5 CFA models with categorical indicators 70
2.6 The item response theory (IRT) model and the graded response model (GRM) 77
2.7 Higher-order CFA models 91
2.8 Bifactor models 96
2.9 Bayesian CFA models 102
2.10 Plausible values of latent variables 110
Appendix 2.A BSI-18 instrument 113
Appendix 2.B Item reliability 114
Appendix 2.C Cronbach’s alpha coefficient 116
Appendix 2.D Calculating probabilities using probit regression coefficients 117
3 Structural equation models 119
3.1 Introduction 119
3.2 Multiple indicators, multiple causes (MIMIC) model 120
3.3 General structural equation models 137
3.4 Correcting for measurement error in single indicator variables 144
3.5 Testing interactions involving latent variables 150
3.6 Moderated mediating effect models 153
3.7 Using plausible values of latent variables in secondary analysis 164
3.8 Bayesian structural equation modeling (BSEM) 167
Appendix 3.A Influence of measurement errors 173
Appendix 3.B Fraction of missing information (FMI) 175
4 Latent growth modeling (LGM) for longitudinal data analysis 177
4.1 Introduction 177
4.2 Linear LGM 178
4.3 Nonlinear LGM 192
4.4 Multiprocess LGM 216
4.5 Two-part LGM 221
4.6 LGM with categorical outcomes 229
4.7 LGM with individually varying times of observation 238
4.8 Dynamic structural equation modeling (DSEM) 241
5 Multigroup modeling 253
5.1 Introduction 253
5.2 Multigroup CFA models 254
5.3 Multigroup SEM 316
5.4 Multigroup latent growth modeling (LGM) 327
6 Mixture modeling 339
6.1 Introduction 339
6.2 Latent class analysis (LCA) modeling 340
6.3 Extending LCA to longitudinal data analysis 373
6.4 Growth mixture modeling (GMM) 392
6.5 Factor mixture modeling (FMM) 411
Appendix 6.A Including covariates in LTA model 418
Appendix 6.B Manually implementing three-step mixture modeling 434
7 Sample size for structural equation modeling 443
7.1 Introduction 443
7.2 The rules of thumb for sample size in SEM 444
7.3 The Satorra-Saris method for estimating sample size 445
7.4 Monte Carlo simulation for estimating sample sizes 458
7.5 Estimate sample size for SEM based on model fit indexes 473
7.6 Estimate sample sizes for latent class analysis (LCA) model 479
References 483
Index 507
