Jichuan Wang, PhD, is Professor in the Department of Pediatrics, Epidemiology, and Biostatistics at the George Washington University (GWU) School of Medicine. He also serves as Senior Biostatistician in the National Children's Medical Center (CNMC) in Washington, DC. Xiaoqian Wang, PhD, is a Principle Consultant at Mobley Group Pacific Ltd., P.R. China.

• Preface ix1 Introduction to structural equation modeling 11.1 Introduction 11.2 Model formulation 31.2.1 Measurement models 41.2.2 Structural models 61.2.3 Model formulation in equations 71.3 Model identification 111.4 Model estimation 141.4.1 Bayes estimator 171.5 Model fit evaluation 191.5.1 The model 𝜒2 statistic 201.5.2 Comparative fit index (CFI) 201.5.3 Tucker Lewis index (TLI) or non-normed fit index (NNFI) 211.5.4 Root mean square error of approximation (RMSEA) 221.5.5 Root mean-square residual (RMR), standardized RMR (SRMR), and weighted RMR (WRMR) 221.5.6 Information criteria indices 241.5.7 Model fit evaluation with Bayes estimator 251.5.8 Model comparison 261.6 Model modification 271.7 Computer programs for SEM 28Appendix 1.A Expressing variances and covariances among observed variables as functions of model parameters 30Appendix 1.B Maximum likelihood function for SEM 322 Confirmatory factor analysis 332.1 Introduction 332.2 Basics of CFA models 342.2.1 Latent variables/factors 392.2.2 Indicator variables 392.2.3 Item parceling 402.2.4 Factor loadings 422.2.5 Measurement errors 422.2.6 Item reliability 442.2.7 Scale reliability 442.3 CFA models with continuous indicators 452.3.1 Alternative methods for factor scaling 522.3.2 Model estimated item reliability 572.3.3 Model modification based on modification indices 572.3.4 Model estimated scale reliability 582.3.5 Item parceling 602.4 CFA models with non-normal and censored continuous indicators 612.4.1 Testing non-normality 612.4.2 CFA models with non-normal indicators 622.4.3 CFA models with censored data 672.5 CFA models with categorical indicators 702.5.1 CFA models with binary indicators 722.5.2 CFA models with ordinal categorical indicators 762.6 The item response theory (IRT) model and the graded response model (GRM) 772.6.1 The item response theory (IRT) model 772.6.2 The graded response model (GRM) 862.7 Higher-order CFA models 912.8 Bifactor models 962.9 Bayesian CFA models 1022.10 Plausible values of latent variables 110Appendix 2.A BSI-18 instrument 113Appendix 2.B Item reliability 114Appendix 2.C Cronbach’s alpha coefficient 116Appendix 2.D Calculating probabilities using probit regression coefficients 1173 Structural equation models 1193.1 Introduction 1193.2 Multiple indicators, multiple causes (MIMIC) model 1203.2.1 Interaction effects between covariates 1263.2.2 Differential item functioning (DIF) 1273.3 General structural equation models 1373.3.1 Testing indirect effects 1413.4 Correcting for measurement error in single indicator variables 1443.5 Testing interactions involving latent variables 1503.6 Moderated mediating effect models 1533.6.1 Bootstrap confidence intervals 1593.6.2 Estimating counterfactual-based causal effects in Mplus 1603.7 Using plausible values of latent variables in secondary analysis 1643.8 Bayesian structural equation modeling (BSEM) 167Appendix 3.A Influence of measurement errors 173Appendix 3.B Fraction of missing information (FMI) 1754 Latent growth modeling (LGM) for longitudinal data analysis 1774.1 Introduction 1774.2 Linear LGM 1784.2.1 Unconditional linear LGM 1784.2.2 LGM with time-invariant covariates 1844.2.3 LGM with time-invariant and time-varying covariates 1894.3 Nonlinear LGM 1924.3.1 LGM with polynomial time functions 1924.3.2 Piecewise LGM 2034.3.3 Free time scores 2104.3.4 LGM with distal outcomes 2114.4 Multiprocess LGM 2164.5 Two-part LGM 2214.6 LGM with categorical outcomes 2294.7 LGM with individually varying times of observation 2384.8 Dynamic structural equation modeling (DSEM) 2414.8.1 DSEM using observed centering for covariates 2414.8.2 Residual DSEM (RDSEM) using observed centering for covariates 2454.8.3 Residual DSEM (RDSEM) using latent variable centering for covariates 2485 Multigroup modeling 2535.1 Introduction 2535.2 Multigroup CFA models 2545.2.1 Multigroup first-order CFA 2585.2.2 Multigroup second-order CFA 2895.2.3 Multigroup CFA with categorical indicators 3065.3 Multigroup SEM 3165.3.1 Testing invariance of structural path coefficients across groups 3225.3.2 Testing invariance of indirect effects across groups 3265.4 Multigroup latent growth modeling (LGM) 3275.4.1 Testing invariance of the growth function 3325.4.2 Testing invariance of latent growth factor means 3356 Mixture modeling 3396.1 Introduction 3396.2 Latent class analysis (LCA) modeling 3406.2.1 Description of LCA models 3416.2.2 Defining the latent classes 3476.2.3 Predicting class membership 3476.2.4 Unconditional LCA 3486.2.5 Directly including covariates into LCA models 3606.2.6 Approaches for auxiliary variables in LCA models 3636.2.7 Implementing the PC, three-step, Lanza’s, and BCH methods 3656.2.8 LCA with residual covariances 3706.3 Extending LCA to longitudinal data analysis 3736.3.1 Longitudinal latent class analysis (LLCA) 3736.3.2 Latent transition analysis (LTA) models 3756.4 Growth mixture modeling (GMM) 3926.4.1 Unconditional growth mixture modeling (GMM) 3946.4.2 GMM with covariates and a distal outcome 4026.5 Factor mixture modeling (FMM) 4116.5.1 LCFA models 417Appendix 6.A Including covariates in LTA model 418Appendix 6.B Manually implementing three-step mixture modeling 4347 Sample size for structural equation modeling 4437.1 Introduction 4437.2 The rules of thumb for sample size in SEM 4447.3 The Satorra-Saris method for estimating sample size 4457.3.1 Application of The Satorra-Saris method to CFA models 4467.3.2 Application of the Satorra-Saris’s method to latent growth models 4547.4 Monte Carlo simulation for estimating sample sizes 4587.4.1 Application of a Monte Carlo simulation to CFA models 4597.4.2 Application of a Monte Carlo simulation to latent growth models 4637.4.3 Application of a Monte Carlo simulation to latent growth models with covariates 4677.4.4 Application of a Monte Carlo simulation to latent growth models with missing values 4697.5 Estimate sample size for SEM based on model fit indexes 4737.5.1 Application of the MacCallum–Browne–Sugawara’s method 4747.5.2 Application of Kim’s method 4777.6 Estimate sample sizes for latent class analysis (LCA) model 479References 483Index 507