Structural Equation Modeling

Sik-Yum Lee is a professor of statistics at the Chinese University of Hong Kong. He earned his Ph.D. in biostatistics at the University of California, Los Angeles, USA. He received a distinguished service award from the International Chinese Statistical Association, is a former president of the Hong Kong Statistical Society, and is an elected member of the International Statistical Institute and a Fellow of the American Statistical Association. He serves as Associate Editor for Psychometrika and Computational Statistics & Data Analysis, and as a member of the Editorial Board of British Journal of Mathematical and Statistical Psychology, Structural Equation Modeling, Handbook of Computing and Statistics with Applications and Chinese Journal of Medicine. his research interests are in structural equation models, latent variable models, Bayesian methods and statistical diagnostics. he is editor of Handbook of Latent Variable and Related Models and author of over 140 papers.

"This book is a welcome addition to any library and should be a valuable resource for research and teaching." (Technometrics, August 2008)

• About the Author xiPreface xiii1 Introduction 11.1 Standard Structural Equation Models 11.2 Covariance Structure Analysis 21.3 Why a New Book? 31.4 Objectives of the Book 41.5 Data Sets and Notations 6Appendix 1.1 7References 102 Some Basic Structural Equation Models 132.1 Introduction 132.2 Exploratory Factor Analysis 152.3 Confirmatory and Higher-order Factor Analysis Models 182.4 The LISREL Model 222.5 The Bentler–Weeks Model 262.6 Discussion 27References 283 Covariance Structure Analysis 313.1 Introduction 313.2 Definitions, Notations and Preliminary Results 333.3 GLS Analysis of Covariance Structure 363.4 ml Analysis of Covariance Structure 413.5 Asymptotically Distribution-free Methods 443.6 Some Iterative Procedures 47Appendix 3.1: Matrix Calculus 53Appendix 3.2: Some Basic Results in Probability Theory 57Appendix 3.3: Proofs of Some Results 59References 654 Bayesian Estimation of Structural Equation Models 674.1 Introduction 674.2 Basic Principles and Concepts of Bayesian Analysis of SEMs 704.3 Bayesian Estimation of the CFA Model 814.4 Bayesian Estimation of Standard SEMs 954.5 Bayesian Estimation via WinBUGS 98Appendix 4.1: The Metropolis–Hastings Algorithm 104Appendix 4.2: EPSR Value 105Appendix 4.3: Derivations of Conditional Distributions 106References 1085 Model Comparison and Model Checking 1115.1 Introduction 1115.2 Bayes Factor 1135.3 Path Sampling 1155.4 An Application: Bayesian Analysis of SEMs with Fixed Covariates 1205.5 Other Methods 1275.6 Discussion 130Appendix 5.1: Another Proof of Equation (5.10) 131Appendix 5.2: Conditional Distributions for Simulating (θ, ΩlY, t) 133Appendix 5.3: PP p-values for Model Assessment 136References 1366 Structural Equation Models with Continuous and Ordered Categorical Variables 1396.1 Introduction 1396.2 The Basic Model 1426.3 Bayesian Estimation and Goodness-of-fit 1446.4 Bayesian Model Comparison 1556.5 Application 1: Bayesian Selection of the Number of Factors in EFA 1596.6 Application 2: Bayesian Analysis of Quality of Life Data 164References 1727 Structural Equation Models with Dichotomous Variables 1757.1 Introduction 1757.2 Bayesian Analysis 1777.3 Analysis of a Multivariate Probit Confirmatory Factor Analysis Model 1867.4 Discussion 190Appendix 7.1: Questions Associated with the Manifest Variables 191References 1928 Nonlinear Structural Equation Models 1958.1 Introduction 1958.2 Bayesian Analysis of a Nonlinear SEM 1978.3 Bayesian Estimation of Nonlinear SEMs with Mixed Continuous and Ordered Categorical Variables 2158.4 Bayesian Estimation of SEMs with Nonlinear Covariates and Latent Variables 2208.5 Bayesian Model Comparison 230References 2399 Two-level Nonlinear Structural Equation Models 2439.1 Introduction 2439.2 A Two-level Nonlinear SEM with Mixed Type Variables 2449.3 Bayesian Estimation 2479.4 Goodness-of-fit and Model Comparison 2559.5 An Application: Filipina CSWs Study 2599.6 Two-level Nonlinear SEMs with Cross-level Effects 2679.7 Analysis of Two-level Nonlinear SEMs using WinBUGS 275Appendix 9.1: Conditional Distributions: Two-level Nonlinear Sem 279Appendix 9.2: MH Algorithm: Two-level Nonlinear SEM 283Appendix 9.3: PP p-value for Two-level NSEM with Mixed Continuous and Ordered-categorical Variables 285Appendix 9.4: Questions Associated with the Manifest Variables 286Appendix 9.5: Conditional Distributions: SEMs with Cross-level Effects 286Appendix 9.6: The MH algorithm: SEMs with Cross-level Effects 289References 29010 Multisample Analysis of Structural Equation Models 29310.1 Introduction 29310.2 The Multisample Nonlinear Structural Equation Model 29410.3 Bayesian Analysis of Multisample Nonlinear SEMs 29710.4 Numerical Illustrations 302Appendix 10.1: Conditional Distributions: Multisample SEMs 313References 31611 Finite Mixtures in Structural Equation Models 31911.1 Introduction 31911.2 Finite Mixtures in SEMs 32111.3 Bayesian Estimation and Classification 32311.4 Examples and Simulation Study 33011.5 Bayesian Model Comparison of Mixture SEMs 344Appendix 11.1: The Permutation Sampler 351Appendix 11.2: Searching for Identifiability Constraints 352References 35212 Structural Equation Models with Missing Data 35512.1 Introduction 35512.2 A General Framework for SEMs with Missing Data that are Mar 35712.3 Nonlinear SEM with Missing Continuous and Ordered Categorical Data 35912.4 Mixture of SEMs with Missing Data 37012.5 Nonlinear SEMs with Nonignorable Missing Data 37512.6 Analysis of SEMs with Missing Data via WinBUGS 386Appendix 12.1: Implementation of the MH Algorithm 389References 39013 Structural Equation Models with Exponential Family of Distributions 39313.1 Introduction 39313.2 The SEM Framework with Exponential Family of Distributions 39413.3 A Bayesian Approach 39813.4 A Simulation Study 40213.5 A Real Example: A Compliance Study of Patients 40413.6 Bayesian Analysis of an Artificial Example using WinBUGS 41113.7 Discussion 416Appendix 13.1: Implementation of the MH Algorithms 417Appendix 13.2 419References 41914 Conclusion 421References 425Index 427