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Contents Preface Chapter 1 Introduction 1.1 Standard structural equation models 1.2 Covariance structure analysis 1.3 Why a new book? 1.4 Objectives of the book 1.5 Data sets and notations Appendix 1.1 References Chapter 2 Some Basic Structural Equation Models 2.1 Introduction 2.2 Exploratory factor analysis 2.2.1 Model definition 2.2.2 Identification and analysis of the model 2.3 Confirmatory and higher-order factor analysis models 2.3.1 Confirmatory factor analysis model 2.3.2 Estimation of factor scores 2.3.3 Higher-order factor analysis model 2.4 The LISREL model 2.5. The Bentler-Weeks model 2.6. Discussion References Chapter 3 Covariance Structure Analysis 3.1 Introduction 3.2 Definition, notations and preliminary results 3.3 GLS analysis of covariance structure 3.3.1 The GLS approach 3.3.2 Asymptotic properties of the GLS estimator 3.4 ML analysis of covariance structure 3.5 Asymptotically distribution-free methods 3.6 Some iterative procedures 3.6.1 Numerical examples Appendix 3.1 Matrix calculus Appendix 3.2 Some basic results in probability theory Appendix 3.3 References Chapter 4 Bayesian Estimation of Structural Equation Models 4.1 Introduction 4.2 Basic principles and concepts of Bayesian estimation 4.2.1 Bayesian estimation 4.2.2 Prior distributions 4.2.3 Posterior analysis 4.3 Bayesian estimation of the CFA model 4.3.1 Conditional distributions 4.3.2 A numerical example 4.3.3 Robustness to small sample sizes 4.4 Bayesian estimation of standard SEMs 4.5 Bayesian estimation via WinBUGS Appendix 4.1 The Metropolis-Hastings algorithm Appendix 4.2 Appendix 4.3 References Chapter 5 Model Comparison and Model Checking 5.1 Introduction 5.2 Bayes factor 5.3 Path sampling 5.4 An application: Bayesian analysis of SEMs with fixed covariates 5.5 Other methods 5.5.1 Bayesian information criterion and Akaike information criterion 5.5.2 Deviance information criterion 5.5.3 Posterior predictive p-value 5.5.4 Residuals and outlier analysis 5.6 Discussion Appendix 5.1 Appendix 5.2 Appendix 5.3 References Chapter 6 Structural Equation Models with Continuous and Ordered Categorical Variables 6.1 Introduction 6.2 The basic model 6.3 Bayesian estimation and goodness-of-fit 6.3.1 Conditional distribution 6.3.2 Implementation 6.3.3 Bayesian estimates 6.3.4 Goodness-of-fit of the model 6.3.5 An illustrative example 6.4 Bayesian model comparison 6.5 Application 1: Bayesian selection of the number of factors in EFA 6.5.1 A simulation study 6.5.2 A real example 6.6 Application 2: Bayesian analysis of quality of life data 6.6.1 A synthetic illustrative example 6.6.2 Application of WinBUGS References Chapter 7 Structural Equation Models with Dichotomous Variables 7.1 Introduction 7.2 Bayesian analysis 7.2.1 Illustrative example 1 7.3 Analysis of a multivariate probit confirmatory factor analysis model 7.3.1 Illustrative example 2 7.4 Discussion Appendix 7.1 Reference Chapter 8 Nonlinear Structural Equation Models 8.1 Introduction 8.2 Bayesian analysis of a nonlinear SEM 8.2.1 The model 8.2.2 The Gibbs sampler for posterior simulation 8.2.3 Full conditional distributions 8.2.4 Bayesian estimates 8.2.5 Illustrative example 1 8.2.6 Comparison with a product indicator method 8.2.7 Comparison with the LMS approach via the Kenny-Judd model 8.3 Bayesian estimation of nonlinear SEMs with mixed continuous and ordered categorical variables 8.3.1 Posterior analysis 8.3.2 Illustrative Example 2 8.4 Bayesian estimation of SEMs with nonlinear covariates and latent variables 8.4.1 A model with ordered categorical variables, and nonlinear covariates and latent variables 8.4.2 Illustrative example 3 8.4.3 Analysis of an artificial example using WinBUGS 8.5 Bayesian model comparison 8.5.1 Path sampling procedure for computing the Bayes factor 8.5.2 Illustrative example 4 8.5.3 Model comparison using DIC and WinBUGS 8.5.4 Remarks on goodness-of-fit assessment References Chapter 9 Two-level Nonlinear Structural Equation Models 9.1 Introduction 9.2 A two-level nonlinear SEM with mixed type variables 9.3 Bayesian estimation 9.3.1 Posterior simulation and Bayesian estimates 9.3.2 Simulation studies 9.4 Goodness-of-fit and model comparison 9.5 An application: Filipina CSWs study 9.6 Two-level nonlinear SEMs with cross level effects 9.6.1 The model 9.6.2 Bayesian analysis 9.6.3 An application 9.7 Analysis of two-level nonlinear SEMs using WinBUGS Appendix 9.1 Appendix 9.2 Appendix 9.3 Appendix 9.4 Appendix 9.5 Appendix 9.6 References Chapter 10 Multisample Analysis of Structural Equation Models 10.1 Introduction 10.2 The multisample nonlinear structural equation model 10.3 Bayesian analysis of multisample nonlinear SEMs 10.3.1 Bayesian estimation 10.3.2 Bayesian model comparison 10.4 Numerical Illustrations 10.4.1 Analysis of multisample management data 10.4.2 Analysis of multisample quality of life data via WinBUGS Appendix 10.1 References Chapter 11 Finite Mixtures in Structural Equation Models 11.1 Introduction 11.2 Finite mixtures in SEMs 11.3 Bayesian estimation and classification 11.4 Examples and simulation study 11.4.1 Analysis of an artificial example 11.4.2 A simulation study 11.4.3 An example on ?Job? and ?Home life? 11.5 Bayesian model selection of mixture SEMs 11.5.1 A model selection procedure through path sampling 11.5.2 A simulation study 11.5.3 An illustrative example Appendix 11.1 Appendix 11.2 References Chapter 12 Structural Equation Models with Missing Data 12.1 Introduction 12.2 A general framework for SEM with missing data that are MAR 12.3 Nonlinear SEM with missing continuous and ordered categorical data 12.3.1 A simulation study 12.3.2 An illustrative example 12.4 Mixture of SEMs with missing data 12.5 Nonlinear SEMs with nonignorable missing data 12.5.1 The model and the nonignorable missing mechanism 12.5.2 Bayesian analysis of the model 12.5.3 An illustrative real example 12.6 Analaysis of SEMs with missing data via WinBUGS Appendix 12.1 References Chapter 13 Structural Equation Models with Exponential Family of Distributions 13.1 Introduction 13.2 The SEM framework with exponential family of distributions 13.2.1 The model 13.2.2 The nonignorable missing mechanism 13.3 A Bayesian approach 13.3.1 Prior distributions 13.3.2 Full conditional distributions 13.3.3 Model comparison 13.4 A simulation study 13.5 A real example: A compliance study of patients 13.6 Bayesian analysis of an artificial example using WinBUGS 13.7 Discussion Appendix 13.1 Appendix 13.2 Reference Chapter 14 Conclusion Index

Library of Congress Subject Headings for this publication:

Structural equation modeling.

Bayesian statistical decision theory.