紹介
Basic and Advanced Structural Equation Models for Medical and Behavioural Sciences introduces the Bayesian approach to SEMs, including the selection of prior distributions and data augmentation, and offers an overview of the subject's recent advances. This book takes a Bayesian approach to SEMs allowing the use of prior information resulting in improved parameter estimates, latent variable estimates, and statistics for model comparison, as well as offering more reliable results for smaller samples.
目次
About the Authors Preface 1 Introduction 1.1 Observed and Latent Variables 1.2 Structural Equation Model 1.3 Objectives of the Book 1.4 The Bayesian Approach 1.5 Real Data Sets and Notation Appendix 1.1: Information on Real Data Sets References 2 Basic Concepts and Applications of Structural Equation Models 2.1 Introduction 2.2 Linear SEMs 2.3 SEMs with Fixed Covariates 2.4 Nonlinear SEMs 2.5 Discussion and Conclusions References 3 Bayesian Methods for Estimating Structural Equation Models 3.1 Introduction 3.2 Basic Concepts of the Bayesian Estimation and Prior Distributions 3.3 Posterior Analysis Using Markov Chain Monte Carlo Methods 3.4 Application of Markov Chain Monte Carlo Methods 3.5 Bayesian Estimation via WinBUGS Appendix 3.1: The Gamma, Inverted Gamma, Wishart, and Inverted Wishart Distributions and Their Characteristics Appendix 3.2: The Metropolis{Hastings Algorithm Appendix 3.3: Conditional Distributions [jY
-] and [-jY
] Appendix 3.4: Conditional Distributions [jY
-] and [-jY
] in Nonlinear SEMs with Covariates Appendix 3.5: WinBUGS Code Appendix 3.6: R2WinBUGS Code References 4 Bayesian Model Comparison and Model Checking 4.1 Introduction 4.2 Bayes Factor 4.3 Other Model Comparison Statistics 4.4 Illustration 4.5 Goodness-of-Fit and Model Checking Methods Appendix 4.1: WinBUGS Code Appendix 4.2: R code in Bayes Factor Example Appendix 4.3: Posterior Predictive p-value for Model Assessment References 5 Practical Structural Equation Models 5.1 Introduction 5.2 SEMs with Continuous and Ordered Categorical Variables 5.3 SEMs with Variables from Exponential Family Distributions 5.4 SEMs with Missing Data Appendix 5.1: Conditional Distributions and Implementation of the MH Algorithm for SEMs with Continuous and Ordered Categorical Variables Appendix 5.2: Conditional Distributions and Implementation of MH Algorithm for SEMs with EFDs Appendix 5.3: WinBUGS Code Related to Section 5.3.4 Appendix 5.4: R2WinBUGS Code Related to Section 5.3.4 Appendix 5.5: Conditional Distributions for SEMs with Non-ignorable Missing Data References 6 Structural Equation Models with Hierarchical and Multisample Data 6.1 Introduction 6.2 Two-Level Structural Equation Models 6.3 Structural Equation Models with Multisample Data Appendix 6.1: Conditional Distributions: Two-Level Nonlinear SEM Appendix 6.2: The MH Algorithm: Two-Level Nonlinear SEM Appendix 6.3: PP p-value for Two-level Nonlinear SEM with Mixed Continuous and Ordered Categorical Variables Appendix 6.4: WinBUGS Code Appendix 6.5: Conditional Distributions: Multisample SEMs References 7 Mixture Structural Equation Models 7.1 Introduction 7.2 Finite Mixture SEMs 7.3 A Modified Mixture SEM Appendix 7.1: The Permutation Sampler Appendix 7.2: Searching for Identifiability Constraints Appendix 7.3: Conditional Distributions: Modified Mixture SEMs References 8 Structural Equation Modeling for Latent Curve Models 8.1 Introduction 8.2 Background to the Real Studies 8.3 Latent Curve Models 8.4 Bayesian Analysis 8.5 Applications to Two Longitudinal Studies 8.6 Other Latent Curve Models Appendix 8.1: Conditional Distributions Appendix 8.2: WinBUGS Code for the Analysis of Cocaine Use Data References 9 Longitudinal Structural Equation Models 9.1 Introduction 9.2 A Two-Level SEM for Analyzing Multivariate Longitudinal Data 9.3 Bayesian Analysis of the Two-Level Longitudinal SEM 9.4 Simulation Study 9.5 Application: Longitudinal Study of Cocaine Use 9.6 Discussion Appendix 9.1: Full Conditional Distributions for Implementing the Gibbs Sampler Appendix 9.2: Approximation of the L--Measure in Equation via MCMC Samples References 10 Semiparametric Structural Equation Models with Continuous Variables 10.1 Introduction 10.2 Bayesian Semiparametric Hierarchical Modeling of SEMs with Covariates 10.3 Bayesian Estimation and Model Comparison 10.4 Application: Kidney Disease Study 10.5 Simulation Studies 10.6 Discussion Appendix 10.1: Conditional Distributions for Parametric Components Appendix 10.2: Conditional Distributions for Nonparametric Components References 11 Structural Equation Models with Mixed Continuous and Unordered Categorical Variables 11.1 Introduction 11.2 Parametric SEMs with Continuous and Unordered Categorical Variables 11.3 Bayesian Semiparametric SEM with Continuous and Unordered Categorical Variables Appendix 11.1: Full Conditional Distributions Appendix 11.2: Path Sampling Appendix 11.3: A Modified Truncated DP Related to Equation Appendix 11.4: Conditional Distributions and the MH Algorithm for the Bayesian Semiparametric Model References 12 Structural Equation Models with Nonparametric Structural Equations 12.1 Introduction 12.2 Nonparametric SEMs with Bayesian P-Splines 12.3 Generalized Nonparametric Structural Equation Models 12.4 Discussion Appendix 12.1: Conditional Distributions and the MH Algorithm: Nonparametric SEMs Appendix 12.2: Conditional Distributions in Generalized Nonparametric EMs References 13 Transformation Structural Equation Models 13.1 Introduction 13.2 Model Description 13.3 Modeling Nonparametric Transformations 13.4 Identifiability Constraints and Prior Distributions 13.5 Posterior Inference with MCMC Algorithms 136 Simulation Study 13.7 A Study on the Intervention Treatment of Polydrug Use 13.8 Discussion References 14 Conclusion References Index
