Basic and Advanced Bayesian Structural Equation Modeling

With Applications in the Medical and Behavioral Sciences

Sik-Yum Lee, Xin-Yuan Song

• Publisher: Wiley
• Year: 2012
• Print ISBN: 9780470669525
• eBook ISBN: 9781118358870
• Edition: 1
• Topic: Mathematik
• Subtopic: Wahrscheinlichkeitsrechnung & Statistiken

This book provides clear instructions to researchers on how to apply Structural Equation Models (SEMs) for analyzing the inter relationships between observed and latent variables.

Basic and Advanced Bayesian Structural Equation Modeling introduces basic and advanced SEMs for analyzing various kinds of complex data, such as ordered and unordered categorical data, multilevel data, mixture data, longitudinal data, highly non-normal data, as well as some of their combinations. In addition, Bayesian semiparametric SEMs to capture the true distribution of explanatory latent variables are introduced, whilst SEM with a nonparametric structural equation to assess unspecified functional relationships among latent variables are also explored.

Statistical methodologies are developed using the Bayesian approach giving reliable results for small samples and allowing the use of prior information leading to better statistical results. Estimates of the parameters and model comparison statistics are obtained via powerful Markov Chain Monte Carlo methods in statistical computing.

• Introduces the Bayesian approach to SEMs, including discussion on the selection of prior distributions, and data augmentation.
• Demonstrates how to utilize the recent powerful tools in statistical computing including, but not limited to, the Gibbs sampler, the Metropolis-Hasting algorithm, and path sampling for producing various statistical results such as Bayesian estimates and Bayesian model comparison statistics in the analysis of basic and advanced SEMs.
• Discusses the Bayes factor, Deviance Information Criterion (DIC), and $L_\nu$-measure for Bayesian model comparison.
• Introduces a number of important generalizations of SEMs, including multilevel and mixture SEMs, latent curve models and longitudinal SEMs, semiparametric SEMs and those with various types of discrete data, and nonparametric structural equations.
• Illustrates how to use the freely available software WinBUGS to produce the results.
• Provides numerous real examples for illustrating the theoretical concepts and computational procedures that are presented throughout the book.

Researchers and advanced level students in statistics, biostatistics, public health, business, education, psychology and social science will benefit from this book.

Table of contents

• Cover
• Series
• Title Page
• Copyright
• Dedication
• About the authors
• Preface
• Chapter 1: Introduction
• Chapter 2: Basic concepts and applications of structural equation models
• Chapter 3: Bayesian methods for estimating structural equation models
• Chapter 4: Bayesian model comparison and model checking
• Chapter 5: Practical structural equation models
• Chapter 6: Structural equation models with hierarchical and multisample data
• Chapter 7: Mixture structural equation models
• Chapter 8: Structural equation modeling for latent curve models
• Chapter 9: Longitudinal structural equation models
• Chapter 10: Semiparametric structural equation models with continuous variables
• Chapter 11: Structural equation models with mixed continuous and unordered categorical variables
• Chapter 12: Structural equation models with nonparametric structural equations
• Chapter 13: Transformation structural equation models
• Chapter 14: Conclusion
• Index
• Series