Structural Equation Modeling: A Bayesian Approach(Wiley Series in Probability and Statistics)

***Winner of the 2008 Ziegel Prize for outstanding new book of the year*** Structural equation modeling (SEM) is a powerful multivariate method allowing the evaluation of a series of simultaneous hypotheses about the impacts of latent and manifest variables on other variables, taking measurement errors into account. As SEMs have grown in popularity in recent years, new models and statistical methods have been developed for more accurate analysis of more complex data. A Bayesian approach to SEMs allows 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. Structural Equation Modeling 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. Demonstrates how to utilize powerful statistical computing tools, including the Gibbs sampler, the Metropolis-Hasting algorithm, bridge sampling and path sampling to obtain the Bayesian results. Discusses the Bayes factor and Deviance Information Criterion (DIC) for model comparison. Includes coverage of complex models, including SEMs with ordered categorical variables, and dichotomous variables, nonlinear SEMs, two-level SEMs, multisample SEMs, mixtures of SEMs, SEMs with missing data, SEMs with variables from an exponential family of distributions, and some of their combinations. Illustrates the methodology through simulation studies and examples with real data from business management, education, psychology, public health and sociology. Demonstrates the application of the freely available software WinBUGS via a supplementary website featuring computer code and data sets. Structural Equation Modeling: A Bayesian Approach is a multi-disciplinary text ideal for researchers and students in many areas, including: statistics, biostatistics, business, education, medicine, psychology, public health and social science.

Table of Contents:
About the Author xi Preface xiii 1 Introduction 1 1.1 Standard Structural Equation Models 1 1.2 Covariance Structure Analysis 2 1.3 Why a New Book? 3 1.4 Objectives of the Book 4 1.5 Data Sets and Notations 6 Appendix 1.1 7 References 10 2 Some Basic Structural Equation Models 13 2.1 Introduction 13 2.2 Exploratory Factor Analysis 15 2.3 Confirmatory and Higher-order Factor Analysis Models 18 2.4 The LISREL Model 22 2.5 The Bentler–Weeks Model 26 2.6 Discussion 27 References 28 3 Covariance Structure Analysis 31 3.1 Introduction 31 3.2 Definitions, Notations and Preliminary Results 33 3.3 GLS Analysis of Covariance Structure 36 3.4 ml Analysis of Covariance Structure 41 3.5 Asymptotically Distribution-free Methods 44 3.6 Some Iterative Procedures 47 Appendix 3.1: Matrix Calculus 53 Appendix 3.2: Some Basic Results in Probability Theory 57 Appendix 3.3: Proofs of Some Results 59 References 65 4 Bayesian Estimation of Structural Equation Models 67 4.1 Introduction 67 4.2 Basic Principles and Concepts of Bayesian Analysis of SEMs 70 4.3 Bayesian Estimation of the CFA Model 81 4.4 Bayesian Estimation of Standard SEMs 95 4.5 Bayesian Estimation via WinBUGS 98 Appendix 4.1: The Metropolis–Hastings Algorithm 104 Appendix 4.2: EPSR Value 105 Appendix 4.3: Derivations of Conditional Distributions 106 References 108 5 Model Comparison and Model Checking 111 5.1 Introduction 111 5.2 Bayes Factor 113 5.3 Path Sampling 115 5.4 An Application: Bayesian Analysis of SEMs with Fixed Covariates 120 5.5 Other Methods 127 5.6 Discussion 130 Appendix 5.1: Another Proof of Equation (5.10) 131 Appendix 5.2: Conditional Distributions for Simulating (θ, ΩlY, t) 133 Appendix 5.3: PP p-values for Model Assessment 136 References 136 6 Structural Equation Models with Continuous and Ordered Categorical Variables 139 6.1 Introduction 139 6.2 The Basic Model 142 6.3 Bayesian Estimation and Goodness-of-fit 144 6.4 Bayesian Model Comparison 155 6.5 Application 1: Bayesian Selection of the Number of Factors in EFA 159 6.6 Application 2: Bayesian Analysis of Quality of Life Data 164 References 172 7 Structural Equation Models with Dichotomous Variables 175 7.1 Introduction 175 7.2 Bayesian Analysis 177 7.3 Analysis of a Multivariate Probit Confirmatory Factor Analysis Model 186 7.4 Discussion 190 Appendix 7.1: Questions Associated with the Manifest Variables 191 References 192 8 Nonlinear Structural Equation Models 195 8.1 Introduction 195 8.2 Bayesian Analysis of a Nonlinear SEM 197 8.3 Bayesian Estimation of Nonlinear SEMs with Mixed Continuous and Ordered Categorical Variables 215 8.4 Bayesian Estimation of SEMs with Nonlinear Covariates and Latent Variables 220 8.5 Bayesian Model Comparison 230 References 239 9 Two-level Nonlinear Structural Equation Models 243 9.1 Introduction 243 9.2 A Two-level Nonlinear SEM with Mixed Type Variables 244 9.3 Bayesian Estimation 247 9.4 Goodness-of-fit and Model Comparison 255 9.5 An Application: Filipina CSWs Study 259 9.6 Two-level Nonlinear SEMs with Cross-level Effects 267 9.7 Analysis of Two-level Nonlinear SEMs using WinBUGS 275 Appendix 9.1: Conditional Distributions: Two-level Nonlinear Sem 279 Appendix 9.2: MH Algorithm: Two-level Nonlinear SEM 283 Appendix 9.3: PP p-value for Two-level NSEM with Mixed Continuous and Ordered-categorical Variables 285 Appendix 9.4: Questions Associated with the Manifest Variables 286 Appendix 9.5: Conditional Distributions: SEMs with Cross-level Effects 286 Appendix 9.6: The MH algorithm: SEMs with Cross-level Effects 289 References 290 10 Multisample Analysis of Structural Equation Models 293 10.1 Introduction 293 10.2 The Multisample Nonlinear Structural Equation Model 294 10.3 Bayesian Analysis of Multisample Nonlinear SEMs 297 10.4 Numerical Illustrations 302 Appendix 10.1: Conditional Distributions: Multisample SEMs 313 References 316 11 Finite Mixtures in Structural Equation Models 319 11.1 Introduction 319 11.2 Finite Mixtures in SEMs 321 11.3 Bayesian Estimation and Classification 323 11.4 Examples and Simulation Study 330 11.5 Bayesian Model Comparison of Mixture SEMs 344 Appendix 11.1: The Permutation Sampler 351 Appendix 11.2: Searching for Identifiability Constraints 352 References 352 12 Structural Equation Models with Missing Data 355 12.1 Introduction 355 12.2 A General Framework for SEMs with Missing Data that are Mar 357 12.3 Nonlinear SEM with Missing Continuous and Ordered Categorical Data 359 12.4 Mixture of SEMs with Missing Data 370 12.5 Nonlinear SEMs with Nonignorable Missing Data 375 12.6 Analysis of SEMs with Missing Data via WinBUGS 386 Appendix 12.1: Implementation of the MH Algorithm 389 References 390 13 Structural Equation Models with Exponential Family of Distributions 393 13.1 Introduction 393 13.2 The SEM Framework with Exponential Family of Distributions 394 13.3 A Bayesian Approach 398 13.4 A Simulation Study 402 13.5 A Real Example: A Compliance Study of Patients 404 13.6 Bayesian Analysis of an Artificial Example using WinBUGS 411 13.7 Discussion 416 Appendix 13.1: Implementation of the MH Algorithms 417 Appendix 13.2 419 References 419 14 Conclusion 421 References 425 Index 427

About the Author :
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.

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