***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.

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.

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.

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.

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 L…