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E-raamat: Structural Equation Modeling: A Bayesian Approach illustrated edition [Wiley Online]

(Chinese University of Hong Kong)
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Structural Equation Modeling: A Bayesian Approach illustrated editionSuurem pilt
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Lee (statistics, Chinese U. of Hong Kong) describes this multivariate method that allows the evaluation of a series of simultaneous hypotheses about the effects of latent and manifest variables on other variables, taking measurement errors into account, and shows how a Bayesian approach allows the inclusion of prior information. The results are improved parameter estimates, latent variable estimates, and statistics for model comparison with more reliable results using smaller samples. He describes standard structural equation models, such as exploratory factor analysis and the Bentler-Weeks model, examines covariance structure analysis, then presents the Bayesian approach. He covers model comparison and model checking, structural equation models with continuous and ordered categorical variables, structural equation models with dichotomous variables, nonlinear structural equation models, two-level nonlinear structural equation models, multisample analysis, finite mixtures, structural equation models with missing data, and structured equation models with an exponential family of distributions. Annotation ©2007 Book News, Inc., Portland, OR (booknews.com)

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 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, ΩY, 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


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.
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