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El. knyga: Basic and Advanced Bayesian Structural Equation Modeling - With Applications in the Medical and Behavioral Sciences: With Applications in the Medical and Behavioral Sciences [Wiley Online]

(Chinese University of Hong Kong), (Chinese University of Hong Kong)
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Basic and Advanced Bayesian Structural Equation Modeling - With Applications in the Medical and Behavioral Sciences: With Applications in the Medical and Behavioral SciencesDidesnis paveikslėlis
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Partnerių interneto svetainė: https://onlinelibrary.wiley.com/doi/book/10.1002/9781118358887
"This book 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"--

Song and Lee (both statistics, Chinese U. of Hong Kong) explore the Bayesian analysis of structural equation models (SEM), which are the technique of choice to assess various inter-relationships among observed and latent variables. Their topics include basic concepts and applications of structural equation models, Bayesian model comparison and model checking, structural equation modeling for latent curve models, structural equation models with mixed continuous and unordered categorical variables, and transformation structural equation models. Annotation ©2012 Book News, Inc., Portland, OR (booknews.com)

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.

About the authors xiii
Preface xv
1 Introduction
1(15)
1.1 Observed and latent variables
1(2)
1.2 Structural equation model
3(1)
1.3 Objectives of the book
3(1)
1.4 The Bayesian approach
4(1)
1.5 Real data sets and notation
5(2)
Appendix 1.1 Information on real data sets
7(7)
References
14(2)
2 Basic concepts and applications of structural equation models
16(18)
2.1 Introduction
16(1)
2.2 Linear SEMs
17(6)
2.2.1 Measurement equation
18(1)
2.2.2 Structural equation and one extension
19(1)
2.2.3 Assumptions of linear SEMs
20(1)
2.2.4 Model identification
21(1)
2.2.5 Path diagram
22(1)
2.3 SEMs with fixed covariates
23(2)
2.3.1 The model
23(1)
2.3.2 An artificial example
24(1)
2.4 Nonlinear SEMs
25(4)
2.4.1 Basic nonlinear SEMs
25(2)
2.4.2 Nonlinear SEMs with fixed covariates
27(2)
2.4.3 Remarks
29(1)
2.5 Discussion and conclusions
29(4)
References
33(1)
3 Bayesian methods for estimating structural equation models
34(30)
3.1 Introduction
34(1)
3.2 Basic concepts of the Bayesian estimation and prior distributions
35(5)
3.2.1 Prior distributions
36(1)
3.2.2 Conjugate prior distributions in Bayesian analyses of SEMs
37(3)
3.3 Posterior analysis using Markov chain Monte Carlo methods
40(3)
3.4 Application of Markov chain Monte Carlo methods
43(2)
3.5 Bayesian estimation via WinBUGS
45(8)
Appendix 3.1 The gamma, inverted gamma, Wishart, and inverted Wishart distributions and their characteristics
53(1)
Appendix 3.2 The Metropolis-Hastings algorithm
54(1)
Appendix 3.3 Conditional distributions [ Ω|Y, θ] and [ θ|Y, Ω]
55(3)
Appendix 3.4 Conditional distributions [ Ω|Y, θ] and [ θ|Y, Ω] in nonlinear SEMs with covariates
58(2)
Appendix 3.5 WinBUGS code
60(1)
Appendix 3.6 R2WinBUGS code
61(1)
References
62(2)
4 Bayesian model comparison and model checking
64(22)
4.1 Introduction
64(1)
4.2 Bayes factor
65(8)
4.2.1 Path sampling
67(3)
4.2.2 A simulation study
70(3)
4.3 Other model comparison statistics
73(3)
4.3.1 Bayesian information criterion and Akaike information criterion
73(1)
4.3.2 Deviance information criterion
74(1)
4.3.3 Lv-measure
75(1)
4.4 Illustration
76(2)
4.5 Goodness of lit and model checking methods
78(2)
4.5.1 Posterior predictive p-value
78(1)
4.5.2 Residual analysis
78(2)
Appendix 4.1 WinBUGS code
80(1)
Appendix 4.2 R code in Bayes factor example
81(2)
Appendix 4.3 Posterior predictive p-value for model assessment
83(1)
References
83(3)
5 Practical structural equation models
86(44)
5.1 Introduction
86(1)
5.2 SEMs with continuous and ordered categorical variables
86(9)
5.2.1 Introduction
86(2)
5.2.2 The basic model
88(2)
5.2.3 Bayesian analysis
90(1)
5.2.4 Application: Bayesian analysis of quality of life data
90(4)
5.2.5 SEMs with dichotomous variables
94(1)
5.3 SEMs with variables from exponential family distributions
95(7)
5.3.1 Introduction
95(1)
5.3.2 The SEM framework with exponential family distributions
96(1)
5.3.3 Bayesian inference
97(1)
5.3.4 Simulation study
98(4)
5.4 SEMs with missing data
102(13)
5.4.1 Introduction
102(1)
5.4.2 SEMs with missing data that are MAR
103(2)
5.4.3 An illustrative example
105(3)
5.4.4 Nonlinear SEMs with nonignorable missing data
108(3)
5.4.5 An illustrative real example
111(4)
Appendix 5.1 Conditional distributions and implementation of the MH algorithm for SEMs with continuous and ordered categorical variables
115(4)
Appendix 5.2 Conditional distributions and implementation of MH algorithm for SEMs with EFDs
119(3)
Appendix 5.3 WinBUGS code related to section 5.3.4
122(1)
Appendix 5.4 R2WinBUGS code related to section 5.3.4
123(3)
Appendix 5.5 Conditional distributions for SEMs with nonignorable missing data
126(1)
References
127(3)
6 Structural equation models with hierarchical and multisample data
130(32)
6.1 Introduction
130(1)
6.2 Two-level structural equation models
131(10)
6.2.1 Two-level nonlinear SEM with mixed type variables
131(2)
6.2.2 Bayesian inference
133(3)
6.2.3 Application: Filipina CSWs study
136(5)
6.3 Structural equation models with multisample data
141(9)
6.3.1 Bayesian analysis of a nonlinear SEM in different groups
143(4)
6.3.2 Analysis of multisample quality of life data via WinBUGS
147(3)
Appendix 6.1 Conditional distributions: Two-level nonlinear SEM
150(3)
Appendix 6.2 The MH algorithm: Two-level nonlinear SEM
153(2)
Appendix 6.3 PP p-value for two-level nonlinear SEM with mixed continuous and ordered categorical variables
155(1)
Appendix 6.4 WinBUGS code
156(2)
Appendix 6.5 Conditional distributions: Multisample SEMs
158(2)
References
160(2)
7 Mixture structural equation models
162(34)
7.1 Introduction
162(1)
7.2 Finite mixture SEMs
163(15)
7.2.1 The model
163(1)
7.2.2 Bayesian estimation
164(4)
7.2.3 Analysis of an artificial example
168(2)
7.2.4 Example from the world values survey
170(3)
7.2.5 Bayesian model comparison of mixture SEMs
173(3)
7.2.6 An illustrative example
176(2)
7.3 A Modified mixture SEM
178(11)
7.3.1 Model description
178(2)
7.3.2 Bayesian estimation
180(2)
7.3.3 Bayesian model selection using a modified DIC
182(1)
7.3.4 An illustrative example
183(6)
Appendix 7.1 The permutation sampler
189(1)
Appendix 7.2 Searching for identifiability constraints
190(1)
Appendix 7.3 Conditional distributions: Modified mixture SEMs
191(3)
References
194(2)
8 Structural equation modeling for latent curve models
196(28)
8.1 Introduction
196(1)
8.2 Background to the real studies
197(2)
8.2.1 A longitudinal study of quality of life of stroke survivors
197(1)
8.2.2 A longitudinal study of cocaine use
198(1)
8.3 Latent curve models
199(6)
8.3.1 Basic latent curve models
199(1)
8.3.2 Latent curve models with explanatory latent variables
200(1)
8.3.3 Latent curve models with longitudinal latent variables
201(4)
8.4 Bayesian analysis
205(1)
8.5 Applications to two longitudinal studies
206(7)
8.5.1 Longitudinal study of cocaine use
206(4)
8.5.2 Health-related quality of life for stroke survivors
210(3)
8.6 Other latent curve models
213(5)
8.6.1 Nonlinear latent curve models
214(1)
8.6.2 Multilevel latent curve models
215(1)
8.6.3 Mixture latent curve models
215(3)
Appendix 8.1 Conditional distributions
218(2)
Appendix 8.2 WinBUGS code for the analysis of cocaine use data
220(2)
References
222(2)
9 Longitudinal structural equation models
224(23)
9.1 Introduction
224(2)
9.2 A two-level SEM for analyzing multivariate longitudinal data
226(2)
9.3 Bayesian analysis of the two-level longitudinal SEM
228(3)
9.3.1 Bayesian estimation
228(2)
9.3.2 Model comparison via the Lv-measure
230(1)
9.4 Simulation study
231(1)
9.5 Application: Longitudinal study of cocaine use
232(4)
9.6 Discussion
236(5)
Appendix 9.1 Full conditional distributions for implementing the Gibbs sampler
241(3)
Appendix 9.2 Approximation of the Lv-measure in equation (9.9) via MCMC samples
244(1)
References
245(2)
10 Semiparametric structural equation models with continuous variables
247(24)
10.1 Introduction
247(2)
10.2 Bayesian semiparametric hierarchical modeling of SEMs with covariates
249(2)
10.3 Bayesian estimation and model comparison
251(1)
10.4 Application: Kidney disease study
252(7)
10.5 Simulation studies
259(6)
10.5.1 Simulation study of estimation
259(3)
10.5.2 Simulation study of model comparison
262(2)
10.5.3 Obtaining the Lv-measure via WinBUGS and R2WinBUGS
264(1)
10.6 Discussion
265(2)
Appendix 10.1 Conditional distributions for parametric components
267(1)
Appendix 10.2 Conditional distributions for nonparametric components
268(1)
References
269(2)
11 Structural equation models with mixed continuous and unordered categorical variables
271(35)
11.1 Introduction
271(1)
11.2 Parametric SEMs with continuous and unordered categorical variables
272(8)
11.2.1 The model
272(2)
11.2.2 Application to diabetic kidney disease
274(2)
11.2.3 Bayesian estimation and model comparison
276(1)
11.2.4 Application to the diabetic kidney disease data
277(3)
11.3 Bayesian semiparametric SEM with continuous and unordered categorical variables
280(15)
11.3.1 Formulation of the semiparametric SEM
282(1)
11.3.2 Semiparametric hierarchical modeling via the Dirichlet process
283(2)
11.3.3 Estimation and model comparison
285(1)
11.3.4 Simulation study
286(3)
11.3.5 Real example: Diabetic nephropathy study
289(6)
Appendix 11.1 Full conditional distributions
295(3)
Appendix 11.2 Path sampling
298(1)
Appendix 11.3 A modified truncated DP related to equation (11.19)
299(1)
Appendix 11.4 Conditional distributions and the MH algorithm for the Bayesian semiparametric model
300(4)
References
304(2)
12 Structural equation models with nonparametric structural equations
306(35)
12.1 Introduction
306(1)
12.2 Nonparametric SEMs with Bayesian P-splines
307(13)
12.2.1 Model description
307(1)
12.2.2 General formulation of the Bayesian P-splines
308(1)
12.2.3 Modeling nonparametric functions of latent variables
309(1)
12.2.4 Prior distributions
310(2)
12.2.5 Posterior inference via Markov chain Monte Carlo sampling
312(1)
12.2.6 Simulation study
313(3)
12.2.7 A study on osteoporosis prevention and control
316(4)
12.3 Generalized nonparametric structural equation models
320(11)
12.3.1 Model description
320(2)
12.3.2 Bayesian P-splines
322(2)
12.3.3 Prior distributions
324(1)
12.3.4 Bayesian estimation and model comparison
325(2)
12.3.5 National longitudinal surveys of youth study
327(4)
12.4 Discussion
331(2)
Appendix 12.1 Conditional distributions and the MH algorithm: Nonparametric SEMs
333(3)
Appendix 12.2 Conditional distributions in generalized nonparametric SEMs
336(2)
References
338(3)
13 Transformation structural equation models
341(17)
13.1 Introduction
341(1)
13.2 Model description
342(1)
13.3 Modeling nonparametric transformations
343(1)
13.4 Identifiability constraints and prior distributions
344(1)
13.5 Posterior inference with MCMC algorithms
345(3)
13.5.1 Conditional distributions
345(1)
13.5.2 The random-ray algorithm
346(1)
13.5.3 Modifications of the random-ray algorithm
347(1)
13.6 Simulation study
348(2)
13.7 A study on the intervention treatment of polydrug use
350(4)
13.8 Discussion
354(1)
References
355(3)
14 Conclusion
358(3)
References
360(1)
Index 361
Xin-Yuan Song and Sik-Yum Lee, Department of Statistics, The Chinese University of Hong Kong
Pastovi nuoroda: https://www.kriso.lt/db/9781118358887_pe.html
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