Dunson Random Effect and Latent Variable Model Selection

1. Auflage 2010
ISBN: 978-0-387-76721-5
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 192, 170 Seiten

Reihe: Lecture Notes in Statistics

Random Effect and Latent Variable Model Selection In recent years, there has been a dramatic increase in the collection of multivariate and correlated data in a wide variety of ?elds. For example, it is now standard pr- tice to routinely collect many response variables on each individual in a study. The different variables may correspond to repeated measurements over time, to a battery of surrogates for one or more latent traits, or to multiple types of outcomes having an unknown dependence structure. Hierarchical models that incorporate subje- speci?c parameters are one of the most widely-used tools for analyzing multivariate and correlated data. Such subject-speci?c parameters are commonly referred to as random effects, latent variables or frailties. There are two modeling frameworks that have been particularly widely used as hierarchical generalizations of linear regression models. The ?rst is the linear mixed effects model (Laird and Ware , 1982) and the second is the structural equation model (Bollen , 1989). Linear mixed effects (LME) models extend linear regr- sion to incorporate two components, with the ?rst corresponding to ?xed effects describing the impact of predictors on the mean and the second to random effects characterizing the impact on the covariance. LMEs have also been increasingly used for function estimation. In implementing LME analyses, model selection problems are unavoidable. For example, there may be interest in comparing models with and without a predictor in the ?xed and/or random effects component.

Autoren/Hrsg.

Dunson, David

Inhaltsverzeichnis

1;Preface Random Effect and Latent Variable Model Selection;5
2;Contents;8
3;Part I: Random Effects Models;9
3.1;Chapter 1;10
3.1.1;Likelihood Ratio Testing for Zero Variance Components in Linear Mixed Models;10
3.1.1.1;1 Examples;11
3.1.1.1.1;1.1 Loa loa Prevalence in West Africa;11
3.1.1.1.2;1.2 Onion Density in Australia;12
3.1.1.1.3;1.3 Coronary Sinus Potassium;14
3.1.1.2;2 Model and Testing Framework;16
3.1.1.3;3 Standard Asymptotic Results for LMMs;17
3.1.1.4;4 Finite Sample and Asymptotic Results for General Design LMMs with One Variance Component;17
3.1.1.5;5 Linear Mixed Models with Multiple Variance Components;18
3.1.1.5.1;5.1 Fast Finite Sample Approximation;20
3.1.1.5.2;5.2 Mixture Approximation to the Bootstrap;20
3.1.1.6;6 Revisiting the Applications;21
3.1.1.7;7 Discussion;22
3.1.2;References;24
3.2;Chapter 2;25
3.2.1;Variance Component Testing in Generalized Linear Mixed Models for Longitudinal/Clustered Data and other Related Topics;25
3.2.1.1;1 Introduction;25
3.2.1.2;2 Generalized Linear Mixed Models for Longitudinal/Clustered Data;26
3.2.1.3;3 The Likelihood Ratio Test for Variance Components in GLMMs;27
3.2.1.4;4 The Score Test for Variance Components in GLMMs;31
3.2.1.5;5 Simulation Study to Compare the Likelihood Ratio Test and the Score Test for Variance Components;35
3.2.1.6;6 Polynomial Test in Semiparametric Additive Mixed Models;36
3.2.1.7;7 Application;39
3.2.1.8;8 Discussion;40
3.2.1.9;References;41
3.3;Chapter 3;43
3.3.1;Bayesian Model Uncertainty in Mixed EffectsModels;43
3.3.1.1;1 Introduction;43
3.3.1.1.1;1.1 Motivation;43
3.3.1.1.2;1.2 Frequentist Literature;44
3.3.1.1.3;1.3 Bayesian Approach;45
3.3.1.2;2 Bayesian Model Uncertainty;46
3.3.1.2.1;2.1 Subset Selection in Linear Regression;46
3.3.1.2.2;2.2 Bayes Factors and Default Priors;48
3.3.1.3;3 Bayesian Subset Selection for Mixed Effects Models;49
3.3.1.3.1;3.1 Bayes Factor Approximations;49
3.3.1.3.2;3.2 Stochastic Search Variable Selection;50
3.3.1.4;4 Linear Mixed Models;51
3.3.1.4.1;4.1 Priors;51
3.3.1.4.2;4.2 Posterior Computation;53
3.3.1.5;5 Binary Logistic Mixed Models;55
3.3.1.5.1;5.1 Priors and Posterior Computation;57
3.3.1.5.2;5.2 Importance Weights;59
3.3.1.6;6 Simulation Examples;60
3.3.1.7;7 Epidemiology Application;63
3.3.1.8;8 OtherModels;64
3.3.1.8.1;8.1 Logistic Models for Ordinal Data;64
3.3.1.8.2;8.2 Probit Models;65
3.3.1.9;9 Discussion;65
3.3.1.10;References;66
3.4;Chapter 4;69
3.4.1;Bayesian Variable Selection in Generalized Linear Mixed Models;69
3.4.1.1;1 Introduction;69
3.4.1.1.1;1.1 Background and Motivation;69
3.4.1.1.2;1.2 Time to Pregnancy Application;71
3.4.1.1.3;1.3 Background on Model Selection in GLMMs;72
3.4.1.2;2 Bayesian Subset Selection in GLMMs;73
3.4.1.2.1;2.1 Generalized Linear Mixed Models;73
3.4.1.2.2;2.2 Description of Approach;75
3.4.1.2.3;2.3 Reparameterization and Mixture Prior Specification;76
3.4.1.2.4;2.4 An Approximation;78
3.4.1.3;3 Posterior Computation;80
3.4.1.3.1;3.1 General Strategies;80
3.4.1.3.2;3.2 Updating Parameters;81
3.4.1.3.3;3.3 Calculation of Quantities;83
3.4.1.4;4 Simulation Examples;84
3.4.1.4.1;4.1 Simulation Setup;84
3.4.1.4.2;4.2 Results;86
3.4.1.4.3;4.3 Assessment of Accuracy of the Approximation;90
3.4.1.5;5 Time-to-Pregnancy Application;91
3.4.1.5.1;5.1 Data and Model Selection Problem;91
3.4.1.5.2;5.2 Prior Specification, Implementation and Results;91
3.4.1.6;6 Discussion;94
3.4.1.7;References;95
3.4.1.8;Appendix;97
4;Part II: Factor Analysis and Structural Equations Models;98
4.1;Chapter 5;99
4.1.1;A Unified Approach to Two-Level Structural Equation Models and Linear Mixed Effects Models;99
4.1.1.1;1 Introduction;99
4.1.1.2;2 Model Formulation;101
4.1.1.3;3 The EM Algorithm;104
4.1.1.3.1;3.1 Maximum Likelihood Estimation;104
4.1.1.3.2;3.2 Asymptotic Properties;110
4.1.1.4;4 Examples;112
4.1.1.5;5 Goodness-of-Fit and Related Issues;118
4.1.1.6;Appendix. EQS Input Program for the Model in Example 2;119
4.1.1.7;References;122
4.2;Chapter 6;124
4.2.1;Bayesian Model Comparison of Structural Equation Models;124
4.2.1.1;1 Introduction;124
4.2.1.2;2 Bayes Factor and other Model Comparison Statistics;125
4.2.1.2.1;2.1 Bayes Factor;125
4.2.1.2.2;2.2 Other Alternatives;127
4.2.1.3;3 Computation of Bayes Factor through Path Sampling;129
4.2.1.4;4 Model Comparison of Nonlinear SEMs;130
4.2.1.4.1;4.1 Model Description;130
4.2.1.4.2;4.2 Model Comparison via Bayes Factor;131
4.2.1.4.3;4.3 A Simulation Study;133
4.2.1.5;5 Model Comparison of an Integrated SEM;136
4.2.1.5.1;5.1 The Integrated Model;138
4.2.1.5.2;5.2 Model Comparison;139
4.2.1.5.3;5.3 An Illustrative Example;141
4.2.1.6;6 Discussion;146
4.2.1.7;Appendix: Full Conditional Distributions;148
4.2.1.8;References;151
4.3;Chapter 7;154
4.3.1;Bayesian Model Selection in Factor Analytic Models;154
4.3.1.1;1 Introduction;154
4.3.1.2;2 Specification of the Model;156
4.3.1.3;3 Bayesian Uncertainty in the Number of Factors;158
4.3.1.4;4 Simulation Study;160
4.3.1.4.1;4.1 One-Factor Model;160
4.3.1.4.2;4.2 Three-Factor Model;161
4.3.1.5;5 Application to Rodent Organ Weight Data;161
4.3.1.6;6 Discussion;163
4.3.1.7;References;164
4.3.1.8;Appendix: Full Conditional Distributions for the Gibbs Sampler;165
5;Index;167