Random Effect and Latent Variable Model Selection (eBook)

David Dunson (Herausgeber)

eBook Download: PDF

2010 | 2008
X, 170 Seiten
Springer New York (Verlag)
978-0-387-76721-5 (ISBN)

Infos

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.

Inhalt

Preface Random Effect and Latent Variable Model Selection 5
Contents 8
Part I: Random Effects Models 9
Chapter 1 10
Likelihood Ratio Testing for Zero Variance Components in Linear Mixed Models 10
1 Examples 11
1.1 Loa loa Prevalence in West Africa 11
1.2 Onion Density in Australia 12
1.3 Coronary Sinus Potassium 14
2 Model and Testing Framework 16
3 Standard Asymptotic Results for LMMs 17
4 Finite Sample and Asymptotic Results for General Design LMMs with One Variance Component 17
5 Linear Mixed Models with Multiple Variance Components 18
5.1 Fast Finite Sample Approximation 20
5.2 Mixture Approximation to the Bootstrap 20
6 Revisiting the Applications 21
7 Discussion 22
References 24
Chapter 2 25
Variance Component Testing in Generalized Linear Mixed Models for Longitudinal/Clustered Data and other Related Topics 25
1 Introduction 25
2 Generalized Linear Mixed Models for Longitudinal/Clustered Data 26
3 The Likelihood Ratio Test for Variance Components in GLMMs 27
4 The Score Test for Variance Components in GLMMs 31
5 Simulation Study to Compare the Likelihood Ratio Test and the Score Test for Variance Components 35
6 Polynomial Test in Semiparametric Additive Mixed Models 36
7 Application 39
8 Discussion 40
References 41
Chapter 3 43
Bayesian Model Uncertainty in Mixed EffectsModels 43
1 Introduction 43
1.1 Motivation 43
1.2 Frequentist Literature 44
1.3 Bayesian Approach 45
2 Bayesian Model Uncertainty 46
2.1 Subset Selection in Linear Regression 46
2.2 Bayes Factors and Default Priors 48
3 Bayesian Subset Selection for Mixed Effects Models 49
3.1 Bayes Factor Approximations 49
3.2 Stochastic Search Variable Selection 50
4 Linear Mixed Models 51
4.1 Priors 51
4.2 Posterior Computation 53
5 Binary Logistic Mixed Models 55
5.1 Priors and Posterior Computation 57
5.2 Importance Weights 59
6 Simulation Examples 60
7 Epidemiology Application 63
8 OtherModels 64
8.1 Logistic Models for Ordinal Data 64
8.2 Probit Models 65
9 Discussion 65
References 66
Chapter 4 69
Bayesian Variable Selection in Generalized Linear Mixed Models 69
1 Introduction 69
1.1 Background and Motivation 69
1.2 Time to Pregnancy Application 71
1.3 Background on Model Selection in GLMMs 72
2 Bayesian Subset Selection in GLMMs 73
2.1 Generalized Linear Mixed Models 73
2.2 Description of Approach 75
2.3 Reparameterization and Mixture Prior Specification 76
2.4 An Approximation 78
3 Posterior Computation 80
3.1 General Strategies 80
3.2 Updating Parameters 81
3.3 Calculation of Quantities 83
4 Simulation Examples 84
4.1 Simulation Setup 84
4.2 Results 86
4.3 Assessment of Accuracy of the Approximation 90
5 Time-to-Pregnancy Application 91
5.1 Data and Model Selection Problem 91
5.2 Prior Specification, Implementation and Results 91
6 Discussion 94
References 95
Appendix 97
Part II: Factor Analysis and Structural Equations Models 98
Chapter 5 99
A Unified Approach to Two-Level Structural Equation Models and Linear Mixed Effects Models 99
1 Introduction 99
2 Model Formulation 101
3 The EM Algorithm 104
3.1 Maximum Likelihood Estimation 104
3.2 Asymptotic Properties 110
4 Examples 112
5 Goodness-of-Fit and Related Issues 118
Appendix. EQS Input Program for the Model in Example 2 119
References 122
Chapter 6 124
Bayesian Model Comparison of Structural Equation Models 124
1 Introduction 124
2 Bayes Factor and other Model Comparison Statistics 125
2.1 Bayes Factor 125
2.2 Other Alternatives 127
3 Computation of Bayes Factor through Path Sampling 129
4 Model Comparison of Nonlinear SEMs 130
4.1 Model Description 130
4.2 Model Comparison via Bayes Factor 131
4.3 A Simulation Study 133
5 Model Comparison of an Integrated SEM 136
5.1 The Integrated Model 138
5.2 Model Comparison 139
5.3 An Illustrative Example 141
6 Discussion 146
Appendix: Full Conditional Distributions 148
References 151
Chapter 7 154
Bayesian Model Selection in Factor Analytic Models 154
1 Introduction 154
2 Specification of the Model 156
3 Bayesian Uncertainty in the Number of Factors 158
4 Simulation Study 160
4.1 One-Factor Model 160
4.2 Three-Factor Model 161
5 Application to Rodent Organ Weight Data 161
6 Discussion 163
References 164
Appendix: Full Conditional Distributions for the Gibbs Sampler 165
Index 167

Produkt-Details

• Erscheint lt. Verlag: 18.3.2010
• Reihe/Serie: Lecture Notes in Statistics
• Reihe/Serie: Lecture Notes in Statistics
• Zusatzinfo: X, 170 p.
• Verlagsort: New York
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Statistik
• Themenwelt: Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
• Themenwelt: Technik
• Schlagworte: Factor Analysis • Generalized Linear Model • Latent variable model • Latent Variables • likelihood • Model Selection • random effects • structural equation models • subset selection • Variable selection • Variance
• ISBN-10: 0-387-76721-5 / 0387767215
• ISBN-13: 978-0-387-76721-5 / 9780387767215