Linear and Generalized Linear Mixed Models and Their Applications (Springer Series in Statistics)

✍ Scribed by Jiming Jiang

• Publisher: Springer
• Year: 2007
• Tongue: English
• Leaves: 273
• Edition: Springer Series in Statistics
• Category: Library

✦ Synopsis

This book covers two major classes of mixed effects models, linear mixed models and generalized linear mixed models. It presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. The book offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it includes recently developed methods, such as mixed model diagnostics, mixed model selection, and jackknife method in the context of mixed models. The book is aimed at students, researchers and other practitioners who are interested in using mixed models for statistical data analysis.

✦ Table of Contents

LINEAR AND GENERALIZED LINEAR MIXED MODELS AND THEIR APPLICATIONS......Page 1
Springerlink......Page 0
Springer Series in Statistics......Page 3
Title Page......Page 4
Copyright Page......Page 5
Dedication......Page 7
Preface......Page 8
Contents......Page 12
1.1 Introduction......Page 16
1.1.1 Effect of Air Pollution Episodes on Children......Page 17
1.1.3 Small Area Estimation of Income......Page 18
1.2.1 Gaussian Mixed Models......Page 19
1.2.2 Non-Gaussian Linear Mixed Models......Page 23
1.3.1 Maximum Likelihood......Page 24
1.3.2 Restricted Maximum Likelihood......Page 27
1.4 Estimation in Non-Gaussian Models......Page 30
1.4.1 Quasi-Likelihood Method......Page 31
1.4.2 Partially Observed Information......Page 33
1.4.3 Iterative Weighted Least Squares......Page 35
1.4.4 Jackknife Method......Page 39
1.5.1 Analysis of Variance Estimation......Page 40
1.5.2 Minimum Norm Quadratic Unbiased Estimation......Page 43
1.6.1 Notes on Computation......Page 44
1.6.2 Notes on Software......Page 48
1.7 Real-Life Data Examples......Page 49
1.7.1 Analysis of Birth Weights of Lambs......Page 50
1.7.2 Analysis of Hip Replacements Data......Page 52
1.8 Further Results and Technical Notes......Page 54
1.9 Exercises......Page 63
2.1.1 Tests in Gaussian Mixed Models......Page 66
2.1.2 Tests in Non-Gaussian Linear Mixed Models......Page 71
2.2.1 Confidence Intervals in Gaussian Mixed Models......Page 81
2.2.2 Confidence Intervals in Non-Gaussian Linear Mixed Models......Page 87
2.3.1 Prediction of Mixed Effect......Page 89
2.3.2 Prediction of Future Observation......Page 95
2.4.1 Model Diagnostics......Page 103
2.4.2 Model Selection......Page 108
2.5 Bayesian Inference......Page 114
2.5.1 Inference about Variance Components......Page 115
2.5.2 Inference about Fixed and Random Effects......Page 116
2.6.1 Analysis of the Birth Weights of Lambs (Continued)......Page 117
2.6.2 The Baseball Example......Page 118
2.7 Further Results and Technical Notes......Page 120
2.8 Exercises......Page 128
3.1 Introduction......Page 134
3.2 Generalized Linear Mixed Models......Page 135
3.3.1 The Salamander Mating Experiments......Page 137
3.3.3 Small Area Estimation of Mammography Rates......Page 139
3.4 Likelihood Function under GLMM......Page 140
3.5.1 Laplace Approximation......Page 142
3.5.2 Penalized Quasi-Likelihood Estimation......Page 143
3.5.3 Tests of Zero Variance Components......Page 147
3.5.4 Maximum Hierarchical Likelihood......Page 149
3.6.1 Joint Estimation of Fixed and Random Effects......Page 151
3.6.2 Empirical Best Prediction......Page 157
3.6.3 A Simulated Example......Page 164
3.7.1 More on NLGSA......Page 166
3.7.2 Asymptotic Properties of PQWLS Estimators......Page 167
3.7.3 MSE of EBP......Page 170
3.7.4 MSPE of the Model-Assisted EBP......Page 173
3.8 Exercises......Page 176
4.1 Likelihood-Based Inference......Page 178
4.1.1 A Monte Carlo EM Algorithm for Binary Data......Page 179
4.1.2 Extensions......Page 182
4.1.3 MCEM with I.I.D. Sampling......Page 185
4.1.4 Automation......Page 186
4.1.5 Maximization by Parts......Page 189
4.1.6 Bayesian Inference......Page 193
4.2 Estimating Equations......Page 198
4.2.1 Generalized Estimating Equations (GEE)......Page 199
4.2.2 Iterative Estimating Equations......Page 201
4.2.3 Method of Simulated Moments......Page 205
4.2.4 Robust Estimation in GLMM......Page 211
4.3 GLMM Selection......Page 214
4.3.1 A General Principle for Model Selection......Page 215
4.3.2 A Simulated Example......Page 218
4.4.1 Fetal Mortality in Mouse Litters......Page 220
4.4.2 Analysis of Gc Genotype Data: An Application of the Fence Method......Page 222
4.4.3 The Salamander-Mating Experiments: Various Applications of GLMM......Page 224
4.5.2 Linear Convergence and Asymptotic Properties of IEE......Page 229
4.5.3 Incorporating Informative Missing Data in IEE......Page 232
4.5.4 Consistency of MSM Estimator......Page 233
4.5.5 Asymptotic Properties of First and Second-Step Estimators......Page 236
4.5.6 Further Results of the Fence Method......Page 240
4.6 Exercises......Page 244
Appendix A. List of Notations......Page 246
B.2 Matrix Differentiation......Page 248
B.3 Projection......Page 249
B.5 Decompositions of Matrices......Page 250
B.6 The Eigenvalue Perturbation Theory......Page 251
C.2 Quadratic Forms......Page 252
C.4 Convolution......Page 253
C.5 Exponential Family and Generalized Linear Models......Page 254
References......Page 256
Index......Page 270
Springer Series in Statistics (continued from p. ii)......Page 273