Generalized Linear Models with Random Effects: Unified Analysis Via H-Likelihood, Second Edition

Cover......Page 1
Half Title......Page 2
Title......Page 8
Copyright......Page 9
Contents......Page 10
List of notations......Page 16
Preface to first edition......Page 18
Preface......Page 20
Introduction......Page 22
 1.1 Definition......Page 26
 1.2 Quantities derived from the likelihood......Page 31
 1.3 Profile likelihood......Page 35
 1.4 Distribution of the likelihood ratio statistic......Page 37
 1.5 Distribution of the MLE and the Wald statistic......Page 41
 1.6 Model selection......Page 45
 1.7 Marginal and conditional likelihoods......Page 46
 1.8 Higher-order approximations......Page 51
 1.9 Adjusted profile likelihood......Page 53
 1.10 Bayesian and likelihood methods......Page 55
 1.11 Confidence distribution......Page 57
 2.1 Linear models......Page 60
 2.2 Generalized linear models......Page 65
 2.3 Model checking......Page 72
 2.4 Examples......Page 76
3 Quasi–likelihood......Page 88
 3.1 Examples......Page 91
 3.2 Iterative weighted least squares......Page 95
 3.3 Asymptotic inference......Page 96
 3.4 Dispersion models......Page 100
 3.5 Extended quasi–likelihood......Page 103
 3.6 Joint GLM of mean and dispersion......Page 108
 3.7 Joint GLMs for quality improvement......Page 113
4 Extended likelihood inferences......Page 120
 4.1 Two kinds of likelihoods......Page 121
 4.2 Wallet game and extended likelihood......Page 127
 4.3 Inference about the fixed parameters......Page 129
 4.4 Inference about the random parameters......Page 131
 4.5 Canonical scale, h-likelihood and joint inference......Page 132
 4.6 Prediction of random parameters......Page 139
 4.7 Prediction of future outcome......Page 142
 4.8 Finite sample adjustment......Page 143
 4.10 Summary: likelihoods in extended framework......Page 147
5 Normal linear mixed models......Page 152
 5.1 Developments of normal mixed linear models......Page 155
 5.2 Likelihood estimation of fixed parameters......Page 158
 5.3 Classical estimation of random effects......Page 163
 5.4 H-likelihood approach......Page 172
 5.5 Example......Page 180
 5.6 Invariance and likelihood inference......Page 183
 6.1 HGLMs......Page 188
 6.2 H-likelihood......Page 190
 6.3 Inferential procedures using h-likelihood......Page 198
 6.4 Penalized quasi–likelihood......Page 204
 6.5 Deviances in HGLMs......Page 208
 6.6 Examples......Page 209
 6.7 Choice of random effect scale......Page 214
 7.1 Description of model......Page 218
 7.2 Quasi–HGLMs......Page 220
 7.3 Examples......Page 228
 8.1 HGLMs with correlated random effects......Page 244
 8.2 Random effects described by fixed L matrices......Page 246
 8.3 Random effects described by a covariance matrix......Page 248
 8.4 Random effects described by a precision matrix......Page 249
 8.6 Examples......Page 250
 8.7 Twin and family data......Page 265
 8.8 Ascertainment problem......Page 278
9 Smoothing......Page 280
 9.1 Spline models......Page 281
 9.2 Mixed model framework......Page 285
 9.3 Automatic smoothing......Page 291
 9.4 Smoothing via a model with singular precision matrix......Page 294
 9.5 Non–Gaussian smoothing......Page 299
 10.1 Model description......Page 310
 10.2 Models for finance data......Page 314
 10.3 Joint splines......Page 315
 10.4 H-likelihood procedure for fitting DHGLMs......Page 316
 10.5 Random effects in the λ component......Page 320
 10.6 Examples......Page 321
11 Variable selection and sparsity models......Page 334
 11.1 Penalized least squares......Page 335
 11.2 Random effect variable selection......Page 337
 11.3 Implied penalty functions......Page 339
 11.4 Scalar β case......Page 341
 11.5 Estimating the dispersion and tuning parameters......Page 344
 11.6 Example: diabetes data......Page 345
 11.7 Numerical studies......Page 346
 11.8 Asymptotic property of HL method......Page 349
 11.9 Sparse multivariate methods......Page 350
 11.10 Structured variable selection......Page 353
 11.11 Interaction and hierarchy constraints......Page 356
12 Multivariate and missing data analysis......Page 362
 12.1 Multivariate models......Page 363
 12.2 Missing data problems......Page 370
 12.3 Missing data in longitudinal studies......Page 376
 12.4 Denoising signals by imputation......Page 382
 13.1 Single hypothesis testing......Page 388
 13.2 Multiple testing......Page 391
 13.3 Multiple testing with two states......Page 393
 13.4 Multiple testing with three states......Page 395
 13.5 Examples......Page 398
 14.1 Proportional-hazard model......Page 402
 14.2 Frailty models and the associated h-likelihood......Page 404
 14.3 ∗Mixed linear models with censoring......Page 416
 14.4 Extensions......Page 422
 14.5 Proofs......Page 424
References......Page 428
Data Index......Page 448
Author Index......Page 450
Subject Index......Page 456