1 Classical likelihood theory 5
1.1 Definition 5
1.2 Quantities derived from the likelihood 10
1.3 Profile likelihood 14
1.4 Distribution of the likelihood-ratio statistic 16
1.5 Distribution of the MLE and the Wald statistic 20
1.6 Model selection 24
1.7 Marginal and conditional likelihoods 25
1.8 Higher-order approximations 30
1.9 Adjusted profile likelihood 32
1.10 Bayesian and likelihood methods 34
1.11 Jacobian in likelihood methods 36
2 Generalized Linear Models 37
2.1 Linear models 37
2.2 Generalized linear models 42
2.3 Model checking 49
2.4 Examples 53
3 Quasi-likelihood 65
3.1 Examples 68
3.2 Iterative weighted least squares 72
3.3 Asymptotic inference 73
3.4 Dispersion models 77
3.5 Extended quasi-likelihood 80
3.6 Joint GLM of mean and dispersion 85
3.7 Joint GLMs for quality improvement 90
4 Extended Likelihood Inferences 97
4.1 Two kinds of likelihood 98
4.2 Inference about the fixed parameters 103
4.3 Inference about the random parameters 105
4.4 Optimality in random-parameter estimation 108
4.5 Canonical scale, h-likelihood and joint inference 112
4.6 Statistical prediction 119
4.7 Regression as an extended model 121
4.8 *Missing or incomplete-data problems 122
4.9 Is marginal likelihood enough for inference about fixed
parameters? 130
4.10 Summary: likelihoods in extended framework 131
5 Normal linear mixed models 135
5.1 Developments of normal mixed linear models 138
5.2 Likelihood estimation of fixed parameters 141
5.3 Classical estimation of random effects 146
5.4 H-likelihood approach 155
5.5 Example 163
5.6 Invariance and likelihood inference 166
CONTENTS
6 Hierarchical GLMs 173
6.1 HGLMs 173
6.2 H-likelihood 175
6.3 Inferential procedures using h-likelihood 183
6.4 Penalized quasi-likelihood 189
6.5 Deviances in HGLMs 192
6.6 Examples 194
6.7 Choice of random-effect scale 199
7 HGLMs with structured dispersion 203
7.1 HGLMs with structured dispersion 203
7.2 Quasi-HGLMs 205
7.3 Examples 213
8 Correlated random effects for HGLMs 231
8.1 HGLMs with correlated random effects 231
8.2 Random effects described by fixed L matrices 233
8.3 Random effects described by a covariance matrix 235
8.4 Random effects described by a precision matrix 236
8.5 Fitting and model-checking 237
8.6 Examples 238
8.7 Twin and family data 251
8.8 *Ascertainment problem 264
9 Smoothing 267
9.1 Spline models 267
9.2 Mixed model framework 273
9.3 Automatic smoothing 278
9.4 Non-Gaussian smoothing 281
10 Random-effect models for survival data 293
10.1 Proportional-hazard model 293
10.2 Frailty models and the associated h-likelihood 295
10.3 *Mixed linear models with censoring 307
10.4 Extensions 313
10.5 Proofs 315
11 Double HGLMs 319
11.1 DHGLMs 319
11.2 Models for finance data 323
11.3 Joint splines 324
11.4 H-likelihood procedure for fitting DHGLMs 325
11.5 Random effects in the A component 328
11.6 Examples 330
12 Further topics 343
12.1 Model for multivariate responses 344
12.2 Joint model for continuous and binary data 345
12.3 Joint model for repeated measures and survival time 348
12.4 Missing data in longitudinal studies 351
12.5 Denoising signals by imputation 357