Correlated Data Analysis: Modeling, Analytics, and Applications (eBook)

Preface 7
Contents 11
1 Introduction and Examples 16
1.1 Correlated Data 16
1.2 Longitudinal Data Analysis 17
1.3 Data Examples 21
1.4 Remarks 34
1.5 Outline of Subsequent Chapters 35
2 Dispersion Models 37
2.1 Introduction 37
2.2 Dispersion Models 39
2.3 Exponential Dispersion Models 44
2.4 Residuals 49
2.5 Tweedie Class 50
2.6 Maximum Likelihood Estimation 51
3 Inference Functions 68
3.1 Introduction 68
3.2 Quasi-Likelihood Inference in GLMs 69
3.3 Preliminaries 71
3.4 Optimal Inference Functions 74
3.5 Multi-Dimensional Inference Functions 78
3.6 Generalized Method of Moments 81
4 Modeling Correlated Data 85
4.1 Introduction 85
4.2 Quasi-Likelihood Approach 88
4.3 Conditional Modeling Approaches 92
4.4 Joint Modeling Approach 96
5 Marginal Generalized Linear Models 98
5.1 Model Formulation 99
5.2 GEE: Generalized Estimating Equations 100
5.3 GEE2 106
5.4 Residual Analysis 112
5.5 Quadratic Inference Functions 114
5.6 Implementation and Softwares 117
5.7 Examples 120
6 Vector Generalized Linear Models 132
6.1 Introduction 132
6.2 Log-Linear Model for Correlated Binary Data 133
6.3 Multivariate ED Family Distributions 136
6.4 Simultaneous Maximum Likelihood Inference 147
6.5 Algorithms 152
6.6 An Illustration: VGLMs for Trivariate Discrete Data 157
6.7 Data Examples 161
7 Mixed-Effects Models: Likelihood-Based Inference 167
7.1 Introduction 167
7.2 Model Specification 171
7.3 Estimation 175
7.4 MLE Based on Numerical Integration 177
7.5 Simulated MLE 184
7.6 Conditional Likelihood Estimation 186
7.7 MLE Based on EM Algorithm 188
7.8 Approximate Inference: PQL and REML 192
7.9 SAS Software 202
8 Mixed-Effects Models: Bayesian Inference 205
8.1 Bayesian Inference Using MCMC Algorithm 205
8.2 An Illustration: Multiple Sclerosis Trial Data 213
8.3 Multi-Level Correlated Data 216
8.4 WinBUGS Software 222
9 Linear Predictors 226
9.1 General Results 226
9.2 Estimation of Random Effects in GLMMs 230
9.3 Kalman Filter and Smoother 231
10 Generalized State Space Models 236
10.1 Introduction 236
10.2 Linear State Space Models 240
10.3 Shift-Mean Model 241
10.4 Monte Carlo Maximum Likelihood Estimation 244
11 Generalized State Space Models for Longitudinal Binomial Data 247
11.1 Introduction 247
11.2 Monte Carlo Kalman Filter and Smoother 248
11.3 Bayesian Inference Based on MCMC 254
12 Generalized State Space Models for Longitudinal Count Data 269
12.1 Introduction 269
12.2 Generalized Estimating Equation 272
12.3 Monte Carlo EM Algorithm 273
12.4 KEE in Stationary State Processes 275
12.5 KEE in Non-Stationary State Processes 283
13 Missing Data in Longitudinal Studies 299
13.1 Introduction 299
13.2 Missing Data Patterns 301
13.3 Diagnosis of Missing Data Types 308
13.4 Handling MAR Mechanism 314
13.5 Handling NMAR Mechanism 328
References 337
Index 351