Correlated Data Analysis

by Song, Peter X. k.

• ISBN13: 9780387713922
• ISBN10: 0387713921
• Format: Hardcover
• Copyright: 2007-07-20
• Publisher: Springer Verlag

Summary

This book presents some recent developments in correlated data analysis. It utilizes the class of dispersion models as marginal components in the formulation of joint models for correlated data. This enables the book to handle a broader range of data types than those analyzed by traditional generalized linear models. One example is correlated angular data. This book provides a systematic treatment for the topic of estimating functions. Under this framework, both generalized estimating equations (GEE) and quadratic inference functions (QIF) are studied as special cases. In addition to marginal models and mixed-effects models, this book covers topics on joint regression analysis based on Gaussian copulas and generalized state space models for longitudinal data from long time series. Various real-world data examples, numerical illustrations and software usage tips are presented throughout the book. This book has evolved from lecture notes on longitudinal data analysis, and may be considered suitable as a textbook for a graduate course on correlated data analysis. This book is inclined more towards technical details regarding the underlying theory and methodology used in software-based applications. Therefore, the book will serve as a useful reference for those who want theoretical explanations to puzzles arising from data analyses or deeper understanding of underlying theory related to analyses.

Author Biography

Peter Song is Professor of Statistics in the Department of Statistics and Actuarial Science at the University of Waterloo.

Table of Contents

Preface	p. vii
Introduction and Examples	p. 1
Correlated Data	p. 1
Longitudinal Data Analysis	p. 2
Data Examples	p. 6
Indonesian Children's Health Study	p. 6
Epileptic Seizures Data	p. 7
Retinal Surgery Data	p. 9
Orientation of Sandhoppers	p. 10
Schizophrenia Clinical Trial	p. 11
Multiple Sclerosis Trial	p. 13
Tretinoin Emollient Cream Trial	p. 13
Polio Incidences in USA	p. 14
Tokyo Rainfall Data	p. 15
Prince George Air Pollution Study	p. 16
Remarks	p. 19
Outline of Subsequent Chapters	p. 20
Dispersion Models	p. 23
Introduction	p. 23
Dispersion Models	p. 25
Definitions	p. 26
Properties	p. 28
Exponential Dispersion Models	p. 30
Residuals	p. 35
Tweedie Class	p. 36
Maximum Likelihood Estimation	p. 37
General Theory	p. 38
MLE in the ED Models	p. 41
MLE in the Simplex GLM	p. 42
MLE in the von Mises GLM	p. 49
Inference Functions	p. 55
Introduction	p. 55
Quasi-Likelihood Inference in GLMs	p. 56
Preliminaries	p. 58
Optimal Inference Functions	p. 61
Multi-Dimensional Inference Functions	p. 65
Generalized Method of Moments	p. 68
Modeling Correlated Data	p. 73
Introduction	p. 73
Quasi-Likelihood Approach	p. 76
Conditional Modeling Approaches	p. 80
Latent Variable Based Approach	p. 80
Transitional Model Based Approach	p. 82
Joint Modeling Approach	p. 84
Marginal Generalized Linear Models	p. 87
Model Formulation	p. 88
GEE: Generalized Estimating Equations	p. 89
General Theory	p. 90
Some Special Cases	p. 93
Wald Test for Nested Models	p. 95
GEE2	p. 95
Constant Dispersion Parameter	p. 96
Varying Dispersion Parameter	p. 100
Residual Analysis	p. 101
Checking Distributional Assumption	p. 102
Checking Constant Dispersion Assumption	p. 102
Checking Link Functions	p. 102
Checking Working Correlation	p. 102
Quadratic Inference Functions	p. 103
Implementation and Softwares	p. 106
Newton-Scoring Algorithm	p. 106
SAS PROC GENMOD	p. 107
SAS MACRO QIF	p. 108
Examples	p. 109
Longitudinal Binary Data	p. 110
Longitudinal Count Data	p. 112
Longitudinal Proportional Data	p. 116
Vector Generalized Linear Models	p. 121
Introduction	p. 121
Log-Linear Model for Correlated Binary Data	p. 122
Multivariate ED Family Distributions	p. 125
Copulas	p. 126
Construction	p. 127
Interpretation of Association Parameter	p. 129
Simultaneous Maximum Likelihood Inference	p. 136
General Theory	p. 136
VGLMs for Correlated Continuous Outcomes	p. 137
VGLMs for Correlated Discrete Outcomes	p. 138
Scores for Association Parameters	p. 139
Algorithms	p. 141
Algorithm I: Maximization by Parts	p. 142
Algorithm II: Gauss-Newton Type	p. 146
An Illustration: VGLMs for Trivariate Discrete Data	p. 146
Trivariate VGLMs	p. 147
Comparison of Asymptotic Efficiency	p. 148
Data Examples	p. 150
Analysis of Two-Period Cross-Over Trial Data	p. 150
Analysis of Hospital Visit Data	p. 152
Analysis of Burn Injury Data	p. 153
Mixed-Effects Models: Likelihood-Based Inference	p. 157
Introduction	p. 157
Model Specification	p. 161
Estimation	p. 165
MLE Based on Numerical Integration	p. 167
Simulated MLE	p. 174
Conditional Likelihood Estimation	p. 176
MLE Based on EM Algorithm	p. 178
Approximate Inference: PQL and REML	p. 182
SAS Software	p. 192
PROC MIXED	p. 192
PROC NLMIXED	p. 193
PROC GLIMMIX	p. 194
Mixed-Effects Models: Bayesian Inference	p. 195
Bayesian Inference Using MCMC Algorithm	p. 195
Gibbs Sampling: A Practical View	p. 195
Diagnostics	p. 198
Enhancing Burn-in	p. 201
Model Selection	p. 202
An Illustration: Multiple Sclerosis Trial Data	p. 203
Multi-Level Correlated Data	p. 206
WinBUGS Software	p. 212
WinBUGS Code in Multiple Sclerosis Trial Data Analysis	p. 213
WinBUGS Code for the TEC Drug Analysis	p. 214
Linear Predictors	p. 217
General Results	p. 217
Estimation of Random Effects in GLMMs	p. 221
Estimation in LMMs	p. 221
Estimation in GLMMs	p. 221
Kalman Filter and Smoother	p. 222
General Forms	p. 222
Generalized State Space Models	p. 227
Introduction	p. 227
Linear State Space Models	p. 231
Shift-Mean Model	p. 232
Monte Carlo Maximum Likelihood Estimation	p. 235
Generalized State Space Models for Longitudinal Binomial Data	p. 239
Introduction	p. 239
Monte Carlo Kalman Filter and Smoother	p. 240
Bayesian Inference Based on MCMC	p. 246
Generalized State Space Models for Longitudinal Count Data	p. 261
Introduction	p. 261
Generalized Estimating Equation	p. 264
Monte Carlo EM Algorithm	p. 265
KEE in Stationary State Processes	p. 267
Setup	p. 267
Kalman Filter and Smoother	p. 269
Godambe Information Matrix	p. 271
Analysis of Polio Incidences Data	p. 272
KEE in Non-Stationary State Processes	p. 275
Model Formulation	p. 275
Kalman Filter and Smoother	p. 278
Parameter Estimation	p. 280
Model Diagnosis	p. 281
Analysis of Prince George Data	p. 283
Missing Data in Longitudinal Studies	p. 291
Introduction	p. 291
Missing Data Patterns	p. 293
Patterns of Missingness	p. 293
Types of Missingness and Effects	p. 297
Diagnosis of Missing Data Types	p. 300
Graphic Approach	p. 301
Testing for MCAR	p. 302
Handling MAR Mechanism	p. 306
Simple Solutions and Limitations	p. 307
Multiple Imputation	p. 307
EM Algorithm	p. 311
Inverse Probability Weighting	p. 317
Handling NM AR Mechanism	p. 320
Parametric Modeling	p. 320
A Semiparametric Pattern Mixture Model	p. 322
References	p. 329
Index	p. 343
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