Song Correlated Data Analysis: Modeling, Analytics, and Applications

1. Auflage 2007
ISBN: 978-0-387-71393-9
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 352 Seiten

Reihe: Springer Series in Statistics

This book covers 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 cover a broader range of data types than the traditional generalized linear models. The reader is provided with a systematic treatment for the topic of estimating functions, and both generalized estimating equations (GEE) and quadratic inference functions (QIF) are studied as special cases. In addition to the discussions on marginal models and mixed-effects models, this book covers new topics on joint regression analysis based on Gaussian copulas.

Autoren/Hrsg.

Song, Peter X. -K.

Inhaltsverzeichnis

1;Preface;7
2;Contents;11
3;1 Introduction and Examples;16
3.1;1.1 Correlated Data;16
3.2;1.2 Longitudinal Data Analysis;17
3.3;1.3 Data Examples;21
3.4;1.4 Remarks;34
3.5;1.5 Outline of Subsequent Chapters;35
4;2 Dispersion Models;37
4.1;2.1 Introduction;37
4.2;2.2 Dispersion Models;39
4.3;2.3 Exponential Dispersion Models;44
4.4;2.4 Residuals;49
4.5;2.5 Tweedie Class;50
4.6;2.6 Maximum Likelihood Estimation;51
5;3 Inference Functions;68
5.1;3.1 Introduction;68
5.2;3.2 Quasi-Likelihood Inference in GLMs;69
5.3;3.3 Preliminaries;71
5.4;3.4 Optimal Inference Functions;74
5.5;3.5 Multi-Dimensional Inference Functions;78
5.6;3.6 Generalized Method of Moments;81
6;4 Modeling Correlated Data;85
6.1;4.1 Introduction;85
6.2;4.2 Quasi-Likelihood Approach;88
6.3;4.3 Conditional Modeling Approaches;92
6.4;4.4 Joint Modeling Approach;96
7;5 Marginal Generalized Linear Models;98
7.1;5.1 Model Formulation;99
7.2;5.2 GEE: Generalized Estimating Equations;100
7.3;5.3 GEE2;106
7.4;5.4 Residual Analysis;112
7.5;5.5 Quadratic Inference Functions;114
7.6;5.6 Implementation and Softwares;117
7.7;5.7 Examples;120
8;6 Vector Generalized Linear Models;132
8.1;6.1 Introduction;132
8.2;6.2 Log-Linear Model for Correlated Binary Data;133
8.3;6.3 Multivariate ED Family Distributions;136
8.4;6.4 Simultaneous Maximum Likelihood Inference;147
8.5;6.5 Algorithms;152
8.6;6.6 An Illustration: VGLMs for Trivariate Discrete Data;157
8.7;6.7 Data Examples;161
9;7 Mixed-Effects Models: Likelihood-Based Inference;167
9.1;7.1 Introduction;167
9.2;7.2 Model Specification;171
9.3;7.3 Estimation;175
9.4;7.4 MLE Based on Numerical Integration;177
9.5;7.5 Simulated MLE;184
9.6;7.6 Conditional Likelihood Estimation;186
9.7;7.7 MLE Based on EM Algorithm;188
9.8;7.8 Approximate Inference: PQL and REML;192
9.9;7.9 SAS Software;202
10;8 Mixed-Effects Models: Bayesian Inference;205
10.1;8.1 Bayesian Inference Using MCMC Algorithm;205
10.2;8.2 An Illustration: Multiple Sclerosis Trial Data;213
10.3;8.3 Multi-Level Correlated Data;216
10.4;8.4 WinBUGS Software;222
11;9 Linear Predictors;226
11.1;9.1 General Results;226
11.2;9.2 Estimation of Random Effects in GLMMs;230
11.3;9.3 Kalman Filter and Smoother;231
12;10 Generalized State Space Models;236
12.1;10.1 Introduction;236
12.2;10.2 Linear State Space Models;240
12.3;10.3 Shift-Mean Model;241
12.4;10.4 Monte Carlo Maximum Likelihood Estimation;244
13;11 Generalized State Space Models for Longitudinal Binomial Data;247
13.1;11.1 Introduction;247
13.2;11.2 Monte Carlo Kalman Filter and Smoother;248
13.3;11.3 Bayesian Inference Based on MCMC;254
14;12 Generalized State Space Models for Longitudinal Count Data;269
14.1;12.1 Introduction;269
14.2;12.2 Generalized Estimating Equation;272
14.3;12.3 Monte Carlo EM Algorithm;273
14.4;12.4 KEE in Stationary State Processes;275
14.5;12.5 KEE in Non-Stationary State Processes;283
15;13 Missing Data in Longitudinal Studies;299
15.1;13.1 Introduction;299
15.2;13.2 Missing Data Patterns;301
15.3;13.3 Diagnosis of Missing Data Types;308
15.4;13.4 Handling MAR Mechanism;314
15.5;13.5 Handling NMAR Mechanism;328
16;References;337
17;Index;351