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Generalized Estimating Equations
Comment from the Stata technical groupThe method of generalized linear models (GLM) is an integral part of the data analyst's toolkit, as it encompasses many models under one roof: logistic and probit regressions, ordinary least squares, ordinal outcome regression, and regression models for the analysis of survival data, to name a few. Nominal GLM, however, is inadequate when the data are longitudinal or are otherwise grouped so that observations within the same group are expected to be correlated. The method of generalized estimating equations (GEE) is a generalization of GLM that takes into account this within-group correlation. This text is the sequel to the 2001 text, Generalized Linear Models and Extensions, by the same authors, and provides the first complete treatment of GEE methodology. As with the previous text on GLM, this text is filled with examples on using this methodology with Stata. In fact, the principal author, James Hardin, developed much of the Stata software for fitting GEE models while he was a senior statistician at StataCorp. This text is heavy in mathematical and computational detail, but the mathematics is balanced by an array of real-world datasets and analyses. Thus the text should appeal to a wide audience, from the mathematical statistician wishing to glean the current state of the GEE literature to the professional researcher needing to fit a GEE model to solve a particular problem. Table of contents1 Introduction
1.1 Notational conventions
1.2 A short review of generalized linear models
1.2.1 Historical review
1.3 Software 1.2.2 Basics 1.2.3 Link and variance functions 1.2.4 Algorithms
1.3.1 S-PLUS
1.4 Exercises 1.3.2 SAS 1.3.3 Stata 1.3.4 SUDAAN 2 Model Construction and Estimating Equations
2.1 Independent data
2.1.1 The FIML estimating equation for linear regression
2.2 Estimating the variance of the estimates2.1.2 The FIML estimating equation for Poisson regression 2.1.3 The FIML estimating equation for Bernoulli regression 2.1.4 The LIML estimating equation for GLMs 2.1.5 The LIMQL estimating equation for GLMs 2.3 Panel data
2.3.1 Pooled estimators
2.4 Estimation2.3.2 Fixed-effects and random-effects models
2.3.2.1 Unconditional fixed-effects models
2.3.3 Population-averages and subject-specific models2.3.2.2 Conditional fixed-effects models 2.3.2.3 Random-effects models 2.5 Summary 2.6 Exercises 3 Generalized Estimating Equations
3.1 Population-averaged (PA) and subject-specific (SS) models
3.2 The PA-GEE for GLMs
3.2.1 Parameterizing the working correlation matrix
3.3 The SS-GEE for GLMs
3.2.1.1 Exchangeable correlation
3.2.2 Estimating the scale variance (dispersion parameter)
3.2.1.2 Autoregressive correlation 3.2.1.3 Stationary correlation 3.2.1.4 Nonstationary correlation 3.2.1.5 Unstructured correlation 3.2.1.6 Fixed correlation 3.2.1.7 Free specification
3.2.2.1 Independence models
3.2.3 Estimating the PA-GEE model3.2.2.2 Exchangeable models 3.2.4 Convergence of the estimation routine 3.2.5 ALR: Estimating correlations for binomial models 3.2.6 Summary
3.3.1 Single random-effects
3.4 The GEE2 for GLMs3.3.2 Multiple random-effects 3.3.3 Applications of the SS-GEE 3.3.4 Estimating the SS-GEE model 3.3.5 Summary 3.5 GEEs for extensions of GLMs
3.5.1 Generalized logistic regression
3.6 Further developments and applications3.5.2 Cumulative logistic regression
3.6.1 The PA-GEE for GLMs with measurement error
3.7 Missing data3.6.2 The PA-EGEE for GLMs 3.6.3 The PA-REGEE for GLMs 3.8 Choosing an appropriate model 3.9 Summary 3.10 Exercises 4 Residuals, Diagnostics, and Testing
4.1 Criterion measures
4.1.1 Choosing the best correlation structure
4.2 Analysis of residuals4.1.2 Choosing the best subset of covariates
4.2.1 A nonparametric test of the randomness of residuals
4.3 Deletion diagnostics4.2.2 Graphical assessment 4.2.3 Quasivariance functions for PA-GEE models
4.3.1 Influence measures
4.4 Goodness of fit (population-averaged models)4.3.2 Leverage measures
4.4.1 Proportional reduction in variation
4.5 Testing coefficients in the PA-GEE model4.4.2 Concordance correlation 4.4.3 A x2 goodness of fit test for PA-GEE binomial models
4.5.1 Likelihood ratio tests
4.6 Assessing the MCAR assumption of PA-GEE models4.5.2 Wald tests 4.5.3 Score tests 4.7 Summary 4.8 Exercises 5 Programs and Datasets
5.1 Programs
5.1.1 Fitting PA-GEE models in Stata
5.2 Datasets
5.1.2 Fitting PA-GEE models in SAS 5.1.3 Fitting PA-GEE models in S-PLUS 5.1.4 Fitting ALR models in SAS 5.1.5 Fitting PA-GEE models in SUDAAN 5.1.6 Calculating QIC in Stata 5.1.7 Calculating QICu in Stata 5.1.8 Graphing the residual runs test in S-PLUS 5.1.9 Using the fixed correlation structure in Stata 5.1.10 Fitting quasivariance PA-GEE models in S-PLUS
5.2.1 Wheeze data
5.2.2 Ship accident data 5.2.3 Progabide data 5.2.4 Simulated logistic data 5.2.5 Simulated user-specific correlated data 5.2.6 Simulated measurement error data for the PA-GEE References
Author Index
Subject Index
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