Preface

1 Introduction

1.1 Notational conventions and acronyms

1.2 A short review of generalized linear models

1.2.1 A brief history of GLMs

1.2.1.1 GLMs as likelihood-based models

1.2.1.2 GLMs and correlated data

1.2.2 GLMs and overdispersed data

1.2.2.1 Scaling standard errors

1.2.2.2 The modified sandwich variance estimator

1.2.3 The basics of GLMs

1.2.4 Link and variance functions

1.2.5 Algorithms

1.3 Software

1.3.1 R

1.3.2 SAS

1.3.3 Stata

1.3.4 SUDAAN

1.4 Exercises

2 Model Construction and Estimating Equations

2.1 Independent data

2.1.1 Optimization

2.1.2 The FIML estimating equation for linear regression

2.1.3 The FIML estimating equation for Poisson regression

2.1.4 The FIML estimating equation for Bernoulli regression

2.1.5 The LIML estimating equation for GLMs

2.1.6 The LIMQL estimating equation for GLMs

2.2 Estimating the variance of the estimates

2.2.1 Model-based variance

2.2.2 Empirical variance

2.2.3 Pooled variance

2.3 Panel data

2.3.1 Pooled estimators

2.3.2 Fixed-effects and random-effects models

2.3.2.1 Unconditional fixed-effects models

2.3.2.2 Conditional fixed-effects models

2.3.2.3 Random-effects models

2.3.3 Population-averaged and subject-specific models

2.4 Estimation

2.5 Summary

2.6 Exercises

2.7 R code for selected output

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

3.2.1.1 Exchangeable correlation

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 Estimating the scale variance (dispersion parameter)

3.2.2.1 Independence models

3.2.2.2 Exchangeable models

3.2.3 Estimating the PA-GEE model

3.2.4 The robust variance estimate

3.2.5 A historical footnote

3.2.6 Convergence of the estimation routine

3.2.7 ALR: Estimating correlations for binomial models

3.2.8 Quasi-least squares

3.2.9 Summary

3.3 The SS-GEE for GLMs

3.3.1 Single random-effects

3.3.2 Multiple random-effects

3.3.3 Applications of the SS-GEE

3.3.4 Estimating the SS-GEE model

3.3.5 Summary

3.4 The GEE2 for GLMs

3.5 GEEs for extensions of GLMs

3.5.1 Multinomial logistic GEE regression

3.5.2 Proportional odds GEE regression

3.5.3 Penalized GEE models

3.5.4 Cox proportional hazards GEE models

3.6 Further developments and applications

3.6.1 The PA-GEE for GLMs with measurement error

3.6.2 The PA-EGEE for GLMs

3.6.3 The PA-REGEE for GLMs

3.6.4 Quadratic inference function for marginal GLMs

3.7 Missing data

3.8 Choosing an appropriate model

3.9 Marginal effects

3.9.1 Marginal effects at the means

3.9.2 Average marginal effects

3.10 Summary

3.11 Exercises

3.12 R code for selected output

4 Residuals, Diagnostics, and Testing

4.1 Criterion measures

4.1.1 Choosing the best correlation structure

4.1.2 Alternatives to the original QIC

4.1.3 Choosing the best subset of covariates

4.2 Analysis of residuals

4.2.1 A nonparametric test of the randomness of residuals

4.2.2 Graphical assessment

4.2.3 Quasivariance functions for PA-GEE models

4.3 Deletion diagnostics

4.3.1 Influence measures

4.3.2 Leverage measures

4.4 Goodness of fit (population-averaged models)

4.4.1 Proportional reduction in variation

4.4.2 Concordance correlation

4.4.3 A *χ*^{2} goodness of fit test for PA-GEE
binomial models

4.5 Testing coefficients in the PA-GEE model

4.5.1 Likelihood ratio tests

4.5.2 Wald tests

4.5.3 Score tests

4.6 Assessing the MCAR assumption of PA-GEE models

4.7 Summary

4.8 Exercises

5 Programs and Datasets

5.1 Programs

5.1.1 Fitting PA-GEE models in Stata

5.1.2 Fitting PA-GEE models in SAS

5.1.3 Fitting PA-GEE models in R

5.1.4 Fitting ALR models in SAS

5.1.5 Fitting PA-GEE models in SUDAAN

5.1.6 Calculating QIC(P) in Stata

5.1.7 Calculating QIC(HH) in Stata

5.1.8 Calculating QICu in Stata

5.1.9 Graphing the residual runs test in R

5.1.10 Using the fixed correlation structure in Stata

5.1.11 Fitting quasivariance PA-GEE models in R

5.1.12 Fitting GLMs in R

5.1.13 Fitting FE models in R using the GAMLSS package

5.1.14 Fitting RE models in R using the LME4 package

5.2 Datasets

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-specified correlated data

5.2.6 Simulated measurement error data for the PA-GEE

References

Author index

Subject index