Although powerful and flexible, the method of generalized linear models (GLM) is limited in its ability to accurately deal with longitudinal and clustered data. Developed specifically to accommodate these data types, the method of Generalized Estimating Equations (GEE) extends the GLM algorithm to accommodate the correlated data encountered in health research, social science, biology, and other related fields.Generalized Estimating Equations provides the first complete treatment of GEE methodology in all of its variations. After introducing the subject and reviewing GLM, the authors examine the different varieties of generalized estimating equations and compare them with other methods, such as fixed and random effects models. The treatment then moves to residual analysis and goodness of fit, demonstrating many of the graphical and statistical techniques applicable to GEE analysis.With its careful balance of origins, applications, relationships, and interpretation, this book offers a unique opportunity to gain a full understanding of GEE methods, from their foundations to their implementation. While equally valuable to theorists, it includes the mathematical and algorithmic detail researchers need to put GEE into practice.
Author(s): James W. Hardin, Joseph M. Hilbe
Edition: 1
Publisher: Chapman & Hall/CRC
Year: 2003
Language: English
Pages: 224
City: Boca Raton, Fla
Tags: Математика;Теория вероятностей и математическая статистика;Математическая статистика;
Generalized Estimating Equations......Page 2
Preface......Page 5
Contents......Page 8
CHAPTER 1: Introduction......Page 11
1.1 Notational conventions......Page 12
1.2.1 Historical review......Page 13
1.2.2 Basics......Page 16
1 .2.3 Link and variance functions......Page 18
1.2.4 Algorithms......Page 19
1.3 Software......Page 21
1.3.1 S-PLUS......Page 22
1.3.3 Stata......Page 23
1.3.4 SUDAAN......Page 24
1.4 Exercises......Page 25
2 .1 Independent data......Page 26
2.1 .1 The FIML estimating equation for linear regression......Page 27
2.1 .2 The FIML estimating equation for Poisson regression......Page 30
2.1 .3 The FIML estimating equation for Bernoulli regression......Page 31
2.1 .4 The LIML estimating equation for GLMs......Page 33
2.1 .5 The LIMQL estimating equation for GLMs......Page 36
2 .2 Estimating the variance of the estimates......Page 37
2 .3 Panel data......Page 41
2.3.1 Pooled estimators......Page 42
2.3.2 Fixed-effects and random-effects models......Page 43
2.3.2.1 Unconditional fixed-effects models......Page 44
2.3.2.2 Conditional fixed-effects models......Page 45
2.3.2.3 Random-effects models......Page 51
2.3.3 Population-averaged and subject-specific models......Page 58
2 .5 Summary......Page 59
2 .6 Exercises......Page 61
3.1 Population-averaged (PA) and subject-specific (SS) models......Page 63
3.2 The PA-GEE for GLMS......Page 65
3.2.1 Parameterizing the working correlation matrix......Page 66
3.2.1 .1 Exchangeable correlation......Page 67
3.2.1 .2 Autoregressive correlation......Page 74
3.2.1 .3 Stationary correlation......Page 76
3.2.1 .4 Nonstationary correlation......Page 79
3.2.1 .5 Unstructured correlation......Page 80
3.2.1.7 Free specification......Page 81
3.2.2 Estimating the scale variance (dispersion parameter)......Page 84
3.2.2.1 Independence models......Page 85
3.2.2.2 Exchangeable models......Page 90
3.2.3 Estimating the PA-GEE model......Page 93
3.2.5 ALR: Estimating correlations for binomial models......Page 97
3.2.6 Summary......Page 101
3.3 The SS-GEE for GLMS......Page 103
3.3.1 Single random-effects......Page 104
3.3.2 Multiple random-effects......Page 106
3.3.3 Applications of the SS-GEE......Page 107
3.3.4 Estimating the SS-GEE model......Page 111
3.4 The GEE2 for GLMs......Page 112
3.5.1 Generalized logistic regression......Page 114
3.5.2 Cumulative logistic regression......Page 116
3.6.1 The PA-GEE for GLMs with measurement error......Page 118
3.6.2 The PA-EGEE for GLMs......Page 125
3.6.3 The PA-REGEE for GLMs......Page 127
3.7 Missing data......Page 130
3.8 Choosing an appropriate model......Page 136
3.9 Summary......Page 139
3.10 Exercises......Page 142
CHAPTER 4: Residuals, Diagnostics, and Testing......Page 144
4, .1 .1 Choosing the best correlation structure......Page 146
4.2 Analysis of residuals......Page 149
4.2.2 Graphical assessment......Page 150
4.2.3 Quasivariance functions for PA-GEE models......Page 161
4.3 Deletion diagnostics......Page 165
4 .3.1 Influence measures......Page 166
4 .4 .1 Proportional reduction in variation......Page 172
4 .4 .2 Concordance correlation......Page 173
4.4.3 A x2 goodness of fit test for PA-GEE binomial models......Page 174
4.5 Testing coefficients in the PA-GEE model......Page 176
4, .5.1 Likelihood ratio tests......Page 177
4 .5.2 Wald tests......Page 179
4.6 Assessing the MCAR assumption of PA-GEE models......Page 181
4.7 Summary......Page 184
4.8 Exercises......Page 186
5 .1 Programs......Page 187
5.1 .1 Fitting PA-GEE models in Stata......Page 188
5.1.2 Fitting PA-GEE models in SAS......Page 189
5.1 .3 Fitting PA-GEE models in S-PLUS......Page 190
5.1 .4, Fitting ALR models in SAS......Page 191
5.1 .5 Fitting PA-GEE models in SUDAAN......Page 192
5.1.6 Calculating QIC in Stata......Page 193
5.1.7 Calculating QICu in Stata......Page 194
5.1 .8 Graphing the residual runs test in S-PL US......Page 195
5.1 .9 Using the fixed correlation structure in Stata......Page 196
5.1.10 Fitting quasivariance PA-GEE models in S-PL US......Page 197
5.2.1 Wheeze data......Page 198
5.2.2 Ship accident data......Page 200
5.2.3 Progabide data......Page 202
5.2.4, Simulated logistic data......Page 208
5.2.5 Simulated user-specified correlated data......Page 215
5.2.6 Simulated measurement error data for the PA-GEE......Page 218
References......Page 221
