Prediction of Random Effects in the Generalized Linear Model

Abstract

This article develops an estimating function-based approach to component estimation in the two-stage generalized linear model with univariate random effects and a vector of fixed effects. The novelty and unifying feature of the method is the use of estimating functions in the estimation of both the random effects and their variance. Two separate estimating procedures based on the method are proposed that differ in the intensity of numerical computation required. The estimating function approach is especially valuable in the longitudinal setting where the response variable is discrete and the number of repeated observations on each unit is small. Other key features of this empirical Bayes technique are that it uses all available data, it yields familiar forms for the estimators as special cases, and it is less computationally intensive than other methods designed to address the same problem. An application to the estimation of trends in acquired immune deficiency syndrome (AIDS) incidence across risk groups and geographical regions is presented.

KEY WORDS:

• Empirical Bayes estimation
• Estimating function
• Generalized linear model
• Longitudinal studies
• Two-stage random effects model