A modification of the restricted maximum likelihood method in generalized linear models with random effects

Abstract

The existing Restricted Maximum Likelihood Method of obtaining variance component estimates in generalized linear models with random effects is a complicated procedure requiring the value of the parameter it is intended to estimate. This paper addresses this problem by providing a modification to the existing Restricted Maximum Likelihood Method (REML) for the estimation of variance components, fixed and random effects parameters. This modification arises from a generalization of the Cramer-Rao inequality to include a vector-valued parameter. The algorithm is applied to a data set on the treatment and management of hypertensive patients by different doctors to illustrate the level of contribution to variability by the random effects factors.

KEY WORDS: Random effects, Variance components, Weight matrix, Link function, Information matrix.