A Conditional Likelihood Approach to Residual Maximum Likelihood Estimation in Generalized Linear Models

Abstract

Residual maximum likelihood (REML) estimation is often preferred to maximum likelihood estimation as a method of estimating covariance parameters in linear models because it takes account of the loss of degrees of freedom in estimating the mean and produces unbiased estimating equations for the variance parameters. In this paper it is shown that REML has an exact conditional likelihood interpretation, where the conditioning is on an appropriate sufficient statistic to remove dependence on the nuisance parameters. This interpretation clarifies the motivation for REML and generalizes directly to non-normal models in which there is a low dimensional sufficient statistic for the fitted values. T..