The derivation of blup, ML, REML estimation methods for generalised linear mixed models

This paper presents a unified derivation of BLUP, ML and REML estimation procedures for normally distributed response variables with possibly correlated random components occurring in the mixed model for the mean. The theory is extended to generalised linear mixed models, where the response variable is not necessarily normally distributed but the model may be fitted using a penalised quasi-likelihood approach which mirrors the development in normal theory models. The method is applied to binomially distributed response variables with logit link to a mixed model containing a random component distributed as an AR(1) process.