Maximum posterior estimation of random effects in generalized linear mixed models

Given a vector of observations and a vector of dispersion parameters (variance components), the fixed and random effects in a generalized linear mixed model are estimated by maximizing the posterior density. Although such estimates of the fixed and random effects depend on the (unknown) vector of variance components, we demonstrate both numerically and theoretically that in certain large sample situations the consistency of a restricted version of these estimates is not affected by variance components at which they are computed. The method is applied to a problem of small area estimation using data from a sample survey.