Maximum posterior estimation of random effects in generalized linear mixedmodels

Given a vector of observations and a vector of dispersion parameters (varia nce components), the fixed and random effects in a generalized linear mixed model are estimated by maximizing the posterior density. Although such est imates of the fixed and random effects depend on the (unknown) vector of va riance components, we demonstrate both numerically and theoretically that i n certain large sample situations the consistency of a restricted version o f 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.