Statistica Sinica 11(2001), 97-120

MAXIMUM POSTERIOR ESTIMATION OF RANDOM EFFECTS

IN GENERALIZED LINEAR MIXED MODELS

Jiming Jiang, Haomiao Jia and Hegang Chen

Case Western Reserve University, University of Tennessee

and University of Minnesota

Abstract: 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.

Key words and phrases: Consistency, GLMM, maximum posterior, small area estimation.