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 com- ponents, we demonstrate both numerically and theoretically that in certain large sample situations the consistency of a restricted version of these estimates is not af- fected 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.

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