Abstract: Although Bayesian methodologies have been successful in drawing inference about random effects, the frequentist literature has been limited. In this paper we consider inferences on random effects in hierarchical generalized linear models from a frequentist point of view using their summarizability. We show asymptotic distributional properties for the conditional and the marginal inference when the number of subunits is large. We conduct simulation studies when the number of subunits is small to moderate. A seizure study and an infertility study are used to illustrate the conditional and the marginal inference of random effects.

Key words and phrases: Conditional inference, confidence interval, marginal inference, nested generalized linear mixed models, random-effect inference.