http://projecteuclid.org/euclid.ejs/1423229753

Abstract

The likelihood for the parameters of a generalized linear mixed model involves an integral which may be of very high dimension. Because of this intractability, many approximations to the likelihood have been proposed, but all can fail when the model is sparse, in that there is only a small amount of information available on each random effect. The sequential reduction method described in this paper exploits the dependence structure of the posterior distribution of the random effects to reduce substantially the cost of finding an accurate approximation to the likelihood in models with sparse structure.

I have written an R package glmmsr, which may be used to fit Generalized Linear Mixed Models, with a choice of which method to use to approximate the likelihood, including the sequential reduction method described in this paper.