  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.
