A sequential reduction method for inference in generalized linear mixed models
This work addresses a computational bottleneck for statisticians and researchers using sparse generalized linear mixed models, offering an incremental improvement over existing approximation methods.
The paper tackles the challenge of intractable high-dimensional integrals in generalized linear mixed models, especially under sparse data conditions, by introducing a sequential reduction method that leverages the posterior dependence structure to significantly lower computational costs for accurate likelihood approximations.
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.