%HPGLIMMIX: A High-PerformanceSASMacro for GLMM Estimation

Generalized linear mixed models (GLMMs) comprise a class of widely used statistical tools for data analysis with fixed and random effects when the response variable has a conditional distribution in the exponential family. GLMM analysis also has a close relationship with actuarial credibility theory. While readily available programs such as the GLIMMIX procedure in SAS and the lme4 package in R are powerful tools for using this class of models, these progarms are not able to handle models with thousands of levels of fixed and random effects. By using sparse-matrix and other high performance techniques, procedures such as HPMIXED in SAS can easily fit models with thousands of factor levels, but only for normally distributed response variables. In this paper, we present the %HPGLIMMIX SAS macro that fits GLMMs with large number of sparsely populated design matrices using the doubly-iterative linearization (pseudo-likelihood) method, in which the sparse-matrix-based HPMIXED is used for the inner iterations with the pseudo-variable constructed from the inverse-link function and the chosen model. Although the macro does not have the full functionality of the GLIMMIX procedure, time and memory savings can be large with the new macro. In applications in which design matrices contain many zeros and there are hundreds or thousands of factor levels, models can be fitted without exhausting computer memory, and 90% or better reduction in running time can be observed. Examples with a Poisson, binomial, and gamma conditional distribution are presented to demonstrate the usage and efficiency of this macro.