Restricted likelihood inference for generalized linear mixed models

We aim to promote the use of the modified profile likelihood for estimating the variance parameters of a GLMM in analogy to the REML criterion for linear mixed models. Our approach is based on both Quasi-Monte Carlo integration and numerical quadrature, obtaining in either case simulation-free inferential results. The method is illustrated for regression models with binary response and independent clusters, covering also the case of two-part models. Real-data examples and simulations studies support the use of the proposed solution as a natural extension of REML for GLMMs