A nonlinear Gauss-Seidel algorithm for inference about GLMM

SummaryA nonlinear Gauss-Seidel type algorithm is proposed for computing the maximum posterior estimates of the random effects in a generalized linear mixed model. We show that the algorithm converges in virtually all typical situations of generalized linear mixed models. A numerical example shows the superiority of the proposed algorithm over the standard Newton-Raphson procedure when the number of random effects is large.