MAXIMUM-LIKELIHOOD ALGORITHMS FOR GENERALIZED LINEAR MIXED MODELS

Maximum likelihood algorithms are described for generalized linear mix ed models. I show how to construct a Monte Carlo version of the EM alg orithm, propose a Monte Carlo Newton-Raphson algorithm, and evaluate a nd improve the use of importance sampling ideas. Calculation of the ma ximum likelihood estimates is feasible for a wide variety of problems where they were not previously. I also use the Newton-Raphson algorith m as a framework to compare maximum likelihood to the ''joint-maximiza tion'' or penalized quasi-likelihood methods and explain why the latte r can perform poorly.