Implementation and performance issues in Bayesian and likelihood fitting of multilevel models. Computational Statistics 15:391420

We use simulation studies (a) to compare Bayesian and likelihood tting methods, in terms of validity of conclusions, in two-level random-slopes regression (RSR) models, and (b) to compare several Bayesian estimation methods based on Markov chain Monte Carlo, in terms of computational eÆciency, in random-eects logistic regression (RELR) models. We nd (a) that the Bayesian approach with a particular choice of diuse inverse Wishart prior distribution for the (co)variance parameters performs at least as well|in terms of bias of estimates and actual coverage of nominal 95% intervals|as maximum likelihood methods in RSR models with medium sample sizes (expressed in terms of the number J of level{2 units), but neither approach performs as well as might be hoped with small J; and (b) that an adaptive hybrid Metropolis-Gibbs sampling method we have developed for use in the multilevel modeling package MlwiN outperforms adaptive rejection Gibbs sampling in the RELR models we have considered, sometimes by a wide margin