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Fitting cross-classified multilevel models with binary response ischallenging. In this setting a promising method is Bayesian inference throughIntegrated Nested Laplace Approximations (INLA), which performs well in severallatent variable models. Therefore we devise a systematic simulation study toassess the performance of INLA with cross-classified logistic data underdifferent scenarios defined by the magnitude of the random effects variances,the number of observations, the number of clusters, and the degree ofcross-classification. In the simulations INLA is systematically compared withthe popular method of Maximum Likelihood via Laplace Approximation. By anapplication to the classical salamander mating data, we compare INLA with thebest performing methods. Given the computational speed and the generally goodperformance, INLA turns out to be a valuable method for fitting the consideredcross-classified models.

Fitting logistic multilevel models with crossed random effects via Bayesian Integrated Nested Laplace Approximations: a simulation study