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

Fitting cross-classified multilevel models with binary response is\nchallenging. In this setting a promising method is Bayesian inference through\nIntegrated Nested Laplace Approximations (INLA), which performs well in several\nlatent variable models. Therefore we devise a systematic simulation study to\nassess the performance of INLA with cross-classified logistic data under\ndifferent scenarios defined by the magnitude of the random effects variances,\nthe number of observations, the number of clusters, and the degree of\ncross-classification. In the simulations INLA is systematically compared with\nthe popular method of Maximum Likelihood via Laplace Approximation. By an\napplication to the classical salamander mating data, we compare INLA with the\nbest performing methods. Given the computational speed and the generally good\nperformance, INLA turns out to be a valuable method for fitting the considered\ncross-classified models.\n