Fitting logistic multilevel models with crossed random effects via   Bayesian Integrated Nested Laplace Approximations: a simulation study
  Fitting cross-classified multilevel models with binary response is challenging. In this setting a promising method is Bayesian inference through Integrated Nested Laplace Approximations (INLA), which performs well in several latent variable models. Therefore we devise a systematic simulation study to assess the performance of INLA with cross-classified logistic data under different scenarios defined by the magnitude of the random effects variances, the number of observations, the number of clusters, and the degree of cross-classification. In the simulations INLA is systematically compared with the popular method of Maximum Likelihood via Laplace Approximation. By an application to the classical salamander mating data, we compare INLA with the best performing methods. Given the computational speed and the generally good performance, INLA turns out to be a valuable method for fitting the considered cross-classified models. 
Leonardo Grilli (1) and Francesco Innocenti ((1) Dipartimento di   Statistica, Informatica, Applicazioni "G. Parenti", Unive...
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