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

TL;DR

This paper evaluates the effectiveness of Bayesian INLA for fitting cross-classified logistic multilevel models through extensive simulations and real data application, highlighting its speed and accuracy.

Contribution

It systematically compares INLA with traditional methods for cross-classified logistic models and demonstrates its advantages in speed and performance.

Findings

INLA performs well across various simulation scenarios.

INLA is faster than traditional maximum likelihood methods.

Application to salamander data confirms practical utility.

Abstract

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.