Bayesian estimation with integrated nested Laplace approximation for binary logit mixed models

Abstract

In multilevel models for binary responses, estimation is computationally challenging due to the need to evaluate intractable integrals. In this paper, we investigate the performance of integrated nested Laplace approximation (INLA), a fast deterministic method for Bayesian inference. In particular, we conduct an extensive simulation study to compare the results obtained with INLA to the results obtained with a traditional stochastic method for Bayesian inference (MCMC Gibbs sampling), and with maximum likelihood through adaptive quadrature. Particular attention is devoted to the case of small number of clusters. The specification of the prior distribution for the cluster variance plays a crucial role and it turns out to be more relevant than the choice of the estimation method. The simulations show that INLA has an excellent performance as it achieves good accuracy (similar to MCMC) with reduced computational times (similar to adaptive quadrature).

Keywords:

• adaptive Gaussian quadrature
• generalized linear mixed model
• INLA
• MCMC
• multilevel model
• prior distribution
• random effects

AMS Subject Classification:

• 62F15
• 62J12
• 65C60

Acknowledgements

The research has been supported by Italian FIRB 2012 project n. RBFR12SHVV_003 Mixture and latent variable models for causal inference and analysis of socio-economic data.