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).
Bayesian estimation with integrated nested Laplace approximation for binary logit mixed models / L. Grilli; S. Metelli; C. Rampichini. - In: JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION. - ISSN 0094-9655. - STAMPA. - 85:(2015), pp. 2718-2726. [10.1080/00949655.2014.935377]
Bayesian estimation with integrated nested Laplace approximation for binary logit mixed models
GRILLI, LEONARDO;RAMPICHINI, CARLA
2015
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).I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.