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

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. We devise a systematic simulation study to assess the performance of INLA with cross-classified binary data under different scenarios defined by the magnitude of the variances of the random effects, 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 logistic cross-classified models.

KEYWORDS:

• Binary response
• crossed random effects
• generalized linear mixed models
• INLA
• maximum Likelihood via Laplace approximation
• non-hierarchical data
• random effects
• salamander mating data

AMS SUBJECT CLASSIFICATION:

• 62F15
• 62J12
• 65C60

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Leonardo Grilli http://orcid.org/0000-0002-3886-7705.

Francesco Innocenti http://orcid.org/0000-0001-6113-8992.

Additional information

Funding

The research has been supported by the grant Finite mixture and latent variable models for causal inference and analysis of socio-economic data (FIRB – Futuro in ricerca) funded by the Italian government $[$RBFR12SHVV$]$.