Bayesian inference for generalized linear mixed models: A comparison of different statistical software procedures

ABSTRACT

Bayesian inference for generalized linear mixed models (GLMM) is appealing, but its widespread use has been hampered by the lack of a fast implementation tool and the difficulty in specifying prior distributions. In this paper, we conduct an extensive simulation study to evaluate the performance of INLA for estimation of the hierarchical Poisson regression models with overdispersion in comparison with JAGS and Stan while assuming a variety of prior specifications for variance components. Further, we analysed the influence of different factors such as small number of observations per cluster, different values of the cluster variance and estimation from a misspecified model. A simulation study has shown that the approximation strategy employed by INLA is accurate in general and that all software leads to similar results for most of the cases considered. Estimation of the variance components, however, is difficult when their true value is small for all estimation methods and prior specifications. The estimates obtained for all software tend to be biased downward or upward depending on the assumed priors.

Keywords:

• Clustering
• Bayesian modelling
• overdispersion
• GLMM
• count data
• INLA
• JAGS
• stan

PUBLIC INTEREST STATEMENT

Longitudinal count data are now an integral part of experimental and empirical studies across a range of disciplines from the medical to the social and business sciences. Special models for longitudinal data are required when there are repeated measurements of the count outcome from the same individual over time, which leads to a dependence structure in the data. Generalized linear mixed models (GLMM) are one of the most used models for modeling longitudinal count data. Bayesian inference for generalized linear mixed effect models (GLMM) is appealing, but its widespread use has been hampered by the lack of a fast implementation tool and the difficulty in specifying prior distributions. In this paper, we conduct an extensive simulation study to evaluate the performance of INLA for estimation of the hierarchical Poisson regression models with overdispersion in comparison with JAGS and Stan while assuming a variety of prior specifications for variance components.

Acknowledgements

The authors gratefully acknowledge the support from VLIR-UOS. For the simulations, the Flemish Supercomputer Centre, funded by the Hercules Foundation and the Flemish Government of Belgium – department EWI, was used.

Disclosure statement

No potential conflict of interest was reported by the authors.

Supplemental data

Supplemental data for this article can be accessed here.

Additional information

Funding

The authors received no direct funding for this research.

Notes on contributors

Belay Birlie Yimer

Belay Birlie Yimer is currently a research associate at Versus Arthritis Centre for Epidemiology, Division of Musculoskeletal and Dermatological Sciences, The University of Manchester, UK. Prior to joining the University of Manchester, Belay was an assistant professor in the Department of Statistics, Jimma University, Ethiopia. He has completed his B.Sc. and M.Sc. in statistics and is currently pursuing his PhD in statistics. His main research area focuses on Bayesian methods and modelling complex time-to-event data with applications to infectious and chronic diseases.

Ziv Shkedy

Ziv Shkedy is a Professor of Biostatistics and bioinformatics at the University of Hasselt in Belgium.