A semiparametric Bayesian approach to binomial distribution logistic mixed-effects models for longitudinal data

Abstract

Logistic mixed-effects models are widely used to study the relationship between the binary response and covariates for longitudinal data analysis, where the random effects are typically assumed to have a fully parametric distribution. As this assumption is likely limited or unreasonable in a multitude of practical researches, a semiparametric Bayesian approach for relaxing it is developed in this paper. In the context of binomial distribution logistic mixed-effects models, a general Bayesian framework is presented in which a semiparametric hierarchical modelling with an approximate truncated Dirichlet process prior distribution is specified for the random effects. The stick-breaking prior and the blocked Gibbs sampler using Pólya-Gamma mixture are employed to efficiently sample in the posterior analysis. Besides, a procedure calculating DIC for Bayesian model comparison is addressed. The methodology is demonstrated through simulation studies and a real example.

Keywords:

• Longitudinal binomial data
• Dirichlet process
• Gibbs sampler
• model comparison
• Pólya-Gamma mixture

Acknowledgments

We sincerely thank the editor, the associate editor and two anonymous referees for their insightful comments and suggestions that led to a greatly improved manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Zhao's work was supported by National Natural Science Foundation of China [No.11761016], by the Project of High Level Creative Talents in Guizhou Province of China, and by Discipline and Master's Site Construction Project of Guiyang University by Guiyang City Financial Support Guiyang University [2021-xk04]. Xu's work was supported by National Natural Science Foundation of China (No. 11801514). Duan's work was supported by National Natural Science Foundation of China (No. 12161014), by the Science and Technology Foundation of Guizhou Province of China ([2020]1Y009). Du's work was supported by National Natural Science Foundation of China (Nos. 11971045,11771032).