Open Access
June 2023 Normal Approximation for Bayesian Mixed Effects Binomial Regression Models
Brandon Berman, Wesley O. Johnson, Weining Shen
Author Affiliations +
Bayesian Anal. 18(2): 415-435 (June 2023). DOI: 10.1214/22-BA1312

Abstract

Bayesian inference for generalized linear mixed models implemented with Markov chain Monte Carlo (MCMC) sampling methods have been widely used. In this paper, we propose to substitute a large sample normal approximation for the intractable full conditional distribution of the latent effects (of size k) in order to simplify the computation. In addition, we develop a second approximation involving what we term a sufficient reduction (SR). We show that the full conditional distributions for the model parameters only depend on a small, say rk, dimensional function of the latent effects, and also that this reduction is asymptotically normal under mild conditions. Thus we substitute the sampling of an r dimensional multivariate normal for sampling the k dimensional full conditional for the latent effects. Applications to oncology physician data, to cow abortion data and simulation studies confirm the reasonable performance of the proposed approximation method in terms of estimation accuracy and computational speed.

Acknowledgments

The authors thank the editor Michele Guindani, the associate editor, and anonymous reviewers for their valuable comments and suggestions that greatly improved the paper.

Citation

Download Citation

Brandon Berman. Wesley O. Johnson. Weining Shen. "Normal Approximation for Bayesian Mixed Effects Binomial Regression Models." Bayesian Anal. 18 (2) 415 - 435, June 2023. https://doi.org/10.1214/22-BA1312

Information

Published: June 2023
First available in Project Euclid: 2 May 2022

MathSciNet: MR4578059
Digital Object Identifier: 10.1214/22-BA1312

Keywords: Asymptotic approximation , Binomial regression , generalized linear mixed models , Markov chain Monte Carlo , sufficient reduction

Vol.18 • No. 2 • June 2023
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