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Bayesian analysis of a finite mixture of bivariate Poisson regression models: An application to Australia health care data
Journal of the Korean Data & Information Science Society 2022;33:491-503
Published online May 31, 2022;  https://doi.org/10.7465/jkdi.2022.33.3.491
© 2022 Korean Data and Information Science Society.

Jae Hwan Choi1 · Beom Seuk Hwang2

12Department of Applied Statistics, Chung-Ang University
Correspondence to: This research was supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Science and ICT (NRF-2019R1C1C1011710), and supported by the Korea Institute of Energy Technology Evaluation and Planning(KETEP) and the Ministry of Trade, Industry & Energy(MOTIE) of the Republic of Korea (No. 20199710100060). This paper was prepared by extracting part of Jae Hwan Choi’s master’s thesis.
1 Graduate student, Department of Applied Statistics, Chung-Ang University, 84 Heukseok-ro, Dongjakgu, Seoul 06974, Korea.
2 Associate professor, Department of Applied Statistics, Chung-Ang University, 84 Heukseok-ro, Dongjak-gu, Seoul 06974, Korea. E-mail: bshwang@cau.ac.kr
Received March 4, 2022; Revised March 15, 2022; Accepted March 15, 2022.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Excess zero data are observed in various research fields such as social science, natural science, medicine, and engineering. In these data, if two response variables are correlated, we can consider a bivariate Poisson model and random effects may be included to take into account the heterogeneity of unobserved data. Furthermore, a finite mixture of bivariate Poisson models can be applied to explain the overdispersion of zero inflated data. We propose a Bayesian infernece for the finite mixture of bivariate Poisson models with random effects when there is a correlation between the two response variables. In order to determine a model with the optimal number of components, the deviance information criterion was computed in the models. We applied the proposed model to the Australian health survey data, and checked the performance of the model.
Keywords : Bayesian inference, health care data, Markov chain Monte Carlo, mixture model, zero inflated data.