Bayesian hierarchical joint model for analyzing zero-inflated count and binary data

Count and binary outcomes frequently occur in public health, economics, and social sciences, but joint modeling is difficult due to heterogeneous data, random effects, over-dispersion, and excess zeros. Traditional approaches that model these outcomes separately often fail to capture dependencies, resulting in biased estimates. This study proposes a Bayesian hierarchical joint modeling framework that simultaneously analyzes zero-inflated count and binary outcomes through shared random effects and conditional modeling. The framework accommodates zero-inflated counts (ZIP, ZINB, ZIGP-2) with a binomial mixed model via shared random effects to capture heterogeneity and outcome dependencies. Parameter estimation is conducted within a Bayesian framework using Markov Chain Monte Carlo (MCMC) methods, combining Gibbs sampling and Metropolis–Hastings algorithms for efficient posterior inference. Sensitivity analysis is conducted to assess robustness to prior choices and model assumptions. The proposed model is evaluated through simulation studies and applied to infant mortality and breastfeeding data. The results demonstrate that the joint ZIGP-binary modeling outperforms separate models, capturing dependence, unobserved heterogeneity, and excess zeros with higher accuracy and efficiency. The findings further reveal important socio-demographic determinants of infant mortality and the protective role of breastfeeding. Overall, the proposed framework offers a flexible and powerful tool for analyzing complex mixed outcomes.