Modeling Zero-Inflated Poisson Invers Gaussian Regression Bayesian Approach

Berliana Jannah; Ni Wayan Surya Wardhani; Eni Sumarminingsih

doi:10.31764/jtam.v10i1.34068

Modeling Zero-Inflated Poisson Invers Gaussian Regression Bayesian Approach

Berliana Jannah, Ni Wayan Surya Wardhani, Eni Sumarminingsih

Abstract

Deaths due to dengue hemorrhagic fever (DHF) remains one of the most pressing public health issues in Indonesia, especially in urban areas such as Semarang City, which has a high population density and diverse environmental conditions that potentially increase the risk of transmission and death from DHF. This study aims to model the number of DHF in Semarang City using a Bayesian-based Zero-Inflated Poisson Inverse Gaussian Regression (ZIPIGR) approach. The research data was obtained from the Semarang City Health Office and the Central Statistics Agency (BPS) in 2024, with the response variable being the number of DHF deaths and five predictor variables. The data showed overdispersion and a high proportion of zeros (around 50%), indicating the presence of excess zeros in count data with a small sample size. The Bayesian ZIPIGR method was chosen because it can produce more stable parameter estimates than classical methods such as Maximum Likelihood Estimation (MLE), especially for data with complex likelihood functions, small sample sizes, and many zero values. Parameter estimation was performed using Gibbs Sampling simulation in the Markov Chain Monte Carlo (MCMC) framework. The results show that the Bayesian ZIPIGR model performs better than the MLE ZIPIGR model based on the Root Mean Square Error (RMSE) value. Factors that significantly influence DHF mortality are population density, slum area, and number of health workers. These results confirm that regional density and health worker capacity play an important role in increasing the risk of DHF mortality in urban areas. The developed model has been proven to be highly accurate in modeling count data with excess zero characteristics and makes an important contribution to health policy formulation. In practical terms, this model can be used to improve early warning systems and DHF control strategies in densely populated urban areas such as the city of Semarang.

Keywords

ZIPIGR; Overdispersion; Bayesian; Excess Zero; Gibbs Sampling.

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DOI: https://doi.org/10.31764/jtam.v10i1.34068