Negative Binomial Modeling of District-Level Diarrhea Incidence in West Java Province - Nurul Nabilah; A'yunin Sofro (Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang, 2026)
This study investigated district-level diarrhea incidence in West Java Province during 2022–2024 and identified an appropriate count-data regression model for longitudinal epidemiological data. The response variable was the annual number of diarrhea cases, while explanatory variables included sanitation access, inpatient health centers, community health workers, nutritional indicators, drinking water facilities, and households implementing clean and healthy living behavior (PHBS). A population offset term was incorporated to account for differences in population exposure across districts/cities. Poisson Regression was initially fitted as a baseline model; however, severe overdispersion was detected. Therefore, Negative Binomial Regression and Generalized Linear Mixed Models (GLMM) were estimated and compared using Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), log-likelihood values, and simulation-based residual diagnostics. The results showed that Negative Binomial Regression provided the best overall fit, yielding substantially lower AIC and BIC values than competing models. Residual diagnostics indicated no evidence of remaining overdispersion, zero inflation, or serious outliers. Sanitation access was significantly associated with lower diarrhea incidence rates, with a one-standard-deviation increase corresponding to an estimated 15.7% reduction in incidence. These findings highlight the importance of accounting for overdispersion and suggest that Negative Binomial Regression is an appropriate framework for modeling regional diarrhea incidence data.