Negative Binomial Regression Modeling of Stunting Cases in Central Java: Handling Overdispersion in Count Data
Abstract
This study aims to identify factors associated with the number of stunting cases across districts and cities in Central Java Province using count data regression models. Secondary data from 35 districts/cities in 2025 were analyzed within the generalized linear modeling framework. Poisson regression was initially applied, followed by exhaustive subset selection using the corrected Akaike Information Criterion (AICc) to obtain a parsimonious model. Model adequacy was evaluated through goodness-of-fit assessment, information criteria, and overdispersion diagnostics. The results indicated severe overdispersion in the Poisson model, suggesting that the equidispersion assumption was violated and that the model was unsuitable as the primary inferential framework. Consequently, a Negative Binomial regression model was estimated to accommodate the extra-Poisson variation. Model comparison demonstrated that the Negative Binomial model provided substantially better statistical performance, as reflected by lower AIC and AICc values, a dispersion statistic closer to one, and satisfactory diagnostic results. Based on the Negative Binomial model, exclusive breastfeeding coverage was the only variable that remained statistically significant, with an incidence rate ratio (IRR) of 1.0258 (95% CI: 1.0090–1.0426). Meanwhile, the dependency ratio and doctor ratio exhibited marginal significance. These findings highlight the importance of selecting appropriate count data models when overdispersion is present and suggest that stunting cases across Central Java are associated with complex nutritional, demographic, and healthcare-related conditions.
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DOI: http://dx.doi.org/10.30829/zero.v10i2.29471
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