Geographically weighted negative binomial regression for spatial count data: Methodology and application

This study presents a reproducible methodological framework of Geographically Weighted Negative Binomial Regression (GWNBR) for modeling spatially overdispersed count data. The framework integrates Negative Binomial Regression (NBR) model with spatial weighting to capture overdispersion and spatial heterogeneity. The modeling procedure begins with Poisson regression, followed by an overdispersion test to justify the use of NBR. Spatial dependence and heterogeneity are then evaluated using Moran's I and Breusch-Pagan diagnostics. The GWNBR model is subsequently constructed using kernel-based spatial weighting with bandwidth selection through cross-validation. Model performance is assessed using Akaike Information Criterion (AIC) to compare Poisson, NBR, and GWNBR. A real-data application involving HIV case in Indonesia illustrates the capability of GWNBR to produce spatially localized estimates, offering enhanced interpretability and model accuracy over global approaches. This study contributes transparent and step-by-step analytical workflow that enhances reproducibility in spatial count data modeling.