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

This study presents a methodological implementation of Geographically Weighted Negative Binomial Regression (GWNBR) for modeling spatially overdispersed count data. The GWNBR framework integrates classical Negative Binomial Regression (NBR) model with spatial weighting to capture both overdispersion and spatial heterogeneity. Model development begins with Poisson regression, followed by overdispersion testing. To address observed overdispersion, a NBR model is employed. Then, spatial dependency and heteroskedasticity are examined. Upon confirming spatial effects, GWNBR is implemented using a kernel weighting. Model performance is evaluated using Akaike Information Criterion (AIC), enabling comparison between Poisson, NBR, and GWNBR. A real-data application illustrates the capability of GWNBR to produce spatially localized estimates, offering enhanced interpretability and model accuracy over global approaches. This method contributes to spatial modeling literature by providing a practical and replicable approach to analyze overdispersed spatial count data. The highlight of this research are:Count data modeling was initiated using Poisson regression, and overdispersion was tested to justify the use of NBR.Spatial dependence and heterogeneity were tested using Moran’s I and Breusch–Pagan tests, followed by modeling with GWNBR.Model performance was compared using the AIC to evaluate improvements from global to spatially weighted count models.