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

Area of Science:

• Spatial statistics
• Geographic Information Systems (GIS)
• Epidemiological modeling

Background:

• Count data often exhibit overdispersion and spatial heterogeneity, challenging standard regression models.
• Existing spatial regression models may not adequately capture localized variations in count data.
• Reproducible methodologies are crucial for advancing spatial data analysis.

Purpose of the Study:

• To present a reproducible methodological framework for Geographically Weighted Negative Binomial Regression (GWNBR).
• To model spatially overdispersed count data by integrating Negative Binomial Regression (NBR) with spatial weighting.
• To enhance the interpretability and accuracy of spatial count data analysis through localized estimates.

Main Methods:

• The framework starts with Poisson regression, followed by an overdispersion test to validate NBR.
• Spatial dependence and heterogeneity are assessed using Moran's I and Breusch-Pagan diagnostics.
• GWNBR is constructed with kernel-based spatial weighting and cross-validation for bandwidth selection.

Main Results:

• Akaike Information Criterion (AIC) was used to compare Poisson, NBR, and GWNBR models.
• The GWNBR model demonstrated superior performance and accuracy over global models.
• Application to HIV cases in Indonesia highlighted GWNBR's ability to provide spatially localized estimates.

Conclusions:

• The proposed GWNBR framework offers a transparent and reproducible analytical workflow for spatial count data.
• GWNBR effectively models overdispersion and spatial heterogeneity, leading to improved model accuracy.
• This methodology enhances the interpretability of spatial patterns in count data, valuable for public health and epidemiology.