Geographically Weighted Poisson Regression (GWPR) Model with Fixed Gaussian Kernel and Fixed Bi-square Kernel Weights

Abstract

This study aims to model the spatial distribution of tuberculosis (TB) cases in Makassar City in 2022 using the Geographically Weighted Poisson Regression (GWPR) approach. This method extends Poisson regression by incorporating spatial heterogeneity, weighting each location based on its geographical proximity. Two types of kernel weighting functions, fixed Gaussian kernel and fixed bi-square kernel, were used to determine the most effective model for identifying key factors influencing TB case numbers. The parameter estimation results indicate that the GWPR model with fixed bi-square kernel performs better than the global Poisson regression model, achieving an Akaike’s Information Criterion (AIC) value of 97.69 and a coefficient of determination (R²) of 99.93%. The findings reveal that the relationship between predictor variables and TB cases varies across districts, with the percentage of the productive-age population and population density emerging as dominant factors. These results highlight the advantages of the GWPR approach in capturing spatial dynamics more effectively than conventional regression models, making it a powerful analytical tool for designing targeted, region-specific public health interventions.