Bandwidth Selection in Geographically Weighted Poisson Regression Model Using Firefly Optimization Algorithm with Application to Cancer Rate Data

Abstract

Geographically Weighted Poisson Regression (GWPR) is an extension of the standard Poisson regression model designed to handle spatial count data by accounting for local associations among variables. However, the GWPR model faces several challenges that can affect its accuracy and reliability-one of the most critical being bandwidth selection. An inappropriate bandwidth may either overfit the model to noise or produce unrealistically low estimates. Specifically, a small bandwidth may capture excessive local variability, while a large bandwidth could smooth over meaningful local patterns. Meta-heuristic algorithms are optimization techniques designed to find approximate solutions to complex problems by efficiently exploring the solution space. The application of meta-heuristic algorithms for bandwidth selection in the GWPR model is relatively novel, as it introduces an optimization-based approach to this critical task. In this paper, the Firefly Algorithm (FA), a nature-inspired meta-heuristic method, is utilized to determine the optimal bandwidth value in the GWPR model. The FA algorithm searches for the bandwidth that minimizes prediction error, based on a defined objective function. Using cancer incidence data as a real-world case study, comparative analysis demonstrated that the proposed FA-based method outperforms traditional approaches in terms of pseudo-R² and Deviance metrics. The results suggest that employing meta-heuristic optimization-specifically the Firefly Algorithm-for bandwidth selection in GWPR models is a promising and effective strategy that enhances spatial modeling through the integration of advanced optimization techniques.