Modeling Mortality Data Using Multi-Scale Geographically Weighted Regression

Abstract

Insurance is a contractual agreement in which the insurer provides financial protection against uncertain risks in exchange for a premium paid by the insured. In the context of life insurance, accurate estimation of mortality rates is essential, as it directly influences premium determination. This study aims to develop a Multi-scale Geographically Weighted Regression (MGWR) model and compare its performance with Multiple Linear Regression (MLR) and Geographically Weighted Regression (GWR) in the spatial analysis of mortality data. While MLR assumes a constant relationship between predictor and response variables across all locations, it fails to account for spatial heterogeneity. GWR addresses this limitation by constructing local regression models using geographical weights. However, GWR applies a single bandwidth for all parameters, which may reduce estimation accuracy. MGWR overcomes this limitation by assigning distinct bandwidths to each parameter through a back-fitting algorithm, resulting in greater model flexibility and precision. The proposed model is applied to the logarithm of mortality counts data in Japan, and the analysis indicates that MGWR with a fixed bandwidth and tricube kernel function yields the best performance, achieving the lowest corrected Akaike Information Criterion (AICc) and the highest adjusted coefficient of determination, outperforming both GWR and MLR. Moreover, MGWR produces lower and more evenly distributed residuals, demonstrating its capability to capture complex spatial variations. These results highlight MGWR’s superiority in estimating mortality rates, thereby enabling more accurate, region-specific life insurance premium calculations.