Estimation of geographically weighted panel nonparametric regression models with spline estimators

Abstract

Geographical regression modeling approaches have developed rapidly in addressing spatial variation in data analysis. Geographically Weighted Regression (GWR) and Geographically Weighted Panel Regression (GWPR) models are widely used to accommodate spatial heterogeneity, but they still have limitations in capturing nonlinear relationships between variables. Therefore, this study proposes a Geographically Weighted Panel Nonparametric Regression approach with a truncated spline estimator (GWPRS) as an extension of the GWPR model. This model integrates nonparametric regression with spatial and temporal weighting in panel data. The selection of optimal knot points is performed using Generalized Cross Validation (GCV). The case study was applied to Human Development Index (HDI) data in South Sulawesi Province for the period 2019–2023 with a Fixed Gaussian Kernel weighting function and a Fixed Effect Model approach. The results show that the optimal model is obtained at order m=1 with two knot points, and the independent variables that affect HDI differ between districts/cities, forming seven regional groups based on significant variables.