Selection of optimal knot point and best geographic weighted on geographically weighted spline nonparametric regression model

Abstract

This study proposes the development of a nonparametric regression model combined with geographically weighted regression. The regression model considers geographical factors and has a data pattern that does not follow a parametric form to overcome the problem of spatial heterogeneity and unknown regression functions. This study aims to model provincial food security index data in Indonesia with the GWSNR model, so finding the optimal knot point and the best geographic weighting is necessary. We propose the selection of optimal knot points using the Cross Validation (CV) and Generalized Cross Validation (GCV) methods. The optimal knot point will control the accuracy of the regression curve as we also consider the MSE value in showing the ability of the model. In addition, we determine the best geographic weighting and test the significance of the model parameters. We demonstrate the GWSNR model on food security index data. The best GWSNR model uses the Gaussian kernel weighting function and selects the optimal knot point as one-knot point based on the lowest CV and GCV values. Simultaneous and partial parameter test results show that there are 10 area classifications with different effects on each group of classification results. Some of the highlights of the proposed approach are:•The method is the development of a nonparametric regression model with geographic weighting, which combines nonparametric and spatial regression in modeling the national food security index.•There are three-knot points tested in nonparametric truncated spline regression and three geographic weightings in spatial regression. Then the optimal knot point and best bandwidth are determined using Cross Validation and Generalized Cross Validation.•This article will determine regional groupings in Indonesia in 2022 based on significant predictors in modeling the national food security index numbers.