CAUCHY: Jurnal Matematika Murni dan Aplikasi
Vol 10, No 1 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI

Modelling Geographically Weighted Truncated Spline Regression Using Maximum Likelihood Estimation for Human Development Disparities

Saris, Laode Muhammad (Unknown)
Pramoedyo, Henny (Unknown)
Fernandes, Adji Achmad Rinaldo (Unknown)



Article Info

Publish Date
22 Mar 2025

Abstract

A development of nonparametric truncated spline regression, Geographically Weighted Regression Spline Truncated (GWSTR) incorporates spatial effects in the modelling of nonlinear relationships between the response and predictor variables. This research utilizes the Maximum Likelihood Estimation (MLE) technique to estimate the parameters of the model. The first-order truncated spline with a single knot yielded a minimal Generalized cross-validation (GCV) value of 1. 729781, suggesting a high level of accuracy in the model.  Four weighting functions were evaluated: Gaussian Kernel, Exponential Kernel, Bi-Square Kernel, and Tri-Cube Kernel. Among these, the Bi-Square weighting function performed the best, achieving a coefficient of determination of 99.999%, demonstrating the model’s capability to explain nearly all data variability effectively. GWSTR proves to be a robust method for capturing complex nonlinear relationships while accounting for spatial variations, making it a valuable tool for spatial data analysis across various disciplines.

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Journal Info

Abbrev

Math

Publisher

Subject

Mathematics

Description

Jurnal CAUCHY secara berkala terbit dua (2) kali dalam setahun. Redaksi menerima tulisan ilmiah hasil penelitian, kajian kepustakaan, analisis dan pemecahan permasalahan di bidang Matematika (Aljabar, Analisis, Statistika, Komputasi, dan Terapan). Naskah yang diterima akan dikilas (review) oleh ...