Year: 2026
Type: article
Abstract: In several fields such as ecological, climate, and environmental studies, modeling three-dimensional (3D) spatial heterogeneity, including altitude, is essential for capturing complex geographic variation. Geographically and altitudinal weighted regression (GAWR) is widely used for this purpose, extending traditional geographically weighted regression into three dimensions. However, GAWR cannot perform local variable selection—it assumes all predictors are relevant at every location - which can make the resulting models less accurate and difficult to interpret when true local sparsity exists. To address this limitation, we propose $$L_0$$ L 0 -GAWR, a novel framework that integrates GAWR with an $$L_0$$ L 0 -norm penalty for strict location-specific variable selection. This framework simultaneously models 3D spatial effects, including altitude, while identifying regionally relevant predictors in a data-driven manner. Since optimizing the $$L_0$$ L 0 penalty involves a computationally challenging NP-hard problem, we employ an iterative adaptive splicing algorithm to search for near-optimal solutions with stable convergence efficiently. Simulation studies demonstrate that $$L_0$$ L 0 —GAWR outperforms conventional GAWR in estimation accuracy and interpretability by correctly identifying zero coefficients. Application to South Korean air temperature data shows that the proposed model effectively captures altitude-driven spatial variations and produces sparse, interpretable coefficient estimates, demonstrating its strength in analyzing complex 3D spatial heterogeneity.
Authors: Seungjun Park, Danhyang Lee, Myungjin Kim
Institutions: Kyungpook National University, Southern Methodist University
Language: English
Subfield: Economics and Econometrics
Domain: Social Sciences
SDG: Climate action
Open Access status: hybrid
Estimated APC paid: $2,290
Award: G908433232
OpenAlex ID: W7165936896