Geographically weighted sparse regression using counting norm regularization for environmental data

초록

Spatial heterogeneity refers to the variation in patterns, relationships, or characteristics across different spatial locations, and it is a common phenomenon in spatial data. This phenomenon occurs because environmental factors such as water quality can vary substantially from one place to another. Geographically weighted regression (GWR) effectively captures such spatial heterogeneity by allowing coefficients to vary across locations. In GWR, local variable selection is crucial as it helps capture the most relevant spatial relationships and enhances the interpretation of local features. This study applies geographically weighted sparse regression with counting norm ($L_0$-GWR) to enhance model sparsity and performance. The method distinguishes between regionally activated and non-activated local features in an adaptive way. Biochemical oxygen demand (BOD), a key indicator of river water pollution, exhibits distinct spatial patterns in South Korea, influenced by local environmental factors. However, some local factors are expected to have minimal impact on BOD in certain regions. This study aims to demonstrate the effectiveness of applying the L_0-GWR method in the spatially varying coefficient model for BOD data. To evaluate its performance, we compare L_0-GWR with GWR and geographically weighted LASSO regression using performance and interpretation measures. The L_0-GWR approach demonstrates competitive performance and provides clear interpretability.

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