M-SGWR: Multiscale Similarity and Geographically Weighted Regression

TL;DR

M-SGWR introduces a multiscale local regression model that combines geographic proximity and attribute similarity to better capture complex spatial relationships, outperforming traditional models.

Contribution

The paper proposes M-SGWR, a novel multiscale regression framework that integrates geographic and attribute-based similarities with predictor-specific weighting.

Findings

M-SGWR outperforms GWR, SGWR, and MGWR in goodness-of-fit metrics.

The model effectively captures both spatial and attribute-based interactions.

Simulation and empirical results validate the model's superior performance.

Abstract

The first law of geography is a cornerstone of spatial analysis, emphasizing that nearby and related locations tend to be more similar, however, defining what constitutes "near" and "related" remains challenging, as different phenomena exhibit distinct spatial patterns. Traditional local regression models, such as Geographically Weighted Regression (GWR) and Multiscale GWR (MGWR), quantify spatial relationships solely through geographic proximity. In an era of globalization and digital connectivity, however, geographic proximity alone may be insufficient to capture how locations are interconnected. To address this limitation, we propose a new multiscale local regression framework, termed M-SGWR, which characterizes spatial interaction across two dimensions: geographic proximity and attribute (variable) similarity. For each predictor, geographic and attribute-based weight matrices are constructed separately and then combined using an optimized parameter, alpha, which governs their relative contribution to local model fitting. Analogous to variable-specific bandwidths in MGWR, the optimal alpha varies by predictor, allowing the model to flexibly account for geographic, mixed, or non-spatial (remote similarity) effects. Results from two simulation experiments and one empirical application demonstrate that M-SGWR consistently outperforms GWR, SGWR, and MGWR across all goodness-of-fit metrics.