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.

翻译：地理学第一定律是空间分析的基石，它强调邻近且相关的位置往往更为相似。然而，如何定义“邻近”与“相关”仍具挑战性，因为不同现象呈现出各异的空间模式。传统的局部回归模型，如地理加权回归（GWR）与多尺度地理加权回归（MGWR），仅通过地理邻近性来量化空间关系。然而，在全球化与数字互联的时代，仅凭地理邻近性可能不足以捕捉位置间的相互关联。为克服这一局限，我们提出了一种新的多尺度局部回归框架，称为M-SGWR，该框架从两个维度刻画空间交互作用：地理邻近性与属性（变量）相似性。对于每个预测变量，分别构建基于地理和基于属性的权重矩阵，随后通过优化参数α将其组合，该参数控制二者对局部模型拟合的相对贡献。类似于MGWR中变量特定的带宽，最优α值因预测变量而异，使得模型能够灵活地考虑地理效应、混合效应或非空间（远程相似性）效应。两项模拟实验和一项实证应用的结果表明，在所有拟合优度指标上，M-SGWR均一致优于GWR、SGWR和MGWR。