arXiv:2601.19888stat.MEcs.AI2026-01

新模型M-SGWR融合地理距离与变量相似性,提升空间预测精度。

M-SGWR: Multiscale Similarity and Geographically Weighted Regression

  • 用地理距离和变量相似性双维度构建权重矩阵
  • 在模拟与实证中均优于传统模型,提升拟合效果
  • 适合研究跨区域关联的地理、城市或环境问题

地理学第一定律强调相近位置具有相似性,但何为‘近’与‘相关’仍具挑战,因不同现象的空间模式各异。传统局部回归模型如地理加权回归(GWR)和多尺度地理加权回归(MGWR)仅依赖地理邻近性刻画空间关系。在全球化与数字互联背景下,仅靠地理距离已不足以捕捉位置间的真实联系。为此,本文提出新型多尺度局部回归框架M-SGWR,从地理邻近性和属性相似性两个维度表征空间交互。对每个预测变量,分别构建地理与属性权重矩阵,并通过可优化参数α融合,控制二者贡献比例。类似MGWR中的变量特定带宽,最优α随变量变化,使模型灵活捕捉地理、混合或非空间(远程相似)效应。两项模拟实验与一项实证应用结果表明,M-SGWR在所有拟合优度指标上均持续优于GWR、SGWR和MGWR。

原文摘要 · Abstract (English)

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.

空间分析回归模型多尺度建模

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