In spatial regression models, spatial heterogeneity may be considered with either continuous or discrete specifications. The latter is related to delineation of spatially connected regions with homogeneous relationships between variables (spatial regimes). Although various regionalization algorithms have been proposed and studied in the field of spatial analytics, methods to optimize spatial regimes have been largely unexplored. In this paper, we propose two new algorithms for spatial regime delineation, two-stage K-Models and Regional-K-Models. We also extend the classic Automatic Zoning Procedure to spatial regression context. The proposed algorithms are applied to a series of synthetic datasets and two real-world datasets. Results indicate that all three algorithms achieve superior or comparable performance to existing approaches, while the two-stage K-Models algorithm largely outperforms existing approaches on model fitting, region reconstruction, and coefficient estimation. Our work enriches the spatial analytics toolbox to explore spatial heterogeneous processes.

翻译：在空间回归模型中，空间异质性可以通过连续或离散设定加以考虑。后者涉及划定具有变量间同质关系的空间连通区域（空间体制）。尽管在空间分析领域已有多种区域化算法被提出并研究，但优化空间体制的方法在很大程度上尚未被探索。本文提出了两种新的空间体制划定算法：两阶段K模型和区域K模型。我们还将经典的自动分区方法扩展到空间回归的语境中。所提出的算法应用于一系列合成数据集和两个真实世界数据集。结果表明，所有三种算法均达到优于或与现有方法相当的性能，其中两阶段K模型算法在模型拟合、区域重建和系数估计方面大幅超越现有方法。我们的工作丰富了探索空间异质过程的空间分析工具箱。