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的设定来加以考虑。后者涉及描绘变量间关系具有同质性的空间连通区域（空间体制）。尽管空间分析领域已提出并研究了各种区域化算法，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分算法：两阶段K-Models和区域K-Models。同时，我们将经典的自动分区程序扩展至空间回归背景下。所提出的算法被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，这三种算法均能达到优于或等同于现有方法的性能，其中两阶段K-Models算法在模型拟合、区域重建和系数估计方面大幅优于现有方法。我们的工作丰富了探索空间异质性过程的空间分析工具箱。