  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.
