Extending regionalization algorithms to explore spatial process heterogeneity

AbstractIn 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 a 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.Keywords: Regionalizationspatial heterogeneityspatial regimespatial regression NotesAcknowledgmentsThe authors thank members of Spatial Analysis Group, Spatio-temporal Social Sensing Lab for helpful discussion. The constructive comments from anonymous reviewers are gratefully acknowledged.Data and codes availability statementThe data and codes that support the findings of this study are available at https://github.com/Nithouson/regreg.Disclosure statementThe authors declare that they have no conflict of interest.Notes1 For example, the population in each region is required to be as similar as possible or above a predefined value (see Duque et al. (Citation2012), Folch and Spielman (Citation2014), Wei et al. (Citation2021)).2 Note that the optimization of spatial regimes differs from Openshaw (Citation1978), where spatial units are aggregated into areas, and each area is treated as an observation in a global regression model.3 Note that in EquationEquation 1(1) L(R)=∑j=1p∑1≤i1