A generalized regionalization framework for geographical modelling and its application in spatial regression

In presence of spatial heterogeneity, models applied to geographic data face a trade-off between producing general results and capturing local variations. Modelling at a regional scale may allow the identification of solutions that optimize both accuracy and generality. However, most current regionalization algorithms assume homogeneity in the attributes to delineate regions without considering the processes that generate the attributes. In this paper, we propose a generalized regionalization framework based on a two-item objective function which favors solutions with the highest overall accuracy while minimizing the number of regions. We introduce three regionalization algorithms, which extend previous methods that account for spatially constrained clustering. The effectiveness of the proposed framework is examined in regression experiments on both simulated and real data. The results show that a spatially implicit algorithm extended with an automatic post-processing procedure outperforms spatially explicit approaches. Our suggested framework contributes to better capturing the processes associated with spatial heterogeneity with potential applications in a wide range of geographical models.