Spatially Clustered Regression
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Spatial regression or geographically weighted regression models have been widely adopted to capture the effects of auxiliary information on a response variable of interest over a region, while relationships between response and auxiliary variables are expected to exhibit complex spatial patterns in many applications. In this paper, we propose a new approach for spatial regression, called spatially clustered regression, to estimate possibly clustered spatial patterns of the relationships. We combine K-means based clustering formulation and penalty function motivated from a spatial process known as Potts model for motivating similar clustering in neighboring locations. We provide a simple iterative algorithm to fit the proposed method which is scalable for large spatial datasets. We also discuss two potential extensions of the proposed approach, regularized estimation for variable selection, and semiparametric additive modeling. Through simulation studies, the proposed method is demonstrated to show its superior performance to existing methods even under the true structure does not admit spatial clustering. Finally, the proposed method is applied to crime event data in Tokyo and produces interpretable results for spatial patterns. The R code is available at https://github.com/sshonosuke/SCR.
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