Spatially Clustered Regression

TL;DR

This paper introduces a novel spatially clustered regression method that combines clustering and spatial penalties to better capture complex spatial relationships in data, demonstrated through simulations and real crime data analysis.

Contribution

It proposes a new spatial regression approach integrating K-means clustering with Potts model-inspired penalties, scalable for large datasets and effective even without true spatial clustering.

Findings

Outperforms existing methods in simulations

Produces interpretable spatial patterns in crime data

Scalable algorithm for large spatial datasets

Abstract

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. In contrast, relationships between response and auxiliary variables are expected to exhibit complex spatial patterns in many applications. This paper proposes 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 encouraging similar clustering in neighboring locations. We provide a simple iterative algorithm to fit the proposed method, scalable for large spatial datasets. Through simulation studies, the proposed method demonstrates 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.