Spatially clustered regression

Shonosuke Sugasawa, Daisuke Murakami

Research output: Contribution to journalArticlepeer-review


Spatial regression and 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

Original languageEnglish
Article number100525
JournalSpatial Statistics
Publication statusPublished - 2021 Aug
Externally publishedYes


  • Geographically weighted regression
  • K-means algorithm
  • Penalized likelihood
  • Potts model
  • Spatially varying parameters

ASJC Scopus subject areas

  • Statistics and Probability
  • Computers in Earth Sciences
  • Management, Monitoring, Policy and Law


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