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.
翻译:空间回归或地理加权回归模型已被广泛采用,以捕捉辅助信息对一个区域感兴趣的响应变量的影响。相反,反应变量和辅助变量之间的关系预计将在许多应用中呈现复杂的空间模式。本文件提出了一种新的空间回归方法,称为空间集群回归,以估计可能存在的关系组合空间模式。我们结合了K- means基于集群的配制和从被称为Potts 的空间进程驱动的处罚功能,即鼓励邻近地点类似集群的波茨模型。我们提供了一种简单的迭代算法,以适应拟议的方法,对大型空间数据集而言,可以伸缩。通过模拟研究,拟议方法显示其优于现有方法,即使根据真实结构,也不允许空间集群。最后,拟议方法适用于东京的犯罪事件数据,并产生空间模式的可解释结果。R代码可在https://github.com/shonosuke/SCR查阅。