Anisotropic Variance Functions in Geographically Weighted Regression Models

Abstract

Most standard methods of statistical analysis used in the social and environmental sciences are built upon the basic assumptions of independence, homogeneity, and isotropy. A notable exception to this rule is the collection of methods used in geographical analysis, which have been designed to take into account serial dependence often observed in spatial data. In addition, recent developments, in particular the method of geographically weighted regression, have provided the tools to model non‐stationary processes, and thus evidence that challenges the assumption of homogeneity. The assumption of isotropy, however, although suspect, has received considerably less attention, and there is thus a need for tools to study anisotropy in a more systematic fashion. In this paper we expand the method of geographically weighted regression in a simple yet effective way to explore the topic of anisotropy in spatial processes. We discuss two different estimation situations and exemplify the proposed technical development by means of a case study. The results suggest that anisotropy issues might be a fairly common occurrence in spatial processes and/or in the statistical modeling of spatial processes.