Measuring Spatial Variations in Relationships with Geographically Weighted Regression

Abstract

A frequent aim of data analysis is to identify relationships between pairs of variables, often after negating the effects of other variables. By far the most common type of analysis used to achieve this aim is that of regression in which relationships between one or more independent variables and a single dependent variable are estimated. In spatial analysis, the data are drawn from geographical units and a single regression equation is estimated. This has the effect of producing 'average' or 'global' parameter estimates which are assumed to apply equally over the whole region. That is, the relationships being measured are assumed to be stationary over space. Relationships which are not stationary, and which are said to exhibit spatial nonstationarity, create problems for the interpretation of parameter estimates from a regression model. It is the intention of this paper to describe a statistical technique, which we refer to as Geographically Weighted Regression (GWR), which can be used both to account for and to examine the presence of spatial non-stationarity in relationships.