C.5 Geographically Weighted Regression

Geographically weighted regression (GWR) was introduced to the geography literature by Brunsdon et al. (1996) to study the potential for relationships in a regression model to vary in geographical space, or what is termed parametric nonstationarity. GWR is based on the non-parametric technique of locally weighted regression developed in statistics for curve-fitting and smoothing applications, where local regression parameters are estimated using subsets of data proximate to a model estimation point in variable space. The innovation with GWR is using a subset of data proximate to the model calibration location in geographical space instead of variable space. While the emphasis in traditional locally weighted regression in statistics has been on curve-fitting, that is estimating or predicting the response variable, GWR has been presented as a method to conduct inference on spatially varying relationships, in an attempt to extend the original emphasis on prediction to confirmatory analysis (Páez and Wheeler 2009). In GWR, a regression model can be fitted at each observation location in the dataset, although the model calibration locations are not restricted to observation locations. The spatial coordinates of the data points, either individual data points or areal centroids, are used to calculate inter-point distances, which are input into a kernel function to calculate weights that represent spatial dependence between observations. For each model calibration location, i = 1, ..., n, the GWR model is