Geographically Weighted Regression

Geographically weighted regression (GWR) is a local form of spatial analysis introduced in 1996 in the geographical literature drawing from statistical approaches for curve-fitting and smoothing applications. The method works based on the simple yet powerful idea of estimating local models using subsets of observations centered on a focal point. Since its introduction, GWR rapidly captured the attention of many in geography and other fields for its potential to investigate nonstationary relations in regression analysis. The basic concepts have also been used to obtain local descriptive statistics and other models such as Poisson regression and probit. The method has been instrumental in highlighting the existence of potentially complex spatial relationships. At the same time, there have been a number of debates concerning the nature and range of applications of the method, including its use for inferential analysis or interpolation. The evidence available suggests that GWR is a useful, if imperfect, tool for inferring spatial processes, and a relatively simple and effective tool for spatial interpolation. Related technical developments enhance GWR (e.g., autocorrelation tests and multiple comparison adjustments) and/or complement it (e.g., the expansion method). Other approaches provide alternatives to the use of GWR (e.g., kriging and Bayesian models).