A modification to geographically weighted regression

Background: Geographically weighted regression (GWR) is a modelling technique designed to deal with spatial non-stationarity, e.g., the mean values vary by locations. It has been widely used as a visualization tool to explore the patterns of spatial data. However, the GWR tends to produce unsmooth surfaces when the mean parameters have considerable variations, partly due to that all parameter estimates are derived from a fixed-range (bandwidth) of observations. In order to deal with the varying bandwidth problem, this paper proposes an alternative approach, namely Conditional geographically weighted regression (CGWR). Methods: The estimation of CGWR is based on an iterative procedure, analogy to the numerical optimization problem. Computer simulation, under realistic settings, is used to compare the performance between the traditional GWR, CGWR, and a local linear modification of GWR. Furthermore, this study also applies the CGWR to two empirical datasets for evaluating the model performance. The first dataset consists of disability status of Taiwan's elderly, along with some social-economic variables and the other is Ohio's crime dataset. Results: Under the positively correlated scenario, we found that the CGWR produces a better fit for the response surface. Both the computer simulation and empirical analysis support the proposed approach since it significantly reduces the bias and variance of data fitting. In addition, the response surface from the CGWR reviews local spatial characteristics according to the corresponded variables. Conclusions: As an explanatory tool for spatial data, producing accurate surface is essential in order to provide a first look at the data. Any distorted outcomes would likely mislead the following analysis. Since the CGWR can generate more accurate surface, it is more appropriate to use it exploring data that contain suspicious variables with varying characteristics.