A Closer Examination of Spatial-Filter-Based Local Models

Abstract

GIScience 2016 Short Paper Proceedings A Closer Examination of Spatial-Filter-Based Local Models Taylor Oshan, A. Stewart Fotheringham Arizona State University, Tempe, Arizona 85281 Email: {toshan; stewart.fotheringham}@asu.edu Abstract Local modeling is a spatial analysis technique that explores spatial non-stationarity in data- generating processes. Geographically weighted regression (GWR) is one method that has been widely applied across domains, which has helped uncover local spatial relationships and gener- ally increases model goodness-of-fit. Despite this, some have criticized GWR for being extra susceptible to issues such as multicollinearity and spatial autocorrelation. Spatial-filtering- based local regression (SFLR) has been suggested as a solution. While SFLR is claimed to be approximately equivalent to GWR, it is also touted as superior. Therefore, it is of interest to compare the output from these two techniques. We do this by examining how well both techniques replicate the known coefficient values derived by simulating data that is represen- tative of spatially varying processes. The results indicate that the original SFLR specification is prone to overfitting, while an alternative specification that minimizes the mean square error produces coefficients similar to GWR. Introduction and Background Non-stationarity in data-generating processes goes largely undetected in traditional global models. Hence, local models, which explicitly allow regression coefficients to vary over space, are necessary to capture such heterogenous processes. One local modeling technique that has become particularly popular is geographically weighted regression (GWR) (Fotheringham et al. 2002). Despite its usefulness, GWR has been critiqued as being highly susceptible to multicollinearity (Wheeler & Tiefelsdorf 2005), whereby multicollinearity amongst explana- tory variables causes intolerable levels of correlation amongst GWR coefficients. However, results show that when the sample size is large, GWR is robust to even remarkably high levels of multicollinearity (Paez et al. 2011; Fotheringham & Oshan Submitted). Still, the work of Wheeler and Tiefelsdorf (Wheeler & Tiefelsdorf 2005) sparked much subsequent critiques of GWR. Specifically, spatial-filter-based local regression (SFLR) has been suggested as a supe- rior alternative to GWR (Griffith 2008). While Griffith (2008) posits that SFLR and GWR are approximately equivalent, he also points out that local coefficients produced from GWR and SFLR are minimally correlated, suggesting that the two models are producing much different results, thereby implying a contradiction within the SFLR method. To the knowledge of the authors, the SFLR method has not been applied outside its original conception (Griffith 2008), while GWR has produced agreeable results in many studies. Therefore, the primarily goal of this paper is to employ simulated data in order to test which of the techniques can more reliably estimate the true coefficients of non-stationary processes. Some modifications of the SFLR routine are investigated and several issues of the SFLR framework are highlighted. A basic GWR model may be specified as p y i = b i0 + Â b ik x ik + e i , k=1 i = 1, ..., n,