Comparative Spatial Filtering in Regression Analysis

TLDR

Spatial autocorrelation in regression can be addressed by filtering variables to separate spatial effects from total effects. This study compares two filtering approaches that enable conventional linear regression models. The authors evaluate Getis’s G_i‑based filter and Griffith’s eigenfunction decomposition filter using economic data to assess their performance. Both filters produce effective, comparable regression models, though each is best suited to specific contexts.

Abstract

One approach to dealing with spatial autocorrelation in regression analysis involves the filtering of variables in order to separate spatial effects from the variables’ total effects. In this paper we compare two filtering approaches, both of which allow spatial statistical analysts to use conventional linear regression models. Getis’ filtering approach is based on the autocorrelation observed with the use of the G i local statistic. Griffith's approach uses an eigenfunction decomposition based on the geographic connectivity matrix used to compute a Moran's I statistic. Economic data are used to compare the workings of the two approaches. A final comparison with an autoregressive model strengthens the conclusion that both techniques are effective filtering devices, and that they yield similar regression models. We do note, however, that each technique should be used in its appropriate context.