Spatial Filtering

Abstract

One approach to dealing with spatial autocorrelation in regression analysis involves filtering, which seeks to transform a spatially dependent variable into an independent variable by removing the spatial dependence embedded in it. In doing so, the original georeferenced attribute variable is partitioned into two synthetic variables: a filtered nonspatial variable and a residual spatial variable. Haining (1991) shows that the temporal-type filtering approach is equivalent to a spatial autocorrelation adjustment for the case of bivariate correlation. He employs one of the family of autoregressive models, such as the simultaneous (SAR), of the general form discussed in Anselin (1988) and Griffith (1988) to implement his version of spatial filtering. In essence, these models depend on one or more spatial structural matrices that remove (filter) spatial autocorrelation from the georeferenced data from which model parameters are estimated: e.g., from equation (1.3), (I- ρW)^-1Y = μ_Y 1 + ε _Y. The filtering devices are constructed from geographic weights matrices, which are used to capture the covariation among values of one or more random variables associated with the depiction of the configuration of areal units.