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Spatial Filtering using the Eigenvector Approach

by Michael Tiefelsdorf and Daniel A. Griffith


What is spatial filtering?                                                                  

Spatial filtering is a novel spatial statistical methodology to capture the inherent autocorrelation in geo-referenced observations. In essence, spatial filtering uses a set of spatial proxy variables, which usually are extracted as eigenvectors from an underlying spatial relationship matrix that ties the spatial objects together, and adds these vectors as control variables to a model. These control variables identify and isolate the stochastic spatial dependencies among the observations, thus allowing model building to proceed as if the observations were independent.



Where can spatial filtering be applied?                                                  

Spatial filtering using eigenvectors can be applied:

  •  To non-parametrically and semi-parametrically model several autoregressive linear specifications that are predominately used in spatial econometrics,

  •  To generalized linear models with autocorrelated observations such as logistic and Poisson regression that are frequently applied in spatial ecology and epidemiology,

  •  To model spatial heterogeneities in regression parameters,

  •  To general spatial link matrices such as spatial interaction flows or network structures among interaction flows, which embed spatial link matrices into a more theory driven domain,

  •   To many more exploratory and explanatory methods in spatial and geographical analysis.


Which software tools for spatial filtering are available?                              

Prototypes for performing spatial filtering are developed in the open source statistical environment R (see http://www.r-project.org). A good collection of these spatial filtering tools can be found in Roger Bivand's R-package spdep. If you want to learn more on R's spatial and GIS functionality please see http://sal.uiuc.edu/csiss/Rgeo/. Additional spatial filtering tools are under development by several groups of spatial statisticians.


Is there a reference text-book?                                                           

No, not at the present time because the spatial filtering methodology is still under active development. However, there is a good collection of academic publications. For an overview please begin with

  •   Tiefelsdorf, M., and Griffith, D.A. (2007). Semiparametric filtering of spatial autocorrelation: the eigenvector approach. Environment and Planning A, 39:1193-1221


page last updated: July 03, 2008