What is spatial filtering?
Spatial filtering is a novel spatial
statistical methodology to capture the inherent
autocorrelation in georeferenced 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 nonparametrically and
semiparametrically 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.rproject.org).
A good collection of these spatial filtering tools can
be found in
Roger Bivand's Rpackage
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 textbook?
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, 39:11931221
