Message-ID: <1193863597.4728e9ae0050b@webmail.pobox.upenn.edu>
Date: 2007-10-31T20:46:38Z
From: Sam Field
Subject: centering explanatory variables around spatial lag
In-Reply-To: <4728B219.8020707@zevross.com>
List,
When the influence of explanatory variables "spills over" into adjacent or
proximate spatial units, one way to model this would be to include a spatially
lagged explanatory variable (WX). If there exists a significant spatially lagged
association, then (it would seem to me) the influence of X would be biased if it
is correlated with WX (which it would be if X was non_randomly distributed in
space). In other words, the effect of X is confounded with WX if the two are
correlated AND both have independent impacts on the outcome. It would seem that
a properly specified model would include both the effects of X and WX. One
potential problem is that X and WX maybe highly correlated leading to
instability in the estimation of their independent effects. It seems a
solution, analogous to what is often done in multi-level models, is to center X
on its spatial average, WX. Thus,
yhat = b0 + b1(X - WX) + b2(WX).
where the influence of WX is now a function of two parameters: (b2-b1)WX and the
null H0:b2-b1 = 0
Is there a reason not to do this with spatially lagged explanatory variables?
Is there any literature on this? I have an empirical example in which the
results from centering versus non centering differ dramatically, so I want to
make sure that the situation is analogous to the multi-level case before
proceeding. I could do some simulation, but I thought I would ask the list first.
thanks!
Sam
--
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Samuel H. Field, Ph.D.
Senior Research Investigator
CHERP/Division of Internal Medicine - University of Pennsylvania
Philadelphia VA Medical Center
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