[R-sig-Geo] centering explanatory variables around spatial lag

[Sam Field]

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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