centering explanatory variables around spatial lag

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