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

[Roger Bivand]

On Wed, 31 Oct 2007, Sam Field wrote:

> 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.
>

I'm not aware of work that has reported this approach, though use of WX 
and WWX as instruments for WY is known. I think that it would be 
interesting to pursue, if only to conclude that it doesn't help. One would 
still need to be fairly sure that there were no substantive missing X, and 
no X with the wrong functional form, in addition to choosing a likely and 
parsimonious W.

Roger

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> Sam
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-- 
Roger Bivand
Economic Geography Section, Department of Economics, Norwegian School of
Economics and Business Administration, Helleveien 30, N-5045 Bergen,
Norway. voice: +47 55 95 93 55; fax +47 55 95 95 43
e-mail: Roger.Bivand at nhh.no