[R-sig-Geo] Trouble with Durbin Model

[Roger Bivand]

On Sun, 14 Dec 2008, adjemian wrote:

> Hey everyone,
>
> I'm puzzled about a recent result, and I'm wondering if
> anyone can help explain it.  Essentially, I have a set of
> data that is positively spatially autocorrelated (Moran's I
> is highly significant).

You mean that the residuals in a *null* model show spatial 
autocorrelation, but do you know the "real" data generating process?

> According to LM tests on the OLS
> residuals, I find that the spatial lag model is preferred.

That is for the chosen covariates and spatial weights - but could be 
misled by the choice of variables wrt. the "real" data generation process 
(and/or the weights).

> After estimating the lag specification with a group of
> covariates, the spatial parameter is positive and
> significant at the 1% level.  This indicates that the
> spatial clustering in the dependent variable is robust to
> the potential confounding influence of the covariates.
>

This is an overly strong assertion, isn't it? Could there be relevant 
omitted covariates? Could there be omitted case weights and/or 
heteroskedasticity, or other misspecification?

> However, when I estimate the spatial Durbin specification by
> including a set of distanced covariates, the spatial
> parameter is still significant, but with the *opposite*
> sign.  Something that may be of interest: the errors of the
> lag model are not spatially autocorrelated; while the errors
> of the Durbin model are.
>
> I wonder why the sign of spatial influence flips.  Has
> anybody faced a similar situation?  How should I select the
> proper model?

It does look as though the model is misspecified as it stands. The Spatial 
Durbin is more general - does comparing the AIC values say anything? If 
the Spatial Durbin fits "better" for a chosen criterion, then it looks 
like a missing variable or equivalently inappropriate functional form in 
one of the covariates.

Sorry not to be more help,

Roger

>
> Software used: Geoda, R.
>
> Thanks!
> Mike
>
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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