[R-sig-Geo] LM test in a spatial lag model

[Roger Bivand]

On Mon, 15 Dec 2008, Annachiara Saguatti wrote:

> Hello,
>
> I have question about the interpretation of the results of my regression.
> I'm estimating the convergence between European regions with spatial
> regimes. I have first run an OLS regression for the whole set of regions and
> I have found evidence of residual autocorrelation through the LMerr and
> LMlag tests.
> This was the result:
>
> LMerr = 5.4816, df = 1, p-value = 0.01922
>
> RLMerr = 0.2422, df = 1, p-value = 0.6226
>
> LMlag = 6.3184, df = 1, p-value = 0.01195
>
>
> RLMlag = 1.079, df = 1, p-value = 0.2989
>
> SARMA = 6.5606, df = 2, p-value = 0.03762
>
> I'm modelling spatial heterogeneity through the estimation of two separate
> models for Objective 1 regions and the rest of the regions. According to the
> results of the LM tests I have decided to use a spatial lag model (is this
> correct in your opinion?). I did so because I find that the LMlag test is a
> little more significant than the LMerr... which is the decision rule in this
> case (both LM test significant and both RLM test non significant)?
>

Please note that neither of the robust LM tests are significant. It may 
very well be the case that there is no spatial "story" in your residuals 
for the chosen spatial weights.

> After running the first ML regression I see that there is another LM test
> computed at the end of the results of the regression:
>
> Log likelihood: 176.7501 for lag model
> ML residual variance (sigma squared): 4.7437e-05, (sigma: 0.0068875)
> Number of observations: 50
> Number of parameters estimated: 7
> AIC: -339.5, (AIC for lm: -334.18)
> *LM test for residual autocorrelation
> test value: 3.4731 p-value: 0.062373 *
>
> Which is the interpretation to give to it? Is this relative to a spatial
> error or to a spatial lag?

This is a test for residual error autocorrelation for the same spatial 
weights. It does appear from the AIC values that the spatial lag model 
fits the data better than the aspatial model, but it isn't clear why.

Have you tried fitting a spatial Durbin model (lagsarlm(..., 
type="mixed")), and maybe considered testing the Common Factor hypothesis 
(Mur & Angulo, Spatial Economic Analysis, 2006)? There is a growing 
literature on this.

Another possibility is to look at the Kosfeld & Lauridsen approach to look 
at the non-stationarity question (Papers in Regional Science, 2006).

However, the tests are borderline, so only spend time on this if you have 
to, it may be what in macroecology is known as a "red herring".

Hope this helps,

Roger

>
> Thank you very much for your help!
> Annachiara Saguatti
>
> 	[[alternative HTML version deleted]]
>
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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