[R-sig-Geo] predict.spautolm

[Roger Bivand]

On Thu, 24 Sep 2009, Bjarke Christensen wrote:

> Roger Bivand wrote:
>> If you want simulations around
>> those point estimates, you can introduce spatial autocorrelation with the
>> lambda term, but lambda will not impact the predictions unless the model
>> was misspecified, I believe.
>
> I'm not quite sure I understand why. If lambda does not impact the
> predictions, would its estimate not converge to zero?

Not the estimate of lambda, but the expectation of the spatially 
autocorrelated errors will (I think) be zero - it is their covariance that 
isn't \sigma^2 I.

>
> Is it wrong to do out-of-sample validation using the method used for
> in-sample fitted values in spautolm itself, where
> yhat = Xb + lambda  W  (y-Xb)

This is Cressie (1993) p. 564. Validation maybe, because you have the 
observed y values not used in fitting, but this is not generally the case 
for prediction, so one is left with yhat = Xb, with the possibility of 
adding in the simulated \sigma (I - lambda W)^{-1} e for getting a 
distribution (see Kaluzny et al. (1998) S-plus SpatialStats manual).

>
> (My background is in econometrics, not spatial statistics, so I apologize
> if this is obvious to those with a more acute understanding of spatial
> statistics).

The only difference might be that people coming from econometrics seem to 
believe their formulae more than the applied statisticians(?)

Roger

>
> Thanks for your help,
> Bjarke Christensen
>
>

-- 
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