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: [email protected]
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