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st: predictions out of sample with spatial regression

Subject   st: predictions out of sample with spatial regression
Date   Fri, 21 Jun 2013 00:16:24 -0300 (BRT)

Dear Stata List members

I have a sample of n observations of the dependent variable y and independent
variables X1, X2, ..., Xk. I wish to estimate a spatial lag model for a sample
of n observations with the following specification:

y = rho * W * X * beta + y + u

where W is a neighborhood binary matrix (or inverse distances matrix) and rho is
a spatial autoregressive parameter.

I realize the estimation of this model for n observations and wish to make
predictions within and outside the sample. To make estimates within the sample
is simple, but how to realize the estimation of a set of observations (out of
sample) that surround the original n observations? One idea is to rebuild the
neighborhood matrix for each point outside the sample and from each new matrix W
'(with one more row and column than W) I would apply the expression. with the
same parameters estimates:

ypred = rho*W'y'  + beta *X

Assuming this space  is structural homogeneous, this procedure is valid?
If it is true, are there any Stata command to automatically  perform these
predictions out of sample or I have to develop a specific routine for this? But
I guess that have some problems with this procedure. Any help is wellcome.

Best regards

Henrique Neder

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