[R-sig-Geo] Spatial Regression with two Weights matrix (SAR)

[Roger Bivand]

On Fri, 25 Jul 2014, Linus Holtermann wrote:

> Hello,
>
> is there a R function that could estimate the following spatial regression:
>
> y = rho_1*W1*y + rho_2*W2*y + XB + e
>
> W1 and W2 are not identical, of course.

No, not least because the mutual constraints on \rho_* are unknown. Too 
little is known about (I - (\sum{i=1}{k}\rho_i W_i)) in the literature as 
far as I am aware. It may seem attractive to see W_i as bands of 
increasing distances, or graph steps, but these models actually work 
through (I - \rho W)^{-1}, which includes all higher order 
relationships implicitly. The same lack of knowledge about constraints 
applies to the SEM error case:

y = X\beta + u, u = \sum{i=1}{k}(\rho_i W_i u) + e

but this is more like the case of a collection of variogram models.

In the SAR (lag), you also face the problem of finding the impacts, as the 
\beta values should not be interpreted directly, as the reduced form is:

y = (I - (\sum{i=1}{k}\rho_i W_i))^{-1} (X\beta + e)

and the \rho's and \beta interact.

Contributions welcome,

Roger

>
> Bests,
>
>
> Linus Holtermann
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-- 
Roger Bivand
Department of Economics, Norwegian School of Economics,
Helleveien 30, N-5045 Bergen, Norway.
voice: +47 55 95 93 55; fax +47 55 95 91 00
e-mail: Roger.Bivand at nhh.no