[R-sig-Geo] Spatial Durbin Model (lagsarlm) with two different Weight Matrices

[Roger Bivand]

On Sun, 3 May 2020, Wingeier, Dominik wrote:

> Dear Community
>
> I hope you are all doing well despite the special circumstances.
>
> I would like to estimate the following spatial durbin model by making 
> use of the lagsarlm(...,type ="mixed") function in R:
>
> y = ???W1y+X???+W2X??? +???

Please post plain text only, if need be using LaTeX markup for symbols. 
This is illegible.

>
> where W1 and W2 have the same dimension and are both row standardized 
> but different weights are assigned to the elements. I found two older 
> posts in the archive with similar problems 
> (https://stat.ethz.ch/pipermail/r-sig-geo/2015-May/022852.html and 
> https://stat.ethz.ch/pipermail/r-sig-geo/2015-May/022821.html) but I am 
> struggling to understand the proposed solution and how to correctly 
> implement the create_WX() in connection with the lagsarlm() function. 
> Therefore, I would like to kindly ask you for help on how to deal with 
> two different weight matrices in the case of a spatial durbin model in 
> R.

Don't apply advive given in a different setting to a different problem. 
Your model may be:

y = \rho W_1 y + X \beta + W_2 X \gamma + \varepsillon

This is not a Durbin model unless W_1 == W_2; if it was a Durbin model, 
you would use

spatialreg::lagsarlm(y ~ X, ..., Durbin=TRUE, ...)

with the DGP

y = (I - \rho W)^{-1} (X \beta + W X \gamma + \varepsillon).

Your DGP is equivalent to X_a = [X, W_2 X] and

y = (I - \rho W_1)^{-1} (X_a \beta + \varepsillon)

So construct your formula something like:

spatialreg::lagsarlm(y ~ X_1 + I(lag(lw_2, X_1)) + ..., ...)

not using Durbin, by creating the spatial lags of each continuous X 
variable one-by-one. If any X are factors, your job will be even more 
involved. I would doubt strongly that you have a motivation for mixing 
spatial weights in this way, I cannot see any obvious reason for using W_1 
for y and W_2 for X.

Hope this clarifies,

Roger

>
> In advance many thanks for any help and suggestions.
> Best regards
> Dominik
>
>
> 	[[alternative HTML version deleted]]
>
>

-- 
Roger Bivand
Department of Economics, Norwegian School of Economics,
Helleveien 30, N-5045 Bergen, Norway.
voice: +47 55 95 93 55; e-mail: Roger.Bivand using nhh.no
https://orcid.org/0000-0003-2392-6140
https://scholar.google.no/citations?user=AWeghB0AAAAJ&hl=en