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Spatial Durbin Model (lagsarlm) with two different Weight Matrices

2 messages · Wingeier, Dominik, Roger Bivand

Original
Wingeier, Dominik
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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? +?

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.

In advance many thanks for any help and suggestions.
Best regards
Dominik
Roger Bivand
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On Sun, 3 May 2020, Wingeier, Dominik wrote:

            

      
      
      
    

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