Dear All,

I have a little confusion about the use of spatial weight matrix that I want to get clarity on. I created two inverse distance weight matrices ( 0.5 mile and 1mile radius) using spmat as follows:

The 0.5 mile radius matrix is:

Code:
spmat idistance M05 lon lat , id(ID_) dfunction(dhaversine, miles) norm(row) vtruncate(1/0.5)

The 1 mile radius matrix is:
Code:
spmat idistance M1 lon lat , id(ID_) dfunction(dhaversine, miles) norm(row) vtruncate(1)
Let say I use M05 to run a spatial regression, specifically, Spatial Durbin Model (SDM) as:

Code:
xtset ID year
   xsmle y x1 x2 x3 x4,  wmat(M05) dmatrix(M05) ///
  model(sdm) durbin(x1 x2 x3 x4) re vce(cluster ID) effect nolog
And let say I use M1 to run a spatial regression, specifically, Spatial Durbin Model (SDM) as:

Code:
xtset ID year
   xsmle y x1 x2 x3 x4,  wmat(M1) dmatrix(M1) ///
  model(sdm) durbin(x1 x2 x3 x4) re vce(cluster ID) effect nolog

My question is, would it be correct to have the indirect (spillover) marginal effects of any of the covariates in the M05 model to be less than its counterpart from the M1 model? The basis of my question is that I thought the M05 model which defines a closer relation should produce bigger estimates than the M1 model. At least that's what Tobler's first law of geography implies: “everything is related to everything else, but near things are more related than distant things” (Tobler 1970).

Any help to remove my confusion is highly appreciated.