CSPATIALREG Procedure
Spatial Durbin Error Models
The spatial Durbin error model (SDEM) accounts for spatial dependence among the error terms and the exogenous interaction effect. Let 
denote the observation that is associated with the spatial unit 
for 
. For these spatial units, let 
be an 
spatial weights matrix. Further, let 
be a 
vector that denotes values of p regressors that are recorded at unit , and let 
be a 
vector that denotes values of q regressors that are measured at unit .
The SDEM can be described in vector form by using the following two-stage formulation (LeSage and Pace 2009),
where 
, 
with 
, 
is an 
matrix where each row consists of 
, 
is an 
matrix where each row consists of 
, and 
and 
are and parameter vectors, respectively.
By letting 
and 
, you can rewrite the SDEM as
where 
.
The log-likelihood function for the SDEM is
For the SDEM, the gradients are
