CSPATIALREG Procedure
Spatial Error Models
The spatial error model (SEM) accounts for spatial dependence in the error terms rather than in the dependent variable. 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 .
The SEM 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 
, and 
is a parameter vector.
The log-likelihood function for the SEM is
where 
.
For the SEM, the gradients are
In addition to the interaction effects among error terms, you might also want to include exogenous interaction effects in the model. In such cases, you need to consider a spatial Durbin error model.