CSPATIALREG Procedure
Spatial Lag of X Models
The spatial lag of X (SLX) model assumes no endogenous interaction effects or spatial dependence in the error terms. Instead, it incorporates only exogenous interaction effects into the linear regression model. Let 
denote the observation that is associated with the spatial unit 
for 
. For these spatial units, let 
be a spatial weights matrix. Further, let 
be a 
vector that denotes values of p regressors recorded at unit , and let 
be a 
vector that denotes values of q regressors measured at unit .
The SLX model can be described in vector form as
where 
, 
with 
, 
is an 
matrix where each row consists of 
, 
is an 
matrix where each row consists of 
, and 
is a parameter vector.
By letting 
and 
, you can rewrite the SLX model as
The log-likelihood function for the SLX model is
For the SLX model, the gradients are
The Hessians take the following forms:
