CSPATIALREG Procedure
Spatial Durbin Moving Average Models
The term spatial Durbin moving average (SDMA) model is used to refer to the SMA model that accommodates exogenous interaction effects. 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 covariates that are measured at unit .
The SDMA model can be described in vector form as
where 
; 
with 
; 
and 
are 
and 
matrices, where each row consists of 
and 
, respectively; 
is a parameter vector; and 
is a 
parameter vector.
By letting 
and 
, the SDMA model can be written as
The log-likelihood function for the SDMA model is
where 
and 
denotes the determinant of matrix 
.
For the SDMA model, the gradients are
