SPATIALREG Procedure
Spatial Moving Average Models
The spatial moving average (SMA) model accounts for spatial dependence among the error terms; thus it is similar to the SEM model but with a different autocorrelation structure. The SMA model is used for modeling local autocorrelation. Let 
denote the observation 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 recorded at unit .
The SMA model can be described in vector form by using the following two-stage formulation,
where 
and 
, with 
. Moreover, 
is an 
matrix that has 
in each row, and 
is an 
matrix that has of 
in each row. In addition, 
is a parameter vector.
The log-likelihood function for the SMA model is
where 
.
For the SMA model, the gradients are
