SPATIALREG Procedure
Spatial Autoregressive Confused Models
The spatial autoregressive confused (SAC) model, like the SARMA model, can accommodate spatial dependence in both the dependent variable and error terms. However, the covariance structure for the error terms in a SAC model is different from that of the SARMA model. Let 
denote the observation associated with the spatial unit 
for 
. For these spatial units, let 
and 
be two spatial weights matrices. Further, let 
be a 
vector that denotes values of p regressors recorded at unit .
The SAC model can be described in vector form by using the following two-stage formulation (LeSage and Pace 2009),
where 
and 
, with 
. Moreover, 
is an 
matrix that has 
in each row. In addition, 
is a parameter vector.
The log-likelihood function for the SAC model is
where 
and 
.
For the SAC model, the gradients are
