The SPATIALREG Procedure
Spatial Durbin Autoregressive Confused Models
The SAC model can be extended to account for exogenous interaction effects. The term spatial Durbin autoregressive confused (SDAC) model is used to refer to such an extension of the SAC 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 . Similarly, assume that is a vector that denotes values of q regressors measured at unit .
The SDAC 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, is an matrix that has in each row. In addition, is a parameter vector.
By letting and , the SDAC model can be rewritten as
The log-likelihood function for the SDAC model is
For the SDAC model, the gradients are