MAXIMUM LIKELIHOOD ESTIMATION FOR SPATIAL DURBIN MODEL

Spatial Durbin Model (SDM) is one method of spatial autoregressive. This model was developed because the dependencies in the spatial relationships not only occur in the dependent variable, but also on the independent variables. In the assessment of parameter estimation, the process is carried out by Maximum Likelihood Estimation (MLE). This estimation can be approximation by Spatial Autoregressive Models (SAR). By MLE, the matrix of independent variable in SAR is X and in SDM is [I X W₁X], so that the estimation in SDM was done by replace matrix X in SAR by [I X W₁X]. This estimation perform the unbiased estimator for β and σ². Estimate ρ was done by optimize the concentrated log-likelihood function with respect to ρ.