Application of Lasso to the Eigenvector Selection Problem in Eigenvector Based Spatial Filtering

Eigenvector based spatial filtering is one of the well-used approaches to model spatial autocorrelation among the observations or errors in a regression model. In this approach, subset of eigenvectors extracted from a modified spatial weight matrix is added to the model as explanatory variables. The subset is typically specified via the forward stepwise model selection procedure, but it is disappointingly slow when the number of observations n takes a large number. Hence as a complement or alternative, the present paper proposes the use of the LASSO (L1-penalized regression) to select the eigenvectors. The LASSO model selection procedure is applied to the well-known Boston housing dataset and simulation dataset, and its performance is compared with that of the stepwise procedure. The obtained results suggest that the LASSO is fairly fast compared the stepwise procedure, and can select eigenvectors effectively even if dataset is relatively large (n = 10000), to which the forward stepwise procedure is uneasy to apply.