A quality assessment of eigenvector spatial filtering based parameter estimates for the normal probability model

Abstract

Eigenvector spatial filtering, which introduces a subset of eigenvectors extracted from a spatial weights matrix as synthetic control variables in a regression model specification, furnishes a solution to extraordinarily intricate statistical modeling problems involving spatial dependences. It accounts for spatial autocorrelation in standard specifications of regression models. But the quality of the resulting regression parameter estimates has yet to be ascertained. The estimator properties to establish include unbiasedness, efficiency, and consistency. The purpose of this paper is to demonstrate these estimator properties for linear regression parameters based on eigenvector spatial filtering, including a comparison with the simultaneous autoregressive (SAR) model. Eigenvector spatial filtering methodology requires the judicious selection of eigenvectors, whose number tends to increase with both level of linear regression residual spatial autocorrelation and the number of areal units. A logistic regression description of the number of eigenvectors selected in a simulation pilot study suggests estimator consistency.