Some Guidelines for Specifying the Geographic Weights Matrix Contained in Spatial Statistical Models 1

This chapter provides some explicit guidance on specification of the geographic weights matrix contained in spatial autoregressive models. Specification of a geographic weights matrix represents a priori knowledge of the range and intensity of a spatial field effect for a set of areal units constituting a geographic system. Stetzer, F. found that misspecification of the weights matrix introduces bias into mean response estimation, a finding that is incorrect, as Theorem subsequently proves. Florax and Rey have studied impacts of the misspecification of a geographic weights matrix in terms of statistical power in spatial econometric hypothesis testing. Stetzer's conclusion that over-specification leads to inflation while under-specification leads to suppression of variance is reflected here in results for the conditional autoregressive model, but is not supported by results for the simultaneous autoregressive model, which is a second-order model having a greater dependency range. Hopefully the rules-of-thumb will prove helpful in guiding specification of geographic weights matrices for a myriad of spatial landscapes.