Linear Models with Spatially Distributed Data

This article deals with linear models for which data have been aggregated over well-defined geographic areas. Such data may be generated by spatial processes, and these may be represented in the form of spatial autocorrelation in the disturbance term or directly in the form of a spatial effect. This article details the derivation of Ord's (1975) MLEprocedurefor the spatial disturbances model and contrasts it with this MLE procedure for the spatial effects model. These alternative model specifications and estimation procedures are then illustrated by a variety of examples. These MLEprocedures for the spatial models are also contrasted with conventional regression procedures (which ignored geographical space). If there is spatial autocorrelation present, an MLE procedure is preferable.