Popular Spatial Autoregressive And Geostatistical Models

Abstract

Abstract Parallels between spatial autoregression and geostatistics are outlined in §1.2. To recapitulate, discussions of spatial series tend to focus on either spatial autocorrelation (geostatistics) or partial spatial autocorrelation (spatial autoregression). Although these two subfields have been evolving autonomously and in parallel, they are closely linked. Recalling Figure 1.1, both spatial statistics and geostatistics fall under the heading of multivariate analysis. The former frequently is concerned with aggregations of phenomena into discrete regions, while the latter principally is concerned with more or less continuously occurring attributes. By exploiting latent spatial autocorrelation in georeferenced data, spatial autoregression usually seeks to enhance statistical description and increase statistical precision, whereas geostatistics often seeks to generate spatial predictions. The prediction focus of the latter provides a link between these two subdisciplines through the missing data problem. The exact algebraic correspondence established with this spatial prediction/missing data linkage emphasizes that spatial autoregression directly deals with the inverse-variance covariance matrix while geostatistics directly deals with the variance-covariance matrix itself(§1.1).