Spatial autocorrelation and spatial filtering

Abstract

This chapter provides an introductory discussion of spatial autocorrelation (SA), which refers to correlation existing and observed in geospatial data, and which characterizes data values that are not independent, but rather are tied together in overlapping subsets within a given geographic landscape. This chapter summarizes the various interpretations of SA, one being map pattern. SA can be quantified in a number of different ways, too, one being with the Moran Coefficient. Spatial filtering is a statistical method whose goal is to obtain enhanced and robust results in a spatial data analysis by decomposing a spatial variable into trend, a spatially structured random component (i.e., spatial stochastic signal), and random noise. Its aim is to separate spatially structured random components from both trend and random noise, and, consequently, leads statistical modeling to sounder statistical inference and useful visualization. This separation procedure can involve eigenfunctions of the matrix version of the numerator of the Moran Coefficient. This chapter summarizes the eigenvector spatial filtering (ESF) conceptual material, and presents the computer code for implementing ESF in R, Matlab, MINITAB, FORTRAN, and SAS. Next, it demonstrates that eigenvector spatial filter estimators are unbiased, efficient, and consistent. Finally, it summarizes an ESF empirical example application, and the extension of ESF to spatial interaction modeling.