The Analysis of Spatial Association by Use of Distance Statistics

TLDR

The paper introduces a family of G statistics for measuring spatial association in various contexts. The authors derive the basic G statistic, detail its properties and advantages, compare it to Moran's I under hypothetical and empirical scenarios, and apply it to studies of sudden infant death syndrome in North Carolina and housing prices in San Diego. The results show that G statistics, when used alongside Moran's I, uncover local dependence patterns—particularly with G_i and G_i*—that global statistics alone miss.

Abstract

Introduced in this paper is a family of statistics, G , that can be used as a measure of spatial association in a number of circumstances. The basic statistic is derived, its properties are identified, and its advantages explained. Several of the G statistics make it possible to evaluate the spatial association of a variable within a specified distance of a single point. A comparison is made between a general G statistic and Moran's I for similar hypothetical and empirical conditions. The empirical work includes studies of sudden infant death syndrome by county in North Carolina and dwelling unit prices in metropolitan San Diego by zip‐code districts. Results indicate that G statistics should be used in conjunction with I in order to identify characteristics of patterns not revealed by the I statistic alone and, specifically, the G i and G i * statistics enable us to detect local “pockets” of dependence that may not show up when using global statistics.