A new information theoretical measure of global and local spatial association

In this paper a new measure of spatial association, the S statistics, is developed. The proposed measure is based on information theory by defining a spatially weighted information measure (entropy measure) that takes the spatial configuration into account. The proposed S-statistics has an intuitive interpretation, and furthermore fulfills properties that are expected from an entropy measure. Moreover, the S statistics is a global measure of spatial association that can be decomposed into Local Indicators of Spatial Association (LISA). This new measure is tested using a dataset of employment in the culture sector that was attached to the wards over Stockholm County and later compared with the results from current global and local measures of spatial association. It is shown that the proposed S statistics share many properties with Moran's I and Getis-Ord Gi statistics. The local Si statistics showed significant spatial association similar to the Gi statistic, but has the advantage of being possible to aggregate to a global measure of spatial association. The statistics can also be extended to bivariate distributions. It is shown that the commonly used Bayesian empirical approach can be interpreted as a Kullback-Leibler divergence measure. An advantage of S-statistics is that this measure select only the most robust clusters, eliminating the contribution of smaller ones composed by few observations and that may inflate the global measure.