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 defininga spatially weighted information measure (entropy measure) that takes thespatial configuration into account. The proposed S-statistics has an intuitiveinterpretation, and furthermore fulfils properties that are expected from anentropy measure. Moreover, the S statistics is a global measure of spatialassociation that can be decomposed into Local Indicators of Spatial Association(LISA). This new measure is tested using a dataset of employmentin the culture sector that was attached to the wards over Stockholm Countyand later compared with the results from current global and local measuresof spatial association. It is shown that the proposed S statistics share manyproperties with Moran’s I and Getis-Ord Gi statistics. The local Si statisticsshowed significant spatial association similar to the Gi statistic, but has the advantage of being possible to aggregate to a global measure of spatialassociation. The statistics can also be extended to bivariate distributions.It is shown that the commonly used Bayesian empirical approach can beinterpreted as a Kullback-Leibler divergence measure. An advantage of Sstatisticsis that this measure select only the most robust clusters, eliminatingthe contribution of smaller ones composed by few observations and that mayinflate the global measure.

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