Configurational Entropy: An Application Involving Census Tract Data for the City of Birmingham, Alabama

abstract:A variation of Shannon's relative entropy statistic is presented as a measure of configurational entropy for variables known to exhibit spatial autocorrelation using census tract data for the city of Birmingham, Alabama. Standardized and non-standardized configurational entropy indices (CEIs) are introduced to measure the amount of spatial order in a geographic distribution. As the degree of spatial autocorrelation increases and the amount of entropy or uncertainty decreases, the CEIs produce values that diverge from Shannon's statistic, which tends to overstate the degree of disorder or uncertainty in the presence of spatial autocorrelation. The CEIs incorporate a spatial covariance approach to estimating spatial order based on connectivity and the differencing of values for adjacent areal units. While Shannon's entropy statistic is insensitive to spatial arrangement, the CEIs provide a scale-targeted quantification of the amount of inherent spatial order in a distribution as defined by the connective structure of the areal units and the degree to which a variable is spatially autocorrelated. The amount of spatial order, as manifested within an autocorrelated pattern at a given geographic scale and for a given connectivity structure, is directly proportional to the difference between Shannon's measure and the CEIs.