Some Practical Applications Of Moran'S I'S Exact Conditional Distribution

This article uses statistical results on ratios of quadratic forms to present a closed theory of Moran's I's exact conditional distribution, its moments and feasible range subject to a significant underlying Gaussian spatial process. These results allow one (i) to give by means of the conditional expectation a direct link of an observed value of Moran's I to the autocorrelation level of an underlying spatial process, (ii) to calculate the distribution of local Moran's Ii subject to the forces of a global spatial process which permits the exploration of local heterogeneities within the global process, and (iii) to distinguish between two competing spatial processes. A preliminary regression model to describe the spatial distribution of bladder cancer incidence rates in 219 counties of the former German Democratic Republic is used to demonstrate the feasibility and flexibility of the proposed exact conditional approach. Furthermore, a theoretical basis to address the migration problem in spatial epidemiology is given and tested against simple spatial clustering.