On Moran’s II coefficient under heterogeneity

Moran’s II is the most popular spatial test statistic, but its inability to incorporate heterogeneous populations has been long recognized. This article provides a limiting distribution of the Moran’s II coefficient which can be applied to heterogeneous populations. The method provides a unified framework of testing for spatial autocorrelation for both homogeneous and heterogeneous populations, thereby resolving a long standing issue for Moran’s II. For Poisson count data, a variance adjustment method is provided that solely depends on populations at risk. Simulation results are shown to be consistent with theoretical results. The application of Nebraska breast cancer data shows that the variance adjustment method is simple and effective in reducing type I error rates, which in turn will likely reduce potential misallocation of limited resources.