Examining tail distributions of Moran’s I statistic through intensive simulations

Abstract

Moran’s I statistic is arguably the most widely applied method for testing spatial autocorrelation in areal datasets. This study examines its probability distribution through intensive simulation experiments with a specific focus on its tails, which are the most important for statistical testing. While Moran’s I statistic is known to be asymptotically normal when the number of zones in a study region is sufficiently large, results of this study indicate that the normality is hardly achievable even when the number of zones is increased up to 2,500. Our results also suggest that discrepancies from the normality are more serious for target variables with larger skewness and kurtosis. Simulation-based testing, which does not rely upon the assumed normality of I, is thus recommended. This study proposes to carry out multiple sets of simulations and use the mean of simulated percentage point values as critical values to reduce instability inherent in simulation-based approaches.