Power calculations for global and local Moran’s II

As in any statistical test, a power analysis can help in assessing the outcomes of whether global or local spatial dependencies exist. This point was briefly addressed with respect to global Moran’s II, but it has not been widely used. One reason may be that the most commonly used spatial analysis and GIS software packages do not support power analysis. Thus, apart from using the code for saddle-point approximation, applications have been restricted to employing normal approximations. An implementation of the exact distributions for global and local Moran’s II, which are integrated into the R-package spdep, is presented. Furthermore, assuming a simultaneous autoregressive spatial data generating scheme, substantial cases are provided, demonstrating the drawbacks and potential flaws of using the normal approximation in power calculations. The results confirm that, particularly for local Moran’s II, due to the smallness of sets of neighborhoods, this practice may potentially lead to errors of inference. An example concerned with Upper-Austrian migration, where using the exact distribution leads to different conclusions, is presented as well.