Most exploratory data analysis projects dealing with spatial data start by looking for, and potentially filtering, spatial autocorrelation. In simple terms, this means that we are looking for spatial effects in the data—for instance, the similarities of some data points can be (partly) explained by the short distance between them; further points seem to differ a lot more. There is nothing surprising in this statement; probably all of you agree with this. But how can we test this on real data with analytical tools?

Moran's I index is a well-known and generally used measure to test whether spatial autocorrelation is present or not in the variable of interest. This is a quite simple statistical test with the null hypothesis that there is no spatial autocorrelation in the dataset.

With the current data structure we have, probably the easiest way to compute Moran's I is to load the ape package, and pass the similarity matrix along with the variable of interest to the Moran.I...