Ok, I now understand what's happening. The defaults produce only 2 bins which turns
- cat1 and cat2 into 1 2 2 1 2 2 1 2 2
- cat3 into 2 2 1 2 2 1 2 2 1
which explains the lower mutual information value (it is indeed not related to sort order!). Allowing 3 bins by modifying one line of code like so
cor.matrix.nats <- (mutinformation(discretize(df, disc="equalwidth", nbins=NROW(df)^(1/2))))
bins
- cat1 and cat2 into 1 2 3 1 2 3 1 2 3
- cat3 into 3 2 1 3 2 1 3 2 1
and now mutual information cat1 vs. cat2 = cat1 vs. cat3 = 1.0986123.
Guess I need to think about how to get a robust value for nbins in discretize not knowing in advance how many real bins across how many samples are coming in...