[Question] Understanding why CLR -> Correlation is not compositionally-valid

[jolespin]

A colleague of mine asked me why use proportionality when they could instead use CLR transformation followed by Pearson/spearman/biweight midcorrelation. I vaguely remember reading why this isn't compositionally-valid but I can't seem to recall the exact details on why this shouldn't be pursued and can lead to spurious associations.

[suzannejin]

Hi @jolespin There is actually an nature issue about this : https://doi.org/10.1038/s41592-020-01006-1