Hi @kam,
Thanks for reaching out. The way RPCA and CTF produce their distances matrix is not the same as traditional beta-diversity methods. The distance matrix is calculated from the ordination itself, specifically the Euclidean distance of U (the sample/subject/time loadings) and itself. Since it is transformed via the robust centered log-ratio transform ahead of that, we call it the Aitchison distance rather than Euclidean. So, with that background, to answer your three questions above directly.
- No, I would not suggest running PCoA on the distance matrix. As you guessed, we really only produce it to assist in statistical evaluations like PERMANOVA.
- Well you can also view PC2-PCN (depending on the number of components you specified in the command). But that is its purpose to give you a view of differences in the dynamics across groups that contribute the most variance to the dataset in question.
- Yes, that is correct. Also, you may want to read this previous answer about interpreting those proportions explained, although the question was for RPCA it also applies to CTF.
Even though the workflow order occurs differently your analysis/interpretation workflow can be the same. CTF just outputs everything you need at once. I hope that helps.
Thanks,
Cameron