[R] The RV coinertia coefficient to interpret multivariate analysis plots

[David Bars]

Dear all community,

My issue is related to the R package (made4) that permits me to calculate
the RV coefficient of co-inertia. However, it is a theoretical question.
And if I am not mistaken, the list Usenet groups sci.stat.consult is not
currently active.

Let me explain briefly:

Through different microbiota datasets, I have plotted PCoA, db-RDA and
sPLS-DA using 3 different types of normalization methods (Total sum of
squares, cumulative sum of squares and rarefaction). For each dataset and
multivariate analysis (PCoA, db-RDA or sPLS-DA) in order to easily
interpret if the different normalization strategies creates me different or
equivalent PCoA for example, I have calculated the Procrustes sum of
squares and the RV coefficient of co-inertia. However, for the RV
coefficient of co-inertia, I have obtained the value 1 (perfect
equivalence) for the PCoA comparisons amongst the 3 methods of
normalization, and also for the db-RDA. For the sPLS-DA I have not obtained
1 for all the comparisons.

Then, my concern, it is why the comparison of 3 normalization methods
within their PCoA plots and within db-RDA plots it is always 1, meaning
that the all PCoA plots between them (the 3 normalization methods compared)
are identical and the same for the db-RDA plots.. This scenario tells me
something at a theorically level?

Why could obtain 1 for PCoA and db-RDA and not for sPLS-DA?

Thanks on advance for your comments...

David

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