R help - Oct 2024 - The RV coinertia coefficient to interpret multivariate analysis plots

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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? Sun, 13 Oct 2024 13:19:09 +0200
David Bars <el.segarrenc at gmail.com> ?????:
> 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.
 
> Why could obtain 1 for PCoA and db-RDA and not for sPLS-DA?
It's hard to give a precise answer without seeing the details. For
example, how exactly was sPLS-DA calculated? Isn't it a supervised
_classification_ method, unlike the distance-based methods PCoA
(unsupervised dimensionality reduction) and db-RDA (correlation
analysis between two blocks of data)?

Perhaps the reason you couldn't get an RV coefficient of exactly 1 for
sPLS-DA with different scalings is because the method is sparse, i.e.,
it sacrifices some of its ability to explain the data in order to
obtain loadings that are exactly 0 for "unimportant" variables.
Different scalings may have resulted in different subsets of related
variables passing the "importance" threshold.

-- 
Best regards,
Ivan