[R] Estimate "between-axes" vs "within-axes heterogeneity of multivariate matrices

[Nikos Alexandris]

This time with a more-R oriented question:

Is the mrpp {vegan} package [1] useful in trying to check, or get a clue about 
the differences between- and within-axes (or variables or dimensions or 
columns) of a multivariate matrix?


The description explains:

" ...(MRPP) provides a test of whether there is a significant difference 
between two "or more groups of sampling units. ..."

"... difference may be one of location (differences in mean) or one of spread 
(differences in within-group distance) ..."

and 

"... Function mrpp operates on a data.frame matrix where rows are observations 
and responses data matrix. The response(s) may be uni- or multivariate. ..."


Question: what about the observations being actually the columns? Is a simple 
transposing of the matrix enough? Any other alternatives or hints?

Thak you, Nikos
---

[1] <http://cc.oulu.fi/~jarioksa/softhelp/vegan/html/mrpp.html>


--%<---
Nikos:
> My question(s) in the end might be silly but I am no expert on this, so
> here it goes:
> 
> Noy-Meir (1973), Pielou (1984) and a few others have pointed to
> non-centered PCA being in some cases useful. They clearly explain that "it
> is the case" when multi-dimensional data display distinct clusters (which
> have zero, or near-zero, projections in some subset of the axes) and the
> task is (exactly) to separate this clusters among the principal
> components.
> 
> I have done my complete work using prcomp() and tested combinations of
> center=FALSE/TRUE and scale=FALSE/TRUE. I would like to now check this
> "between-axes" vs "within-axes" heterogeneity of my data and cross-check
> results with the various tested PCA-versions.
> 
> Is there any (official or custom) function available in R that could answer
> this question? Some relative/comparative (preferrable simple and intuitive)
> measure(s)? Something that would graphically perhaps give an indication
> without time-consuming clustering, sampling or whatsoever processing?
> 
> Even though the above mentoined authors mention some measure for the
> assymetry of the yielded compoenents ( uncentered -> unipolar, centered ->
> bipolar) I find the concept a bit hard to understand.
> 
> Isn't there a quick way (function) to just say (with numbers of plots of
> course) "well, it seems that the data are heterogenous looking at between-
> axes" or  the other way around "it looks like the variables differ within,
> more than between"?
> 
> Apologies for repeating the same question (trying to understand the problem
> myself). Thank you, Nikos