[R-sig-eco] pca or nmds (with which normalization and distance ) for abundance data ?

[Gavin Simpson]

On Fri, 2012-12-14 at 06:22 -0600, Stephen Sefick wrote:
<snip />
> >>> a) Which ordination method would be better for my data : PCA knowing
> >>> that the represented inertia is 35.62% or NMDS with a stress value about
> >>> 0.22?
> >>>
> >> My opinion is PCA on hellinger transformed relative proportions "means"
> >> more than an NMDS
> >
> > ?? NMDS with Hellinger distances could optimise a k-D PCA with Hellinger
> > transform.
> 
> Gavin, maybe I have spoken beyond my knowledge.  My though was that a 
> PCA has a unique solution and is therefore "better" (as long as an 
> appropriate distance is used that deals with the double zero problem 
> effectively).  I am sure that this is too simple for the reality of the 
> situation.  I don't know what a k-D PCA is.  Would you mind explaining 
> or directing me to some reading material?

By k-D PCA I meant that in nMDS you need to state the dimensionality; in
metaMDS() we start the process from a Principal Coordinates of the data
(PCoA == PCA when Euclidean distances used). I meant that nMDS for say
2d solutions can optimise the configuration arising from the first two
PCA axes.

I don't see the unique solution of PCA as an implicit advantage of that
method. It has a unique solution because the possible solutions are
constrained by the approach; linear combinations of the variables which
best approximate the Euclidean distances between samples. NMDS
generalises this idea extensively into a problem of best preserving the
mapping of the dissimilarities. As such it can do a better job of
drawing the map but that comes at a price.

Again though; horses for courses.

> >
> > Given that NMDS essentially subsumes PCA I'm not sure what you are
> > getting at.
> 
> I don't understand.  Would you mind explaining this?
> many thanks,

I meant in the sense that PCA is special case of Principal Coordinates
and that nMDS generalises Principal coordinates.

I don't get the point of saying one method is "better" than any other.
Each has uses etc. I certainly don't think any one method "means" more
than the other.

G

> Stephen
> 
> >
> > G
> >
> >>> b) If NMDS is more adapted which one is the better? with Hellinger
> >>> normalization and Bray-Curtis distance, or with the normalization
> >>> recommended by Legendre and Legendre and Kulcynski distance ?
> >>>
> >> I sounds like the normalization you are referring to is relative
> >> proportion which is si/sum(s); s is a vector of taxon at a site.
> >>
> >>> c) Is there other method to apply? I’m going to try co-inertia with
> >>> ade4 package
> >>>
> >>>
> >>>
> >> I am reading about co-inertia analysis now as it may be useful for some
> >> of the things that I am planning on doing.  This method looks promising.
> >>
> >> You are going to have to decide on what type of ordination to use with
> >> COIA...
> >>
> >> HTH,
> >>
> >> Stephen
> >>
> >>> Thanks in advance.
> >>>
> >>> Cheers.
> >>>
> >>> Claire Della Vedova
> >>>
> >>>
> >>>
> >>>
> >>> [[alternative HTML version deleted]]
> >>>
> >>>
> >>>
> >>> _______________________________________________
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> >>> -- 
> >>> Stephen Sefick
> >>> **************************************************
> >>> Auburn University
> >>> Biological Sciences
> >>> 331 Funchess Hall
> >>> Auburn, Alabama
> >>> 36849
> >>> **************************************************
> >>> sas0025 at auburn.edu
> >>> http://www.auburn.edu/~sas0025
> >>> **************************************************
> >>>
> >>> Let's not spend our time and resources thinking about things that are so little or so large that all they really do for us is puff us up and make us feel like gods.  We are mammals, and have not exhausted the annoying little problems of being mammals.
> >>>
> >>>                                   -K. Mullis
> >>>
> >>> "A big computer, a complex algorithm and a long time does not equal science."
> >>>
> >>>                                 -Robert Gentleman
> >>>
> >>
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