[R-sig-eco] PCA - omission of attributes in percentage data

[Jari Oksanen]

Roy,

Did the referee say *which* species to remove? 

The selection of a species to be removed will influence the results, so it is crucial to pick the "correct" species. Conclusion: the referee got it wrong.

There is a special theory of PCA of proportional data, but only removing one species does not make data non-proportional.

If you have more observations than species (and full rank data), then the maximum number of above-zero eigenvalues can be one less with proportional data than with non-proportional data. Removing one species does not change the number of above-zero eigenvalues in such a case, but it will change the sum of all eigenvalues, as well as eigenvalues of axes, and scores. So it is only the rank of the solution that is invariant with removing one species, but all other results will change. Don't do this if you can.  

Cheers, Jari Oksanen
________________________________________
From: r-sig-ecology-bounces at r-project.org [r-sig-ecology-bounces at r-project.org] on behalf of Roy Sanderson [roy.sanderson at newcastle.ac.uk]
Sent: 01 May 2012 11:51
To: r-sig-ecology at r-project.org
Subject: [R-sig-eco] PCA - omission of attributes in percentage data

Dear list

I've had a query from a referee arguing that in PCA and other multivariate methods, one attribute (typically spp) should be omitted when the sum of all attributes in each sample is 100%.  This might make sense if you only had two or three spp (not that you'd be doing a PCA with so few), but I'm less clear on why it is needed with larger numbers of spp.

Many thanks
Roy

Roy Sanderson
School of Biology
Ridley Building
Newcastle University
Newcastle upon Tyne NE1 7RU
roy.sanderson at ncl.ac.uk
Tel: 0191 222 3044

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