Graham's right of course. Sorry about that.
You might do something like:
Si<-(Xi-matrix(1,nrow(Xi),1)%*%phyl.vcv(Xm,vcv(tree),
1)$alpha[,1])%*%pca$Evec
I also agree with Joe that you can take the phylogeny into account
whilst accounting for sampling error using his approach or that of Ives
et al. In either case you will obtain a covariance matrix among traits
the decomposition of which could be employed to compute scores for
individuals in the original space as Joe suggests. I'm not sure whether
or not it will make a difference. That probably depends on how much
uncertainty in the values of species means has been ignored.
All the best, Liam
Liam J. Revell, Associate Professor of Biology
University of Massachusetts Boston
& Profesor Asociado, Programa de Biología
Universidad del Rosario
web: http://faculty.umb.edu/liam.revell/
On 3/12/2018 11:29 AM, Graham Slater wrote:
Hi Rafael,
You need to mean-center your traits before multiplying by the matrix of
eigenvectors. Compute the vector of phylogenetic means (under BM or
Pagel’s lambda), subtract each value from the relevant column of Xm and
then compute Si. The result should be identical to the scores from your
phylogenetic PCA.
Graham
------------------------------------------------------
Graham J. Slater
Assistant Professor
Department of the Geophysical Sciences
University of Chicago
5734 S. Ellis Avenue
Chicago, IL 60637 USA
Tel: (773) 702-0249
email: gsla...@uchicago.edu <mailto:gsla...@uchicago.edu>
www.fourdimensionalbiology.com <http://www.fourdimensionalbiology.com>
On Mar 12, 2018, at 11:11 AM, Rafael S Marcondes
<raf.marcon...@gmail.com <mailto:raf.marcon...@gmail.com>> wrote:
Hi Liam,
Thank you very much for the very fast response (as usual). To try out
if I was using your approach correctly, I ran it with the
species-level data, expecting that I would get the same PC scores as
from phyl.PCA. That didn't happen though. Am I understanding/doing
something wrong?
pca<-phyl.pca(tree,Xm)
Si<-Xm%*%pca$Evec
Expected that Si would be identical to pca$S. But they aren't.
I have attached my species-level data, individual-level data, and
output of phyl.pca
Thank you,
*--
*
*Rafael Sobral Marcondes*
PhD Candidate (Systematics, Ecology and Evolution/Ornithology)
Museum of Natural Science <http://sites01.lsu.edu/wp/mns/>
Louisiana State University
119 Foster Hall
Baton Rouge, LA 70803, USA
Twitter: @brown_birds <https://twitter.com/brown_birds>
On Sun, Mar 11, 2018 at 5:16 PM Liam J. Revell <liam.rev...@umb.edu
<mailto:liam.rev...@umb.edu>> wrote:
Hi Rafael.
So far as I know, there is currently no way to explicitly take into
account sampling error in computing principal components while also
accounting for the phylogeny. However, it is relatively
straightforward
to compute scores for individuals from a PCA conducted on species
means.
This would look as follows (in which Xm is a matrix containing values
for species for each trait, and Xi is a matrix with the same number of
columns but containing values for individuals):
pca<-phyl.pca(tree,Xm)
Si<-Xi%*%pca$Evec
Then, if you have a separate vector containing species ID as a factor,
you could compute means and variances for each component by species.
I hope this is some help. All the best, Liam
Liam J. Revell, Associate Professor of Biology
University of Massachusetts Boston
& Profesor Asociado, Programa de Biología
Universidad del Rosario
web: http://faculty.umb.edu/liam.revell/
On 3/11/2018 5:06 PM, Rafael S Marcondes wrote:
> Dear all,
>
> Does anyone have any advice on how to calculate measurement
error in an
> analysis using phylogenetic principal components? Or, in other
words, after
> I run a phylogenetic PCA on species-level data, how can I
"project" my
> individual-level data into the phylogenetic PCs so I can calculate a
> standard error? I'm running my pPCA using the lambda method and the
> covariance matrix.
>
> I would think this would be an usual, simple procedure, and that
there
> would be an R function for it, but I can't for the life of me find
> anything. The recent paper by Jonathan Drury et al linked below does
> mention doing it, but without going into any detail.
>
>
http://journals.plos.org/plosbiology/article?id=10.1371/journal.pbio.2003563
>
> Thank you very much for any help,
>
>
> *--*
> *Rafael Sobral Marcondes*
> PhD Candidate (Systematics, Ecology and Evolution/Ornithology)
>
> Museum of Natural Science <http://sites01.lsu.edu/wp/mns/>
> Louisiana State University
> 119 Foster Hall
> Baton Rouge, LA 70803, USA
>
> Twitter: @brown_birds <https://twitter.com/brown_birds>
>
> [[alternative HTML version deleted]]
>
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