[R-sig-phylo] Phylogenetic Canonical Correlations
Hello all, I'm trying to perform a canonical correlations analysis that takes phylogenetic non-independence into account properly (a la what Revall 2009 did for PCA). To this effect, I've written a script to do canonical correlates in R based entirely on SVD instead of QR decomp. (because I understand SVD better) that recapitulates the cancor() function ( http://nr.com/whp/notes/CanonCorrBySVD.pdf). The way I'm currently approaching this is, I'm centering each column of X and Y on their phylogenetic mean instead of their numeric mean, and multiplying the centered matrices by the inverse of the vcv. Is this appropriate/correct? Is there a better way? Simplified example code posted below: tree - rtree(10) X - replicate(5, rnorm(10)) Y - replicate(6, rnorm(10)) rownames(X) - rownames(Y) - tree$tip.label C - vcv(tree) inC - solve(C) Ones - rep(1, nrow(X)) PMx - t(solve(t(Ones) %*% inC %*% Ones) %*% t(Ones) %*%inC %*% X) PMy - t(solve(t(Ones) %*% inC %*% Ones) %*% t(Ones) %*%inC %*% Y) pcX - invC %*% (X - Ones %*% t(PMx)) pcY - invC %*% (Y - Ones %*% t(PMy)) #SVD of X, Y and Ux'Uy Xs - svd(pcX) Ys - svd(pcY) uTu - t(Xs$u) %*% Ys$u uTus - svd(uTu) #Canonical coefficients for X A - Xs$v %*% solve(diag(Xs$d)) %*% uTus$u #Canonical coefficients for Y B - Ys$v %*% solve(diag(Ys$d)) %*% uTus$v -- Jon _ Jonathan S. Mitchell http://home.uchicago.edu/~mitchelljs/ PhD Student Committee on Evolutionary Biology The University of Chicago 1025 57th Str, Culver Hall 402 Chicago, IL 60637 Geology Department The Field Museum of Natural History 1400 S. Lake Shore Dr. Chicago, IL 60605 [[alternative HTML version deleted]] ___ R-sig-phylo mailing list R-sig-phylo@r-project.org https://stat.ethz.ch/mailman/listinfo/r-sig-phylo
Re: [R-sig-phylo] Phylogenetic Canonical Correlations
Hi Jon. phytools (http://cran.r-project.org/package=phytools) has a function, phyl.cca, for phylogenetic canonical correlations. It returns the coefficients scores (in the species space - so, with phylogenetic correlation), correlations, and p-values. You can also just use pic and cancor to get the same coefficients, as follows: # simulate data tree-rtree(50) X-replicate(5,fastBM(tree)) Y-replicate(6,fastBM(tree)) # use phyl.cca result1-phyl.cca(tree,X,Y) # use pic cancor picX-apply(X,2,pic,phy=tree) picY-apply(Y,2,pic,phy=tree) result2-cancor(picX,picY,xcenter=F,ycenter=F) Note that the coefficients from result1 and result2 may not be equal, but scale by a constant (this will not change the correlation between corresponding canonical variables). # e.g. result1$xcoef/result2$xcoef result1$ycoef/result2$ycoef[,1:5] # should produce matrices in which each column of each matrix # is a scalar constant - Liam -- Liam J. Revell, Assistant Professor of Biology University of Massachusetts Boston web: http://faculty.umb.edu/liam.revell/ email: liam.rev...@umb.edu blog: http://phytools.blogspot.com On 7/13/2012 1:32 PM, Jonathan Mitchell wrote: Hello all, I'm trying to perform a canonical correlations analysis that takes phylogenetic non-independence into account properly (a la what Revall 2009 did for PCA). To this effect, I've written a script to do canonical correlates in R based entirely on SVD instead of QR decomp. (because I understand SVD better) that recapitulates the cancor() function ( http://nr.com/whp/notes/CanonCorrBySVD.pdf). The way I'm currently approaching this is, I'm centering each column of X and Y on their phylogenetic mean instead of their numeric mean, and multiplying the centered matrices by the inverse of the vcv. Is this appropriate/correct? Is there a better way? Simplified example code posted below: tree - rtree(10) X - replicate(5, rnorm(10)) Y - replicate(6, rnorm(10)) rownames(X) - rownames(Y) - tree$tip.label C - vcv(tree) inC - solve(C) Ones - rep(1, nrow(X)) PMx - t(solve(t(Ones) %*% inC %*% Ones) %*% t(Ones) %*%inC %*% X) PMy - t(solve(t(Ones) %*% inC %*% Ones) %*% t(Ones) %*%inC %*% Y) pcX - invC %*% (X - Ones %*% t(PMx)) pcY - invC %*% (Y - Ones %*% t(PMy)) #SVD of X, Y and Ux'Uy Xs - svd(pcX) Ys - svd(pcY) uTu - t(Xs$u) %*% Ys$u uTus - svd(uTu) #Canonical coefficients for X A - Xs$v %*% solve(diag(Xs$d)) %*% uTus$u #Canonical coefficients for Y B - Ys$v %*% solve(diag(Ys$d)) %*% uTus$v -- Jon _ Jonathan S. Mitchell http://home.uchicago.edu/~mitchelljs/ PhD Student Committee on Evolutionary Biology The University of Chicago 1025 57th Str, Culver Hall 402 Chicago, IL 60637 Geology Department The Field Museum of Natural History 1400 S. Lake Shore Dr. Chicago, IL 60605 [[alternative HTML version deleted]] ___ R-sig-phylo mailing list R-sig-phylo@r-project.org https://stat.ethz.ch/mailman/listinfo/r-sig-phylo ___ R-sig-phylo mailing list R-sig-phylo@r-project.org https://stat.ethz.ch/mailman/listinfo/r-sig-phylo
[R-sig-phylo] phylogenetic signal on multistate discrete traits
Hi all,
I am new to this forum and also new to phylogenetic analysis.
I am trying to study phylogenetic signal on traits from plant
communities following an environmental gradient.
Part of my traits are continuous and for them I have used Blomberg's K.
However for the multistate discrete traits I was not able yet to run an
adequate methodology.
When exploring data, I have tried fitDiscrete {geiger} to fit a
Jukes-Cantor model to each trait (i.e. first trait :DEN1) but I always
obtain the following error:
Finding the maximum likelihood solution
[050 100]
[]
Error in fitDiscrete(treeDNNnexus, DEN1) :
ERROR: No solution found. Does your tree contain zero-length tip
branches?
Although I don't have zero-length tip branches in my phylo tree, there
are 3 pairs of species which display very small length tip branches.
Is there any alternative to run this function keeping or modifying the
characteristics of my tree?
Or, if this function couldn't be applied in my case, Does anybody
recommend an alternative methodology that could be implemented in R or
Matlab?
Thank you in advance for your help
Patricia
---
Patricia Rodríguez González
Post Doc at Centro de Estudos Florestais
Instituto Superior de Agronomia
Universidade Técnica de Lisboa
Tapada da Ajuda
1349-017 Lisboa
PORTUGAL
http://www.isa.utl.pt/cef/ForEcoGen/
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