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
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