Hi Ted.
Yes, good point.
I also pointed out in my message that the correlation should be exactly
the same when the error matrix V is a covariance matrix obtained under
pure BM. In Christian's code, however, he also fits Pagel's lambda
(using the function corPagel) - which means that his correlation will
not be the same as in IC if lambda~=1.0. Furthermore, he calculates V
as a correlation matrix (rather than covariance matrix), which means
that his correlation will not be the same as for IC if the tree is not
ultrametric (and his is nearly, but not precisely, ultrametric), even if
lambda is set to 1.0.
However, for the conditions where V is the covariance matrix obtained
under BM (i.e., V<-vcv.phylo(tree.orig);
V<-V[order(dimnames(V)[[1]]),order(dimnames(V)[[2]])];) then the
correlation from IC will be the same as from PGLS.
I hope this clarifies my earlier message!
Thanks, Liam
Liam J. Revell
NESCent, Duke University
web: http://anolis.oeb.harvard.edu/~liam/
NEW email: lrev...@nescent.org
tgarl...@ucr.edu wrote:
Maybe I am missing something here, but as IC = GLS, the correlation coefficient is the
same. GLS will not give you anything different.
Cheers,
Ted
Theodore Garland, Jr., Ph.D.
Professor
Department of Biology
University of California
Riverside, CA 92521
Phone: (951) 827-3524 = Ted's office (with answering machine)
Phone: (951) 827-5724 = Ted's lab
Phone: (951) 827-5903 = Dept. office
Home Phone: (951) 328-0820
FAX: (951) 827-4286 = Dept. office
Email: tgarl...@ucr.edu
http://biology.ucr.edu/people/faculty/Garland.html
List of all publications with PDF files:
http://biology.ucr.edu/people/faculty/Garland/GarlandPublications.html
Garland, T., Jr., and M. R. Rose, eds. 2009. Experimental evolution: concepts, methods,
and applications of selection experiments. University of California Press, Berkeley,
California.
http://www.ucpress.edu/books/pages/10604.php
Associate Director
Network for Experimental Research on Evolution
http://nere.bio.uci.edu/
(A University of California Multicampus Research Project)
---- Original message ----
Date: Sun, 27 Dec 2009 22:06:21 -0500
From: r-sig-phylo-boun...@r-project.org (on behalf of "Liam J. Revell"
<lrev...@nescent.org>)
Subject: Re: [R-sig-phylo] Estimate correlation coefficient of a linear GLS model
To: Christian Arnold <chrarn...@web.de>
Cc: r-sig-phylo@r-project.org
Hi Christian,
There was a previous discussion on the coefficient of determination
(R^2) for PGLS. It can be found in the Oct-2009 R-sig-phylo archive,
here: https://stat.ethz.ch/pipermail/r-sig-phylo/2009-October/thread.html.
Maybe you could also calculate a "generalized correlation coefficient"
as follows (for your case):
V<-corMatrix(Initialize(corStr,DF)); # this gets the correlation matrix
>from corStr (I'm not sure this is precisely right in general)
a.FemMass<-matrix(1,1,5)%*%solve(V)%*%FemMass/sum(solve(V)); # this
computes the "phylogenetic mean" from FemMass
a.HomeRange<-matrix(1,1,5)%*%solve(V)%*%HomeRange/sum(solve(V)); # this
computes the same from HomeRange
# this computes the generalized correlation coefficient
r.gls<-(FemMass-a.FemMass)%*%solve(V)%*%(HomeRange-
a.HomeRange)/sqrt(((FemMass-a.FemMass)%*%solve(V)%*%(FemMass-
a.FemMass))*((HomeRange-a.HomeRange)%*%solve(V)%*%(HomeRange-a.HomeRange)));
Incidentally, this for an ultrametric tree (yours is close to
ultrametric, but not precisely so) and lambda=1;
OR for the following:
V<-vcv.phylo(tree.orig);
V<-V[order(dimnames(V)[[1]]),order(dimnames(V)[[2]])]; # to order rows
and columns;
the previous calculations will give you exactly the same correlation
coefficient as:
pic.FemMass<-pic(FemMass,tree.orig);
pic.HomeRange<-pic(HomeRange,tree.orig);
r.pic<-cor.origin(pic.FemMass,pic.HomeRange);
Try it. - Liam
Liam J. Revell
NESCent, Duke University
web: http://anolis.oeb.harvard.edu/~liam/
NEW email: lrev...@nescent.org
Christian Arnold wrote:
Hello,
I received great support in the past in this mailing list, and I hope
that someone knows the answer to the following question as well:
I want to estimate the correlation coefficient (r) for two continuous
characters X and Y using phylogenetically independent contrasts (PIC)
and phylogenetically generalized least squares (PGLS) (with the gls
function in the nlme package) for a given phylogeny and model of
evolution. This is easy for PIC (using the pic function from the APE
package and cor.origin for example), but I am having troubles with
PGLS. The gls function fits a linear model using generalized least
squares and returns estimates for the coefficients of the linear
regression, but I don't see an estimate of r (the correlation of X and
Y) and I am not sure how to do that in the GLS case...
Here some code that can be pasted into R directly:
____________________________________________________________________
library(ape)
library(nlme)
FemMass=c(80,3.3,3.3,40,37)
HomeRange=c(3200,42,39,1250,410)
names(HomeRange) <- names(FemMass) <- c("a","b","c","d","e")
tree.orig
=read.tree(text="(((a:9.35,d:9.35):7.05,e:16.5):14.51,(b:4.8,c:4.8):26.16):64.2;")
corStr <- corPagel(value = 1,phy = tree.orig, fixed=F)
DF <- data.frame(HomeRange,FemMass)
m1 <- gls(HomeRange ~ FemMass, correlation = corStr,data = DF)
summary(m1)
____________________________________________________________________
If anyone knows how I can calculate r here, I would appreciate any
help...
Thanks,
Christian
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