Hi all,
Simon Blomberg wrote on 27/09/2010 08:10:
Hi Anne, Ted, Liam et al!,
On 25/09/10 02:51, tgarl...@ucr.edu wrote:
Hi Anne,
I am going to put this back online so others might benefit or chime in.
If you literally want to do correlations, then phylogenetically
independent contrasts may be easiest. You just compute the
standardized contrasts for each of your traits, then compute
correlations (through the origin).
The correct statistical term is "noncentral correlation." Correlation
"through the origin" makes no sense, as there is no line involved here.
Nothing is going through the origin. (Although I guess we all know what
we mean.)
You can also handle interactions with contrasts. You just need to
compute the usual 0-1 dummy variables, compute contrasts of them,
etc. This was discussed here:
Garland, T., Jr., P. H. Harvey, and A. R. Ives. 1992. Procedures for
the analysis of comparative data using phylogenetically independent
contrasts. Systematic Biology 41:18-32.
Clobert, J., T. Garland, Jr., and R. Barbault. 1998. The evolution of
demographic tactics in lizards: a test of some hypotheses concerning
life history evolution. Journal of Evolutionary Biology 11:329-364.
However, then you are most likely going to want to be back into
regression models. At this point, I refer you back to what Liam
Revell wrote.
Another interesting technical point. In general, PIC and PGLS are the
same, especially if you stick with a simple Brownian motion model of
character evolution. However, their complete mathematical identity
has not, to my knowledge, been proven.
I have a proof. I have a paper submitted to Sys. Biol. on the topic.
You can find in my book the R code to get exactly the same coefficients
with PICs and PGLS. This works as long as the tree is ultrametric (for
equal variance). It's not a formal proof, of course, but a strong suspicion.
And, some things that can easily be done with PUC cannot easily be
done with PGLS, partly because the proofs don't yet exist but also
because the code to do it does not exist (so far as I am aware). For
example, with PIC you can easily compute contrasts on a hierarchical
tree for one trait, but on star with another. Or, you can use
different sets of branch lengths for different traits if that made
biological or statistical sense to do. We have used this ability
sometimes when we have "nuisance variables" that need to be
incorporated in our set of independent variables in a multiple
regression model. Given that the nuisance variable is not
phylogenetically inherited, it makes sense to compute contrasts on a
star. We have done t!
From a biological point of view, I understand why you would want to do
that. But be aware that this means the resulting estimator will not have
minimum variance. Since the minimum variance property is a very useful
property of PIC/GLS, I don't recommend Ted's approach. Keep the same
tree for response AND explanatory variables. That way you are using the
Minimum Variance Unbiased Estimator (MVUE). If you really want to use
different trees/branch lengths for explanatory and response variables,
then you should ditch GLS/PIC and move to a Measurement Error (Errors in
Variables) model that explicitly incorporates covariance in explanatory
variables. We have developed Bayesian methods to fit ME models for
phylogenetic data in OpenBUGS and JAGS (submitted to Evolution). A good
introduction to ME models is Carrol, Ruppert, Stafanski, Crainiceanu
(2006). Measurement Error in Nonlinear Models. A Modern Perspective.
Chapman & Hall.
I share some of Simon's concern but for a different reason. I see no
problem to build complex models (and what Ted describes seems quite
exciting) as long as you do that in a hierarchical and consistent way
leading to the ability to test whether your added complexity is
statistically significant. For instance, it is not clear to me how to
test that different predictors have distinct correlation structures.
Emmanuel
hi!
!
s sort of thing here:
Wolf, C. M., T. Garland, Jr., and B. Griffith. 1998. Predictors of
avian and mammalian translocation success: reanalysis with
phylogenetically independent contrasts. Biological Conservation
86:243-255.
Perry, G., and T. Garland, Jr. 2002. Lizard home ranges revisited:
effects of sex, body size, diet, habitat, and phylogeny. Ecology
83:1870-1885.
All of this then relates back to what Liam wrote. Anyway, none of
these questions are entirely simple, nor the answers entirely
straightforward.
If the answers were straightforward, it wouldn't be so much fun!
Cheers,
Simon.
Cheers,
Ted
---- Original message ----
Date: Fri, 24 Sep 2010 17:56:46 +0200
From: Anne Kempel<kem...@ips.unibe.ch>
Subject: Re: [R-sig-phylo] (no subject)
To: tgarl...@ucr.edu
>Hi Ted,
>I guess I do regression models, since this GLS method
only does
>regressions (I have an interaction term, thats why I use
the
>phylogenetic GLS and not the PIC method). But
biologically, for those
>species traits I am analysing each one could be dependent
- e.g. the
>plants growth rate might depend on plant resistance, but
plant
>resistance also depends on the growth rate.
>All the best,
>anne
>
>
>On 24.09.2010 17:33, tgarl...@ucr.edu wrote:
>> Are you doing regression models or correlations per se?
>>
>> Cheers,
>> Ted
>>
Date: Fri 24 Sep 08:43:52 PDT 2010
From: r-sig-phylo-boun...@r-project.org Add To Address Book | This is
Spam (on behalf of "Liam J. Revell"<lrev...@nescent.org>)
Subject: Re: [R-sig-phylo] (no subject)
To: Anne Kempel<kem...@ips.unibe.ch>
Cc: r-sig-phylo@r-project.org
Hi Anne,
You should build your model based on your scientific hypothesis - not on
which trait shows phylogenetic signal. However, GLS "corrects for"
non-independence in the residual error of y given X - non-independence
which may be due to (for instance) phylogenetic history. Incidentally,
if our observations for X are non-independent due to the phylogeny, but
the residual error in y given X is uncorrelated, than GLS is not
necessary (and will actually give us an estimate with inflated variance).
I have a paper about exactly this topic that was recently published
online in the new journal "Methods in Ecology and Evolution." The
citation is:
Revell, L. J. 2010. Phylogenetic signal and linear regression on species
data. /Methods in Ecology and Evolution/ Online Early View.
And the article can be found at the following URL:
http://dx.doi.org/10.1111/j.2041-210X.2010.00044.x or on my website (URL
below).
I hope this is of some help.
- Liam
Liam J. Revell
NESCent, Duke University
web: http://anolis.oeb.harvard.edu/~liam/
NEW email: lrev...@nescent.org
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Emmanuel Paradis
IRD, Montpellier, France
ph: +33 (0)4 67 16 64 47
fax: +33 (0)4 67 16 64 40
http://ape.mpl.ird.fr/
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