Hi All,
Responding to two of Emmanuel's points.
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.
You also get the same numbers if you compute standardized independent contrasts
in, say, PDAP of Mesquite and compare with the PGLS results from our
Regressionv2.m Matlab program (Lavin et al., 2008). And, this applies not only
for ultrametric trees (contemporaneous tips). Emmanuel, does your R code not
get the same numbers (e.g., regression equations) if the trees are
non-ultrametric? Why not?
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.
Those are good points. As a heuristic, you can always do a univariate fit of
different independent variables and look at the lm maximum likelihoods on a
star and on hierarchical trees with different sets of branch lengths. If one
independent variable showed a higher ln ML on a star whereas another showed a
higher lm MN on a hierarchical tree, then this would be evidence that their
correlations structures are different. This could be done with our PHYSIG_LL.m
Matlab program (from Blomberg et al., 2003) or with Regressionv2.m (just
pretend you are doing a regression with the trait of interest as the dependent
variable and tell it you have no independent variables). I know that does not
give a statistical test, but it would be an indicator. I am sure you could
figure out a way to do a formal test via randomization or simulation
procedures. But, maybe there is also a good way through what Simon mentioned:
We have developed Bayesian methods to fit ME models for
phylogenetic data in OpenBUGS and JAGS (submitted to Evolution).
Simon, I'd like to see the paper if you are willing to share at this stage.
Cheers,
Ted
---- Original message ----
Date: Mon, 27 Sep 2010 17:39:08 +0200
From: Emmanuel Paradis<emmanuel.para...@ird.fr>
Subject: Re: [R-sig-phylo] PIC vs. PGLS
To: Simon Blomberg<s.blombe...@uq.edu.au>
Cc: r-sig-phylo@r-project.org
>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
>>>
>>> _______________________________________________
>>> R-sig-phylo mailing list
>>> R-sig-phylo@r-project.org
>>> https://stat.ethz.ch/mailman/listinfo/r-sig-phylo
>>>
>>
>
>--
>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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