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.
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.
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
-- Simon Blomberg, BSc (Hons), PhD, MAppStat, AStat Lecturer and Consultant Statistician School of Biological Sciences The University of Queensland St. Lucia Queensland 4072 Australia T: +61 7 3365 2506 email: S.Blomberg1_at_uq.edu.au http://www.uq.edu.au/~uqsblomb/ Policies: 1. I will NOT analyse your data for you. 2. Your deadline is your problem Statistics is the grammar of science - Karl Pearson. _______________________________________________ R-sig-phylo mailing list R-sig-phylo@r-project.org https://stat.ethz.ch/mailman/listinfo/r-sig-phylo