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/ > >_______________________________________________ >R-sig-phylo mailing list >R-sig-phylo@r-project.org >https://stat.ethz.ch/mailman/listinfo/r-sig-phylo _______________________________________________ R-sig-phylo mailing list R-sig-phylo@r-project.org https://stat.ethz.ch/mailman/listinfo/r-sig-phylo