Thanks for the suggestions. I'll see if I can implement them. However, I'm curious if anyone can address my specific questions: Does it make biological sense for one variable "A" to predict another "B" significantly, but for "B" to predict "A"?
-Tom On Jul 26, 2013, at 6:42 PM, Theodore Garland Jr <theodore.garl...@ucr.edu> wrote: > Hi Tom, > > So far I have resisted jumping in here, but maybe this will help. > Come up with a model for how you think your traits of interest might evolve > together in a correlated fashion along a phylogenetic tree. > Now implement it in a computer simulation along a phylogenetic tree. > Also implement the model with no correlation between the traits. > Analyze the data with whatever methods you choose. > Check the Type I error rate and then the power of each method. Also check > the bias and means squared error for the parameter you are trying to estimate. > See what method works best. > Use that method for your data if you have some confidence that the model you > used to simulate trait evolution is reasonable, based on your understanding > (and intuition) about the biology involved. > > Lots of us have done this sort of thing, e.g., check this: > > Martins, E. P., and T. Garland, Jr. 1991. Phylogenetic analyses of the > correlated evolution of continuous characters: a simulation study. Evolution > 45:534-557. > > > > Cheers, > Ted > > Theodore Garland, Jr., Professor > Department of Biology > University of California, Riverside > Riverside, CA 92521 > Office Phone: (951) 827-3524 > Wet Lab Phone: (951) 827-5724 > Dry Lab Phone: (951) 827-4026 > Home Phone: (951) 328-0820 > Skype: theodoregarland > Facsimile: (951) 827-4286 = Dept. office (not confidential) > Email: tgarl...@ucr.edu > http://www.biology.ucr.edu/people/faculty/Garland.html > http://scholar.google.com/citations?hl=en&user=iSSbrhwAAAAJ > > Inquiry-based Middle School Lesson Plan: > "Born to Run: Artificial Selection Lab" > http://www.indiana.edu/~ensiweb/lessons/BornToRun.html > > From: r-sig-phylo-boun...@r-project.org [r-sig-phylo-boun...@r-project.org] > on behalf of Tom Schoenemann [t...@indiana.edu] > Sent: Friday, July 26, 2013 3:21 PM > To: Tom Schoenemann > Cc: r-sig-phylo@r-project.org > Subject: Re: [R-sig-phylo] PGLS vs lm > > OK, so I haven't gotten any responses that convince me that PGLS isn't > biologically suspect. At the risk of thinking out loud to myself here, I > wonder if my finding might have to do with the method detecting phylogenetic > signal in the error (residuals?): > > From: > Revell, L. J. (2010). Phylogenetic signal and linear regression on species > data. Methods in Ecology and Evolution, 1(4), 319-329. > > I note the following: "...the suitability of a phylogenetic regression should > actually be diagnosed by estimating phylogenetic signal in the residual > deviations of Y given our predictors (X1, X2, etc.)." > > Let's say one variable, "A", has a strong evolutionary signal, but the other, > variable "B", does not. Would we expect this to affect a PGLS differently if > we use A to predict B, vs. using B to predict A? > > If so, it would explain my findings. However, given the difference, I can > have no confidence that there is, or is not, a significant covariance between > A and B independent of phylogeny. Doesn't this finding call into question the > method itself? > > More directly, how is one to interpret such a finding? Is there, or is there > not, a significant biological association? > > -Tom > > > On Jul 21, 2013, at 11:47 PM, Tom Schoenemann <t...@indiana.edu> wrote: > > > Thanks Liam, > > > > A couple of questions: > > > > How does one do a hypothesis test on a regression, controlling for > > phylogeny, if not using PGLS as I am doing? I realize one could use > > independent contrasts, though I was led to believe that is equivalent to a > > PGLS with lambda = 1. > > > > I take it from what you wrote that the PGLS in caper does a ML of lambda > > only on y, when doing the regression? Isn't this patently wrong, > > biologically speaking? Phylogenetic effects could have been operating on > > both x and y - we can't assume that it would only be relevant to y. > > Shouldn't phylogenetic methods account for both? > > > > You say you aren't sure it is a good idea to jointly optimize lambda for x > > & y. Can you expand on this? What would be a better solution (if there is > > one)? > > > > Am I wrong that it makes no evolutionary biological sense to use a method > > that gives different estimates of the probability of a relationship based > > on the direction in which one looks at the relationship? Doesn't the fact > > that the method gives different answers in this way invalidate the method > > for taking phylogeny into account when assessing relationships among > > biological taxa? How could it be biologically meaningful for phylogeny to > > have a greater influence when x is predicting y, than when y is predicting > > x? Maybe I'm missing something here. > > > > -Tom > > > > > > On Jul 21, 2013, at 8:59 PM, Liam J. Revell <liam.rev...@umb.edu> wrote: > > > >> Hi Tom. > >> > >> Joe pointed out that if we assume that our variables are multivariate > >> normal, then a hypothesis test on the regression is the same as a test > >> that cov(x,y) is different from zero. > >> > >> If you insist on using lambda, one logical extension to this might be to > >> jointly optimize lambda for x & y (following Freckleton et al. 2002) and > >> then fix the value of lambda at its joint MLE during GLS. This would at > >> least have the property of guaranteeing that the P-values for y~x and x~y > >> are the same.... > >> > >> I previously posted code for joint estimation of lambda on my blog here: > >> http://blog.phytools.org/2012/09/joint-estimation-of-pagels-for-multiple.html. > >> > >> With this code to fit joint lambda, our analysis would then look something > >> like this: > >> > >> require(phytools) > >> require(nlme) > >> lambda<-joint.lambda(tree,cbind(x,y))$lambda > >> fit1<-gls(y~x,data=data.frame(x,y),correlation=corPagel(lambda,tree,fixed=TRUE)) > >> fit2<-gls(x~y,data=data.frame(x,y),correlation=corPagel(lambda,tree,fixed=TRUE)) > >> > >> I'm not sure that this is a good idea - but it is possible.... > >> > >> - Liam > >> > >> Liam J. Revell, Assistant Professor of Biology > >> University of Massachusetts Boston > >> web: http://faculty.umb.edu/liam.revell/ > >> email: liam.rev...@umb.edu > >> blog: http://blog.phytools.org > >> > >> On 7/21/2013 6:15 PM, Tom Schoenemann wrote: > >>> Hi all, > >>> > >>> I'm still unsure of how I should interpret results given that using PGLS > >>> to predict group size from brain size gives different significance > >>> levels and lambda estimates than when I do the reverse (i.e., predict > >>> brain size from group size). Biologically, I don't think this makes any > >>> sense. If lambda is an estimate of the phylogenetic signal, what > >>> possible evolutionary and biological sense are we to make if the > >>> estimates of lambda are significantly different depending on which way > >>> the association is assessed? I understand the mathematics may allow > >>> this, but if I can't make sense of this biologically, then doesn't it > >>> call into question the use of this method for these kinds of questions > >>> in the first place? What am I missing here? > >>> > >>> Here is some results from data I have that illustrate this (notice that > >>> the lambda values are significantly different from each other): > >>> > >>> Group size predicted by brain size: > >>> > >>>> model.group.by.brain<-pgls(log(GroupSize) ~ log(AvgBrainWt), data = > >>>> primate_tom, lambda='ML') > >>>> summary(model.group.by.brain) > >>> > >>> Call: > >>> pgls(formula = log(GroupSize) ~ log(AvgBrainWt), data = primate_tom, > >>> lambda = "ML") > >>> > >>> Residuals: > >>> Min 1Q Median 3Q Max > >>> -0.27196 -0.07638 0.00399 0.10107 0.43852 > >>> > >>> Branch length transformations: > >>> > >>> kappa [Fix] : 1.000 > >>> lambda [ ML] : 0.759 > >>> lower bound : 0.000, p = 4.6524e-08 > >>> upper bound : 1.000, p = 2.5566e-10 > >>> 95.0% CI : (0.485, 0.904) > >>> delta [Fix] : 1.000 > >>> > >>> Coefficients: > >>> Estimate Std. Error t value Pr(>|t|) > >>> (Intercept) -0.080099 0.610151 -0.1313 0.895825 > >>> log(AvgBrainWt) 0.483366 0.136694 3.5361 0.000622 *** > >>> --- > >>> Signif. codes: 0 �***� 0.001 �**� 0.01 �*� 0.05 �.� 0.1 > >>> � � 1 > >>> > >>> Residual standard error: 0.1433 on 98 degrees of freedom > >>> Multiple R-squared: 0.1132, Adjusted R-squared: 0.1041 > >>> F-statistic: 12.5 on 2 and 98 DF, p-value: 1.457e-05 > >>> > >>> > >>> Brain size predicted by group size: > >>> > >>>> model.brain.by.group<-pgls(log(AvgBrainWt) ~ log(GroupSize), data = > >>>> primate_tom, lambda='ML') > >>>> summary(model.brain.by.group) > >>> > >>> Call: > >>> pgls(formula = log(AvgBrainWt) ~ log(GroupSize), data = primate_tom, > >>> lambda = "ML") > >>> > >>> Residuals: > >>> Min 1Q Median 3Q Max > >>> -0.38359 -0.08216 0.00902 0.05609 0.27443 > >>> > >>> Branch length transformations: > >>> > >>> kappa [Fix] : 1.000 > >>> lambda [ ML] : 1.000 > >>> lower bound : 0.000, p = < 2.22e-16 > >>> upper bound : 1.000, p = 1 > >>> 95.0% CI : (0.992, NA) > >>> delta [Fix] : 1.000 > >>> > >>> Coefficients: > >>> Estimate Std. Error t value Pr(>|t|) > >>> (Intercept) 2.740932 0.446943 6.1326 1.824e-08 *** > >>> log(GroupSize) 0.050780 0.043363 1.1710 0.2444 > >>> --- > >>> Signif. codes: 0 �***� 0.001 �**� 0.01 �*� 0.05 �.� 0.1 > >>> � � 1 > >>> > >>> Residual standard error: 0.122 on 98 degrees of freedom > >>> Multiple R-squared: 0.0138, Adjusted R-squared: 0.003737 > >>> F-statistic: 1.371 on 2 and 98 DF, p-value: 0.2586 > >>> > >>> > >>> On Jul 14, 2013, at 6:18 AM, Emmanuel Paradis <emmanuel.para...@ird.fr> > >>> wrote: > >>> > >>>> Hi all, > >>>> > >>>> I would like to react a bit on this issue. > >>>> > >>>> Probably one problem is that the distinction "correlation vs. > >>>> regression" is not the same for independent data and for phylogenetic > >>>> data. > >>>> > >>>> Consider the case of independent observations first. Suppose we are > >>>> interested in the relationship y = b x + a, where x is an environmental > >>>> variable, say latitude. We can get estimates of b and a by moving to 10 > >>>> well-chosen locations, sampling 10 observations of y (they are > >>>> independent) and analyse the 100 data points with OLS. > >>> Here we cannot say anything about the correlation between x and y > >>> because we controlled the distribution of x. In practice, even if x is > >>> not controlled, this approach is still valid as long as the observations > >>> are independent. > >>>> > >>>> With phylogenetic data, x is not controlled if it is measured "on the > >>>> species" -- in other words it's an evolving trait (or intrinsic > >>>> variable). x may be controlled if it is measured "outside the species" > >>>> (extrinsic variable) such as latitude. So the case of using regression > >>>> or correlation is not the same than above. > >>> Combining intrinsic and extinsic variables has generated a lot of debate > >>> in the literature. > >>>> > >>>> I don't think it's a problem of using a method and not another, but > >>>> rather to use a method keeping in mind what it does (and its > >>>> assumptions). Apparently, Hansen and Bartoszek consider a range of > >>>> models including regression models where, by contrast to GLS, the > >>>> evolution of the predictors is modelled explicitly. > >>>> > >>>> If we want to progress in our knowledge on how evolution works, I think > >>>> we have to not limit ourselves to assess whether there is a > >>>> relationship, but to test more complex models. The case presented by Tom > >>>> is particularly relevant here (at least to me): testing whether group > >>>> size affects brain size or the opposite (or both) is an > >>> important question. There's been also a lot of debate whether > >>> comparative data can answer this question. Maybe what we need here is an > >>> approach based on simultaneous equations (aka structural equation > >>> models), but I'm not aware whether this exists in a phylogenetic > >>> framework. The approach by Hansen and Bartoszek could be a step in this > >>> direction. > >>>> > >>>> Best, > >>>> > >>>> Emmanuel > >>>> > >>>> Le 13/07/2013 02:59, Joe Felsenstein a �crit : > >>>>> > >>>>> Tom Schoenemann asked me: > >>>>> > >>>>>> With respect to your crankiness, is this the paper by Hansen that you > >>>>>> are referring to?: > >>>>>> > >>>>>> Bartoszek, K., Pienaar, J., Mostad, P., Andersson, S., & Hansen, T. F. > >>>>>> (2012). A phylogenetic comparative method for studying multivariate > >>>>>> adaptation. Journal of Theoretical Biology, 314(0), 204-215. > >>>>>> > >>>>>> I wrote Bartoszek to see if I could get his R code to try the method > >>>>>> mentioned in there. If I can figure out how to apply it to my data, > >>>>>> that will be great. I agree that it is clearly a mistake to assume one > >>>>>> variable is responding evolutionarily only to the current value of > >>>>>> the other (predictor variables). > >>>>> > >>>>> I'm glad to hear that *somebody* here thinks it is a mistake (because > >>>>> it really is). I keep mentioning it here, and Hansen has published > >>>>> extensively on it, but everyone keeps saying "Well, my friend used it, > >>>>> and he got tenure, so it must be OK". > >>>>> > >>>>> The paper I saw was this one: > >>>>> > >>>>> Hansen, Thomas F & Bartoszek, Krzysztof (2012). Interpreting the > >>>>> evolutionary regression: The interplay between observational and > >>>>> biological errors in phylogenetic comparative studies. Systematic > >>>>> Biology 61 (3): 413-425. ISSN 1063-5157. > >>>>> > >>>>> J.F. > >>>>> ---- > >>>>> Joe Felsenstein j...@gs.washington.edu > >>>>> Department of Genome Sciences and Department of Biology, > >>>>> University of Washington, Box 355065, Seattle, WA 98195-5065 USA > >>>>> > >>>>> _______________________________________________ > >>>>> R-sig-phylo mailing list - R-sig-phylo@r-project.org > >>>>> https://stat.ethz.ch/mailman/listinfo/r-sig-phylo > >>>>> Searchable archive > >>>>> athttp://www.mail-archive.com/r-sig-phylo@r-project.org/ > >>>>> > >>> > >>> _________________________________________________ > >>> P. Thomas Schoenemann > >>> > >>> Associate Professor > >>> Department of Anthropology > >>> Cognitive Science Program > >>> Indiana University > >>> Bloomington, IN 47405 > >>> Phone: 812-855-8800 > >>> E-mail: t...@indiana.edu > >>> > >>> Open Research Scan Archive (ORSA) Co-Director > >>> Consulting Scholar > >>> Museum of Archaeology and Anthropology > >>> University of Pennsylvania > >>> > >>> http://www.indiana.edu/~brainevo > >>> > >>> > >>> > >>> > >>> > >>> > >>> > >>> > >>> > >>> > >>> > >>> [[alternative HTML version deleted]] > >>> > >>> _______________________________________________ > >>> R-sig-phylo mailing list - R-sig-phylo@r-project.org > >>> https://stat.ethz.ch/mailman/listinfo/r-sig-phylo > >>> Searchable archive at > >>> http://www.mail-archive.com/r-sig-phylo@r-project.org/ > >> > > > > _________________________________________________ > > P. Thomas Schoenemann > > > > Associate Professor > > Department of Anthropology > > Cognitive Science Program > > Indiana University > > Bloomington, IN 47405 > > Phone: 812-855-8800 > > E-mail: t...@indiana.edu > > > > Open Research Scan Archive (ORSA) Co-Director > > Consulting Scholar > > Museum of Archaeology and Anthropology > > University of Pennsylvania > > > > http://www.indiana.edu/~brainevo > > > > > > > > > > > > > > > > > > > > > > > > [[alternative HTML version deleted]] > > > > _______________________________________________ > > R-sig-phylo mailing list - R-sig-phylo@r-project.org > > https://stat.ethz.ch/mailman/listinfo/r-sig-phylo > > Searchable archive at http://www.mail-archive.com/r-sig-phylo@r-project.org/ > > _________________________________________________ > P. Thomas Schoenemann > > Associate Professor > Department of Anthropology > Cognitive Science Program > Indiana University > Bloomington, IN 47405 > Phone: 812-855-8800 > E-mail: t...@indiana.edu > > Open Research Scan Archive (ORSA) Co-Director > Consulting Scholar > Museum of Archaeology and Anthropology > University of Pennsylvania > > http://www.indiana.edu/~brainevo > > > > > > > > > > > > [[alternative HTML version deleted]] > > _______________________________________________ > R-sig-phylo mailing list - R-sig-phylo@r-project.org > https://stat.ethz.ch/mailman/listinfo/r-sig-phylo > Searchable archive at http://www.mail-archive.com/r-sig-phylo@r-project.org/ _________________________________________________ P. Thomas Schoenemann Associate Professor Department of Anthropology Cognitive Science Program Indiana University Bloomington, IN 47405 Phone: 812-855-8800 E-mail: t...@indiana.edu Open Research Scan Archive (ORSA) Co-Director Consulting Scholar Museum of Archaeology and Anthropology University of Pennsylvania http://www.indiana.edu/~brainevo [[alternative HTML version deleted]]
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