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/
