Thanks Liam, OK, I'm starting to understand this better. But I'm not sure what now to do. Given that the mathematics are such that a PGLS gives significance in one direction, but not in another, what is the most convincing way to show that the two variables really ARE associated (at some level of probability) independent of phylogeny?
Ultimately I want to investigate the following: Given 2 (or more) behavioral measures, what is the probability that they are independently associated with brain size in my sample, controlling for phylogeny. I'd also like to create a prediction model that allows me to estimate what the behavioral values would be for a given brain size (of course with confidence intervals, so I could assess whether the model is really actually useful at all for prediction). Thanks for any suggestions, -Tom On Jul 11, 2013, at 5:23 PM, Liam J. Revell <liam.rev...@umb.edu> wrote: > Hi Tom. > > This is actually not a property of GLS - but of using different correlation > structures when fitting y~x vs. x~y. When you set > correlation=corPagel(...,fixed=FALSE) (the default for corPagel), gls will > fit Pagel's lambda model to the residual error in y|x. The fitted value of > lambda will almost always be different between y|x and x|y. Since the fitted > correlation structure of the residual error is used to calculate our standard > error for beta, this will affect any hypothesis test about beta. > > By contrast, if we assume a fixed error structure (OLS, as in lm; or > correlation=corBrownian(...) - the latter being the same as contrasts > regression), we will find that the P values are the same for y~x vs. x~y. > > library(phytools) > library(nlme) > tree<-pbtree(n=100) > x<-fastBM(tree) > # note I have intentionally simulated y without phylogenetic signal > y<-setNames(rnorm(n=100),names(x)) > fit.a<-gls(y~x,data.frame(x,y),correlation=corBrownian(1,tree)) > summary(fit.a) > fit.b<-gls(x~y,data.frame(x,y),correlation=corBrownian(1,tree)) > summary(fit.b) > # fit.a & fit.b should have the same P-values > fit.c<-gls(y~x,data.frame(x,y),correlation=corPagel(1,tree)) > summary(fit.c) > fit.d<-gls(x~y,data.frame(x,y),correlation=corPagel(1,tree)) > summary(fit.d) > # fit.c & fit.d will most likely have different P-values > > All the best, 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 7/11/2013 12:03 AM, Tom Schoenemann wrote: >> Hi all, >> >> I ran a PGLS with two variables, call them VarA and VarB, using a >> phylogenetic tree and corPagel. When I try to predict VarA from VarB, I get >> a significant coefficient for VarB. However, if I invert this and try to >> predict VarB from VarA, I do NOT get a significant coefficient for VarA. >> Shouldn't these be both significant, or both insignificant (the actual >> outputs and calls are pasted below)? >> >> If I do a simple lm for these, I get the same significance level for the >> coefficients either way (i.e., lm(VarA ~ VarB) vs. lm(VarB ~ VarA), though >> the values of the coefficients of course differ. >> >> Can someone help me understand why the PGLS would not necessarily be >> symmetric in this same way? >> >> Thanks, >> >> -Tom >> >>> outTree_group_by_brain_LambdaEst_redo1 <- gls(log_group_size_data ~ >>> log_brain_weight_data, correlation = bm.t.100species_lamEst_redo1,data = >>> DF.brain.repertoire.group, method= "ML") >>> summary(outTree_group_by_brain_LambdaEst_redo1) >> Generalized least squares fit by maximum likelihood >> Model: log_group_size_data ~ log_brain_weight_data >> Data: DF.brain.repertoire.group >> AIC BIC logLik >> 89.45152 99.8722 -40.72576 >> Correlation Structure: corPagel >> Formula: ~1 >> Parameter estimate(s): >> lambda >> 0.7522738 >> Coefficients: >> Value Std.Error t-value p-value >> (Intercept) -0.0077276 0.2628264 -0.029402 0.9766 >> log_brain_weight_data 0.4636859 0.1355499 3.420778 0.0009 >> >> Correlation: >> (Intr) >> log_brain_weight_data -0.637 >> Standardized residuals: >> Min Q1 Med Q3 Max >> -1.7225003 -0.1696079 0.5753531 1.0705308 3.0685637 >> Residual standard error: 0.5250319 >> Degrees of freedom: 100 total; 98 residual >> >> >> Here is the inverse: >> >>> outTree_brain_by_group_LambdaEst_redo1 <- gls(log_brain_weight_data ~ >>> log_group_size_data, correlation = bm.t.100species_lamEst_redo1,data = >>> DF.brain.repertoire.group, method= "ML") >>> summary(outTree_brain_by_group_LambdaEst_redo1) >> Generalized least squares fit by maximum likelihood >> Model: log_brain_weight_data ~ log_group_size_data >> Data: DF.brain.repertoire.group >> AIC BIC logLik >> -39.45804 -29.03736 23.72902 >> Correlation Structure: corPagel >> Formula: ~1 >> Parameter estimate(s): >> lambda >> 1.010277 >> Coefficients: >> Value Std.Error t-value p-value >> (Intercept) 1.2244133 0.20948634 5.844836 0.0000 >> log_group_size_data -0.0234525 0.03723828 -0.629796 0.5303 >> Correlation: >> (Intr) >> log_group_size_data -0.095 >> Standardized residuals: >> Min Q1 Med Q3 Max >> -2.0682836 -0.3859688 1.1515176 1.5908565 3.1163377 >> Residual standard error: 0.4830596 >> Degrees of freedom: 100 total; 98 residual >> >> _________________________________________________ >> 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/
