I think the issue is largely one of conceptualizing the problem. People often view body size as an "independent variable" when analyzing brain size, but obviously this is a serious oversimplificaiton -- usually done for statistical convenience -- that does not reflect the biology (yes, I have also done this!). Moreover, brain mass is part of body mass, so if you use body mass per se as an independent variable then you have potential part-whole correlation statistical issues.
I would think carefully about what you are really wanting to do (e.g., regression vs. correlation vs. ANCOVA), and check over this paper: Ives, A. R., P. E. Midford, and T. Garland, Jr. 2007. Within-species variation and measurement error in phylogenetic comparative methods. Systematic Biology 56:252-270. And maybe this one: Garland, T., Jr., A. W. Dickerman, C. M. Janis, and J. A. Jones. 1993. Phylogenetic analysis of covariance by computer simulation. Systematic Biology 42:265-292. 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: Thursday, July 11, 2013 11:19 AM To: Emmanuel Paradis Cc: r-sig-phylo@r-project.org Subject: Re: [R-sig-phylo] PGLS vs lm Thanks Emmanuel, OK, so this makes sense in terms of the math involved. However, from a practical, interpretive perspective, shouldn't I assume this to mean that we actually cannot say (from this data) whether VarA and VarB ARE actually associated with each other? In the real world, if VarA is causally related to VarB, then by definition they will be associated. Doesn't this type of situation - where the associations are judged to be statistically significant in one direction but not in the other - suggest that we actually DON'T have confidence that - independent of phylogeny - VarA is associated with VarB? Putting this in the context of the actual variables involved, doesn't this mean that we actually can't be sure brain size is associated with social group size (in this dataset) independent of phylogeny? I notice that the maximum likelihood lambda estimates are different (though I'm not sure they are significantly so). I understand this could mathematically be so, but I'm concerned with how to interpret this. In the real world, how could phylogenetic relatedness affect group size predicting brain size, more than brain size predicting group size? Isn't this a logical problem (for interpretation - not for the math)? In other words, in evolutionary history, shouldn't phylogeny affect the relationship between two variables in only one way, which would show up whichever way we approached the association? Again, I understand the math may allow it, I just don't understand how it could actually be true over evolutionary time. Thanks in advance for helping me understand this better, -Tom On Jul 11, 2013, at 5:12 AM, Emmanuel Paradis <emmanuel.para...@ird.fr> wrote: > Hi Tom, > > In an OLS regression, the residuals from both regressions (varA ~ varB and > varB ~ varA) are different but their distributions are (more or less) > symmetric. So, because the residuals are independent (ie, their covariance is > null), the residual standard error will be the same (or very close in > practice). > > In GLS, the residuals are not independent, so this difference in the > distribution of the residuals affects the estimation of the residual standard > errors (because we need to estimate the covaraince of the residuals), and > consequently the associated tests. > > Best, > Emmanuel > > Le 11/07/2013 11:03, Tom Schoenemann a �crit : >> 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/ [[alternative HTML version deleted]]
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