OK, I started going through the Ives et al. paper - thanks for that. Note that my data is not brain size vs. body size, but brain size vs. social group size (not a measure for which brain size is a subset).
For our particular dataset, I believe we were not able to find much in the way of within-species variation for one of the variables - typically one report per species, and usually no variation given (but I'm not sure on that - I'll have to check). Regarding what exactly we want to do: 1) is there a significant association between brain size and two other behavioral dimensions (reported in the literature), after taking into account (as best we can) phylogeny. This is why I was trying PGLS. We probably also want to look at the relationship within clades (is there a phylogenetically appropriate version of ANCOVA?). 2) are these two other behavioral measures independently associated with brain size (after controlling for the other) - I'm assuming this would be a phylogenetically appropriate version of multiple regression But my issue is that, if I use PGLS, I get significant coefficients if I do it one direction, and not in the other. This makes me skeptical that there is a significant association in the first place. -Tom On Jul 11, 2013, at 4:32 PM, Theodore Garland Jr <theodore.garl...@ucr.edu> wrote: > 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/ _________________________________________________ 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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