Re: [R-sig-phylo] PGLS vs lm
My goal, it seems to me, is to get a bunch of replications of data in which one trait shows a phylogenetic signal, but the other one does not, but also that both share some predefined correlation with each other (over time). I can then test different kinds of methods to see which would be most appropriate statistical method for this kind of problem. I can see how I could simulate traits evolving with a given correlation value over a given tree, using sim.char() in R. However, won't this leave me with traits in which both have the same phylogenetic signal? Is my only option to simulate huge numbers of traits, half of which are evolving consistent with some tree, and the other half are independent of the tree (i.e., random numbers?), and then correlate pairs (one from each of these groups), retaining just those that have the level of correlation I'm interested in exploring? Thanks for any suggestions, -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=enuser=iSSbrhwJ 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
Re: [R-sig-phylo] PGLS vs lm
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=enuser=iSSbrhwJ 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
Re: [R-sig-phylo] PGLS vs lm
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=enuser=iSSbrhwJ 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
Re: [R-sig-phylo] PGLS vs lm
Dear Santiago, I agree that evolving traits might have all sorts of complicated relationships, but that doesn't mean we shouldn't rule out simple relationships first. And besides, the most basic question one can ask - really the first question to ask - is whether there is any association at all between two variables. If we are trying to find out if such an association exists, independent of phylogeny, then we need a method that gives the same results regardless of whether which variable we look at. Of course the slope of any relationship will be different, depending on whether we are trying to predict x from y, or y from x. But that shouldn't biologically affect the covariance between the two variables. The covariance by definition is not a measure of x specifically from y, or vice-versa, it is a measure of how they both covary (there is no directionality to this). So any method that suggests one degree of confidence in this covariance if we look at x from y, and a different degree of confidence if we look at y from x, is simply not biologically valid for assessing covariance. To put it in the context of brain and group size: Is group size covarying significantly with brain size or not? Well, if you try to predict group size from brain size, then PGLS says the confidence we should have of this covariance is higher than if you try to predict brain size from group size. This makes no biological sense, and I maintain this makes PGLS invalid for assessing the significance of covariance between two variables. -Tom On Jul 22, 2013, at 2:02 AM, Santiago Claramunt sclaramunt...@gmail.com wrote: Dear Tom, If your concept of 'relationship' is a simple correlation analysis, then it may not make sense to get different estimates of the 'probability of the relationship'. But in evolutionary biology things are always more complicated than a simple correlation model. Things are not linear, causality is indirect, and, yes, observations are not independent because of phylogen (and space). We clearly need methods that are more sophisticated than a simple correlation analysis. Brain size and groups size are variables of very different nature, and their relationship may be the product of natural selection acting on lineages over evolutionary time, which form phylogenies. I don't see any problem in obtaining somewhat different results depending on how the relationship is modeled. Santiago On Jul 21, 2013, at 11:47 PM, Tom Schoenemann 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
Re: [R-sig-phylo] PGLS vs lm
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 1.17100.2444 --- 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
Re: [R-sig-phylo] PGLS vs lm
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
Re: [R-sig-phylo] PGLS vs lm
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 écrit : 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 at http://www.mail-archive.com/r-sig-phylo@r-project.org/ ___ 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/
Re: [R-sig-phylo] PGLS vs lm
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. Exactly! And it will need to incorporate measurement error in all variables as well as, eventually, uncertainly in the phylogenetic topology and branch lengths. Good luck, Ted From: r-sig-phylo-boun...@r-project.org [r-sig-phylo-boun...@r-project.org] on behalf of Emmanuel Paradis [emmanuel.para...@ird.fr] Sent: Sunday, July 14, 2013 3:18 AM To: Joe Felsenstein Cc: r-sig-phylo@r-project.org Subject: Re: [R-sig-phylo] PGLS vs lm 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 écrit : 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 at http://www.mail-archive.com/r-sig-phylo@r-project.org/ ___ 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/ ___ 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/
Re: [R-sig-phylo] PGLS vs lm
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=enuser=iSSbrhwJ 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
Re: [R-sig-phylo] PGLS vs lm
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 BIClogLik 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 Q1Med Q3Max -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. log_group_size_data
Re: [R-sig-phylo] PGLS vs lm
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 at http://www.mail-archive.com/r-sig-phylo@r-project.org/
Re: [R-sig-phylo] PGLS vs lm
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 écrit : 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 BIClogLik 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 Q1Med Q3Max -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. log_group_size_data -0.0234525 0.03723828 -0.629796 0.5303 Correlation: (Intr) log_group_size_data -0.095 Standardized residuals: Min Q1Med Q3Max -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/ ___ 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/
Re: [R-sig-phylo] PGLS vs lm
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=enuser=iSSbrhwJ 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
[R-sig-phylo] PGLS vs lm
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 BIClogLik 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 Q1Med Q3Max -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. log_group_size_data -0.0234525 0.03723828 -0.629796 0.5303 Correlation: (Intr) log_group_size_data -0.095 Standardized residuals: Min Q1Med Q3Max -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/
