Thanks Rob and Alejandro,
OK, I did as suggested and ran a PGLS with A ~ B + C. I was hoping for some
clarification of the actual results. Here is a summary:
**************************************************************
Generalized least squares fit by maximum likelihood
Model: variableA ~ variableB + variableC
Data: DF.B.A.C
AIC BIC logLik
-23.49499 -10.46914 16.7475
Correlation Structure: corPagel
Formula: ~1
Parameter estimate(s):
lambda
-0.09862731
Coefficients:
Value Std.Error t-value p-value
(Intercept) 0.5229794 0.04740728 11.031625 0.0000
variableB 0.2200980 0.05012508 4.390976 0.0000
variableC 0.0620030 0.05128472 1.208996 0.2296
Correlation:
(Intr) variableB
variableB -0.813
variableC 0.362 -0.837
Standardized residuals:
Min Q1 Med Q3 Max
-3.2951355 -0.4995948 0.2604608 0.8884995 2.8456205
Residual standard error: 0.2067425
Degrees of freedom: 100 total; 97 residual
**************************************************************
Are the following correct interpretations?:
1) Controlling for the phylogeny I used, variableB is associated with variableA
independent of variableC, because the p-value of the beta weight for variableB
is highly significant (0.0000)
2) Controlling for the phylogeny I used, variableC is not significantly
associated with variableA independent of variableB, because the p-value of its
beta weight is not significant (0.2296)
3) There does not seem to be a significant effect of phylogeny on this
relationship, since the ML lambda estimate is: -0.09862731
Also, what exactly are the values listed in the "Correlation" section? Does the
-0.837 entry indicate that variableB is correlated negatively with variableC
controlling for variableA (and/or my phylogeny)?
Regarding my original plan to assess the independent relationship between
variables using residuals, the Freckleton paper Alejandro kindly forwarded
includes this comment:
"Note that to estimate the true slope for the effect of x2 using residual
regression one would need to regress the residuals of the regression on y on x1
on the residuals of the regression of x2 on x1 (e.g. see Baltagi 1999, pp.
7274 for elaboration of this)." (p. 544)
This was what I remembered about the issue myself, though I haven't kept up on
the literature Rob and Alejandro mentioned.
However, Rob believes the residuals might not be independent of phylogeny, and
that I should do a PGLS on them also. This leads to my next question: what ARE
the residuals of the PGLS then, if not also corrected for phylogeny? In the
case of my specific data, I see that the residuals from a PGLS of variableA ~
variableB are not identical to the residuals of a simple lm of variableA ~
variableB, so I assume that the phylogeny included in the PGLS is having some
effect on the residuals? Or is there another reason for the difference?
Thanks for any clarifications!
-Tom
On Mar 12, 2012, at 8:19 AM, Robert Barton wrote:
>
> Dear Tom,
>
> There is no reason to assume that the residuals from your two PGLS analyses
> will be independent of phylogeny, so if you are going to do this you should
> correlate the residuals phylogenetically (i.e. run them through PGLS).
> General problems with using residuals as data have been commented on in the
> literature by people like Freckleton, but I think that in the situation
> where each variable of interest is regressed on the same confounding
> variable it is valid to use residuals - because the correlation between the
> residuals is the same as the partial correlation between them. However, the
> simplest solution for this analysis would be to regress A on B and C in a
> single PGLS.
>
> Rob Barton
>
> On 12/03/2012 11:00, "r-sig-phylo-requ...@r-project.org"
> <r-sig-phylo-requ...@r-project.org> wrote:
>
>> 3. partial correlation with gls residuals? (Tom Schoenemann)
> Hello,
>
> I was hoping to get some feedback on whether I'm doing something legitimate.
> Basically, I have 3 variables (say: A, B, and C) measured on 100 species,
> and I want to see whether A and B correlate with each other after
> controlling for C, and for phylogeny at the same time.
>
> Here is what I thought seems reasonable:
>
> 1) do a gls with variable A predicted by variable C, using a corPagel
> correlations structure derived from a phylogeny of these species to control
> for phylogenetic effects. The residuals from this are then extracted
>
> 2) do a gls with variable B predicted by variable C, using the same method,
> also extracting the residuals for this comparison
>
> 3) do a simple lm of the residuals from step 1 vs. the residuals from step 2
>
> I guess my question is, are the residuals from the gls independent of my
> phylogeny? If they are, then wouldn't this give me the partial correlation
> between A and B, controlling for C, and for phylogeny?
>
> Or is there a better (or alternative) way to do this?
>
> Thanks for any suggestions,
>
> -Tom
>
> ---------------------------------------------------------
> Professor Robert Barton
>
> Professor of Evolutionary Anthropology
>
> President, European Human Behaviour & Evolution Association
>
> email: r.a.bar...@durham.ac.uk
>
> Address: Department of Anthropology,
> Durham University,
> Dawson Building,
> South Road,
> Durham,
> DH1 3LE
> U.K.
>
> Tel. +44 (0)191 334 1603
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>
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>
>
> Department: http://www.dur.ac.uk/anthropology/
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On Mar 12, 2012, at 6:10 AM, Alejandro Gonzalez V wrote:
> Hello,
>
> Why not simply use multiple regression ie A ~ B + C using gls and a
> correlation structure to control for phylogeny? Are you worried about
> multicolinearity?
> Use of residuals to control for the effects of a variable has been
> criticized, I include one paper on the issue by Rob Freckleton.
>
> Cheers
>
> Alejandro
> __________________________________
>
> Alejandro Gonzalez Voyer
> Post-doc
>
> Estación Biológica de Doñana (CSIC)
> Avenida Américo Vespucio s/n
> 41092 Sevilla
> Spain
>
> Tel: +34- 954 466700, ext 1749
>
> E-mail: alejandro.gonza...@ebd.csic.es
>
> Web-site (Under Construction):
> Group page: http://consevol.org/index.html
> Personal web-page: http://consevol.org/members/alejandro.html
>
_________________________________________________
P. Thomas Schoenemann
Associate Professor
Department of Anthropology
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
Homepage: http://mypage.iu.edu/~toms/
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