Hello Tom,
I will answer some of your questions below, Emmanuel and others may be better
placed to reply to some of your questions:
On 12, Mar 2012, at 7:49 PM, Tom Schoenemann wrote:
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)
Yes, the model estimates a partial regression slope and standard error, that is
the relationship between B and A controlling for the potential effects of C
(that is potential relationship between C and A).
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)
Yes, assuming there is no multicolinearity. See below...
3) There does not seem to be a significant effect of phylogeny on this
relationship, since the ML lambda estimate is: -0.09862731
Yes, when lambda tends to 0, phylogenetic and non phylogenetic methods are
expected to converge. I will note that an advantage of using PGLS methods is
that the evolutionary parameter estimated simultaneously with model fit (in
this case lambda) allows for adequate adjustment for phylogenetic signal. See a
nice paper on this by Revell 2010 in Methods in Ecology and Evolution.
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)?
Maybe Emmanuel can answer this one. You could test whether B and C are strongly
correlated, for example using PGLS. If they are repeating the analysis dropping
B from your model should result in a significant correlation between C and A,
indicating there is multicolinearity. Of course, the proper way to do all this
is to examine your data prior to analyses. What are the two traits, maybe they
are providing very similar information?
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. 72ˆ74 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?
You can look at yet another paper by Revell(2009) on this issue. The issue is
not so much whether traits present phylogenetic signal but rather whether the
residuals of a linear model present phylogenetic signal, or more precisely
whether there is covariance in the residuals because of phylogenetic
relatedness. Hence, even if you extracted the residuals of different PGLS
models you still control for phylogenetic non independence when analyzing the
relationship between those residuals.
Hope this helps!
Alejandro
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,
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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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__________________________________
Alejandro Gonzalez Voyer
Post-doc
Estación Biológica de Doñana
Consejo Superior de Investigaciones Científicas (CSIC)
Av Américo Vespucio s/n
41092 Sevilla
Spain
Tel: + 34 - 954 466700, ext 1749
E-mail: alejandro.gonza...@ebd.csic.es
Web site (Under construction):
Personal page: http://consevol.org/members/alejandro.html
Group page: http://consevol.org/index.html
For PDF copies of papers see:
http://csic.academia.edu/AlejandroGonzalezVoyer
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