Hi Sérgio.
What Simon (& I, in my blog post) suggested is that to test the
'normality assumption' you need to first transform the residuals with
the inverse Cholesky decomposite matrix. This will give you a vector in
which the values should be normal & independent (assuming that the
correlation structure of the residuals is properly given by the tree).
However these values are no longer associated with species(!) so they
cannot be used in subsequent among-species analyses. So, basically, yes
- you should use the residuals before transformation in cross-species
analyses (for instance, as 'size corrected' trait values); however you
need to remember that they are still phylogenetically correlated. I hope
that's clear enough.
All the best, Liam
Liam J. Revell, Assistant Professor of Biology
University of Massachusetts Boston
web: http://faculty.umb.edu/liam.revell/
email: [email protected]
blog: http://blog.phytools.org
On 6/18/2015 6:16 AM, Sergio Ferreira Cardoso wrote:
Hello again,
Thanks for your help. This kind of solved my problem. I normally use
some kind of test (shapiro or komolgorov) to test for normality. I know
histograms or qqnorm plots a more helpful, but they are more
"vulnerable" to each others interpretation.
So, just to make clear one thing: these kind of analysis of the residual
error
(http://blog.phytools.org/2013/02/a-comment-on-distribution-of-residuals.html)
has nothing to do with phylogenetic residuals taken from a regression
(in order to obtain relative values - size-correction as in Revell, L.
J. (2009). Size‐correction and principal components for interspecific
comparative studies. Evolution, 63(12), 3258-3268.). So even if
residuals from a PGLS aren't normal, this means I can still use them as
size-corrected values for a certain trait, correct?
Once again, thank you very much for your advices.
Best regards,
Sérgio.
2015-06-18 4:56 GMT+01:00 Simon Blomberg <[email protected]
<mailto:[email protected]>>:
Hi Sérgio.
Liam is right. But we do expect the normalised residuals to be
approximately Normal. You can calculate the normalised residuals by
pre-multiplying the raw residuals by the inverse of the Cholesky
decomposition of the phylogenetic variance-covariance matrix, and
then dividing by the estimate of the residual standard deviation (ie
sigma). You may have to plug in a value for any parameters that are
co-estimated along with the regression (Pagel's lambda, etc.). If
you use the gls function in the nlme package to fit your model, then
it's all easy:
fit <- gls(response~explanatory, correlation=corPagel(1,
phy=my.tree), data=dat))
res <- residuals(fit, type="normalized")
Then you can do some test for normality on those (I don't ordinarily
recommend such things, although
SnowsPenultimateNormalityTest in the TeachingDemos package is the
best I have seen). More usefully, you can do a normal
quantile-quantile plot to graphically see whether your normalised
residuals are normal enough:
qqnorm(fit, form=~residuals(., type="n"), abline=c(0,1))
See page 239 in Pinheiro and Bates (2000) Mixed-effects models in S
and S-PLUS.
Cheers,
Simon.
On 18/06/15 03:09, Liam J. Revell wrote:
Hi Sérgio.
It might be worth pointing out that we do not expect that the
residuals from a phylogenetic regression to be normal. I
described this with respect to the phylogenetic ANOVA on my blog
(http://blog.phytools.org/2013/02/a-comment-on-distribution-of-residuals.html),
but this applies equally to phylogenetic regression.
All the best, Liam
Liam J. Revell, Assistant Professor of Biology
University of Massachusetts Boston
web: http://faculty.umb.edu/liam.revell/
email: [email protected] <mailto:[email protected]>
blog: http://blog.phytools.org
On 6/17/2015 12:40 PM, Sergio Ferreira Cardoso wrote:
Hello all,
I'm having a problem with a Multiple Regression PGLS
analysis that I'm
performing. The residuals are not normal and it's difficult
to bring them
to normality. In these cases, are there any alternatives to
the linear
model? I know that for non-phylogenetic analyses other
models exist, but is
there any alternative method for phylogenetic analysis?
Thanks in advance.
Best regards,
Sérgio.
_______________________________________________
R-sig-phylo mailing list - [email protected]
<mailto:[email protected]>
https://stat.ethz.ch/mailman/listinfo/r-sig-phylo
Searchable archive at
http://www.mail-archive.com/[email protected]/
--
Simon Blomberg, BSc (Hons), PhD, MAppStat, AStat.
Senior Lecturer and Consultant Statistician
School of Biological Sciences
The University of Queensland
St. Lucia Queensland 4072
Australia
T: +61 7 3365 2506 <tel:%2B61%207%203365%202506>
email: S.Blomberg1_at_uq.edu.au <http://S.Blomberg1_at_uq.edu.au>
http://www.evolutionarystatistics.org
Policies:
1. I will NOT analyse your data for you.
2. Your deadline is your problem.
Basically, I'm not interested in doing research
and I never have been. I'm interested in
understanding, which is quite a different thing.
- David Blackwell
_______________________________________________
R-sig-phylo mailing list - [email protected]
<mailto:[email protected]>
https://stat.ethz.ch/mailman/listinfo/r-sig-phylo
Searchable archive at
http://www.mail-archive.com/[email protected]/
--
Com os melhores cumprimentos,
Sérgio Ferreira Cardoso.
--------------------
Best regards,
Sérgio Ferreira Cardoso
MSc. Paleontology candidate
Departamento de Ciências da Terra - FCT /Universidade Nova de Lisboa
Geociências - Universidade de Évora
Lisboa, Portugal
_______________________________________________
R-sig-phylo mailing list - [email protected]
https://stat.ethz.ch/mailman/listinfo/r-sig-phylo
Searchable archive at http://www.mail-archive.com/[email protected]/
