I think that Cécile' and Theodore' point is important and too often
overlooked. Using GLS models, the BLUP (Best Linear Unbiased Prediction) is
not simply obtained from the fitted line but should incorporates
information from the (evolutionary here) model.
For multivariate linear model you can also do it by specifying a tree
including both the species used to build the model and the ones you want to
predict using the “predict” function in mvMORPH (I think that Rphylopars
can deal with multivariate phylogenetic regression too).
Regarding the model comparison, I would simply avoid it (or limit it) by
fitting models flexible enough to accommodate between your BM and OLS case
and summarize the results obtained across all the trees…
Julien
De : R-sig-phylo <r-sig-phylo-boun...@r-project.org> de la part de
Theodore Garland <theodore.garl...@ucr.edu>
Envoyé : mercredi 30 juin 2021 03:26
À : Cecile Ane <cecile....@wisc.edu>
Cc : mailman, r-sig-phylo <r-sig-phylo@r-project.org>;
neovenatori...@gmail.com <neovenatori...@gmail.com>
Objet : Re: [R-sig-phylo] Model Selection and PGLS
All true. I would just add two things. First, always graph your data and
do ordinary OLS analyses as a reality check.
Second, I think this is the original paper for phylogenetic prediction:
Garland, Jr., T., and A. R. Ives. 2000. Using the past to predict the
present: confidence intervals for regression equations in phylogenetic
comparative methods. American Naturalist 155:346–364.
There, we talk about the Equivalency of the Independent-Contrasts and
Generalized Least Squares Approaches.
Cheers,
Ted
On Tue, Jun 29, 2021 at 5:01 PM Cecile Ane <cecile....@wisc.edu> wrote:
Hi Russel,
What you see is the large uncertainty in “ancestral” states, which is
part
of the intercept here. The linear relationship that you overlaid on top
of
your data is the relationship predicted at the root of the tree (as if
such
a thing existed!). There is a lot of uncertainty about the intercept,
but
much less uncertainty in the slope. It looks like the slope is not
affected
by the inclusion or exclusion of monotremes. (for one possible
reference on
the greater precision in the slope versus the intercept, there’s this:
http://dx.doi.org/10.1214/13-AOS1105 for the BM).
My second cent is that the phylogenetic predictions should be stable.
The
uncertainty in the intercept —and the large effect of including
monotremes
on the intercept— should not affect predictions, so long as you know for
which species you want to make a prediction. If you want to make
prediction
for a species in a small clade “far” from monotremes, say, then the
prediction is probably quite stable, even if you include monotremes:
this
is because the phylogenetic prediction should use the phylogenetic
relationships for the species to be predicted. A prediction that uses
the
linear relationship at the root and ignores the placement of the species
would be the worst-case scenario: for a mammal species with a completely
unknown placement within mammals.
There’s probably a number of software that do phylogenetic prediction. I
know of Rphylopars and PhyloNetworks.
my 2 cents…
Cecile
---
Cécile Ané, Professor (she/her)
H. I. Romnes Faculty Fellow
Departments of Statistics and of Botany
University of Wisconsin - Madison
www.stat.wisc.edu/~ane/<http://www.stat.wisc.edu/~ane/>
CALS statistical consulting lab:
https://calslab.cals.wisc.edu/stat-consulting/
On Jun 29, 2021, at 5:37 PM, neovenatori...@gmail.com<mailto:
neovenatori...@gmail.com> wrote:
Dear All,
So this is the main problem I'm facing (see attached figure, which
should
be small enough to post). When I calculate the best-fit line under a
Brownian model, this produces a best-fit line that more or less bypasses
the distribution of the data altogether. I did some testing and found
that
this result was driven solely by the presence of Monotremata, resulting
in
the model heavily downweighting all of the phylogenetic variation within
Theria in favor of the deep divergence between Monotremata and Theria.
Excluding Monotremata produces a PGLS fit that's comparable enough to
the
OLS and OU model fit to be justifiable (though I can't just throw out
Monotremata for the sake of throwing it out).
I am planning to do a more theoretical investigation into the effect of
Monotremata on the PGLS fit in a future study, but right now what I am
trying to do is perform a study in which I use this data to construct a
regression model that can be used to predict new data. Which is why I am
trying to use AIC to potentially justify going with OLS or an OU model
over
a Brownian model. From a practical perspective the Brownian model is
almost
unusable because it produces systematically biased estimates with high
error rates when applied to new data (error rate is roughly double that
of
both the OLS and OU model). This is especially the case because the data
must be back-transformed into an arithmetic scale to be useable, and
thus a
seemingly minor difference in regression models results in a massive
difference in predicted values. However, I need some objective test to
show
that OLS fits the data better than the Brownian model, hence why I was
going with AIC. Overall, OLS does seem to outperform the Brownian model
on
average, but the variation in AIC is so high it is hard to interpret
this.
This is kind of why I am leery of assuming a null Brownian model. A
Brownian model, if anything, does not seem to accurately model the
relationship between variables.
This is why I am having trouble figuring out how to do model selection.
Just going with accuracy statistics like percent error or standard
error of
the estimate OLS is better from a purely practical sense (it doesn't
work
for the monotreme taxa, but it turns out that estimate error in the
monotremes is only decreased by 10% in a Brownian model when it
overestimates mass by nearly 75%, so the improvement really isn't worth
it
and using this for monotremes isn't recommended in the first place), but
the reviewers are expressing skepticism over the fact that the Brownian
model produces less useable results. And I'm not entirely sure the best
way
to go about the PGLS if using one of the birth-death trees isn't ideal,
perhaps what Dr. Upham says about using the DNA tree might work better.
Ironically, an OU model might be argued to better fit the data, despite
the concerns that Dr. Bapst mentioned. Looking at the distribution of
signal even though signal is not random, it is more accurately
described as
most taxa hewing to a stable equilibrium with rapid, high magnitude
shifts
at certain evolutionary nodes, rather than the covariation between the
two
traits evolving in a Brownian fashion. I did some experiments with a PSR
curve and the results seem to favor an OU model or other models with
uneven
rates of evolution rather than a pure Brownian model.
Of course, the broader issue I am facing is trying to deal with PGLS
succinctly; the scope of the study isn't necessarily an in-depth
comparison
between different regression models, it's more looking at how this
variable
correlates with body mass for practical purposes (for which considering
phylogeny is one part of that). It's definitely something to consider
but I
am trying to avoid manuscript bloat.
Sincerely,
Russell
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