[R-sig-phylo] Multiple regressions with continuous and categorical data

Joe Felsenstein joe at gs.washington.edu
Wed Apr 9 20:05:58 CEST 2008

On Wed, Apr 09, 2008 at 09:00:04AM +0200, Emmanuel Paradis wrote:

> >It is hard to think clearly about environmental variables.  They do
> >not evolve, and I am not sure we can always just treat them as
> >preferences, if they are things like (say) the temperature on an
> >island, whose residents can't move.  We could assume that the
> >environmental variable does a Brownian Motion (or an Ornstein-Uhlenbeck
> >process), but that is somewhat arbitrary, even more than it is for a 
> >phenotype.  If only there were some way to know past environmental
> >variables at interior nodes in the tree!
> >
> >>There is no statistical problem with computing contrasts from 0's and  
> >>1's. It is exactly the same.
> Actually, this sounds like a simplified version of computing the
> (relative) likelihoods of ancestral sates for a discrete two-state
> character assuming a Markovian model.

No, if you use the ordinary contrasts, they are not the same as
reconstructing ancestral states in a discrete two-state model.  Maybe
that is a better thing to do, but it is not the same anyway.

In Pagel's (1994) paper the comparative methods analysis using the
discrete states model used likelihood ratios, not just the likelihoods
of ancestral states.

(I must misunderstand what Emmanuel is saying.)

Joe Felsenstein         joe at gs.washington.edu
 Department of Genome Sciences and Department of Biology,
 University of Washington, Box 355065, Seattle, WA 98195-5065 USA

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