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

Emmanuel Paradis Emmanuel.Paradis at mpl.ird.fr
Thu Apr 10 16:24:16 CEST 2008

Joe Felsenstein a écrit :
> 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.)

No, you understood correctly. I simply did not think enough before
sending my message. Since ICs can be negative, it is clear that my point
was wrong from the beginning. Furthermore, likelihood reconstruction of
discrete characters is done through global optimization of the
parameters whereas contrasts are computed recursively down the tree from
the tips.


> Joe
> ----
> 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

Emmanuel Paradis
Institut de Recherche pour le Développement

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