ednah at mws4.biol.berkeley.edu (Huelsenbeck) wrote:
>> Because the null hypothesis is a subset of the alternative
> hypothesis, this ratio should be asymptotically distributed as a Chi
> square probability density distribution with (n m) degrees of
> freedom
John,
Perhaps I'm misunderstanding something. The topologies aren't really
proper parameters in the classical sense, so I don't see why you
would expect an asymptotic chi-square. If I have two genes for each
of four taxa, it seems to me that I have 5p (5 branches times the
number of parameters per branch) parameters for each gene tree. Under
the full model I might have 10p parameters (5p for each gene). It
also seems that this is the case under the null. We don't add 2
parameters for the two topologies under the full model, and one for
the single topology under the null or something like that. This
problem seems analagous to that of testing two competing topologies.
Please clear this part up for me.
Having said that, it is, of course, of no concern since we must use
a Monte Carlo approach to evaluate the p-values anyway. And as
another somewhat irrelevant aside, it seems that Goldman's claim
about the unsuitability of the chi-squaare approximation was a bit
too strong. A number of us have found this approximation to be quite
good when yop have fully-specified null and alternative models. I
think that slight correction might have even popped up in a Goldman
and Yang paper somewhere along the way.
Spencer Muse