Hi,
can I get more information on exactly how good the approximation might
be?
The different tree models differ from each other in the joint
probability distribution by a linear transformation; therefore, the
goodness of the approximation should depend on the degree of symmetry
in the stochastic model. Worse for more symmetric models since the
alternative models are further away from the null model. Since the chi
square approximation is based on local Taylor expansion, we've
speculated that even under the best case, i.e., when the null model is
in the intersection of different topologies, the chi square
approximation should be off proportional to the subspace codimension
difference between what one assumes to be the degrees of freedom for
the alternative model (I don't know what is normally assumed) and the
actual (which differs depending on the degree of symmetry of the
stochastic model)...
Thank you,
Junhyong