use of a Likelihood Ratio Test

John Harshman harshman.diespamdie at sjm.infi.net
Wed Oct 10 17:30:46 EST 2001

In article <9q27pa$nde$1 at mercury.hgmp.mrc.ac.uk>, Brice Quenoville
<quenovib at naos.si.edu> wrote:

> Hello,
> I am using Modeltest to find the evolutionary model that best fits my
data given an assumed tree, and have a question on how one should apply
the Likelihood Ratio Test.
> My question is the following: are any two models with a different number
of free parameters nested, thus comparable through a LRT, or is there
other restrictions than just having d.f.>0?

No. Two models are nested if one is a special case of the other. For
example, HKY85 is a special case of HKY85-gamma in which the alpha
parameter = infinity. but HKY85-gamma is not a special case of GTR, and
thus is not nested within GTR, even though GTR has more parameters. (HKY85
is a special case of GTR, and HKY85-gamma is a special case of GTR-gamma.)

> Modeltest uses a "step by step with no return" in its procedure based on
LRT, and it seems to me that the model given at the end is not always the
best one. For instance I sometimes have TrN93 better than HKY, but HKY +
gamma better than TrN93 + gamma. The firsts two are compare before the
second two with Modeltest so I will end with a model equal or more complex
than TrN93. I understand this if different parameters have different,
additive and non independent effects on the Likelihood score, but then why
not make a program that would compare all possible nested models without
ordering the comparison. I would then guess that there must be other
restrictions and I am curious to know which one, or it has to do with
computation time.

My guess: non-nested models can't be compared with likelihood ratio tests.
Modeltest follows a single line (but a branching one if I recall). You
have to pick the line because only a line of nested models allows valid


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