use of a Likelihood Ratio Test, new questions

John Harshman harshman.diespamdie at sjm.infi.net
Thu Oct 11 16:00:08 EST 2001

In article <9q4jd9$3kp$1 at mercury.hgmp.mrc.ac.uk>, Brice Quenoville
<quenovib at naos.si.edu> wrote:

> >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.)
> I understand the logic of this if the logic is you can't test two
different types of parameters (above: substitution rate and among site
rate variation) at the same time, but if not, can you not say that
HKY-gamma is a special case of GTR in wich alpha=infinity?

No. HKY-gamma is not a special case of GTR; it's a special case of
GTR-gamma. alpha=infinity is another way of saying that there is no
among-site rate variation. You actually can test two or more different
parameters at the same time, but the models must be nested. That is, the
more complex model must take into account all of the parameters of the
simpler model, and more. GTR has several more rate parameters than HKY:
two types of transitions instead of one, and four types of transversions
instead of one. 

> Linked to that is how  you should test gamma against SSR (site specific
rate).  With HKY for instance, shall I do HKY vsHKY gamma, then HKY-gamma
vs HKY -gamma-SSR, then HKY-gamma-SSR vs HKY-SSR? a model with SSR almost
always gives you a very lower Likelihood value than a model with gamma for
coding region, so there seems not doubt that it is better, but I'd like to
know the formal procedure. Again HKY-SSR may be a special case of
HKY-gamma with alpha=infinity and  d.f.=3 (2 for SSR and 1 for gamma).

No, HKY-SSR is not a special case of HKY-gamma, because the SSR parameters
are not taken into account by HKY-gamma. The two models are not nested.
You can add parameters, but you can't add some and take away others. I'm
afraid the Syst. Biol. article doesn't say anything about a way to test
non-nested models against each other, nor anything about SSR. You can try
testing HKY-gamma-SSR vs. HKY-SSR, if that helps. 

I'm not really familiar with SSR. Are we talking about a different rate
parameter for each site, or a priori site classes, or what? Is it possible
this model is just over-parameterized?
> The last issue of Systematic Biology has not reached Panama yet, and I
am right in the middle of these questions so sorry for the bother, I am
also posting to the entire list because I had  people asking me to forward
> Thank you,
> brice
> ---


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