use of a Likelihood Ratio Test, new questions

Brice Quenoville quenovib at naos.si.edu
Thu Oct 11 11:00:28 EST 2001

>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?

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).

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 answers. 

Thank you,


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