How can I interpret the results of a likelihood ratio test between substitution models?

Question

[Mimmi Ahlmén]

I have estimated the dN/dS ratio with 3 different models: M0, M1a and M2a, this is an assignment, but I am having a hard time understanding why I had to do the following:

With model M0 I fixed the value of dN/dS=1 and then estimated the value which resulted in dN/dS=0.52, LR= What can I say about the result when doing the LRT test? (LR= 4.6, p<0.05). What is the purpose of comparing the one-ratio model (M0) with fixed and estimated value of dN/dS?

(Also I compared models M1a and M2a, and I understand that if M1a can be rejected in favor of M2a, this supports positive selection)

Thanks in advance!

Answer 1

[Asaf]

The concept of LRT tests is to have two nested models and then see if the parameters you add in the more complex model (the one with more parameters) makes the likelihood of the observations higher. Since there are more parameters, by definition, the likelihood has to be higher, if it doesn't help in explaining the observed values then the parameters will be ignored (beta=0). The question is how much they improved the likelihood and this was shown to behave like a chi-square statist.