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?
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.
Thanks for any input,