Trying to understand the pharasing in the documentation.

[Rijan Dhakal]

Hello,

In the "Known limitations" section, in the third/final paragraph there is this line: "Also, the likelihood of models with more parameters should always be lower than models with fewer parameters, which may not be true if [CAFE5 ]{}has failed to find a global maximum."

Does the term likelihood mean the L in negative natural log of L (-LnL) or is this "Model Base Final Likelihood"?

I have a fairly large dataset and want to make sure I understand the "Model Base Final Likelihood" right. Specifically:

1. With the exhaustive list of parameters "Model Base Final Likelihood": 1.13023e+06 (1,130,230?)
2. With reduced list of parameters "Model Base Final Likelihood" : 831,823

So, if likelihood in the above phrasing means "Model Base Final Likelihood", then these results are probably erroneous given that the final number for a reduced set of parameters is lower.

But, if likelihood means the L before the negative logarithm is applied then these results are probably fine given the inverse relationship. Or did I do that math wrong?

I suspect this answer has already been asked but the search bar was not the most useful given how common the keywords at issue are. So, apologies in advance.

Sincerely,
Rijan

[Hahn, Matthew]

Hi Rijan,

Thanks for your question—this is a common confusion about likelihoods (not just in CAFE). 

Indeed, CAFE is reporting -lnL, so lower numbers are better. If you are using the same dataset with different numbers of parameters, then, yes, the likelihood should be lower for the model with more parameters. If it is not, this likely means that CAFE has not converged on a global maximum in its search.

cheers,

matt

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