Nick,
Log-likelihoods are calculated as the logarithm of the product of the
heights of the probability density function. Since the probability
density function must integrate to 1.0, it can have a height that is
much greater than 1.0 if all the probability density is concentrated on
a small interval. (This is why rescaling eliminates this "problem" - it
spreads the probability density out over a larger interval.) Thus,
likelihoods greater than 1.0 (and log-likelihoods greater than zero) are
not impossible and should not be a concern.
- Liam
--
Liam J. Revell
University of Massachusetts Boston
web: http://faculty.umb.edu/liam.revell/
email: liam.rev...@umb.edu
blog: http://phytools.blogspot.com
On 3/7/2011 3:37 PM, Nick Matzke wrote:
Hi all,
It seems to be a popular week for questions!
I am running fitContinuous on a variety of continuous trait data. I am
noticing that when the traits are in units where the max is less than 1
(these are not ratio data, though), many of the various models produce
log-likelihoods that are positive, which ought to be impossible.
If I rescale the trait values, e.g. by multiplying them by 100, the
problem goes away and all log-likelihoods are negative, and come out
somewhat similar to each other between the BM, OU, etc. models, as one
would expect.
Any hint about why this might be?
Cheers,
Nick
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