R help - Mar 2010 - using near-zero probabilities in optimization

Hi there

I am using mle2 for a multinomial likelihood optimization problem. My 
function works fine when I'm using simulated data, however my cell 
probabilities of the true data for the multinomial likelihood are 
sometimes very small (in some cases <0.00...) and the estimated point 
estimates fit the true vlaues quite poorly. Is there a way how to handle 
near zero probabilities in maximum likelihood optimization?

Thanks a lot for the help

best wishes

Benedikt

Benedikt Gehr <benedikt.gehr <at> ieu.uzh.ch> writes:
> 
> Hi there
> 
> I am using mle2 for a multinomial likelihood optimization problem. My 
> function works fine when I'm using simulated data, however my cell 
> probabilities of the true data for the multinomial likelihood are 
> sometimes very small (in some cases <0.00...) and the estimated point 
> estimates fit the true vlaues quite poorly. Is there a way how to handle 
> near zero probabilities in maximum likelihood optimization?
> 
  Hard to say without more detail.  Can you send a reproducible
example (your data, or a small subset of your data, or
some way of simulating the data that *does* create the problem)?

  Since you're using log-likelihoods already (within mle2) the
problem is unlikely (?) to be numerical -- R doesn't have any
problem with very large negative log-likelihoods.  Do your
likelihood profiles look reasonable?  If so then the problem
is more likely that your model doesn't fit the data well than
that you are having convergence problems.

  Have you considered the possibility of overdispersion
(non-homogeneity/non-independence), e.g. via a Dirichlet-multinomial
model?