Hey Ricardo -
I faced this problem myself very recently, and there is a recent exchange on the subject which seems to be an easy solution. Look up R-sig-mixed-models Digest, Vol 47, Issue 53; thread by David Stainbrook. Briefly, you can effect modeling with negative binomial distribution (which takes care of the overdispersion) on counts data by using lognormal poisson distribution. You just have to include a random effect corresponding to every observation in your data (that is, add something like (1|index) to the formula) and specify poisson family (which will by default imply log-link). You will get a warning ("Number of levels of a grouping factor for the random effects is *equal* to n, the number of observations." ) but this does not seem to matter. There is even a reference to a paper laying down the theory: Elston et al, Parasitology (2001), 122, 563-569.
cheers
Misha Matz
Over-dispersion and lmer
4 messages · mikhail matz, Ben Bolker, Ricardo Solar
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3 days later
Ricardo Solar <rrsolar at ...> writes:
Guys; Really thanks for your help!!! Always with lots of solutions! Thanks On 20 December 2011 15:59, mikhail matz <matz at ...> wrote:
Hey Ricardo - I faced this problem myself very recently, and there is a recent exchange on the subject which seems to be an easy solution. Look up R-sig-mixed-models Digest, Vol 47, Issue 53; thread by David Stainbrook. Briefly, you can effect modeling with negative binomial distribution (which takes care of the overdispersion) on counts data by using lognormal poisson distribution.
[snip]
There is even a reference to a paper laying
down the theory: Elston et al, Parasitology (2001), 122, 563-569.
See also http://glmm.wikidot.com/faq , the section on overdispersion (I tried to include a few more references there). Note that the lognormal-Poisson is *not* the same as the negative binomial distribution, although it does have the same mean-variance relation ... Ben Bolker
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