# Fitting a beta-binomial model in the case of overdispersion in R

I'm estimating some count data. I have counts for say $m=100$ individuals. Unfortunately when using the Poisson regression overdispersion occurs. So I was thinking to fit a negbin model. But this is not appropriate in my case. So I assume that I can not fit a Poisson regression, because the way the Poisson distribution arises is not appropriate in my case ($n$ is not growing to infinity and $p$ is not converging to zero). So I found the beta-bin model. But quite honestly I'm absolutely not familiar in estimating beta-binomial models using R?

First of all: Does it make sense to fit a beta-bin model when anyone wants to estimate counts? Btw: If it makes sense, does anybody know a good book where the application is discribed?

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## 1 Answer

Beta binomial does sound like a good choice. Ben Bolker has a nice example of how to do it with his bbmle package here. I believe his book has more, some kind of tadpole-related example. You can get preprints of the book here. Hope this helps!

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Thanks David! But is the beta-bin model really appropriate? What I'd like to do is estimating counts, not probabilities! From this link (en.wikipedia.org/wiki/Overdispersion) the beta bin model seems to be appropriate when overdispersion occurs in a logit model... – MarkDollar Jun 13 '11 at 16:33
@Mark--the output of a beta binomial is a count distribution, just like with the binomial or Poisson. The difference is that the count distribution has mire weight in the tails--the probabilities of large IRS all values is greater. The part about the logit has to do with the guts of how to fit a glm--it would show up if you were using a binomial distribution as well. – David J. Harris Jun 13 '11 at 18:18
btw, sorry about the typos--I typed that response on my phone and didn't notice them until now. – David J. Harris Jun 13 '11 at 22:43
So: why is the negative binomial model "not appropriate in your case"? We need more information. While the negative binomial is (by far) the most commonly used overdispersed count distribution, there are other choices -- lognormal-Poisson and other more obscure distributions like the Neyman type A ... – Ben Bolker Jun 14 '11 at 13:10
PS re-reading your description ("n is not growing to infinity and p is not converging to zero") makes it sound like you do have a known denominator/maximum possible number of counts for each observation, which would indeed suggest a model like the beta-binomial -- but it's still a little hard to tell from your description – Ben Bolker Jun 14 '11 at 17:36