The negative binomial has two parameter in its distribution. Neg bin has a scale and a probability parameter. I’d imagine the scale parameter estimated in poisson regression is only one of them. Does running poisson regression give me those two parameters in the negbin?
1 Answer
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It is indeed the case that if you use family=negative.binomial (from the MASS package) that you need to specify theta. You could try running GEE fits in a loop or an optimizer with a range of theta values and selecting the one that maximizes some goodness-of-fit statistic (this is what MASS::glm.nb does).
I would suggest looking into Zuur et al's book on mixed models in ecology to see if there is anything useful there.
Ben Bolker