[R] over-estimation Negative Binomial models

[D_Tomas]

Hi!

I have fitted a Negative Binomial model (glm.nb) and a Poisson model (glm
family=poisson) to some count data. Both have the same explanatory variables
& dataset

When I call  sum(fitted(model.poisson))  for my GLM-Poisson model, I obtain
exactly the same number of counts as my data. 

However, when I call sum(fitted(model.neg.binomial)) for my Negative
Binomial model I clearly obtain many more count data (approx 27% more
counts).

Can anyone explain why such stark contrast between the two models exist? Why
is the Negative Binomial massively over-estimating the values? 

Does it have to do with the dispersion parameter of the Negative Binomial
model?

Any thoughts or suggestions will be much appreciate it.  

Tomas

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