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?