Generalised Linear Models, Deviance
I have fitted two generalised linear models using SAS PROC GENMOD, one for the poisson distribution and the other for the negative binomial.
I have heard that fitting the poisson distribution with dscale corrects for dispersion in the model and that using the negative binomial will help further with overdispersed data and you assess model fit using deviance.
The deviance/degrees of freedom for the poisson model is about 1.8 which is indicating overdispersion so fitting the negative binomial it is about 0.7. Does this mean that the negative binomial is a better fit. Or is it saying that the negative binomial is now underdispersed? And then which is the better fit?