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Hi, I'm fitting a negative binomial GAM to my data using family=nb() so theta is estimated during the fitting process. When I then extract this theta from the model and refit the same model with family=negbin(theta) it gives a much lower AIC. I know using AIC to compare negative binomial models should be done with caution (http://r.789695.n4.nabble.com/How-to-compare-GLM-and-GAM-models-tt827923.html#a827926) but approximately it is ok. My questions are:
Is it better to do model selection with nb() or with negbin and a known theta. if the latter how do you know what theta is?
can you compare models using AIC if the theta is different for each model?