Theta in negative binomial GAM

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Theta in negative binomial GAM

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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 ( 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?

Thanks in advance, any help is much appreciated