How do you compare a gam model with a gamm model? (mgcv)

Question

I've fitted two models, one with gam and another with gamm.

gam(y ~ x, family= betar)

gamm(y ~ x)

So, the only difference is the distributional assumption. I use betar with gam and normal with gamm.

I would like to compare these two models, but I am guessing AIC will not work since the two models are based on different methods? Is there then some other suitable estimate I can use for comparison?

I know I could just fit the second with gam, but let's ignore that for the sake of this question.

Answer 1

AIC is independent of the type of model used as soon as y is exactly the same observation to be predicted. This is only a computation of deviance explained penalised by the number of parameters fitted.
However, depending on the goal of your model, if you want to be able to use the model for prediction for instance, you should use validation to compare model performance. 10-fold cross-validation would be a good idea for instance.