Thank you. In fact, rate has only been a convenience functionality for adding an offset term to not require users working with offsets. But I see now that this can have more general use as we can adjust the negative binomial distribution in a more principled manner using rate. I will make this change accordingly.
As a side note y | offset(N) won’t work (in fact it should return an error), because there is no offset addition term. I will check why this does not return an error in the first place.