In statistical papers I read about ZOIB models (e.g. liu and eugenio, 2016), if I am understanding correctly, it is parameterized with alpha = p(y=0), gamma = p(y = 1 | y != 0) and a beta distribution conditional on y !=0 and y != 1. In contrast, brms seems to parameterize the model with zoi = p(y = 0 or y = 1), coi = p(y = 1 | y = 0 or y = 1), and beta distribution.

I can’t imagine when that latter parameterization with the p(0 or 1) would be conceptually preferable. Is there some reason, perhaps related to model fitting, that I am missing?