I am trying to understand zero-inflated negative binomial regression. My impression is that if a zero-inflated negative binomial model does not contain any logit part, the model is identical to the one can obtain with just ordinary negative binomial regression. Is this correct?
PS: the logit part I was talking about - well - zero-inflated model assumes that the 0s within the dataset are generated based on two different process: one is negative binomial and the other is, if I remember it correctly, poisson. By "no logit part" I meant what if we take out the effect of the poisson distribution from the zero-inflated model? would it be same as ordinary negative binomial regression?