# Zero-inflated negative binomial regression: 0 probability of a count greater than 0

Zero-inflated negative binomial regression assumes 0s are generated by two processes: a group whose counts are generated by a negative binomial regression and a group who have a "0 probability of a count greater than 0" (source).

A friend told me, that in the "0 probability of a count greater than 0" part of the zero-inflated negative binomial regression, I should only include predictors that might theoretically lead to a "0 probability of a count greater than 0".

Using the example of Karl Ove Hufthammer here, let's we're trying to predict number of cigarettes smoked last week. Non-smokers will have a "0 probability of a count greater than 0" and so the predictor "smoker" (a true/false variable stating whether a person smokes or not) is the only predictor entered into the zero-inflated part of the model.

So the negative binomial regression part of the zero-inflated negative binomial regression would be:

number of cigarettes smoked last week ~ age + smoker


and the zero-inflated part of the zero-inflated negative binomial regression would be:

number of cigarettes smoked last week ~ smoker


My questions: (1) Why only include smoker in zero-inflated part of the zero-inflated negative binomial regression? (2) What are the consequences of this?