Different significance found in zero-inflated negative binomial vs. binomial logistic regression I'm having a hard time reconciling two seemingly contradictory findings:


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*In a binomial logistic regression (where 0 is abstinent and 1 is relapsed), the 7 category nominal predictor showed significant differences between classes

*In a zero-inflated negative binomial model looking at a count dependent variable (representing # of days using drugs or alcohol), the zero-inflation model, which predicts "always 0" (so a corollary for abstinence), the 7 category nominal predictor showed NO significant differences between classes.
Both models controlled for the same covariates, and I'm just struggling with justifying the differences in text. Is it because the zero-inflated negative binomial looks at variables that predict abstinence and the binomial logistic regression looks at variables that predict differences between abstinent and relapsed? Or should they be the same and this suggest something is wrong with one of the models? 
 A: The binary zero inflation part of the model only captures the proability of excess zeros, not the probability of zeros overall. I would expect that in the negative-binomial count component of the model, the mean decreases for some classes of your predictor, thus increasing the probability of zeros.
Moreover, you could consider a hurdle model rather than a zero-inflation model which is often simpler to interpret because all zeros are modeled jointly. In fact, the zero hurdle part would coincide with your first logistic regression model.
A: First, don't just look at significance, look at effect size.
Second, since the two models ask different questions, why would you expect that they give the same answer? The logistic regression model is about abstinence vs. relapsed, the ZINB model is about number of days using a substance. It does not, as you write:

predicts "always 0" (so a corollary for abstinence), 

it predicts the number of days. The fact that one of these days is equivalent to abstinence does not change this.
