7
$\begingroup$

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?

Improve this question
$\endgroup$
3
  • 3
    $\begingroup$ i don't quite understand what you mean by the "logit part". you might want to look at this review: jstatsoft.org/v27/i08 $\endgroup$
    – charles
    Commented Nov 26, 2013 at 17:40
  • $\begingroup$ Zero-inflated models are usually defined as two-component mixture models combining a point mass at zero with a count distribution such as negative binomial. $\endgroup$
    – charles
    Commented Nov 27, 2013 at 3:52
  • $\begingroup$ From that review: "the unobserved probability $\pi$ of belonging to the point mass component is modelled by a binomial GLM" (8). I take it @Jin-Dominique has just confused a binomial GLM with logistic regression. Then they're asking, if $\pi = 0$, isn't a ZIM just an ordinary negative binomial regression? In that case, the RHS of eqn 7 collapses to $f_{count}(y; x, \bet)$, so the first-pass answer is "yes." Differences in the way the models are fit in particular implementations might lead to different estimates, perhaps. $\endgroup$
    – Dan Hicks
    Commented Dec 3, 2017 at 19:48

1 Answer 1

Reset to default
5
$\begingroup$

You remember it wrongly: a zero-inflated negative binomial (ZINB) is a mixture of a point mass at zero and a negative binomial(NB) distribution.

$$ f_{ZINB}(Y;\pi, \mu, \theta) = \pi Z(Y) + (1-\pi)f_{NB}(Y;\mu, \theta) $$

with Z(Y) a point mass at zero. Zero observation can come from either distribution, non-zero ones only from the NB.

The "logit-part" you refer to models the mixing parameter $\pi$ as a function on covariates, assuming a binomial distribution with succes probability $\pi$.

To answer your question: yes if you set $\pi=0$ you're indeed back at the regular NB

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.