One approach to modeling count data with many zeroes, if I understand correctly, is to use a zero-inflated Poisson distribution.

I read about an alternate (to using the zero-inflated Poisson distribution) approach that I am looking for feedback on and insight into, in part because I cannot remember where I read it.

I am considering this alternate because - at least in the software I am using (lme4::lmer() in R) - it is significantly harder to carry out the zero-inflated Poisson distribution approach than the proposed alternate approach.

The approach, in cases where there are many zeroes, is to run two separate models:

  • one for whether the outcome is 0 or 1 (so a binomial distribution)
  • one for - if the outcome is greater than 0 - what the number is (so a Poisson distribution)

I think for both, the predictor variables are exponentiated / the log of the outcome is used (if I understand how log link functions work).

Does this two-step approach sound like a reasonable approach to modeling such data?

In the case that data with many zeroes can be identified through a histogram, here is one of the response variables in my specific use case.

histogram of dv

  • $\begingroup$ the mixture distribution you describe is a 0-inflated Poisson probability model. $\endgroup$
    – AdamO
    Commented Oct 12, 2017 at 17:56
  • $\begingroup$ Oh. Does my approach to estimating that (in two separate steps) differ from how it is normally done (I assume on one step / in one model)? $\endgroup$ Commented Oct 12, 2017 at 17:58
  • 1
    $\begingroup$ I should clarify my comment, thanks. The 0-inflated poisson is superior to your method because it accounts for which proportion of observed 0 counts are due to not having a count, versus having a count which is 0. There is always a non-zero probability that a poisson process generates a 0 count. The 0-inf Poisson uses the EM algorithm to iteratively estimate the Binomial proportion of 0s and the lambda rate by which counts are produced. If you used your method, a reviewer or tester would certainly ask why you didn't just use a 0-inflated poisson model. $\endgroup$
    – AdamO
    Commented Oct 12, 2017 at 18:45
  • $\begingroup$ Sounds a bit like a two part model. $\endgroup$
    – dimitriy
    Commented Oct 13, 2017 at 1:04
  • $\begingroup$ The two-step approach is called a hurdle model. They are not uncommon in my field (ecology). And it's not really the same as a Poisson-bernoulli mixture (aka zero-inflated model). $\endgroup$
    – Nate Pope
    Commented Oct 13, 2017 at 1:06

1 Answer 1


A better solution would be to use Generalized Additive Models for Location, Scale and Shape. There is a R-package gamlss with plenty of documentation available online. There are a manual, a book and a website.

In the R-package, you can include random effects as available in the package lme4 using the function gamlss::re() and you have the two most common options of distribution for zero-inflated count data: Zero-Inflated Poisson and Zero-Inflated Negative Binomial (when Var > Mean).

You also have the Zero-Altered Poisson, Zero-Altered Negative Binomial, and Zero-Altered Logarithmic models that are called Hurdle models.

Thus, if you do not have a strong reason to choose a Zero-Altered Poisson (approach suggest by you), you could fit all these options and find the most appropriate model for your data.


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.