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## Zero-inflated models

Zero-inflated distributions are used to model count data that have many zero counts. For example, the zero-inflated Poisson distribution might be used to model count data for which the proportion of zero counts is greater than expected on the basis of the mean of the non-zero counts.

In recent years, there has been considerable interest in regression models based on zero-inflated distributions. Much of this interest stems from the seminal paper of Lambert [Ref 1], though this type of model appears to have originated in the econometrics literature.

Clarice Demetrio, John Hinde and I wrote a review paper on models for count data with many zeros for the International Biometric Conference, Capetown, December 1998 [Ref 2]. Although this review was reasonably complete at the time, there is a substantial subsequent literature on this topic, including one contribution of our own [Ref 3].

### References

[1] Lambert, D. (1992) Zero-inflated Poisson regression, with an
application to defects in manufacturing. *Technometrics*, 34,
1-14.

[2] Ridout, M.S., Demetrio, C.G.B. and Hinde, J.P. (1998) Models
for counts data with many zeros. *Proceedings of the XIXth
International Biometric Conference*, Cape Town, Invited Papers,
pp. 179-192. [pdf]

[3] Ridout, M.S., Hinde, J.P. and Demetrio, C.G.B. (2001) A
score test for testing a zero-inflated Poisson regression model
against zero-inflated negative binomial alternatives. *Biometrics*,
57, 219-223.
[journal
link]