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Not sure if I am pointing you in the right direction but have a look at this link
Much of the data collected on motor vehicle crashes is count data. The standard Poisson regression approach used to model this type of data does not take into account the fact there are few crash events and hence, many observed zeros. In this paper, we applied the zero-inflated Poisson (ZIP) model (which adjusts for the many observed zeros) and the negative binomial (NB) model to analyze young driver motor vehicle crashes. The results of the ZIP regression model are comparable to those from fitting a NB regression model for general over-dispersion. The findings highlight that driver confidence/adventurousness and the frequency of driving prior to licensing are significant predictors of crash outcome in the first 12 months of driving. We encourage researchers, when analyzing motor vehicle crash data, to consider the empirical frequency distribution first and to apply the ZIP and NB models in the presence of extra zeros due, for example, to under-reporting.