Abstract
In this paper we have considered several regression models to fit the count data that encounter in the field of Biometrical, Environmental, Social Sciences and Transportation Engineering. We have fitted Poisson (PO), Negative Binomial (NB), Zero-Inflated Poisson (ZIP) and Zero-Inflated Negative Binomial (ZINB) regression models to run-off-road (ROR) crash data which collected on arterial roads in south region (rural) of Florida State. To compare the performance of these models, we analyzed data with moderate to high percentage of zero counts. Because the variances were almost three times greater than the means, it appeared that both NB and ZINB models performed better than PO and ZIP models for the zero inflated and over dispersed count data.
Highlights
Many outcomes in traffic accident, clinical medicine, biomedical research that are non-negative and discrete in nature
In that cases the negative binomial (NB) distribution is a natural and more flexible extention of the Poisson distribution and allows for over-dispersion compared to Poisson distribution
Regardless of whether the assumed model is a PO, Negative Binomial (NB), Zero-Inflated Poisson (ZIP) or Zero-Inflated Negative Binomial (ZINB), it will be assumed that the occurrences will be independent of each other
Summary
Many outcomes in traffic accident, clinical medicine, biomedical research that are non-negative and discrete in nature. Several researchers have suggested to use the NB regression model as an alternative to the PO regression model when the count data are over or under dispersed. Both Poisson and Negative Binomial distribution have been used for predicting the accidents related count frequencies by Miaou (1994), Shankar et al (1995, 1997), Poch and Mannering (1996), Milton and Mannering (1998) and Lee and Mannering (2002) among others. Corresponding inflated models, say zero inflated Poisson (ZIP) and zero inflated negative binomial (ZINB) are very useful to describe the zero inflated count data.
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