The problem of modeling (predicting) the number of road accidents on individual road segments (sections) appeared in scientific discussions about 30 years ago. For over a quarter of a century, various models and estimation methods have been used to predict the number of road accidents depending on traffic factors. This paper describes a procedure for modeling road accidents using the negative binomial distribution along with analysis of variance. This analysis demonstrated the effectiveness of the model in explaining (describing) systematic variability (over 60%).Initially, the relationship between external factors and the number of accidents was described by a deterministic linear regression equation. However, as shown by Jovanis and
Chang (1986), the variability of traffic volume over time and the frequent occurrence of zero accident counts in a sector mean that standard linear regression can lead to biased parameter estimators and even predicted negative values. In response to the problem of using linear regression, research began on the use of Poisson regression (Joshua, Garber 1990), the application of which is possible because road accident data consist of non-negative integer values. In subsequent years, extensions of Poisson regression, new models, and further estimation methods appeared. (…)
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Source: Logistyka Magazine
Negative binomial Poisson distribution in road accident modeling – PDF file for download