A New Bivariate Regression Model for the Simultaneous Analysis of Total and Severe Crashes Occurrence

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Abstract
This article presents a new regression model for the joint analysis of total crashes (accidents involving material-damage, injuries, and fatalities) and severe crashes (fatal and injury accidents only) occurring in road sections. This model was then exploited\ud to analyze some total and severe crashes observed in 260 Italian motorway tunnels with unidirectional traffic in a 4-year period. Regression parameters are estimated by the maximum likelihood method, and the cumulative residual method is used to\ud test the adequacy of the regression model through the range of annual average daily traffic (AADT) per lane. The results show that total and severe crashes are positively associated with: tunnel length, AADT per lane, percentage of trucks, and number of\ud lanes. In contrast the presence of sidewalk is not statistically significant. Furthermore, an analysis based on the negative multinomial model is carried out to understand whether the implementation of some actions taken in the last years in Italy have had some positive effects on crash occurrence. Additionally, the regression model equations of total crashes are presented for an easy estimation of the mean number of this type of accidents when traffic and tunnel geometry are known

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