A two-stage bivariate logistic-Tobit model for the safety analysis of signalized intersections

• Crash severity and crash frequency are evaluated sequentially and simultaneously.
• A two-stage bivariate logistic-Tobit model is proposed to address low crashes and heterogeneity.
• Crash severity is estimated by binary logistic model, and crash risks are by bivariate Tobit model.
• The results outperform the bivariate Poisson-lognormal and single bivariate Tobit models.

Crash frequency and crash severity models have explored the factors that influence intersection safety. However, most of these models address the frequency and severity independently, and miss the correlations between crash frequency models at different crash severity levels. We develop a two-stage bivariate logistic-Tobit model of the crash severity and crash risk at different severity levels. The first stage uses a binary logistic model to determine the overall crash severity level. The second stage develops a bivariate Tobit model to simultaneously evaluate the risk of a crash resulting in a slight injury and the risk of a crash resulting in a kill or serious injury (KSI). The model uses 420 observations from 262 signalized intersections in the Hong Kong metropolitan area, integrated with information on the traffic flow, geometric road design, road environment, traffic control and any crashes that occurred during 2002 and 2003. The results obtained from the first-stage binary logistic model indicate that the overall crash severity level is significantly influenced by the annual average daily traffic and number of pedestrian crossings. The results obtained from the second-stage bivariate Tobit model indicate that the factor that significantly influences the numbers of both slight injury and KSI crashes is the proportion of commercial vehicles. The existence of four or more approaches, the reciprocal of the average turning radius and the presence of a turning pocket increase the likelihood of slight injury crashes. The average lane width and cycle time affect the likelihood of KSI crashes. A comparison with existing approaches suggests that the bivariate logistic-Tobit model provides a good statistical fit and offers an effective alternative method for evaluating the safety performance at signalized intersections.