Modeling the service-route-based crash frequency by a spatiotemporal-random-effect zero-inflated negative binomial model: An empirical analysis for bus-involved crashes

Document Type

Journal Article

Publication Date


Subject Area

mode - bus, place - asia, place - urban, planning - safety/accidents, planning - methods


Bus-involved crashes, Crash frequency, Spatiotemporal-random-effect, Bus service route, Zero-inflated data


Previous studies related to bus crash frequencies modeling are limited and the statistical models are usually developed at the road segment or zonal level. This study focuses on modeling crash frequencies specifically at the bus-service-route level, which is useful and important to policymakers and bus operation companies toward the improvement of the safety level of bus networks, especially for developing countries where buses are still a major mode of urban travels. Using the observed data adopted from one of the bus operating companies in Beijing, China, we proposed a spatiotemporal-random-effect zero-inflated negative binomial (spatiotemporal ZINB) model to investigate bus crash occurrence and identity key influential factors at the bus-service-route level. The model was motivated to accommodate the special statistical characteristics of the excessive zeros and, more importantly, the potential spatiotemporal correlations of the data. Three degenerated versions of this model were also developed for comparison purposes. Results indicate that the proposed spatiotemporal ZINB model is statistically superior to the others according to a comprehensive judgment based on the EAIC, EBIC, and RMSE criteria. The estimated coefficients reveal the impacts of related factors on the likelihood of bus-involved crashes from bus operation factors including total passengers, number of drivers, and proportion of male drivers as well as planning factors including route length and stop density. On the other hand, the standard deviations of the introduced structured and unstructured spatiotemporal random-effects are statistically significant indicating that the observations are correlated within each route, between neighbor routes and across years. Corresponding policy and practical implications are provided for bus operating companies and planning departments toward the improvement of bus safety.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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