The traffic safety of students concerning school bus transportation and surrounding traffic is a critical issue that demands attention at every level. To ensure a comprehensive safety analysis, it is essential to consider vehicle safety, driver training, and traffic laws around schools. The advanced safety technologies in school buses play an important role in student traffic safety, such as seat belts and stability controls, notably lowering the chances of injuries2. Additionally, Johansson (2020) ’s research brings to the forefront the necessity for rigorous training programs for bus drivers, emphasizing defensive driving and emergency handling, thereby boosting the safety measures for student commutes3. On another front, legislative efforts focused on reducing speed limits and establishing protected crossing zones have been recognized for their significant impact in curtailing the incidents of traffic-related mishaps involving school-going children4 .By examining student and school bus safety through route design, vehicle, and passage, effective strategies address the potential risks and ensure the well-being of students in their commute.
Compared with other traffic modes, school bus travel can better ensure the safety of students. The crash rate of school bus travel is relatively low, while the injury and death rates of walking and cycling are higher than those of school bus travel 5 .The US has allocated $612 million in federal funds for safe routes to school programs to encourage children to use non-vehicle commuting to school to ensure traffic safety and avoid crashes 6 .According to the study of vehicle crash data in North Carolina from 2005 to 2012, the injury rate of school travel is similar to that of school buses, but the mortality rate is much higher than that of school bus 7 . By conducting an analysis of crash, fatality, and injury rates pertaining to school buses, as well as examining the disparities in crash and injury characteristics between school buses and other vehicles, it was determined that the fatality and injury rates associated with school buses were 3.5 times and 5.4 times lower than those observed for all vehicles, respectively 8 .
The safety of school bus travel is related to many factors, including the design standards of school bus, driver characteristics, and weather. The National Traffic and Motor Vehicle Safety Act gives the federal government the important responsibility of setting safety standards for motor vehicles sold in the United States. In terms of improving the safety of school buses, the study of dividing seats to improve the safety of school bus seats7 .In addition to the design of school buses has an impact on the safety of school travel, the age, driving habits, and whether they are distracted driving also have a great impact on the safety of school travel. The study found that younger school bus drivers had higher crash rates than older drivers8. On the topic of safe school bus travel, there are also studies on whether drivers are distracted during driving, and studies have shown that passenger behavior, such as disruptive behavior of children, has a greater impact on driver driving9.
The existing research on school bus crashes has primarily focused on the biomechanics or crashworthiness of catastrophic crashes, neglecting studies on crash rates. For instance, previous investigations have examined the biomechanics of injuries sustained by school bus occupants and emphasized enhancing internal design features of school buses10, as well as improving vehicle crashworthiness to reduce fatal and severe injuries. These studies have predominantly concentrated on frontal and rollover crashes, which are more likely to result in death or serious injury11 .However, such types of crashes are relatively infrequent11 .Therefore, it is imperative to explore the relationship between school bus crashes and the physical and social attributes of their surrounding environment to mitigate crash occurrences by comprehending the severity and characteristics of both school bus crashes and occupant injuries along with associated risk factors.
While many studies have analyzed crash severity, few have taken into account unobserved heterogeneity and compared different crash severity models12. A large body of literature suggests that there are unobserved effects at the spatial, temporal and severity levels. The unobserved effects of space may be due to unmeasured or hard-to-measure cross-regional variations (e.g., differences in road geometry). Due to traffic laws, economics, weather, and the temporal nature of travel demand and behavior, there may be temporal correlations in crash data13,14. Ignoring such unobserved effects in space and time may reduce the efficiency of the estimator. Therefore, more and more econometric methods have been applied in crash analysis. Using the standard negative binomial model and zero-inflated negative binomial model, Lee et al(2016)15 studied the impact of environmental attributes on the perception of traffic crash risk among school-age children at intersections near elementary schools. And findings suggest that the more students cross the street, the wider the roads, the more pedestrian crossings, and the more student-friendly facilities at intersections, the higher the perceived risk of traffic crashes among school-age children.
Meanwhile, due to the spatial dependence and spatial heterogeneity of traffic crash data16, It is particularly important to explain unobserved heterogeneity through stochastic parameter models and their extended frameworks17,18. Stochastic parameter polynomial method on mean and variance heterogeneity19,20. Random parameter logit model is a popular method to study crash damage severity21,22. Hou et al.(2022)23 compared four logit models and concluded that the heterogeneity of mean and variance of random parameter logit model was superior to the prediction performance of other models. Pathivada et al.(2024) using standard Mixed logit (MXL), Related Mixed logit (CMXL), The associated Mixed logit and Heterogeneity Approach (CMXLHM) model investigates the impact of real-time weather on crash injury severity and identifies risk factors contributing to crash injury severity while taking into account unobserved heterogeneity24. Azimian et al.(2021), studied the impact of accessibility, other spatial and socioeconomic factors on crash severity at county level, taking into account unobserved variables in space and time, and came to the conclusion that the density of major roads is positively correlated with all crash severity while the density of intersection is negatively correlated with the number of injury and non-injury crashes25. Briz-Redon et al.(2019) used several statistical methods, including the ratio of observed to expected, macro-conditional autoregressive model, logistic regression, etc., to estimate the probability of traffic crashes occurring near schools26; Rothman et al. (2017) found through multi-factor Logistic regression analysis that one-way streets, intersection guards, traffic signal density, poor social conditions and other factors are related to the traffic crash rate27. Phuksuksakul et al.(2023) established a random-parameter multinomial logit model to identify crash variables that are significantly associated with child pedestrian crash outcomes. Through data-driven research on child pedestrian crashes, the results of how time characteristics, vehicle type, pedestrian location, traffic operation, environment and human factors affect crashes are obtained28.