## 3 Data  
This study focused on the analysis of crashes on a rural two-lane highway without divider or signal controls in Shandong Province, China. In total, 110 rural highways were selected. A map of the study area is shown in Figure 1. SV crashes related to four motor vehicle types (passenger car, motorcycle, pickup, and truck) from 2015 to 2020 were collected to calibrate the crash model. The studied dataset was composed of the information from three different data sources--(1) a crash database extracted from the Crash Reporting System maintained by the Traffic Administration Bureau of Shandong Department of Public Security; (2) a real-time meteorological dataset collected from the Meteorological Information Management System maintained by Shandong Climate Center; and (3) a geographic dataset of the target road derived from the Traffic Information System maintained by the Shandong Department of Transportation. A total of 29,814 crashes were integrated. After removing data with key information errors, 29,525 crashes were employed for subsequent modeling. Figure 1: Map of region under study. In this research, crash severity and various risk factors were identified as dependent and independent variables, respectively. Both the dependent and independent variables were transformed into discrete variables to fit the regression functions. Generally, there are three methods to determine the crash severity: (1) based on driver injury severity [51]; (2) based on most seriously injured passengers [52]; and (3) based on most serious injury in a crash [53]. Given the substantial differences in safety awareness among passengers as well as between drivers and passengers, the latter two approaches may introduce some additional heterogeneity. Thus, to reduce the potential heterogeneity and improve the reliability of model parameters, driver injury severity was used to measure crash severity for subsequent regression analysis. In the database, crash-related driver injuries were classified into four categories--no injury (70.0%), slight injury (20.1%), serious injury (7.8%) and fatal injury (2.1%). A driver passing away within seven days was regarded as a fatal event. Fatality cases were very limited in the dataset, which may lead to incorrect inference. Considering that the two adjacent injury categories are similar, the combination of fatality and serious injury, called FS injuries, was not expected to have a substantial impact on parameters estimation [54,55]. Thus, the dependent variable was a tripartite injury result (no injury, slight injury, FS injuries), in which the interest response refers to FS injuries, and no injury was considered as reference variable. Descriptive statistics of dependent variables across vehicle types are shown in Figure 2. As shown, a similar proportion of injury severity was maintained by passenger car, pickup, and truck crashes. The percentages of no injury for passenger car, pickup, and truck crashes were 87.7%, 87.0%, and 88.5%, respectively, followed by slight injury (9.6%, 9.4%, and 6.9%, respectively) and FS injuries (2.7%, 3.6% and 4.6%, respectively). Further, there is a significant difference in the proportion of injury severity between motorcycle crashes and other motor vehicle crashes. The percentage of slight injury (57.5%) was highest in motorcycle crashes, followed by FS injuries (23.7%) and no injury (18.8%). This may be related to the fact that motorcycle cannot provide adequate protection for riders. Several risk factors, including driver gender, driver age, drunk driving, weather, road surface, crash type, week, month, season, light, crash time and traffic control, were recorded in the crash dataset. Among them, some continuous variables, such as age, month, and crash time, were discretized. Driver age was divided into three categories, including young driver (<30), middle-aged driver (30-60), and older adult driver (>60). Middle-aged driver was identified as the reference variable. The month was also divided into three categories (early in month, middle of month, and late in month).