## 2 Materials and Methods  
### Data Sources  
Historical accident data were obtained from the National Police Agency of South Korea, including detailed records of vehicle-to-vehicle crash incidents reported at the scene. This study also explicitly includes road segments with no records of accident events. Non-accident road segments were identified as those with no recorded vehicle-to-vehicle crashes in police reports over a one-year period. To ensure comparability, non-accident segments were selected to match accident segments in terms of annual average daily traffic volume (AADT), road geometry (e.g., lane width and shoulder width), and terrain characteristics. By choosing similar traffic conditions between road segments with- and without accidents, this study ensures that safety-related features (e.g., road geometry and traffic conditions) are compared without introducing traffic volume bias. In addition, datasets for road segments were collected from geometric design sketches and field surveys by using probe vehicles. In terms of road segment information, samples from the metropolitan area (i.e., Seoul) and one of the primary rural states (i.e., Jeon-Buk) in South Korea were selected. Specifically, roadway segments in Jeon-Buk, including level and rolling terrain characteristics, were selected to investigate the impacts of road conditions. Figure 1 shows the study sites. In total, 2916 highway road segments, which were segmented from 322.9 km of rural highway, were investigated. Figure 1: Data acquisition region and road location. To minimize inherent biased estimation resulting from the type of crash, only vehicle-to-vehicle crash data were used in this study. In the case of data collection, the variables influencing vehicle crashes were found through literature reviews, and surveyed variables were defined based on these influencing variables. The information on roadway situations, such as roadway geometric conditions, traffic operation factors, and roadside environments, was gathered through on-site surveys and design drawings. In total, 104.4 km of the rural highways outside of Seoul and 218.5 km of the rural highway in Jeonbuk were surveyed. Table 1 presents information about the road segment. In many studies, crash prediction models were developed using only data from road segments where the crashes occurred. The results from the studies using those data can be biased because the prediction model cannot explain the conditions of road segments where crashes did not occur. To solve this problem, both road segments with a crash history and segments without any crash history were surveyed, and data from all segments were used to develop the crash prediction models in this study. In this study, each segment was divided based on homogenous driving conditions. Three variables significantly affecting safety and driver behavior on rural highways were used to identify the homogenous conditions, such as horizontal curve radius, grade, and lane width. This segment of homogenous conditions is illustrated in Figure 2. Through this segment process, a total of 2916 homogenous road segments were made, including 998 segments for multi-lane highway sections and 1918 segments for two-lane highways. Data were collected from two regions: Seoul Metropolitan Area and Jeon-Buk rural highways, comprising 2916 homogenous road segments (998 multi-lane highways and 1918 two-lane highways). To ensure consistency, road segments were categorized based on homogeneous road geometric conditions. All variables affecting traffic safety, including road geometry, traffic operations, and roadside conditions, were measured through field surveys, geometric design sketches, and police crash reports. Table 2 provides a detailed description of the variables used in this article. In addition, all explanatory variables in Table 3 consist of continuous and categorical variables. The data contain 21 variables observed in each vehicle accident. Since the raw data include categorical variables, appropriate pretreatment preprocessing should be preceded.