In this study, we attempted to explain drivers' crash risk variation in car-following for crash avoidance considering the effects of drivers' visual perception, vehicle type, and horizontal curves, with a structural equations model. The model was built by incorporating drivers' speed risk perception and distance risk perception as latent variables. A series of on-road experiments was conducted on the curved segments of a freeway in China to collect naturalistic driving data to approximate the model. The results indicate that (1) the amount of variance in speed risk perception accounted for by the temporal and spatial frequency and the following vehicle type was 21%; (2) the amount of variance in distance risk perception accounted for by the temporal and spatial frequency, leading vehicle type, stopping sight distance (SSD), horizontal sightline offset (HSO), and radius was 29%; and (3) speed risk perception and distance risk perception explained 27% of the total variance in crash risk variation, which is significantly higher than previous similar results that were commonly limited to 10%. The results were explained from the perspective of the effect of line markings, vehicle type (size), and curves on driving behaviors, respectively. In addition, the difference between the effect of speed risk perception and distance perception on crash risk variation was discussed considering the direct and indirect origins of risk in driving. The findings suggests that the incorporation of visual perceptual, vehicular, and roadway factors and its relevant speed risk perception and distance risk perception can better explain the crash risk in car-following. This study also emphasized the possibility and the need of applying the line markings as a visual intervention to prevent the drivers from rear-end crashes on curves, which may provide new insights and be a new solution for roadway safety.