## 5 Modeling Results and Discussion
### Discussion  
Compared with the MN-logit model, RP-logit model, and RI-logit model, the SRP-logit model has better fitting performance and classification accuracy. Hence, only the average marginal effects of significant risk factors in the SRP-logit model were calculated, and only the marginal effects associated with FS injuries were calculated. Inspired by [PERSON] et al. (2019) and [PERSON] et al. (2020), a histogram (Figure 4) was designed as a figure to represent the marginal effects, instead of a table. The aim is to interpret the model estimation results in a user-friendly way. Note that the marginal effects of risk factors that have no significant impact or have been artificially removed are denoted by zero. According to Figure 4, (1) for the same motor vehicle type, different risk factors have different impacts on FS injuries of rural SV crashes; (2) the effect of the same factor on FS injuries varies across motor vehicle types; and (3) among the various risk factors, collision with a fixed object has the greatest effect on FS injuries, which has remained stable across different vehicle types. A detailed discussion of risk factors based on the parameter estimation results and the average marginal effects of the SRP-logit model is provided below. There is significant correlation between male driver and FS injuries in rural SV crashes. However, the sign of correlation (positive or negative correlation) varies with motor vehicle type. Male drivers are significantly and positively associated with FS injuries in passenger car and pickup crashes, with average marginal effects of 1.01% and 4.27%, respectively. A similar finding was obtained by [PERSON] et al. [69], who noted that male drivers were 2.18 times more likely to result in serious passenger car crashes than females. However, there is a significant negative correlation between male drivers and FS injuries in rural motorcycle SV crashes, with average marginal effects of \(-2.73\%\). [PERSON] et al. [37] reached a similar conclusion by analyzing the severity of motorcycle crashes at Australian intersections. These findings are of interest to comprehensively elucidate the variable effects of male driver on rural SV crash severity and validate the necessity of regression analysis based on different vehicle types. Further, for all vehicle types, the parameters of male driver exhibit random effects obeying a normal distribution. This finding is supported by many research studies [16; 21] and highlighted that capturing unobserved heterogeneity is indispensable during the crash severity modeling process. For motorcycle crashes, non-clear weather is significantly and positively associated with FS injuries in rural SV crashes (marginal effect 4.52%), which is consistent with previous research [37], because rural China has poor traffic conditions, such as waterlogged and narrower roads. In addition, motorcycles do not have satisfactory stability because of two tires [70]. Hence, serious motorcycle crashes occur frequently in non-clear weather. However, there is a significant negative correlation between non-clear weather and FS injuries for other vehicle types. The probability of serious rural SV crashes caused by passenger car, pickup, and truck under non-clear weather conditions is reduced by 0.99%, 0.33%, and 0.74% respectively. [PERSON] et al. [71] and [PERSON] et al. [72] reached the same conclusion and pointed out that this phenomenon was caused by cautious driving under unsatisfactory weather conditions. For passenger car, motorcycle, and pickup crashes, the relationship between older adult driver (age > 60) and FS injuries is significant at the 95% BCI, and the probability of serious injury caused by older adult drivers increased by 2.07%, 4.10%, and 2.23%, respectively, compared to mid-age drivers (30-60). The same conclusion was reached by [PERSON] et al.