## 6 Results and Discussions
### Random Parameters with Heterogeneity in Means  
Except for the MTC-MTC pattern, the speed standard deviation of the following vehicle within 3 s (TV\({}_{\text{STD}}\)) and the standard deviation of ETTC of all vehicles in sub-segment (ZE\({}_{\text{STD}}\)) have random effects on collision risk level. According to Tables 7-10, both the means and standard deviations of the two variables are statistically significant, indicating that the effects of the factors vary across different vehicle-following patterns.  
Specifically, TV\({}_{\text{STD}}\) is identified as statistically significant random parameters in all RPOL models with heterogeneity in means for all vehicle-following patterns, indicating that the effect of TV\({}_{\text{STD}}\) has considerable variations across all observations. Overall, the coefficients of TV\({}_{\text{STD}}\) are positive, indicating that larger speed changes will result in higher levels of conflict risk. Regarding the standard deviation of ETTC of vehicles in sub-segment (ZE\({}_{\text{STD}}\)), it produced significant random parameters among models for ETC-ETC, MTC-ETC, and ETC-MTC patterns. The effects of ZEST\({}_{\text{STD}}\) differ greatly across three patterns. To some extent, the larger standard deviation of ETTC reflects the fluctuation of traffic flow near the following vehicle, which may increase the conflict risk level. Nevertheless, a random parameter is not observed in the RPOLMH model for the MTC-MTC vehiclefollowing pattern. The possible reason is that MTC vehicles are required to stop before toll collection lanes and wait in queues, so the conflict risk of vehicles in the MTC-MTC pattern is quite different from that of other patterns.  
Theoretically, vehicles choosing the toll lanes corresponding to their initial lanes directly do not need to change lanes, resulting in fewer conflicts. Interestingly, changing lanes to the left (N\({}_{\text{LLC}}\)1) has significant effects on collision risk level in the RPOLMH models for ETC-ETC and MTC-ETC patterns. It indicates that the lane change operation directly affects the collision risk level. If ETC vehicles change to the inner side of the main-line road in advance, there will be less interweaving between ETC and MTC vehicles in the diverging area. The coefficients of variable changing lanes to the right (N\({}_{\text{RLC}}\)1) are significant in the models for ETC-MTC, MTC-ETC, and MTC-MTC patterns. According to the layout of ETC and MTC lanes, MTC vehicles need to operate more lane changes to pass through the diverging area. Therefore, more vehicle-to-vehicle interactions may increase the conflict risk when MTC vehicles are involved in the vehicle-following groups.  
Another important issue that cannot be overlooked is that some random parameters are not sufficient in measuring conflict risk alone and should be considered together with the other variables. In Tables 7-10, the means of the random parameter for ZEST and TVSTD are associated with lane-marking indicator (L\({}_{\text{M}}\)) and the percentage of vehicles with ETTC less than 4 s in sub-segment (ZNPETC). It is noteworthy that L\({}_{\text{M}}\) can be regarded as a primary contributor to collision risk level. For example, in the model for the ETC-ETC pattern in Table 7, when TVSTD is involved with L\({}_{\text{M}}\), the mean of the random parameter is 0.165 (0.404 \(-\) 0.239 = 0.165). Such a result indicates that the effects of TVSTD on the conflict risk level will greatly differ in sub-segments with and without lane markings to a large extent. One possible reason is that the psychology and behaviors of drivers change with the absence of land markings. Apart from the lane-marking indicator, ZNPETC are also found to have an effect on the mean of the random parameter for TVSTD in the ETC-ETC pattern.