## 3 Results and Discussions
### Collision Likelihood Modeling  
With the friction interpolator developed, the next step is to construct a binary collision model using continuous friction values. A binary collision model is preferred over a frequency model because it reduces the need for safety interpretation. This means there is no need to assess the risk level based on the number of predicted collisions, which could result in road users believing that lower expected collisions indicate lower risk. To construct this model, the continuous friction values were averaged to represent how slippery a road segment is, for which the specific length must be calibrated due to the class imbalance problem [24], where one category dominates most of the input data. Therefore, a calibration process is needed to determine the optimal length. In addition, model implementation also requires continuous measurements to ensure that the friction value assigned to each road segment is representative. Hence, because of the importance of spatially dense measurements, we developed a friction interpolator beforehand to demonstrate how continuous friction values can be obtained. Nevertheless, since we already had extremely dense friction values, interpolated values were not used for model development to prevent interpolation errors from carrying over. In this study, all models were developed using the decision tree algorithm, and segment lengths between 500 m and 20 km (500 m increment) were evaluated to identify the optimal value. Figure 10 shows the obtained results. When evaluating each model, its training and validation dataset, model structure, and validation accuracy were examined. This process ensures that the model performance obtained is genuine and not due to class imbalance. Figure 9: ML hybrid model performance at a separation distance of 300 m.  
Between 500 m and 6 km, validation accuracy fluctuated between 70 and 90%. The models developed at these segment lengths only had one node, meaning regardless of the input, the model always outputted \"collision unlikely\". Consequently, the change in accuracy was not due to model structure but validation dataset differences. The observed accuracy only reflected the percentage of road segments in the validation dataset that did not have an associated collision event. From 6.5 to 8.5 km, due to the increase in the number of segments with collisions, the models utilized friction values as a key explanatory variable to identify \"collision likely\" segments. Other features like AADT, elevation, etc., were also used, though not to the extent of friction (which was used in every model). Between 9 and 11.5 km, a difference in the training dataset caused the accuracy difference observed in this region. The 9 and 9.5 km training dataset contained mostly segments with collisions, resulting in the model only outputting \"collision likely\". In contrast, 10-11.5 km had a much more balanced dataset where the model utilized friction and other supporting variables. Since the validation dataset in this region contained a mix of segments with and without collisions, the 9 and 9.5 km models performed much worse than the 10-11.5 km models. Starting at 12.5 km, friction was no longer used as a feature due to low feature variation resulting from averaging friction over long distances. Now that the main feature was too homogeneous to be useful as a predictor, a drop in accuracy of about 30% was observed. From this point on, most of the models could only predict \"collision likely\", meaning that validation accuracy became a measure of the proportion of road segments in the validation dataset associated with a collision event. Based on the extent to which friction was used in the models developed, it is evident that friction is a crucial predictor of collision events. Excluding the cases where significant class imbalances and friction values became too homogenized, every model had friction as a decision node, which cannot be said about any other variable used in this study.