## 3 Results
### Interpretation of the Marginal Effects  
In contrast with the better prediction performance of the data mining models, the importance of parametric method (e.g., BOL) is in quantifying the effect of the underlying variables on the injury probabilities. Table 4 summarizes the parameter estimations and average marginal effects after excluding multicollinearity among factors. All the listed variables have statistically significant (95% confidence level) effects on crash severity. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Factor 1**} & \multicolumn{2}{c}{**Parameter Estimation**} & \multicolumn{3}{c}{**Average Marginal Effects**} \\ \cline{2-6}  & **Estimate** & **Std** & **SEV1 (\%)** & **SEV2 (\%)** & **SEV3 (\%)** \\ \hline AV & 0.0638 & 0.0002 & \(-\)0.68 & 0.18 & 0.49 \\ CSI & 1.4531 & 0.0152 & \(-\)22.6 & 6.2 & 16.39 \\ CMI & 1.3271 & 0.0210 & \(-\)20.4 & 7.3 & 13.1 \\ EES & 0.0584 & 0.0004 & \(-\)0.54 & 0.10 & 0.44 \\ Light-duty & 0.0357 & 0.2453 & \(-\)0.57 & 0.16 & 0.4 \\ Truck & \(-\)0.2947 & 0.2421 & 2.12 & \(-\)0.62 & \(-\)1.49 \\ Proceeding & \(-\)0.2558 & 0.0893 & 4.02 & \(-\)1.1 & \(-\)2.91 \\ Decelerating & \(-\)0.3289 & 0.0805 & 5.19 & \(-\)1.42 & \(-\)3.76 \\ Overtake/merge & \(-\)0.6687 & 0.1356 & 10.4 & \(-\)2.85 & \(-\)7.54 \\ Wrong side & 0.4047 & 0.0494 & \(-\)6.21 & 1.71 & 4.5 \\ Intersecting & 0.1716 & 0.0486 & \(-\)2.79 & 0.76 & 2.02 \\ Age & 0.2157 & 0.0094 & \(-\)0.34 & 0.09 & 0.24 \\ Female & 0.3739 & 0.0298 & \(-\)5.79 & 1.59 & 4.2 \\ Drink/drugs & 0.4838 & 0.0756 & \(-\)7.50 & 2.06 & 5.44 \\ Speeding & 0.1035 & 0.0347 & \(-\)3.20 & 0.88 & 2.32 \\ Speed limit & 0.0062 & 0.0012 & \(-\)0.09 & 0.03 & 0.06 \\ Head-on & 0.1445 & 0.0695 & \(-\)5.57 & 1.53 & 4.04 \\ Rear-end & \(-\)0.3594 & 0.0541 & 1.16 & \(-\)0.34 & \(-\)0.82 \\ Lane number & \(-\)0.1358 & 0.0151 & 2.10 & \(-\)0.57 & \(-\)1.53 \\ Curve & \(-\)0.1257 & 0.1615 & 1.95 & \(-\)0.53 & \(-\)1.41 \\ Down slope & 0.4302 & 0.1082 & \(-\)6.67 & 1.83 & 4.83 \\ Two-way, undivided & 0.3709 & 0.0803 & \(-\)5.75 & \(-\)0.18 & 5.93 \\ Ramp & 0.3362 & 0.0799 & \(-\)5.21 & \(-\)0.33 & 5.54 \\
0.00–6.00 & 0.2234 & 0.0561 & \(-\)3.46 & 0.95 & 2.51 \\
12:00–17:00 & \(-\)0.0996 & 0.0384 & 1.55 & \(-\)0.42 & \(-\)1.12 \\ Far side & \(-\)0.5598 & 0.0501 & 8.68 & \(-\)2.38 & \(-\)6.29 \\ Rear side & \(-\)0.4606 & 0.0747 & 7.14 & \(-\)1.96 & \(-\)5.18 \\ Near side & 0.5286 & 0.0556 & \(-\)8.19 & 2.25 & 5.94 \\ Cut1 & 4.3961 & 0.3376 & & & \\ Cut2 & 6.4116 & 0.3395 & & & \\ \hline \multicolumn{6}{l}{Prob \(>\) chi\({}^{2}\) = 0.0001} \\ Pseudo R\({}^{2}\) = 0.2971 & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of the parameter estimation and average marginal effects. Although most BF variables are not applied for ML models, various factors directly or indirectly influence the probability of severity. PCI, occupant attributes, driving behavior, crash type, environment, and roadway factors may influence the probability of injury severity. Specifically, higher speed-based (\(\Delta\)V and EES) and system-based (CMI and CSI) crash indicators will result in more severe injuries. Taking \(\Delta\)V as an example, the probability of moderate and major severity will increase by about 0.18% and 0.49%, respectively, for every 1 km/h increase in \(\Delta\)V. Meanwhile, the probability of minor severity will decrease by 0.57%, with all other factors being equal. This notion explains the positive correlation between PCIs and IR. Furthermore, the driving maneuver before crash events directly influenced the severity thresholds. Deceleration before crashes and driving on wrong side may result in an increase and decrease in the probability of minor injury by about 5.19% and 6.21%, respectively. Although some studies regard improper overtaking as risky behavior, lane changing or merging will decrease the probability of SEV3 by 7.54%. A plausible reason is that overtaking may result in the proximity to a crash, but it is not highly related to potential overcomes.