## 5 Results and Discussions
These trends were corroborated by Figure 9. Hence, it can be said that fatal crashes are more likely to occur when drivers are not following road regulations properly or do not have enough time to respond to events. It can be observed that the overall weight for each severity type remained the same whether they are taken on the basis of crash types or reasons as shown in Table 8. This was expected, since it would have related to their overall proportion in the available sample. Figures 10 and 11 show the combined weights for the severity of the crash based on each crash type and reason. Figure 10 shows that collisions and vehicles overturning are the two most common types of crashes which cause fatality or serious injury in a crash. These weights were calculated as the cross product of the relative weights of a factor (provided in Table 4 for crash type and Table 5 for crash reason) and the relative weight of factor with the severity level (Table 6 or Table 7). These weights indicate the relative chance of a severity type, among the entire dataset of crashes, with a particular type or reason for the crash. The weight or relative importance of \"collision\" to cause a serious injury crash was at least 10% higher than any other crash type. Similarly, it also had the highest weight for fatal crashes as well; however, the difference in its weight (approximately 5%), compared to other types, \begin{table}
\begin{tabular}{l c c} \hline \hline \multirow{2}{*}{**Contributing Factor**} & \multicolumn{2}{c}{**Crash Severity**} \\ \cline{2-3}  & **Fatal** & **Serious Injury** \\ \hline Crash Types & 0.322 & 0.686 \\ \hline Crash Reasons & 0.321 & 0.669 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Total weights for each crash severity type. Figure 10: Combined weight for different crash severities based upon crash types. was not so prominent for fatal crashes as it was for serious injury crashes. Motorcycle riders were proven to be vulnerable road users because of their greater involvement in crashes of higher severity [41]. Figure 11 shows that sudden lane changing was the most common reason for serious injury and fatal crashes, followed by speeding. The importance of \"sudden turning\" was at least 20% higher than any crash reason for serious injury crashes, while it was at least 10% higher than any other crash reason for fatal crashes. The least common reason for serious injury and fatal crashes was driver distraction. This could be because distracted drivers tend to become slower and keep a higher headway between the vehicles, as has been proven by other studies [42]. The combined weights could be used to form a utility function for the prediction of crashes, as proposed by [43]. Hence, the utility function for different crash severities can be listed as Equations (7) and (8). The development of such utility functions would have been unlikely with traditional statistical approaches for the type of data available, because of their statistical constraints. \[ \begin{array}{l}\text{U}_{\text{Fatal}}=0.129\text{ (Collision) + 0.012 (Hitmotorcycle) + 0.017 (Hitroadfence) + 0.042 (Hitpedestrian) + }\\ 0.088\text{ (Vehicle overturned) + 0.035 (Otherstypes) + 0.016 (Driverdistraction) + 0.058 (Speeding) + }\\ 0.042\text{ (Notgivingway) + 0.163 (Suddenanechanging) + 0.019 (Insufficientsafedistance) + 0.023 (Otherstypes) }\\ \end{array}  \tag{7}\]  
\[ \begin{array}{l}\text{U}_{\text{Seriousinjury}}=0.261\text{ (Collision) + 0.038 (Hitmotorcycle) + 0.053(Hitroadfence) + 0.106 (Hitpedestrian) + }\\ 0.132\text{ (Vehicle overturned) + 0.095 (Othetypes) + 0.044 (Driverdistraction) + 0.122 (Speeding) + }\\ 0.108\text{ (Notgivingway) + 0.317 (Suddenanechanging) + 0.041 (Insufficientsafedistance) + 0.037 (Otherreasons) }\\ \end{array}  \tag{8}\]