# Traffic Collision Severity Modeling Using Multi-Level Multinomial Logistic Regression Model
## 5 Results and Discussion
### Multi-Level Multinomial Logistic Regression
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Variables Bike-Vehicle** & \multicolumn{4}{c}{**Fatality**} & \multicolumn{4}{c}{**Major Injury**} & \multicolumn{4}{c}{**Minor Injury**} \\ \cline{2-10}  & **Coef.** & \(p\)**-Value** & **Odds Ratio** & **(expcoef)** & **Coef.** & \(p\)**-Value** & **Odds Ratio** & **(expcoef)** & **Coef.** & \(p\)**-Value** & **Odds Ratio** \\ \hline Intercept & \(-10.4\) & \(<\)0.01 & & \(-7.01\) & \(<\)0.01 & & \(-0.7\) & \(<\)0.01 & & **(expcoef)** \\ \hline X\({}_{1}\): Collision Type (Head-On) & \(1.85\) & \(0.06\) & \(1.9\) & \(1.4\) & \(<\)0.01 & \(3.6\) & \(0.62\) & \(<\)0.5 & \(1.2\) \\ \hline X\({}_{2}\): Collision Type (Rear-End) & \(-0.34\) & \(<\)0.01 & \(0.75\) & \(-0.69\) & \(0.04\) & \(0.65\) & - & - & - \\ \hline X\({}_{3}\): Collision Type (Gidswipe) & \(-0.38\) & \(<\)0.01 & \(0.68\) & \(-1.1\) & \(0.02\) & \(0.38\) & - & - & - \\ \hline X\({}_{4}\): Traffic Control (Yes) & \(1.6\) & \(<\)0.01 & \(46\) & \(4.1\) & \(<\)0.01 & \(431\) & \(-0.64\) & \(<\)0.01 & \(1\) \\ \hline X\({}_{5}\): Traffic Control (Other) & \(0.25\) & \(<\)0.01 & \(18\) & \(4.4\) & \(<\)0.01 & \(345\) & \(-0.41\) & \(<\)0.01 & \(0.84\) \\ \hline X\({}_{6}\): Related (No) & \(3.8\) & \(<\)0.01 & \(44.70\) & \(2.3\) & \(<\)0.01 & \(10\) & \(1.2\) & \(<\)0.01 & \(4\) \\ \hline X\({}_{2}\): Bike (Yes) & \(4.5\) & \(<\)0.01 & \(13\) & \(3.6\) & \(<\)0.01 & \(67\) & \(2.9\) & \(<\)0.01 & \(41\) \\ \hline X\({}_{6}\): Animal (Yes) & \(-0.76\) & \(<\)0.01 & \(5.7\) & \(-0.46\) & \(<\)0.01 & \(0.56\) & - & - & - \\ \hline X\({}_{7}\): Pedestrian (Yes) & \(9.2\) & \(<\)0.01 & \(354\) & \(7.0\) & \(<\)0.01 & \(436\) & \(5.7\) & \(<\)0.01 & \(258\) \\ \hline X\({}_{10}\): Area Type & \(-1.6\) & \(0.10\) & \(0.60\) & - & - & - & - & - \\ \hline Rural \({}^{*}\) & \(-1.6\) & \(0.10\) & \(0.60\) & - & - & - & - & - & - \\ \hline X\({}_{11}\): Roadway & \multirow{2}{*}{\(2.8\)} & \multirow{2}{*}{\(<\)0.03} & \multirow{2}{*}{\(1.7\)} & \multirow{2}{*}{\(0.49\)} & \multirow{2}{*}{\(0.06\)} & \multirow{2}{*}{\(2.7\)} & \multirow{2}{*}{-} & \multirow{2}{*}{-} & \multirow{2}{*}{-} \\ Description (Two-way divide) & & & & & & & & & \\ (One-way) \({}^{*}\) & & & & & & & & \\ \hline Randomeffect code: & \multirow{2}{*}{\(0.67\)} & \multirow{2}{*}{\(0.64\)} & \multirow{2}{*}{\(0.64\)} & \multirow{2}{*}{\(0.86\)} & \multirow{2}{*}{\(0.86\)} & \multirow{2}{*}{\(0.86\)} & \multirow{2}{*}{\(0.86\)} \\ War (V\({}_{\text{-}}\)odd) & & & & & & & & \\ \hline Goodness of fit: & \multirow{2}{*}{\(421\),\(118\)} & \multirow{2}{*}{\(0.86\)} & \multirow{2}{*}{\(0.86\)} & \multirow{2}{*}{\(0.86\)} & \multirow{2}{*}{\(0.86\)} & \multirow{2}{*}{\(0.86\)} \\ AIC & & & & & & & & \\ \hline BIC & \multirow{2}{*}{\(422\),\(365\)} & \multirow{2}{*}{\(0.86\)} & \multirow{2}{*}{\(0.86\)} & \multirow{2}{*}{\(0.86\)} & \multirow{2}{*}{\(0.86\)} \\ \hline \hline \end{tabular}  
\({}^{*}\) Reference category  
\end{table} 
Table 3: Output from Multi-Level MNL model, including coefficients, \(p\)-value, and odds ratio. As shown in Table 3, when 'Animal (Yes)' is involved, the odds ratios of 5.7 for fatality, 0.56 for major injuries, and 1.5 for minor injuries indicate a measured elevation in risk, especially for fatality. Pedestrian-involved collisions display striking odds ratios of 354 for fatality, 436 for major injuries, and 258 for minor injuries. This underscores the significantly heightened risk across all injury severity levels in such collisions. Finally, 'Area Type (Urban)' scenarios demonstrate odds ratios of 0.6 for fatality, 0.67 for major injuries, and 0.87 for minor injuries, highlighting the protective nature of urban areas. These findings underscore the critical role of various factors in shaping collision severity outcomes, with implications for safety interventions and policy measures. Seatbelt use greatly lowers severe outcomes, and accident type--often associated with driver conduct like speeding or distraction--defines driver-dependent factors determining collision severity.