# Traffic Collision Severity Modeling Using Multi-Level Multinomial Logistic Regression Model
## 4 Modelling  
### Multinomial Logistic Regression  
The Multinomial Logistic Regression model is valuable for analyzing and understanding contributing factors across multiple categories. In the context of traffic accidents, this model allows for a comprehensive exploration of the various factors influencing crash severity, encompassing aspects of human behaviour and the environment highlighted by [PERSON], [PERSON]; [PERSON] [34]. The application of the Multinomial Logistic Regression model in this study focuses on understanding the influence of behavioural factors on traffic collision severity. Specifically, the model is designed to show how different contributing factors affect the severity of traffic accidents, including fatalities, sever injuries, and minor injuries, in comparison to PDO. The model development process involved breaking down the analysis into distinct segments. Specifically, the dataset was divided into Multiple Binary Logistic Regression \begin{table}
\begin{tabular}{l l c} \hline \multicolumn{1}{c}{**Variables**} & \multicolumn{1}{c}{**Description**} & \multicolumn{1}{c}{**Percentage/Mean**} \\ \hline Weather condition & Collision in rainy condition & 16\% (Adverse) \\ \hline Roadway alignment & Collision at different alignment like straight & 14.71\% (Curve) \\  & or intersection & 85\% (Straight) \\ \hline Roadway description & Collision based on road type & 3.19\% (One-Way)57\% (Two-Way Divided) \\  & Collision based on road type & 39.73\% (Two-Way Undivided) \\  & & 26.22\% (Angle) \\  & & 21.7\% (Fixed) \\ Collision type & In what way did the collision happen & 2.3\% (Head-On) \\  & & 1.6\% (No Collision) \\  & & 27.51\% (Rear-End) \\  & & 10.04\% (Sideswipe) \\ \hline Alcohol & Driver under influence of alcohol at the time & 5.8\% \\  & of collision & \\ \hline Unbelted & At the time of collision if the seat belts were & 4.6\% \\  & on or not & 0.48\% \\ \hline Bike & Collision with bike or not & 0.48\% \\ \hline Traffic signal & If the traffic control signal were present in the & 80.4\% \\  & area & \\ \hline Area type (urban) & If the collision happened in urban or rural & 74.27\% (Urban) \\  & area & 25.77\% (Rural) \\ \hline Distracted & Any distractions in external environment for & 17.43\% \\  & driver & \\ \hline Drowsy & Sleepy & 2.7\% \\ \hline Crash date & Collision happened on weekday or weekend & 73.61\% (Weekday) \\  & & 26.38\% (Weekend) \\ \hline Drug & Driver under influence of drugs/medicine at & 1.01\% \\  & the time of collision & \\ \hline Motor & Were any cars or motor vehicles involved in & 1.71\% \\  & the collision & \\ \hline Ped & Any pedestrian involved & 1.18\% \\ \hline Speed & Driver speeding or not at the time of collision & 20.77\% \\ \hline Animal & Collision involving animals & 6.4\% \\ \hline \end{tabular}
\end{table} 
Table 1: Modelling dataset variables. sub-models, each comparing a particular severity category with the reference category (e.g., minor severity vs. reference, severe severity vs. reference). This approach ensured that the model captured the nuanced differences that defined each severity level, as discussed by [PERSON] et al. [35]. The primary objective was to train Multiple Binary Logistic Regression sub-models, each shedding light on the intricate relationships between predictor variables and crash severity. By segmenting the dataset in this manner, the data was navigated precisely, enabling a deeper understanding of the key factors influencing collision outcomes, as described by [PERSON] et al. [24]. The Multinomial Logistic Regression model estimates the log odds of each crash severity category relative to a reference category. The general equation for the Multinomial Logistic Regression model can be expressed as follows, as shown by [PERSON] et al. [36]:  
\[\log\,P(Y=j\mid X)=\beta_{j0}+\beta_{j1}X_{1}+\beta_{j2}X_{2}+\cdots+\beta_{jk} X_{k} \tag{1}\]  
The Multinomial Logistic Regression model estimates the log odds of each crash severity category relative to a reference category.