# Factors Affecting Rear-End Collisions in Underground Road Junctions Using VISSIM
## 4 Results
### Logistic Regression Result  
To identify accident factors in the \"with\" scenario, logistic regression analysis was performed using Python's sklearn_linear_model tool. Sixteen variables, including traffic dummy variables, were used in the logistic regression analysis. The variance inflation factor (VIF) test was performed to check for multicollinearity problems between the variables [38]. VIF is used to test whether the correlation between predictor variables affects the accuracy of the model and reflects the severity of multicollinearity. VIF measures the effects on model accuracy by evaluating the correlation between predictor variables (which reflects the severity of multicollinearity). Typically, a VIF value \(\geq\) 5 means high collinearity. If VIF \(>\) 10, the correlation between variables is high, affecting the prediction accuracy of the model [39]. Here, the VIF values of all variables were \(<\) 1, indicating a low correlation. The VIFs of the average speed and average lateral position variables were 0.347 and 0.001, respectively, demonstrating a very low correlation. Table 7 presents the estimated coefficients, Wald Chi-square, odds ratio, and \(p\)-value. The Wald Chi-square statistic and \(p\)-value were used to test the significance of variables used in the logistic regression analysis. The odds ratio is a measure that shows how many times the accident frequency increases when the unit of a variable increases by 1, assuming \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Mean** & **LOS B** & **LOS C** & **LOS D** & **LOS E** \\ \hline \multirow{10}{*}{Without} & AccelerationMean [m/s\({}^{2}\)] & \(-0.1\) & \(-0.1\) & \(-0.1\) & \(-0.1\) & \(-0.1\) \\  & SpeedMean [km/h] & 61.6 & 70.0 & 68.9 & 63.0 & 47.8 \\  & PosLatMean [m] & 314.9 & 332.6 & 339.5 & 332.7 & 266.8 \\  & SpacingMean [m] & 55.9 & 66.2 & 64.2 & 55.6 & 41.4 \\  & DensityMean [veh/km] & 40.3 & 18.4 & 21.3 & 36.6 & 76.0 \\  & AccelerationStd [m/s\({}^{2}\)] & 1.1 & 0.7 & 0.8 & 1.0 & 1.6 \\  & SpeedStd [km/h] & 16.6 & 12.6 & 12.8 & 15.9 & 23.2 \\  & PosLatStd [m] & 316.5 & 329.7 & 331.1 & 324.2 & 288.1 \\  & SpacingStd [m] & 54.6 & 65.2 & 60.8 & 51.6 & 43.5 \\  & DensityStd [veh/km] & 30.3 & 15.6 & 17.0 & 27.4 & 55.0 \\ \hline \multirow{10}{*}{With} & AccelerationMean [m/s\({}^{2}\)] & \(-0.1\) & 0.0 & \(-0.1\) & \(-0.1\) & \(-0.1\) \\  & SpeedMean [km/h] & 32.2 & 40.7 & 34.0 & 27.1 & 27.0 \\  & PosLatMean [m] & 0.5 & 0.5 & 0.5 & 0.5 & 0.5 \\  & SpacingMean [m] & 29.6 & 40.3 & 31.1 & 23.5 & 23.4 \\  & DensityMean [veh/km] & 75.6 & 48.9 & 65.0 & 93.9 & 94.7 \\  & AccelerationStd [m/s\({}^{2}\)] & 1.8 & 1.4 & 1.7 & 2.0 & 2.0 \\  & SpeedStd [km/h] & 21.7 & 22.6 & 22.4 & 21.0 & 20.9 \\  & PosLatStd [m] & 0.0 & 0.1 & 0.1 & 0.0 & 0.0 \\  & SpacingStd [m] & 35.5 & 45.7 & 37.9 & 29.4 & 29.1 \\  & DensityStd [veh/km] & 35.8 & 26.4 & 32.0 & 42.5 & 42.5 \\ \hline \end{tabular}
\end{table} 
Table 6: Analysis results by scenario. Figure 6: Conflict rate by scenario by location. that the values of all variables, except for that one variable, are the same. The odds ratio was used to determine the effects of variables on accidents. The logistic regression analysis revealed that the variables that affected the increase in accidents were the average acceleration, average density, acceleration standard deviation, and lateral standard deviation. In R1, where the diverging area exists, the possibility of an accident was found to increase from LOS B to LOS D. By contrast, the variables that affected the decrease in accidents as their value increased were the average speed, average lateral position, average distance between the vehicles, speed standard deviation, standard deviation of the distance between the vehicles, and density standard deviation. In R2, which includes the merging area, accidents were found to decrease from LOS B to LOS D, but the effect was small. As a result of the odds ratio analysis, the variables that have a large impact per unit are the standard deviation of the lateral position and the standard deviation of acceleration.