# Analyzing the Factors Influencing Time Delays in Korean Railroad Accidents
## 5 Analysis Results
### Human-Related Time Delays
\begin{table}
\begin{tabular}{l r r r r r r} \hline \hline
**Parameter** & \multicolumn{3}{c}{**Two-Stage Model**} & \multicolumn{3}{c}{**ZINB Model**} \\ \cline{2-7}  & **Estimate** & **S.E.** & \(p\)**-Value** & **Estimate** & **S.E.** & \(p\)**-Value** \\ \hline _Negative Binomial Part_ & & & & & & \\ Intercept & 1.589 & 0.099 & 0.000 & 1.767 & 0.068 & 0.000 \\ Type of event & & & & & & \\ High potential event & 0.011 & 0.088 & 0.897 & \(-\)0.044 & 0.061 & 0.478 \\ Human involved & 0.053 & 0.177 & 0.763 & \(-\)0.357 & 0.133 & 0.007 \\ GL & \(-\)0.098 & 0.097 & 0.312 & \(-\)0.234 & 0.072 & 0.001 \\ Season occurred & & & & & & \\ Fall & 0.092 & 0.046 & 0.044 & 0.043 & 0.033 & 0.188 \\ Person type & & & & & & \\ Public & \(-\)0.174 & 0.095 & 0.066 & \(-\)0.104 & 0.066 & 0.114 \\ Passenger & \(-\)0.507 & 0.101 & 0.000 & \(-\)0.229 & 0.072 & 0.001 \\ Crew & \(-\)0.136 & 0.088 & 0.123 & \(-\)0.123 & 0.063 & 0.051 \\ Size of train operator & & & & & & \\ Middle & \(-\)0.165 & 0.177 & 0.350 & \(-\)0.357 & 0.132 & 0.007 \\ Type of train & & & & & & \\ Conventional & 0.189 & 0.047 & 0.000 & 0.243 & 0.034 & 0.000 \\ Cause directly related to & & & & & & \\ Suicide & 0.405 & 0.049 & 0.000 & 0.187 & 0.037 & 0.000 \\ Location occurred & & & & & & \\ Level crossing & 0.032 & 0.135 & 0.812 & 0.169 & 0.101 & 0.094 \\ Between stations & 0.219 & 0.045 & 0.000 & 0.110 & 0.036 & 0.003 \\ \(\alpha\) (_overdispersion_) & 1.949 & 0.049 & 0.000 & 1.942 & 0.083 & 0.000 \\ _Logit Part_ & & & & & & \\ Intercept & 1.170 & 0.199 & 0.000 & 1.202 & 0.210 & 0.000 \\ Type of event & & & & & & \\ High potential event & 2.708 & 0.225 & 0.000 & 2.980 & 0.258 & 0.000 \\ Human involved & \(-\)2.867 & 0.224 & 0.000 & \(-\)2.865 & 0.228 & 0.000 \\ GL & & 0.931 & 0.357 & 0.009 & 1.043 & 0.411 & 0.011 \\ Season occurred & & & & & & \\ Fall & 0.281 & 0.138 & 0.042 & 0.294 & 0.148 & 0.047 \\ Person type & & & & & & \\ Public & 2.215 & 0.203 & 0.000 & 2.382 & 0.216 & 0.000 \\ Passenger & 1.513 & 0.208 & 0.000 & 1.645 & 0.220 & 0.000 \\ Crew & \(-\)0.076 & 0.235 & 0.745 & \(-\)0.124 & 0.256 & 0.627 \\ Size of train operator & & & & & & \\ middle & 0.331 & 0.534 & 0.535 & 0.634 & 0.633 & 0.317 \\ Type of train & & & & & & \\ Conventional & \(-\)0.279 & 0.135 & 0.039 & \(-\)0.359 & 0.144 & 0.013 \\ Cause directly related to & & & & & & \\ Suicide & 1.143 & 0.157 & 0.000 & 1.137 & 0.168 & 0.000 \\ Location occurred & & & & & & \\ Level crossing & \(-\)0.718 & 0.436 & 0.099 & \(-\)0.845 & 0.483 & 0.081 \\ Between stations & 0.817 & 0.156 & 0.000 & 0.842 & 0.169 & 0.000 \\ LL at constant only & & & \(-\)5606 & & & & \\ LL at convergence & & \(-\)4864 & & & & \\ \(\rho^{2}\) & & & & & & 0.151 \\ AIC & & & 9755 & & & 9568 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Modeling outputs (delayed time) for the human-related factors. selected in conjunction with the BP algorithm, as the application of the ReLU activation function failed to converge to optimal values. Throughout the course of this ANN study, an interesting observation emerges, indicating a consensus on the limited performance improvement attained by introducing additional hidden layers. In many instances, a single hidden layer is deemed sufficient to address many problems. However, this study explores the introduction of hidden layers ranging from 1 to 3, revealing that optimal convergence was not achieved with three hidden layers. Given that the efficacy of the BP training algorithm is contingent on the number of neurons within the hidden layer, various neuron counts ranging from 1 to 12 were systematically examined. The investigation concludes that the optimal number of neurons in the hidden layer is eight, resulting in the lowest values for Mean Square Error (MSE) and Root Mean Square Error (RMSE) for the training data. The analysis was conducted using the R 4.3.1 software package. The primary criteria employed to compare the performance superiority among the Two-stage model, ZINB model, and ANN model encompass the coefficients of determination (\(R^{2}\)), MSE, and RMSE.