# Analysis of the Railway Accident-Related Damages in South Korea
## 4 Real Application
As mentioned earlier, we employed two different types of the TPM; (1) ZIP model and ZINB model for discrete variables such as number of delayed trains (Table 4) due to railway accidents and (2) ZIG model and ZILN model for semi-continuous variables. Tables 5 and 6 illustrate the statistical results from the analyses of the TPMs for the two semi-continuous dependent variables: delayed time and the amount of costs due to the railway accidents. Table 5 displays the statistical results of the regression analysis on the amount of delayed time. For every model, both the logit part and the positively continuous part (Gamma part or Log-normal part) have the statistically significant coefficient estimates. Especially, the coefficient estimates in logit parts are quite similar with each other. The possibility that a railway accident causes any time delay increases when the accident is involved in KORAIL (0.580) compared to Metro. Human-related accidents (\(-\)2.777) and number of fatalities (1.810) have meaningful impact on time delay resulting from a railway accident. In case of the other part, the independent variables such as year and number of casualties are only significant in the Gamma part though number of trains derailed due to railway accidents are not significant in either of the two models. KORAIL (\(-\)1.141 in ZIG; \(-\)0.182 in ZILN) tends to be have lesser delayed time and a human-related accident (\(-\)0.110 in ZILN) has a lower probability of having a positive delayed time than a non-human-related accident. Train types such as KTX (\(-\)0.582 in ZIG; \(-\)0.597 in ZILN) and urban trains (\(-\)0.341 in ZIG; \(-\)0.405 in ZILN) result in less delayed time than general trains. Noteworthy in this case is that higher the number of casualties (0.099) due to the railway accidents the longer the hours of train delay, especially in the ZIG model. From the comparison between the two TPMs, the ZILN model slightly outperforms the ZIG model. This is because the log-likelihood value of the former is larger and its AICC is smaller. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{3}{*}{**Independent Variables**} & \multicolumn{6}{c}{**Zero-Inflated Poisson Regression**} & \multicolumn{6}{c}{**Zero-Inflated Negative-Binomial Regression**} \\ \cline{2-13}  & \multicolumn{3}{c}{**Logit Part**} & \multicolumn{3}{c}{**Poisson Part**} & \multicolumn{3}{c}{**Logit Part**} & \multicolumn{3}{c}{**Negative Binomial Part**} \\ \cline{2-13}  & **Est.** & **S.E.** & \(p\)**-Value** & **Est.** & **S.E.** & \(p\)**-Value** & **Est.** & **S.E.** & \(p\)**-Value** & **Est.** & **S.E.** & \(p\)**-Value** \\ \hline Year (2008-2016) & 0.004 & 0.016 & 0.827 & 0.063 & 0.003 & \(<\)0.001 & 0.012 & 0.047 & 0.786 & 0.066 & 0.008 & \(<\)0.001 \\ \hline \multicolumn{13}{c}{Organization (vs. Metro)} \\ \hline KORAIL & 0.004 & 0.016 & 0.827 & \(-\)0.628 & 0.023 & \(-\)0.001 & \(-\)0.002 & 0.091 & 0.998 & \(-\)0.891 & 0.073 & \(<\)0.001 \\ \hline \multicolumn{13}{c}{Accident Factor (vs. Non-human-related)} \\ \hline Human-related & \(-\)0.955 & 0.107 & \(<\)0.001 & \(-\)0.165 & 0.022 & \(<\)0.001 & 0.512 & 0.278 & 0.065 & \(-\)0.706 & 0.045 & \(<\)0.001 \\ \hline \multicolumn{13}{c}{Train Type (vs. General)} \\ \hline KTX & & & \(-\)0.037 & 0.027 & 0.177 & & & 0.005 & 0.056 & 0.936 \\ Urban & & & 0.702 & 0.020 & \(<\)0.001 & & & 0.646 & 0.045 & \(<\)0.001 \\ No. of fatalities & & & 0.024 & 0.024 & 0.328 & & & 0.460 & 0.054 & \(<\)0.001 \\ No. of Trains Deralied & & & 0.063 & 0.009 & \(<\)0.001 & & & 0.442 & 0.095 & \(<\)0.001 \\ Log-likelihood & & & & \(-\)18,647.2 & & & & & \(-\)10.706.0 & \\ AICC & & & & & & & & & 21,438.0 & \\ \hline \multicolumn{13}{c}{Est., Estimate; S.E., standard error; AICC, Akaike Information Criterion Corrected ([PERSON] and [PERSON] [33]).} \\ \end{tabular}
\end{table} 
Table 4: Two-Part Regression Analyses of Number of Trains delayed due to Railway Accidents.