# Analysis of the Railway Accident-Related Damages in South Korea
## 4 Real Application
\begin{table}
\begin{tabular}{c c c} \hline
**Type** & **Information** & **Description** \\ \hline Dependent Variables & No. of Delayed Trains & The number of trains delayed due to railway accidents \\ \cline{2-3}  & Delay Time & Train delay time due to railway accidents (minute) \\ \cline{2-3}  & Amount of Costs & Amount of costs due to railway accidents (million won) \\ \hline  & Year & Year (2008–2016) \\ \cline{2-3}  & Organization & KORAIL (88.8%), Metro (11.2\%) \\ \cline{2-3}  & Railroad Type & KTX (14.7%), Urban (31.4\%), General (53.8\%), missing (0.1\%) \\ \cline{2-3}  & Accident Factor & Human-related (51.6\%), Non-human-related (48.4\%) \\ \cline{2-3}  & Accident Type & Traffic (30.8\%), Safety (13.8\%), Misc. (8.71\%), rolling stock (46.7\%) \\ \cline{2-3}  & No. of Derailed Trains & The number of derailed trains due to railway accidents \\ \cline{2-3}  & No. of Fatalities & The number of fatalities due to railway accidents \\ \cline{2-3}  & No. of Casualties & The number of casualties due to railway accidents \\ \hline \end{tabular}
\end{table} 
Table 2: Description of the Variables in Korea Transportation Safety Authority (KOTSA) Railway Accidents Dataset. random variables includes zero as one of the possible realizations. Therefore, TPMs for semi-continuous data are essential to build both logit part for zero measurements and the gamma (or log-normal) part for non-zero (or positive) measurements. Table 3 shows the frequencies of each of the categorized non-negative count variables such as the number of fatalities (casualties), the number of derailed trains and the number of trains delayed due to the railway accidents. All the variables in Table 3 have a lot of zero measurements (24.0-99.2%). Hence, zero-inflated regression model for the variables is applied for the number of delayed trains. Figure 4: Distribution of Amount of Costs (the measurements above 100 million won (0.6%) are not displayed in the histogram). Figure 3: Distribution of Delay Time (the measurements above 400 min (0.6%) are not displayed in the histogram). \begin{table}
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The values are expressed as number of cases (percentage). Table 4 illustrates the regression analyses of the number of trains delayed due to the railway accidents with some of the independent variables shown in Table 2. In general, positive estimates increase the probability of having more trains delayed (or the number of trains delayed) but negative estimates decrease them. As can be seen in Table 4, the estimation results are quite similar irrespective of the models considered. For example, more trains are estimated to be delayed during the period of our interest due to the railway accidents as the corresponding estimates are positive (0.063 in ZIP; 0.066 in ZINB) and KORAIL has a smaller number of trains delayed than the other railway organizations in that its associated estimates (\(-\)0.628 in ZIP; \(-\)0.891 in ZINB) are negative. Human-related accidents resulted in less trains delayed compared to the non-human related accidents because of the negative estimate (\(-\)0.165 in ZIP; \(-\)0.706 in ZINB). We can also see that the number of derailed trains has a positive impact (0.063 in ZIP; 0.442 in ZINB) on the number of delayed trains. The ZIP model shows that the KTX (0.005) does not cause more delayed trains under the significance level of 0.05 but the urban trains (0.646) result in more delayed time than the general trains. We can also see that number of fatalities increases the number of delayed trains. The interpretation also works for the ZINB model. The logit part in the ZIP model has statistically significant effect of the accident factor (human-related factor vs. non-human-related factor). However, none of the independent variables are of significance in the logit part of ZINB model. In terms of Akaike Information Criterion Corrected (AICC) [24], the ZINB model outperforms the ZIP model.