## 5 Results and Discussion
Both models showed a different fitness performance based on the Akaike Information Criteria (AIC) and Byesian Information Criteria (BIC), indicating improved ZINB model fitness with the field-validated accurate inventory dataset [2; 12]. * The coefficients for Natural log-transformed Maximum Timetable Speed (IMAXTSPD) and Natural log-transformed Average Annual Daily Traffic (IAADT) exhibited positive signs in both models. However, the expected magnitude differed in both models, where the base model gave a higher coefficient expected magnitude for IAADT compared to the comparison model. Moreover, for IMAXTSPD, the comparison model gave a higher coefficient expected magnitude. The average marginal effect estimates presented in Table 8 show that a unit change in IAADT increases predicted crashes by 0.02681 in the base model and 0.02546 in the comparison model. * The coefficients for warning-device-type flashing lights (WDTLIT) were negative for both models (i.e., compared to passive devices, warning flashing lights reduce predicted crashes). However, the coefficient expected magnitudes and average marginal effects (Table 8) of WDTLITs differ in both models, where the base model estimated a higher negative value compared to the comparison model. * The coefficients of Ln-transformed total daily trains (ITDTRAININS) in the zero-inflated part in both the base and comparison models were negative, indicating that the probability of excess zeros decreases with the number of trains, as expected. However, the coefficient expected magnitudes of ITDTRAININS differed in both models. * All the coefficients retained in both models indicated strong statistical significance. However, as shown in Table 9, the results of hypothesis tests revealed that the regression coefficients were not statistically significantly different when utilizing the two inventory datasets. Figure 8 illustrates a \"Predicted crashes versus AADT (natural logarithm)\" chart for a warning-device-type flashing light indicator. The chart indicates that for cases of HRGCS with no flashing lights in the original FRA dataset, the model gave higher crash predictions for maximum timetable speed ranging from 25 to 45 mph. However, the presence of flashing lights decreased predicted crashes, but only for low-speed trains. Additionally, in Figures 8 and 9, the scales for the parameter IMAXTSPD (ranging from 0 to 4) represent the natural log-transformed values for the maximum timetable speed of trains. This transformation serves to normalize the data, handle outliers, and stabilize variance [2,3]. The gray areas in Figures 8 and 9 represent standard errors, and the blue line shows the best-fit line. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Model Type** & **Variable** & **Effect** & **Std. Error** & **Z-Value** & \(p\)**-Value** \\ \hline Base model & IAADT & 0.02681 & 0.01099 & 2.440 & 0.0146774 \\ (based on & WDTLITs & \(-\)0.12232 & 0.04714 & \(-\)2.595 & 0.0094708 \\ original FRA & IMAXTSPD & 0.08008 & 0.03567 & 2.245 & 0.0247619 \\ inventory data) & ITDTRAININS & 0.02431 & 0.01124 & 2.391 & 0.0166414 \\ \hline Comparison & IAADT & 0.02546 & 0.01082 & 2.353 & 0.018636 \\ model (based on & WDTLITs & \(-\)0.11768 & 0.04713 & \(-\)2.497 & 0.012539 \\ field-validated & IMAXTSPD & 0.08714 & 0.03704 & 2.352 & 0.018663 \\ inventory data) & ITDTRAININS & 0.02383 & 0.01124 & 2.2912 & 0.021725 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Average marginal effects for base and comparison models [2]. \begin{table}
\begin{tabular}{l c c} \hline \hline
**Comparing Regression Coefficients of the Base and Comparison ZINB Models** \\
**H0: There is no Statistically Significant Difference between Coefficients of the Two Models** \\
**Compared Parameters** & **Z statistic** & \(p\)**Values** \\ \hline IAADT & 0.00802 & 0.9935 \\ WDTLITs & \(-\)0.10875 & 0.9134 \\ IMAXTSPD & 0.13174 & 0.8951 \\ ITDTRAININS & \(-\)0.14899 & 0.8815 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison of coefficients of the base and comparison ZINB models [2].