## 5 Results and Discussion
The trend of predicted crashes in the field-validation based model was different. Figure 9 illustrates the estimation of higher crash predictions for no flashing lights indicator with higher train speeds. The estimated parameters from both base and comparison model gave intuitive results, as previously shown in the literature. For instance, variables such as average annual daily traffic, flashing light as a warning device, maximum timetable speed, and total daily trains were also indicated in previous studies to be factors associated with crash occurrence at HRGCs [3; 7; 11; 16; 29; 30; 31; 32]. In addition to the United States, several similar studies have been conducted in various other countries worldwide to understand the factors of HRGC crashes [32; 33; 34; 35]. It is believed that with the increase in average annual daily traffic and train traffic, exposure is increased as more vehicles and trains come into contact with the rail crossings, increasing the likelihood of crashes [2; 3; 16]. Increased traffic can result in longer  
Figure 8: Predicted crashes of base model for IMAXTSPD and WDTLITs [2]. Figure 9: Predicted crashes of comparison model for IMAXTSPD and WDTLITs [2]. waiting times at crossings. Impatient drivers may take risks, such as trying to beat a train or going around lowered gates, which can lead to collisions [2; 6; 13; 16]. Furthermore, flashing lights enhance the visibility of a railroad crossing, especially during low-light conditions or inclement weather [2]. This increased visibility alerts drivers and pedestrians to the presence of a railway, reducing the risk of crashes. Flashing lights act as a visual and attention-grabbing cue, directing the attention of motorists to the imminent danger of an approaching train. This heightened awareness reduces the likelihood of individuals attempting to cross the tracks when a train is approaching. Past studies have also observed that flashing lights on rail crossings can reduce crashes at HRGCs [2; 3; 11]. The association between maximum train timetable speed and crashes at highway-rail grade crossings has been a subject of study in the field of railroad safety. There is a well-established link between higher train speeds and an increased risk of crashes at these crossings. Past studies have shown that higher train speeds result in a reduced reaction time for both motorists and pedestrians at crossings [2; 3; 18]. As train speeds increase, the time available for drivers and pedestrians to detect an oncoming train, assess the situation, and safely clear the tracks decreases. This reduced reaction time can lead to a higher likelihood of crashes. Additionally, trains traveling at higher speeds require a longer distance to come to a complete stop [2; 16; 18]. It is noteworthy that the primary focus of this research was not to explore hidden factors beyond what have already been highlighted in past research as factors of crash occurrences at HRGCs. Instead, its primary goal was to emphasize the crucial role of high-quality data in crash modeling and stress the importance of establishing a robust foundation before delving into an investigation of crash factors at HRGCs. Furthermore, the new models developed in our research largely incorporated volume-related and physical factors similar to those observed in the FRA's 2020 Accident Prediction (AP) model. However, the parameters exhibited variations in magnitude when utilizing the two datasets. Also, systematic attempts were undertaken to generate random-parameters and develop robustly fitted ZINB models through several trials. Nevertheless, it is crucial to acknowledge that the constraint imposed by utilizing analogous variables in both model instances, intended for the purpose of conducting a comparative study, ultimately precluded the emergence of any randomly determined parameters.