## 4 Empirical Assessment Using Real-World Data
### Data  
The dataset used in our analysis covers the years 2011 to 2015. This timeframe was chosen to gather a comprehensive set of data related to traffic accidents on general national roads, focusing on understanding the factors contributing to road safety. The primary method for data collection involved the use of the ARASEO (Automated Road Analysis and Safety Evaluation Tool) vehicle, an advanced road inspection vehicle equipped with technology for capturing detailed road geometry [32]. This vehicle collected data on the physical characteristics of the roads, including road geometry data. Measurements were taken at one-meter intervals, providing the high level of detail necessary for accurate safety analysis. The geometric raw data collected by the ARASEO vehicle, along with data from the road registry, were processed and analyzed using geographic information systems (GISs). Additionally, the obtained data were combined with traffic volume and historical accident data to create the final database, which could be used for further analysis. The final data were obtained from the Korea Institute of Civil Engineering and Building Technology (KICT) in South Korea. Following the necessary data preprocessing, which included the removal of redundant and erroneous entries, the finalized dataset consisted of 8636 road segments and encompassed a total of 3182 crashes recorded over the specified period. As depicted in Figure 2, the frequency of crashes across these segments varied, with counts ranging from 0 to 24 incidents. Notably, the dataset displayed a pronounced skew towards zero counts. There were 7052 road segments with no recorded crashes, constituting approximately 81% of the dataset. This high prevalence of zeros poses a particular challenge for predictive modeling and underscores the necessity for a model adept at handling zero-inflated data, a key attribute of the new model proposed in this study. The data include a mix of continuous and categorical variables reflecting the physical characteristics of the road environment and traffic patterns. For continuous factors, we have measurements such as the length of homogeneous road sections, the degree of road slope, the curvature of the road, lane widths, median widths, and the road shoulder width. Traffic volume is quantified by the annual average daily traffic (AADT), providing an indicator of road utilization intensity. A detailed description and summary statistics of continuous variables, including the dependent variable, is provided in Table 1. The categorical data introduce indicators for elements like the number of lanes, the presence of climbing lanes (which allow slower-moving vehicles to move aside), median barriers, and guard trails, all of which are safety features that can potentially influence crash occurrences. The presence of street lights, distinguishing between well-lit and poorly lit stretches of road, is also included. Additionally, the roads are categorized into rural or suburban segments, whichcan inform the analysis based on varying traffic behaviors and environmental conditions. Table 2 shows summary statistics of the categorical variables. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline
**Variable** & **Definition (Unit)** & **Mean** &
\begin{tabular}{l} **Standard** \\ **Deviation** \\ \end{tabular} & **Minimum** & **Maximum** \\ \hline Cash Count & Crash frequency count & 0.37 & 1.21 & 0 & 24 \\ Section Length & Homogeneous section length (meter) & 129.90 & 131.44 & 50 & 3100 \\ SLOPE & Vertical slope absolute value (\%) & 1.94 & 1.76 & 0 & 12.05 \\ Curve Radius & Horizontal curve radius (meter) & 272.21 & 437.62 & 0 & 2000 \\ Road Width & Lane width (meter) & 3.79 & 0.68 & 2.5 & 5 \\ Median Width & Median width (meter) & 0.91 & 0.79 & 0 & 4 \\ Shoulder Width & Shoulder width (meter) & 0.59 & 0.69 & 0 & 11.3 \\ AADT & AADT & 9306.97 & 9253.74 & 321 & 54,307 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary statistics of continuous variables.