## 3 Data  
The data in this study were aggregated from three main sources: traffic, historical crashes, and barriers geometric characteristics. All datasets were aggregated over a period of 2007-2017. The traffic dataset includes various traffic data such as the average annual daily traffic (AADT) and average annual truck traffic (ADTT).  
The crash data is filtered to include only those crashes having \"hitting a barrier\" as their first harmful event. The response of the crash data was crash severity levels, which was converted into equivalent property damage only crashes (EPDO), based on the criteria highlighted with Wyoming department of transportation (WYODOT) as follows:  
\[EPDO\ rate=Fatal\ crashes+suspected\ serious\ injury+suspected\ minor\ injury+possible\ injury+Unknown+PDO \tag{23}\]  
After converting Equation (23) into their monetary values, the above equation could be written as follows:  
\[EPDO\ rate=277\times PDO+13\times PDO+4\times PDO+4\times PDO+4\times PDO+1 \times PDO \tag{24}\]  
Barrier geometrics includes various roadway and barrier geometric characteristics such as barrier types, length, offset, barrier height, and various roadside geometric characteristics such as shoulder width. This dataset also includes the starting and ending mileposts of traffic barriers on roadways, and roadway ID along with their directions. The milepost and roadway ID information were used for aggregating the crashes across various barriers. It should be noted, for the crash dataset, two highway systems, highway and interstate, were considered.  
Few points are worthy to mention from Table 1. Often a barrier experienced more than a crash. For this scenario, while EPDOs are summed across those barriers, an average of various drivers, weather and road conditions were used as explanatory variables across those barriers. For instance, during the 10-year period, if two drivers: one male as 0 and another female driver as 1 hit a barrier, gender would be set as the average of these two observations as 0.5.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Variable** & **Variable Description** & **Mean** & **Variance** & **Min** & **Max** \\ \hline Cluster, alpha & Cluster information through FMM, 4 clusters: 1 to 4 & 3 & 0.545 & 1 & 4 \\ Highway system, b8 & 0 as highway * versus 1 as interstate & 0.5 & 0.497 & 0 & 1 \\ Restrain condition, b1 & 0 as proper restrain * versus 1 others & 0.1 & 0.275 & 0 & 1 \\ Gender, b2 & 0 as male * versus others & 0.3 & 0.396 & 0 & 1 \\ Residency, b3 & 0 as Wyoming residence * versus 1 as others & 0.5 & 0.433 & 0 & 1 \\ Weather condition, b4 & 0 as clear weather conditions * versus 1 as others & 0.5 & 0.424 & 0 & 1 \\ Light condition, b5 & 0 as light * versus 1 as others & 0.4 & 0.414 & 0 & 1 \\ AADT, b6 & Traffic, continuous & 2438 & 1584 & 27 & 8853 \\ \hline \hline \end{tabular}  
* Reference category.  
\end{table}
Table 1: Descriptive summary of the variables that were found to be important.  
Additionally, an average of the predictor highlights the distribution of those characteristics across a specific barrier. For instance, roadway classification for the first part of the table had a mean of 0.5, meaning that half of the barriers were in the highway system while the other half were placed in the interstate system. Only two barriers accounting for more than 95% of barriers were incorporated in the analysis, box-beam and W-beam. Additionally, the cluster in Table 1 is a variable created by the FMM, which would be elaborated in the next section. In total, 1848 barriers with almost equal proportion across two highway systems in Wyoming were considered in this study. The data accounted for 1,373,282 linear feet of barriers.