# Comprehensive Evaluation of a Sparse Dataset, Assessment and Selection of Competing Models
## 3 Data  
The crash data were obtained from the Critical Analysis Reporting Environment (CARE) package, which provides comprehensive information regarding various aspects of variables such as vehicles and drivers being involved in a crash. This dataset does not include information related to the roadside geometric characteristic or geometric features of traffic barriers. Thus, this information was obtained and aggregated to the traffic barrier dataset from another source: the information related to 1.3 million feet of traffic barriers was collected from a field survey performed by a WYDOT contractor. The collected information includes various information such as shoulder width, barrier length, height, and offset. Only single vehicle crashes were considered in this study. This is because the severity of multiple vehicle crashes might be due to unseen confounding factors that the included variables could not account for. In addition, due to significant differences across a variety of roadway classifications such as interstate and highway systems, only interstate crashes were considered in this study. The data set includes barriers crashes between 2007 and 2017. These crashes were matched with barriers based on their mile posts and highway route IDs. This resulted in identification of 1069 barriers along 139 miles of roadway, which experienced at least one crash of any severity level during the time period. A significant portion of barriers in the Wyoming interstate system did not experience any crashes. In addition, some of these barriers have heights below or above the recommended heights based on barrier design guidelines. Having higher barriers could result in underride crashes while the reverse could result in override crashes. These types of crashes are historically more severe that other barrier crashes. The critical values for override and underride crashes are considered in this study as below 27 inches and above 35 inches, respectively [17]. It should be mentioned that the higher height limits do not apply to concrete barriers since underride in not plausible for that barrier type. Almost all concrete barriers experienced some form of crash as these barriers are mainly installed as median barriers, which exposed them to a high number of crashes. Barriers with no crashes were incorporated based on the randomness of crashes. There is a high risk of severe crashes for these barriers due to under- or over-ride crashes. Therefore, these barriers were identified and incorporated in the final model on the interstate system. This resulted in identification of a total of 235 barriers along 20 miles of roadway that did not experience any crashes but were below or above the recommended heights. In summary, the whole dataset used in this study incorporated 1388 traffic barriers including barriers with and without crashes. While the whole dataset included barriers' geometric characteristics and traffic volumes, barriers with crashes have additional information such as driver action characteristics. Since some barriers experienced more than one crash and each crash has various driver, roadway, and weather characteristics, the averages of those values were included in the dataset. In Wyoming, the economic costs for various crashes could be calculated as:  
\[ \begin{split}&\text{\emph{EPDO}}\;\text{\emph{rate}}=277\times \text{\emph{Fatal}}\;\text{\emph{ crashes}}+13\times\text{\emph{suspected}}\;\text{\emph{ serious}}\;\text{\emph{injury}}\\ &+4\times\text{\emph{suspected}}\;\text{\emph{minor}}\;\text{ \emph{injury}}+4\times\text{\emph{possible}}\;\text{\emph{injury}}+4\times \text{\emph{Unknown}}+\text{\emph{PDO}}\end{split}  \tag{11}\]  
Based on the above Equation (11), a fatal crash, for instance, is equivalent to 277 PDO crashes. Table 1 presents the descriptive statistics of the included variables found to be important in the statistical section for both barriers with and without crashes.