Application of Quantile Mixed Model for modeling Traffic Barrier Crash Cost

Run-off the road crashes account for a significant proportion of severe injuries to vehicle occupants. Traffic barriers have been installed with an objective to keep vehicles on the roadway, and prevent them from hitting natural obstacles like trees or boulders. However, still injuries and fatalities of barrier crashes account for high proportion of fatalities on roadway. Due to challenging geometrics characteristics of Wyoming's roadway, a high mileage of barriers has been installed in the state. The high mileages of barriers result in a high number of barrier crashes in terms of crash frequency and severity due to high exposure. Previous studies mainly focused on crash frequency or individual crash severity. However, it has been recognized the importance of accounting for both aspects of crash severity, and crash frequency. So, in this study, crashes are aggregated across different barriers, and those crashes were converted into costs by considering the impacts of both crash severity and frequency. However, one of the main challenges of this type of dataset is highly skewness of crash data due to its sparseness nature. An improper use of model distribution of crash cost would result in biased estimations of the covariates, and erroneous results. Thus, in order to address this issue, a semi-parametric method of quantile regression technique was implemented to account for the skewness of the response by relaxing model distribution parameters. Also, to account for the heterogeneity in the dataset due to barriers' types, a random intercept model accounting for the structure of the data was implemented. In addition, interaction terms between significant predictors were considered. Understanding what factors with which magnitude contribute to the barrier crash costs is crucial for the future barriers' optimization process. Thus, contributory factors to barriers crash cost with high, medium, and low values, corresponding to 95th, 70th, and 60th percentiles were considered, and a comparison was made across these models. It was found, for instance, that although factors such as rollover, driving under the influence, and presence of heavy truck all have contributory impacts on the cost of crashes, their impacts are greater on higher quantiles, or higher barriers' costs. These models were compared from various perspectives such as intra class correlation (ICC), and standard error of coefficients. This study highlights the changes in coefficient estimates while modeling crash costs.