# Two-Component Bayesian Hierarchical Models for Cost-Benefit Analysis of Traffic Barrier Crash [PERSON]
## 14 Conclusions  
This study was conducted with an objective of implementing a cost-benefit analysis of traffic barrier geometric enhancement. The traffic barriers in the state is characterized by a preponderance of zeros due to low traffic volumes. Most of these zero-crash barriers have not received any crashes due to the nature of crash randomness and low traffic volumes. A significant portion of those barriers need an immediate attention since they are not within recommended geometric characteristics. Thus, this project was initiated by WYDOT to find a methodological approach to provide a monetary benefit of optimizing those barriers. In addition, due to limited budget of WYDOT, those barriers need to be prioritized so barriers with higher benefit could be optimized first.  
The main step in conducting an optimization technique is to identify a best fit model that can model sparse EPDO barrier crashes with presence of excess zeroes. To achieve this objective, various two-component models with various count distributions, in addition to a simple count model, were considered. In order to account for the unobserved heterogeneity across various crash observations due to traffic barrier types, the association was introduced through suitable random effects hierarchical model. All the analyses were conducted in the Bayesian framework. The two-component distribution is a mixture of two distribution, Bernoulli and NB or Poisson, while a single-component model was Bayesian hierarchical NB model.  
Deviance information criterion (DIC) was used for model selection. A two-component model with NB as a count part was identified to perform best compared with all other considered models. A comprehensive discussion was made about various scenarios of two popular two-component models, zero inflated and hurdle model. These two models were found to be very similar in prediction of barrier EPDOs, especially in predicting zeroes. The zero-parts of these models include traffic and highway classification type. The first layers of both models could not predict any zero-crash barriers. In other words, no barriers could be predicted by models as safe, even if the current traffic condition persist. This could be justified by the main reason of the randomness of crashes. A barrier at a very low traffic could still be hit by erroneous activities resulted from a careless driver. This is why a model identified a significant portion of most hazardous barriers among those barriers that have not experiences any crash, EPDO = 0, as shown in Table 6. Despite having a lower percentage of interstate barriers in the dataset, based on optimization results, most of the identified barriers to be enhanced first belong to the interstate system.  
The results also indicated that after investing the money into upgrading barriers, WYDOT is not only expected to regain the investment over ten years, but also to gain more than 3 million dollars in crash savings. The results of the implemented cost-benefit analysis presented in this paper do not just provide WYDOT with the expected benefits from upgraded barriers, but it also prioritizes barriers based on higher benefits so that WYDOT can allocate available funding to enhance barriers annually based on available budgets. The process described in this paper can be utilized by other DOTS to optimize the expenditures on updating the road barriers in their states.  
Funding and supervision: K.K.; Methodology and statistical analysis: M.R. All authors have read and agreed to the published version of the manuscript.  
This research was funded by Wyoming Department of Transportation.  
The authors declare no conflict of interest across the authors of this study.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Variance** & **Min** & **Max** \\ \hline Predicted EPDO & 90 & 1 & 198 \\ \hline Real EPDO & 168 & 0 & 287 \\ \hline \multicolumn{4}{c}{Root mean square error = 35,064} \\ \hline \hline \end{tabular}
\end{table}
Table 7: Some statistics about predicted and real EPDO based on ZI method.