# Comprehensive Evaluation of a Sparse Dataset, Assessment and Selection of Competing Models
## 6 Summary and Conclusions  
The installation of traffic barriers would be warranted if they could reduce the severity of fixed object crashes. However, barrier crash severity will still exist when hitting a barrier. Actually, traffic barrier crashes are a major social and economic concern due to their high severe crash rate for policy makers, especially in a mountainous area like Wyoming with significant under/over standard barriers heights needing immediate attention.  
Studies in the literature review only focused on the severity of barrier crashes. However, crashes are random and not experiencing a crash does not indicate that a specific barrier is not hazardous. The condition would be more critical if those barriers were below standard design, and also if they did not experience a crash. In addition to barriers with crashes, this study incorporated barriers with no crashes that were not designed based on the recommended height, posing a danger of underride or override crashes.  
To account for both severity and the frequency of crashes, EPDO was used as a measure that could account for both aspects of crashes. The distribution of responses shows a substantial amount of over-dispersion that cannot be accounted for by a Poisson model. In addition, the number of zeros were so large that just correcting for over-dispersion through the negative binomial model cannot address the issue. Thus, in order to identify the right distribution, various models were considered and the best-fit model was identified based on various measures.  
AIC measure was used for a decision across various model distributions. A comparison was used not only between various goodness-of-fit measures across the included models, but also between the sign and magnitude of various coefficient estimates. The results indicated that considering the wrong distribution would not only result in a biased estimation of the coefficients for some predictors, but the signs of some critical predictors such as barrier height would be reversed. This would result in a tremendous waste of public funds if it would have not been addressed properly.  
The comparison results based on various measures work in the favor of the hurdle model. Rootograms was used to make the decision of the truncated hurdle model by considering negative binomial and Poisson distributions. Although the negative binomial distribution seems to be suitable for the sparse nature of the dataset, the rootograms visualize how various models would fit the observations. These measures highlighted that the negative binomial distribution for the first component of the hurdle model could fit the data quite well. It is recommended for future studies to give attention to a model distribution assessment while considering crash frequency or EPDO. An optimization technique would be considered for barrier optimization in the Wyoming interstate system.  
**Author Contributions:** Supervision and funding: K.K., methodology and analyses: M.R. Both authors have read and agreed to the published version of the manuscript.  
**Funding:** The project was funded by WYDOT.  
**Conflicts of Interest:** The authors declare no conflict of interest.