# Two-Component Bayesian Hierarchical Models for Cost-Benefit Analysis of Traffic Barrier Crash [PERSON]
###### Abstract
However, in order to account for similar characteristics, correlation across same traffic barrier types or heterogeneity resulted from the effects of various barrier types on crash observation, the hierarchical framework was employed. 3. In order to account for the exposures, various variables such as barrier length and traffic were incorporated in the analysis. 4. After a model is trained across all barriers in the highway and interstate systems, the trained model was implemented only on those barriers that are below/above recommended heights. 5. Barrier cost with no enhancement: the trained model was implemented on the current data for 10 years with only traffic as a varied variable during 10-year period: this evaluates how much money due to crashes is expected if barriers are not optimized. 6. Barriers cost with barrier height enhancement: the barriers were enhanced to their optimal values based on the recommended height in the literature review. The trained model was then implemented again over 10 years, while traffic was increased at a constant rate. 7. The cost of barriers enhancement was considered in the cost-benefit analysis when barriers were enhanced, and added to the total cost of 6. 8. As the analysis was based on equivalent property damage only (EPDO), this factor is converted to its monetary value so that the barrier enhancement cost could be added to the EPDO cost. 9. The barriers were ranked based on expected benefit so that WYDOT could first enhance those barriers with more benefits. 10. A main challenge of modeling barriers EPDO was sparsity and excess number of zeroes in the dataset, which was addressed by a two-component model. Most of the studies in the literature review either focused on the severity [3] or the frequency of barrier crashes [4]. However, not many studies have considered both aspects of barriers: namely, crash severity and frequency. Thus, this study was conducted to take into account both aspects of crash frequency and crash severity by using EPDO as a response. One of the challenges of modeling EPDO as a response is its over-dispersion. This problem can be addressed by implementing a negative binomial (NB) (Poisson-gamma) mixture model. However, the situation would be worse if the analysis also incorporates the barriers that did not experience any crash. For this condition, although the NB model might still account for over-dispersion and excess amount of zero, this model might not be an ideal decision for the distribution. Negative binomial has been used extensively in the past studies to account for sparsity, and a hierarchical approach to account for heterogeneity. Few of those studies would be highlighted here. Zero-inflated NB was used to model heterogeneity for a large sparse spatio-temporal data [5]. The model was chosen to account for the sparse and heterogeneous outcome. The count heterogeneous outcome was modeled by NB Bayesian hierarchical model [6]. The method was found to outperform the other considered methods. Traffic barriers in Wyoming tend to contain a large amount of zero crashes due to low traffic in the state. Such data can be referred to two-component models, zero-inflated or hurdle models. Excess number of zeroes and zero inflation result in over-dispersion, meaning that the actual variance of the observations exceeds the nominal variance of the assumed distribution [7]. Consequently, this over-dispersion could result in assumption violation [8]. This is especially important when doing machine learning modeling with an objective of cost-benefit analysis as a wrong use of a model distribution could result in erroneous results. A two-component model might provide an adequate framework by combining two models into a joint model. For this model after examining classes at point mass of zero, the primarily focus would be on count data with count model distribution, e.g. Poisson. Thus, this study was conducted, with the use of various statistical methods, to model traffic barrier crash EPDO.