Contents lists available at ScienceDirect Transportation Research Part C journal homepage: www.elsevier.com/locate/trc Analysis of train derailment severity using vine copula quantile regression modeling Emmanuel Nii Martey, Nii Attoh-Okine ⁎ Department of Civil and Environmental Engineering, University of Delaware, Newark, DE, USA ARTICLE INFO Keywords: Train derailment severity Rail Railroad safety Copulas Vine copulas Quantile regression ABSTRACT Although there is a low frequency of train derailments, they have been a major concern due to their high consequences justifying the need to critically examine the severity of train derailments. Derailments may result in injury, loss of life and property, interruption of services and damage of the environment. Most derailment severity models have utilized point estimation approaches which focus on the central tendency of derailment severity outcomes. However, this approach is not reliable given the high variation in derailment severity. Thus, it is imperative to take into consideration the entire severity distribution by examining other statistics including conditional quantiles. Furthermore, derailment data has been found to exhibit tail dependence, skewness and non-normality of the marginal distributions and joint distribution of the variables. Therefore, it is not appropriate to examine their interrelationships using conventional correlation analysis. For these reasons, this paper employs vine copula quantile regression model, an interval estimation approach, to predict conditional mean and quantiles of derailment severity outcomes. This novel methodology automatically tackles prominent issues in classical quantile regression including quantile crossing at various levels and interactions between covariates. Vine copulas, which are multivariate copulas constructed hierarchically from bivariate copulas as building blocks, permit the modeling of the complex dependences between the variables. The vine copula quantile re- gression model was found to offer better accuracy for analyzing derailment severity at various confidence levels compared to the classical quantile regression approach. The findings provide greater comprehension of the influence of the covariates on train derailment severity. 1. Introduction Despite the relatively low frequency of train derailments, they have been a major concern due to their high consequence justifying the need to critically examine the severity of train derailments in order to minimize and mitigate the resulting damage (Jeong et al., 2007; Liu et al., 2013). Derailments may result in loss of life and property, interruption of services and destruction of the environment (Liu et al., 2013), and are the most frequent kind of Federal Railroad Administration (FRA)-reportable mainline train accident in the United States (Barkan et al., 2003; Liu et al., 2012; Liu, 2015). Derailments made up about three-quarters of freight-train accidents in the United States from 2001 to 2010. Therefore, analyzing the magnitude and variability of derailment severity is as important as estimating the likelihood of derailment (Liu et al., 2013). Derailment severity may be influenced by factors like car mass, derailment speed, residual train length (number of cars after the point of derailment), derailment cause, ground friction, rail friction, proportion of loaded railcars in the train (loading factor) and https://doi.org/10.1016/j.trc.2019.06.015 Received 11 January 2018; Received in revised form 23 April 2019; Accepted 22 June 2019 ⁎ Corresponding author. E-mail addresses: enmartey@udel.edu (E.N. Martey), okine@udel.edu (N. Attoh-Okine). Transportation Research Part C 105 (2019) 485–503 0968-090X/ © 2019 Published by Elsevier Ltd. T