Contents lists available at ScienceDirect Accident Analysis and Prevention journal homepage: www.elsevier.com/locate/aap A Bayesian multivariate hierarchical spatial joint model for predicting crash counts by crash type at intersections and segments along corridors Saif A. Alarifi ⁎ , Mohamed Abdel-Aty, Jaeyoung Lee University of Central Florida, Department of Civil, Environmental, and Construction Engineering, Orlando, FL 32816, United States ARTICLE INFO Keywords: Multivariate hierarchical spatial model Corridor safety analysis Joint model Crash types ABSTRACT The safety and operational improvements of corridors have been the focus of many studies since they carry most traffic on the road network. Estimating a crash prediction model for total crash counts identifies the crash risk factors that are associated with crash counts at a specific type of road entity. However, this may not reveal useful information to detect the road problems and implement effective countermeasures. Therefore, investigating the contributing factors for crash counts by different types is of great importance. This study aims to provide a good understanding of the contributing factors to crash counts by different types at intersections and roadway seg- ments along corridors. Data from 255 signalized intersections and 220 roadway segments along 20 corridors have been used for this study. The investigated crash types include same direction, angle and turning, opposite direction, non-motorized, single vehicle, and other multi-vehicle crashes. Two models have been estimated, which are multivariate hierarchical Poisson-lognormal (HPLN) spatial joint model and univariate HPLN spatial joint model. The significant variables include exposure measures and some geometric design variables at in- tersection, roadway segment, and corridor levels. The results revealed that the multivariate HPLN spatial joint model outperforms the univariate HPLN spatial joint model. Also, the correlations among crash counts of most types exist at individual road entity and between adjacent entities. Additionally, the significant explanatory variables are different across crash types, and the magnitude of the parameter estimates for the same in- dependent variable is different across crash types. The results emphasize the need for estimating crash counts by type in a multivariate form to better detect the problems and provide appropriate countermeasures. 1. Introduction Corridors safety analysis is a major concern since they carry most traffic on the road network, and their safety and operational improve- ments have been the focus of many studies. Corridors mainly contain signalized intersections and roadway segments, and analyzing safety at corridors by having both components provides a good understanding of the crash risk factors at intersections and roadway segments along corridors. Crash risk factors along corridors include some geometric design features, traffic flow characteristics, and traffic control and signal information. Different types of countermeasures at the corridor level have been proposed (e.g. signal coordination, access management, and median treatments) to enhance the safety and operational effi- ciency at corridors. Developing a crash prediction model for total crash counts identifies the crash risk factors that are associated with crash frequencies at specific locations. However, to implement effective countermeasures, it is required to investigate crash counts of different types. Also, different crash types are associated with traffic and geometric characteristics in different ways (Kim et al., 2006, 2007). Therefore, investigating the contributing factors to crash frequencies for different crash types is of great importance since it provides better explanatory power compared to a single total crash counts model. However, estimating a separate crash frequency model for each crash type may result in inefficient and biased parameters because different crash types may share unobserved or omitted variables (Ye et al., 2009; Aguero-Valverde et al., 2016). As a result, estimating a multivariate model, where crash counts by different types are modeled simultaneously, is necessary to handle the common unobserved factors and provide more accurate parameter estimates. While analyzing intersections and roadway segments along corri- dors, there is a potential presence of spatial correlations among the road entities since these road entities have similarities in the roadway and driver characteristics, and accounting for this spatial correlation in the model is essential especially if the distance between the road entities is not large. Ignoring the spatial correlation may lead to biased model parameters (Guo et al., 2010; Lesage and Pace, 2009). In addition, it has https://doi.org/10.1016/j.aap.2018.07.026 Received 8 January 2018; Received in revised form 13 July 2018; Accepted 21 July 2018 ⁎ Corresponding author. E-mail address: Saif.a@knights.ucf.edu (S.A. Alarifi). Accident Analysis and Prevention 119 (2018) 263–273 0001-4575/ © 2018 Elsevier Ltd. All rights reserved. T