A two-stage bivariate logistic-Tobit model for the safety analysis of signalized intersections

Abstract

a b s t r a c tCrash frequency and crash severity models have explored the factors that influence intersection safety. However, most of these models address the frequency and severity independently, and miss the correlations between crash frequency models at different crash severity levels. We develop a two-stage bivariate logistic-Tobit model of the crash severity and crash risk at different severity levels. The first stage uses a binary logistic model to determine the overall crash severity level. The second stage develops a bivariate Tobit model to simultaneously evaluate the risk of a crash resulting in a slight injury and the risk of a crash resulting in a kill or serious injury (KSI). The model uses 420 observations from 262 signalized intersections in the Hong Kong metropolitan area, integrated with information on the traffic flow, geometric road design, road environment, traffic control and any crashes that occurred during 2002 and 2003. The results obtained from the first-stage binary logistic model indicate that the overall crash severity level is significantly influenced by the annual average daily traffic and number of pedestrian crossings. The results obtained from the second-stage bivariate Tobit model indicate that the factor that significantly influences the numbers of both slight injury and KSI crashes is the proportion of commercial vehicles. The existence of four or more approaches, the reciprocal of the average turning radius and the presence of a turning pocket increase the likelihood of slight injury crashes. The average lane width and cycle time affect the likelihood of KSI crashes. A comparison with existing approaches suggests that the bivariate logistic-Tobit model provides a good statistical fit and offers an effective alternative method for evaluating the safety performance at signalized intersections.

Random parameters multivariate tobit and zero-inflated count data models: Addressing unobserved and zero-state heterogeneity in accident injury-severity rate and frequency analysis

“…For the statistical analysis and modeling of accident injury-severity rates, multivariate tobit regression (for the traditional tobit model, see Tobin, 1958) has been found to be an appropriate approach (Anastasopoulos et al, 2008(Anastasopoulos et al, , 2012a(Anastasopoulos et al, , 2012bXu et al, 2014). The multivariate tobit model (Huang et al, 1987;Huang, 1999;Trivedi and Zimmer, 2005) accounts for contemporaneous (cross-equation) error correlation among the accident injury-severity rates (i.e., property damage only crashes per 100-million vehicle miles traveled, injury crashes per 100-million vehicle miles traveled, and fatal crashes per 100-million vehicle miles traveled) on specific roadway segments.…”

Incorporating temporal correlation into a multivariate random parameters Tobit model for modeling crash rate by injury severity

“…In the past decade, much research effort has been devoted to the development of innovative methods to analyze crash rates (such as the number of crashes per 100 million vehicle miles traveled), which can be regarded as good alternatives to the traditional crash-frequency prediction models (Anastasopoulos et al, 2008). Compared with crash frequency, crash rates may be more appealing because they (1) are a standardized measure of the relative safety performance of a roadway site, which is more directly useable for road safety evaluation by traffic agencies (Anastasopoulos et al, 2008); (2) clearly reflect the risk of accident involvement and hence are more understandable to the public (Ma et al, 2015b); (3) may be more effective criteria for ranking sites in terms of safety improvement (Xu et al, 2014); and (4) are commonly used in crash reporting systems. For example, the National Highway Traffic Safety Administration uses fatality and injury rates per 100 million vehicle miles traveled to describe traffic safety in the United States (NHTSA, 2012).…”

Modeling nonlinear relationship between crash frequency by severity and contributing factors by neural networks

“…In the former group, correlation between crash frequencies at various severity levels is the most important issue. To deal with it, a series of techniques have been investigated, such as multivariate regression models (Aguero-Valverde and Jovanis, 2009;Anastasopoulos et al, 2012;Barua et al, 2014Barua et al, , 2016Bijleveld, 2005;El-Basyouny and Sayed, 2009;El-Basyouny et al, 2014;Ma and Kockelman, 2006;Ma et al, 2008;Park and Lord, 2007), simultaneous equations (Ye et al, 2009(Ye et al, , 2013, a joint-probability approach (Pei et al, 2011), two-stage bivariate/multivariate models (Wang et al, 2011;Xu et al, 2014) and multinomial-generalized Poisson models Fu, 2013, 2015;Chiou et al, 2014). The multivariate Poisson regression proposed by Ma and Kockelman (2006) adds a common error term into the Poisson distributions of univariate regressions to account for their correlation, but it does not allow for the commonly observed over-dispersion, and it assumes the identical and positive covariances across crash frequencies (Park and Lord, 2007).…”

“…Compared with multivariate regression models, the formulation of simultaneous 4 equations, the joint probability model and the two-stage bivariate/multivariate models 5 are less complicated (Pei et al, 2011;Wang et al, 2011;Xu et al, 2014;Ye et al, 6 2009Ye et al, 6 , 2013. Besides, the computation burden of simultaneous equations is lighter, 7…”