Modeling correlation and heterogeneity in crash rates by collision types using full bayesian random parameters multivariate Tobit model

doi:10.1016/j.aap.2019.04.013

Accident Analysis & Prevention

Volume 128, July 2019, Pages 164-174

https://doi.org/10.1016/j.aap.2019.04.013 Get rights and content

Highlights

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Factors affecting crash rates by collision type at freeway diverge areas were evaluated.
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A novel random parameters multivariate Tobit model was developed for safety modeling.
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Correlation between collision types and unobserved heterogeneity across observations were accommodated.
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The impact of risk factors on different collision types were estimated to be distinct.
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Heterogeneous effects on crash rates by collision type were found in certain factors.

Abstract

Crashes present different collision types. There usually exist unobserved risk factors which could jointly affect crash rates of different types, resulting in correlation and heterogeneity issues across observations. The primary objective of the study is to propose a novel random parameters multivariate Tobit (RPMV-Tobit) model for evaluating risk factors on crash rates of different collision types. Crash data from 367 freeway diverge areas in a three-year period were obtained for modeling. Three major types of collisions including rear-end, sideswipe, and angle collisions were considered. The RPMV-Tobit model was structured to simultaneously accommodate correlations between crash rates across collision types and unobserved heterogeneity across observations. The RPMV-Tobit model was compared with a multivariate Tobit (MV-Tobit) model, a random effect multivariate Tobit (REMV-Tobit) model, and independent univariate Tobit (IU-Tobit) models under the Bayesian framework. The results showed that MV-Tobit model outperforms the IU-Tobit models on fitting crash rates, indicating that accounting for the correlation between crash types can improve model fit. The RPMV-Tobit model and REMV-Tobit model perform better than the MV-Tobit model, suggesting that accounting for the unobserved heterogeneous can further improve model fit. The improvement of model performance with the RPMV-Tobit model is higher than that with the REMV-Tobit model. The impacts of each risk factor on crash rates were estimated and some differences were found across different collision types. The lane-balanced design, number of lanes on mainline, speed limit, and speed difference present significant heterogeneous effects on crash rates. Findings suggest that the RPMV-Tobit model is a superior approach for comprehensive crash rates modeling and traffic safety evaluation purposes.

Introduction

Freeway diverge areas play an important role in diverging the exiting traffic from the through traffic on freeway mainline. However, they have been considered to be crash-prone locations due to the disturbances caused by the intense lane changes at diverge areas (Chen et al., 2009; Liu et al., 2009; Li et al., 2015). These disturbances may result in many traffic conflicts, leading to high potential of traffic crashes. An efficient way to improve the safety of freeway diverge areas is to understand the risk factors affecting crashes at freeway diverge areas. As such, analytical tools need to be developed that can aid transportation safety professionals in mitigation of crashes. Previous studies have developed several safety performance functions (SPFs) to evaluate the safety performance of freeway exit ramp areas (Bauer and Harwood, 1998; McCartt et al., 2004; Lord and Bonneson, 2005; Moon and Hummer, 2009; Chen et al., 2009; Lu et al., 2010; Wu et al., 2014). Though it is expected that the impact of risk factors on different collision types are different, previous studies did not distinguish the collision types during the modeling analyses of crash rates. This study aims to add to the current literature by proposing a methodological approach that takes into account crash rates by collision types at freeway diverge areas. Moreover, this paper seeks to shed light on possible risk factors related to crash rates of different collision types at freeway diverge areas.

Crash rates analysis is now advocated as an alternative of crash frequency prediction models because of several advantages. Crash rates provide a standardized safety measure of road entities, which is more understandable and acceptable to the public. Moreover, crash rates are commonly used in the accident reporting systems (NHTSA, 2012). As such, the development of crash rates model has many potential applications and benefits. For example, the crash rate models were considered to be a complementary tool for road safety diagnosis in hotspots identification (Ma et al., 2015a; Xu et al., 2014; Ma et al., 2018). The traffic safety evaluations in before-after studies could be enhanced by combining crash count models and crash rates models.

Different from the features of discrete and non-negative for crash frequency, crash rates are continuous data that is usually left-censored at zero because no crashes may be reported over a specified time period. To deal with the censoring problem, the Tobit model was proposed to model crash rates by previous study (Anastasopoulos et al., 2008). The model has attracted considerable interest in recent traffic safety studies (Anastasopoulos et al., 2012a; Xu et al., 2013; Chen et al., 2014; Xu et al., 2014; Ma et al., 2015b; Yu et al., 2015; Caliendo et al., 2016; Bin Islam and Hernandez, 2016; Anastasopoulos, 2016; Zeng et al., 2017a, b; Anderson and Hernandez, 2017; Sarwar and Anastasopoulos, 2017; Zeng et al., 2018).

Crashes present different collision types due to the particular geometric and traffic features at various freeway diverge areas. Compared with analysis of total crash rates at freeway diverge area, modeling crash rates by collision types can provide better understanding of the impact of risk factors on the crash rates with a particular collision type. However, if crash rates are modeled independently irrespective of correlations among crash rates across collision types, significant estimation error could be introduced because unobserved effects at freeway diverge areas are likely to be shared among different types of collisions (Anastasopoulos et al., 2012a; Anastasopoulos, 2016; Zeng et al., 2017a; Sarwar and Anastasopoulos, 2017; Zeng et al., 2018). Meanwhile, the effect of risk factors on crash rates may vary across observations. If such unobserved heterogeneous effect is ignored, the model fit will be reduced and may result in biased parameter estimation and erroneous inferences (Anastasopoulos et al., 2012b; Chen et al., 2014; Yu et al., 2015; Caliendo et al., 2016; Bin Islam and Hernandez, 2016; Zeng et al., 2017b).

The objective of this study is to simultaneously analyze crash rates by collision types at freeway diverge areas via developing a random parameters multivariate Tobit (RPMV-Tobit) model, which accommodates both correlation between crash rates across collision types and unobserved heterogeneity across observations. Three-year period (2004–2006) crash data, including three types of collisions (i.e., rear-end, sideswipe, and angle), from 367 freeway diverge areas are used for the analysis. Four types of freeway diverge areas are identified according to the arrangement of lanes for traffic to exit. Three candidate Tobit models, i.e. multivariate Tobit (MV-Tobit) model, random effect Tobit (REMV-Tobit) model, and independent univariate Tobit (IU-Tobit) model were also estimated and compared with the RPMV-Tobit model under the Bayesian framework.

Section snippets

Safety analysis of freeway diverge areas

Previously, numerous studies have been conducted to evaluate the safety performance of freeway diverge areas using the SPFs such as Poisson and negative binomial (NB) model, Poisson-lognormal model, zero-inflated count model, negative multinomial model, and generalized estimating equation model (Bauer and Harwood, 1998; Bared et al., 1999; McCartt et al., 2004; Golob et al., 2004; Lord and Bonneson, 2005; Garcia and Romero, 2006; Moon and Hummer, 2009; Chen et al., 2009; Liu et al., 2009; Lu et

Data

Crash data for a three-year period were collected from 367 freeway diverge areas in the State of Florida, United States. Risk factors including the road geometries and traffic exposures were collected as explanatory variables (See Table 1). The diverge area defined in this paper covers a deceleration lane and an exit. More specifically, the diverge contains two influence areas, including an area located within 1500 ft upstream of the painted nose, and an area located within 1000 ft downstream

Tobit model

The Tobit model was first proposed by Tobin (1958) for modeling the continuous dependent variable which is left-censored, right-censored, or both. Given that crash rates are usually left-censored at zero, Anastasopoulos et al. (2008) introduced the Tobit model into road safety evaluation. The Tobit model for fitting crash rates is given as $Y_{i}^{*} = β_{0} + β_{1} X_{i 1} + β_{2} X_{i 2} +, \dots, + β_{J} X_{i J} + ε_{i}$ $Y_{i} = \{\begin{array}{c} Y_{i}^{*}, \begin{array}{c} i f \begin{array}{c} Y_{i}^{*} > 0 \end{array} \end{array} \\ 0, \begin{array}{c} i f \begin{array}{c} Y_{i}^{*} \leq 0 \end{array} \end{array} \end{array} \begin{array}{c} , \end{array} i = 1, 2, \dots N$ where Y_i is the dependent variable (observed values of crash rates), X_ij is the jth (j = 1, 2,

Models estimation

Full Bayesian (FB) method has been advocated for model estimation as it can deal with sophisticated models, particularly for those do not have closed-form likelihood functions (Lord and Mannering, 2010). The specification of prior distribution of the model parameters are required before the FB estimates. To be specifically, the model parameters are coefficients (β₀, β_j) and variance $σ_{ε}^{2}$ in the IU-Tobit model; coefficients ( $β_{0}^{k}$ , $β_{j}^{k}$ ) and covariance matrix ∑ in the MV-Tobit model;

Conclusions

This study evaluated the impact of various risk factors on crash rates of three collision types (i.e. rear-end, sideswipe, and angle) at freeway diverge areas by developing a RPMV-Tobit model. The model can accommodate jointly the correlation between crash rates across collision types and unobserved heterogeneity across observations, which are caused by the existence of unobserved risk factors that could jointly affect crash rates of different collision types. Data from 367 freeway diverge

Acknowledgement

This research was sponsored by the National Natural Science Foundation of China (71871057, 71701046, 6521000176,6521000160), and the Fundamental Research Funds for the Central Universities (2242018R20003; 2242017K40130; YBJJ1533).

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