A.S.M. Mohaiminul Islam , Mohammadali Shirazi , Dominique Lord
{"title":"Grouped Random Parameters Negative Binomial-Lindley for accounting unobserved heterogeneity in crash data with preponderant zero observations","authors":"A.S.M. Mohaiminul Islam , Mohammadali Shirazi , Dominique Lord","doi":"10.1016/j.amar.2022.100255","DOIUrl":"10.1016/j.amar.2022.100255","url":null,"abstract":"<div><p>Developing robust and reliable statistical models to estimate, analyze, and understand crash data is a key element in various highway safety evaluation tasks. Crash data have characteristics not found in other data, including but not limited to the excess number of zero responses. The Negative Binomial-Lindley (NB-L) model has been proposed as a method to analyze data with many zero observations. In addition, the differences in various temporal and spatial factors result in variations of model coefficients among different groups of observations. A grouped random parameters model is a strategy to account for such unobserved heterogeneity. In this paper, we proposed the derivations and applications of the grouped random parameters negative binomial-Lindley model (G-RPNB-L) to account for the unobserved heterogeneity in crash data with many zero observations. We first illustrated our proposed model by designing a simulation study. The simulation study showed the ability of the proposed model to correctly estimate the coefficients. Then, we used an empirical dataset in Maine to show the application of the proposed model. We showed that the impact of weather variables denoting “Days with precipitation greater than 1.0 in.”, and “Days with temperature less than 32°F” varies across Maine counties. We also compared the proposed model with the NB, NB-L, and grouped random-parameters NB (G-RPNB) models using different goodness-of-fit metrics. The proposed G-RPNB-L model showed a superior fit compared to the other models.</p></div>","PeriodicalId":47520,"journal":{"name":"Analytic Methods in Accident Research","volume":"37 ","pages":"Article 100255"},"PeriodicalIF":12.9,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43496523","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ashutosh Arun , Md. Mazharul Haque , Simon Washington , Fred Mannering
{"title":"A physics-informed road user safety field theory for traffic safety assessments applying artificial intelligence-based video analytics","authors":"Ashutosh Arun , Md. Mazharul Haque , Simon Washington , Fred Mannering","doi":"10.1016/j.amar.2022.100252","DOIUrl":"10.1016/j.amar.2022.100252","url":null,"abstract":"<div><p>The rapid technological advancements in video analytics and the availability of big data have made traffic conflict techniques a viable tool for road safety assessments. They can potentially overcome many major limitations of conventional road safety practices that use crash-data analyses. However, the current traffic conflict techniques flag serious concerns regarding the context-dependence of the relationship between traffic conflicts and crashes, the lack of consideration of road user and vehicle heterogeneities in their formulation, and the exclusion of crash severity estimation from the analysis process. To overcome these limitations, this study proposes a novel application of the safety field theory to estimate crash risk and severity by modeling the safety-aware interactions of various road users in a road traffic environment. The safety field theory borrows from the Physics concept of electromagnetic fields to mathematically define the safety “buffers” that road users typically maintain around them while moving in traffic. Additionally, the model formulation explicitly accounts for exceptional circumstances (crashes and extreme conflicts) and integrates severity in the risk estimation framework to provide a holistic safety assessment framework. The proposed safety field theory application was tested by analyzing a total of 196 h of traffic movement videos collected from three signalized intersections in Brisbane, Australia and extracting the required road user trajectory information through artificial intelligence-based video analytics. Extreme value modeling of the tail distribution of the risk force generated by the interacting road user safety fields showed that it could predict the crash frequency and outcome severity more accurately than the prevalent traffic conflict indicators. Thus, the proposed approach provides a single, unified, and efficient method of accurately estimating crash risk and injury severities that can be adapted for various application contexts. The study results significantly improve the effectiveness of automated safety analysis for transport facilities and could elevate the safety prediction algorithms of real-time applications like adaptive signal control systems and Connected and Automated Vehicles.</p></div>","PeriodicalId":47520,"journal":{"name":"Analytic Methods in Accident Research","volume":"37 ","pages":"Article 100252"},"PeriodicalIF":12.9,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44234793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chunyang Han , Guangming Xu , Amjad Pervez , Fan Gao , Helai Huang , Xin Pei , Yi Zhang
{"title":"Modeling traveler’s speed-route joint choice behavior with heterogeneous safety concern","authors":"Chunyang Han , Guangming Xu , Amjad Pervez , Fan Gao , Helai Huang , Xin Pei , Yi Zhang","doi":"10.1016/j.amar.2022.100253","DOIUrl":"10.1016/j.amar.2022.100253","url":null,"abstract":"<div><p>In this study, a speed-route joint choice model considering traveler’s safety concerns is proposed to concurrently model traveler’s safety-oriented travel speed and route choice behavior. Specifically, the safe-speed choice behavior is modeled as a trade-off process between perceived traffic safety and efficiency using a disutility function. The safe-route choice behavior is described by the proposed Mean-excess Crash Risk Cost model, where the route safety is modeled as a random variable following a specific distribution, and traveler’s concerns about both reliability and unreliability aspects of safety variability are considered. The model is accommodative to account for the random nature and the traveler’s perception of traffic safety. Also, the travel time cost is considered, which is depicted as a parallel criterion of travel safety in the route choice model. Moreover, the heterogeneities of travelers’ safety concerns in both the choices of speed and route are considered in the proposed joint model. Then, the study formulated the equilibrium problem with the two behavior elements (speed and route) and two choice criteria (safety and time), based on the assumption that all travelers tend to maximize their disutility when choosing speed while minimizing their travel safety variability and travel time. To illustrate the model, Nguyen and Dupuis, Sioux falls, and Changsha arterial networks are conducted as numerical studies. The result demonstrates the model’s capability in depicting travelers’ trade-off between safety and time when selecting the optimal travel speed. Considering the impact of route safety unreliability makes the model sensible to describe travelers’ safety-concerned route choice behavior. The model is also flexible to account for travelers’ crash risk aversion heterogeneity.</p></div>","PeriodicalId":47520,"journal":{"name":"Analytic Methods in Accident Research","volume":"37 ","pages":"Article 100253"},"PeriodicalIF":12.9,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46309074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Modeling endogeneity between motorcyclist injury severity and at-fault status by applying a Bayesian simultaneous random-parameters model with a recursive structure","authors":"Fangrong Chang , Shamsunnahar Yasmin , Helai Huang , Alan H.S. Chan , Md. Mazharul Haque","doi":"10.1016/j.amar.2022.100245","DOIUrl":"10.1016/j.amar.2022.100245","url":null,"abstract":"<div><p>Motorcyclists’ at-fault status is an important factor influencing crash injury severity in that intrinsically unsafe riders tend to be at fault and are the ones likely to be involved in severe crashes. However, this endogeneity issue and its influence on model estimations have seldom been investigated with regard to motorcyclist crash severity analysis. This study proposes a simultaneous model system to account for the endogenous effects of at-fault status in the motorcyclists’ injury severity analysis. Four Bayesian simultaneous models were developed using motorcyclist crash injury data from Queensland, Australia, from the year 2017 through 2018, including an independent binary and independent ordered Probit model, a simultaneous binary-ordered Probit model without recursive structure, a simultaneous binary-ordered Probit model with a recursive structure, and a simultaneous random-parameters binary-ordered Probit model with a recursive structure. The results of all simultaneous models indicate the existence of endogeneity associated with at-fault status in the injury outcome analysis. In particular, the endogenous relationship is detected by the significant cross-equation correlations in the simultaneous models. The model comparison by Deviance Information Criteria highlights the superiority of the simultaneous random-parameters model with a recursive structure. It was found that exogenous variables such as traffic sign-controlled measures, posted speed limits of 100–110 km/h, the presence of vertical grades, rider age 16–24 years, and unlicensed influenced injury severity indirectly through at-fault status, and ignoring these indirect influences could result in biased estimates. The presence of random parameters, such as collisions with heavy vehicles and riders over 59 years, highlights the importance of considering heterogeneity. The simultaneous random-parameters model with a recursive structure model revealed that the critical factors contributing to riders’ at-fault status included unlicensed riders and posted speed limits of 100–110 km/h, and the crucial factors influencing riders’ injury levels included head-on crashes, collisions with heavy vehicles, darkness-unlighted, and riders over 59 years old. The proposed model system demonstrates the importance of considering both endogeneity and heterogeneity for modeling the injury severity of motorcyclists.</p></div>","PeriodicalId":47520,"journal":{"name":"Analytic Methods in Accident Research","volume":"36 ","pages":"Article 100245"},"PeriodicalIF":12.9,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42703766","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Chenzhu Wang , Muhammad Ijaz , Fei Chen , Yunlong Zhang , Jianchuan Cheng , Muhammad Zahid
{"title":"Evaluating gender differences in injury severities of non-helmet wearing motorcyclists: Accommodating temporal shifts and unobserved heterogeneity","authors":"Chenzhu Wang , Muhammad Ijaz , Fei Chen , Yunlong Zhang , Jianchuan Cheng , Muhammad Zahid","doi":"10.1016/j.amar.2022.100249","DOIUrl":"10.1016/j.amar.2022.100249","url":null,"abstract":"<div><p>With rapid growth in motorcycle use and relatively low helmet-wearing usage rates, injuries and fatalities resulting from motorcycle crashes in Pakistan are a critical concern. To investigate possible temporal instability and differences in the factors that determine resulting injury severities between male and female non-helmet wearing motorcyclists, this study estimated male and female injury severity models using a random parameter logit approach with heterogeneity in means and variances. Motorcycle crash data between 2017 and 2019 from Rawalpindi, Pakistan, were used for the model estimation. With four possible crash injury severity outcomes (injury, minor injury, severe injury, and fatal injury), a wide variety of explanatory variables were considered, including the characteristics of riders, vehicles, roadways, environments, crashes, and temporal considerations. Temporal shifts in the effects of explanatory variables were confirmed using a series of likelihood ratio tests. While the effects of several explanatory variables are relatively temporally stable, those of most variables vary considerably across the years. In addition, out-of-sample simulations underscore the temporal shifts from year to year and the differences between male and female motorcyclist-injury severity. The findings suggest that factors such as effective enforcement countermeasures and relevant educational campaigns can be implemented to reduce injury severity. The statistically significant differences between male and female non-helmeted injury severity models underscore the importance of policies that separately target male and female motorcycle rider safety.</p></div>","PeriodicalId":47520,"journal":{"name":"Analytic Methods in Accident Research","volume":"36 ","pages":"Article 100249"},"PeriodicalIF":12.9,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44180255","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Penglin Song , N.N. Sze , Ou Zheng , Mohamed Abdel-Aty
{"title":"Addressing unobserved heterogeneity at road user level for the analysis of conflict risk at tunnel toll plaza: A correlated grouped random parameters logit approach with heterogeneity in means","authors":"Penglin Song , N.N. Sze , Ou Zheng , Mohamed Abdel-Aty","doi":"10.1016/j.amar.2022.100243","DOIUrl":"10.1016/j.amar.2022.100243","url":null,"abstract":"<div><p>Toll plaza is a designated area of controlled-access roads like expressway, bridge, and tunnel for toll collection. A number of toll booths are often placed at the toll plaza accommodating high passing traffic and multiple payment methods. Traffic and safety characteristics of toll plazas are different from that of other road entities. Different conflict risk indicators, which are usually longitudinal, have been adopted for real-time safety assessment. In this study, correlated grouped random parameter logit models with heterogeneity in the means are established to capture the unobserved heterogeneity, with additional flexibility, at road user level for the association between conflict risk and influencing factors. In addition, modified conflict risk indicator is developed to assess the safety of diverging, merging, and weaving movements of traffic, with which vehicles’ dimensions (width and length), and longitudinal and angular movements are considered. Also, prevalence and severity of both rear-end and sideswipe conflicts are assessed. Results indicate that toll collection type, vehicle’s location, average longitudinal speed, angular speed, acceleration, and vehicle class all affect the risk of traffic conflicts. Furthermore, there are significant correlation among the random parameters of severe traffic conflicts. Proposed analytic method can accommodate the conflict risk analysis for different conflict types and account for the correlation of unobserved heterogeneity. Findings should shed light on appropriate remedial measures like traffic signs, road markings, and advanced traffic management system that can improve the safety at tunnel toll plazas.</p></div>","PeriodicalId":47520,"journal":{"name":"Analytic Methods in Accident Research","volume":"36 ","pages":"Article 100243"},"PeriodicalIF":12.9,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47904121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Real-time crash potential prediction on freeways using connected vehicle data","authors":"Shile Zhang, Mohamed Abdel-Aty","doi":"10.1016/j.amar.2022.100239","DOIUrl":"10.1016/j.amar.2022.100239","url":null,"abstract":"<div><p>The real-time crash potential prediction model is one of the important components of proactive traffic management systems<span>. Over the years numerous models have been proposed to predict crash potential and achieved promising results using input data from roadside<span> detectors. However, the detectors are normally installed at certain locations with limited coverage, while the connected vehicle data can provide city-wide mobility information. Previous studies have found that driver event variables such as hard braking, hard accelerations, etc. are correlated with crash potential on the road segments. Nevertheless, the existing studies are mostly conducted at the aggregated level, and the data are mostly collected from commercial vehicles such as taxis or buses traveling in the urban areas. This paper proposes a bidirectional long short-term memory (LSTM) model with two convolutional layers to predict real-time crash potential on freeways. The input data including traffic flow variables from detectors, and driver event variables from connected vehicle (CV) data, are aggregated at the one-minute level. The model achieves a recall value of 0.772 and an AUC value of 0.857. Moreover, to investigate the transferability of the proposed model, the original data are aggregated at the hourly level. The transferred model is developed with fine tuning two convolutional layers of the established model. And the transferred model achieves a recall value of 0.715 and an AUC value of 0.763. This proves that the proposed model can be successfully applied to another similar data set, or when the connected vehicles have lower penetration rate. In this study, we proved the usefulness of the connected vehicle data in the prediction of real-time crash potential, and the possibility of using it without detector data once the penetration rate increases to a reasonable level.</span></span></p></div>","PeriodicalId":47520,"journal":{"name":"Analytic Methods in Accident Research","volume":"36 ","pages":"Article 100239"},"PeriodicalIF":12.9,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42572952","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The impact of weekday, weekend, and holiday crashes on motorcyclist injury severities: Accounting for temporal influence with unobserved effect and insights from out-of-sample prediction","authors":"Chamroeun Se , Thanapong Champahom , Sajjakaj Jomnonkwao , Nopadon Kronprasert , Vatanavongs Ratanavaraha","doi":"10.1016/j.amar.2022.100240","DOIUrl":"https://doi.org/10.1016/j.amar.2022.100240","url":null,"abstract":"<div><p>This paper examines the differences between weekday, weekend, and holiday crashes on the severity of motorcyclist injury using four-year motorcycle crash data in Thailand from 2016 to 2019. While also considering the temporal stability assessment of significant factors, this study adopted a random parameters logit model with possible heterogeneity in means and variances to account for unobserved heterogeneity. Three levels of motorcyclist injury severity were considered including minor injury, severe injury, and fatal injury. Two series of likelihood ratio tests clearly indicated nontransferability between weekday, weekend, and holiday crashes and substantial temporal instability over the four-year study period. Findings also revealed many statistically significant factors that affect motorcyclist injury severity probabilities in various time-of-year and yearly models. In addition, the prediction comparison results (using out-of-sample prediction simulation) clearly illustrated substantial differences between weekday, weekend, and holiday motorcyclist injury severity probabilities, and substantial changes in each injury predicted probabilities over time. This paper highlights the importance of accounting for day-of-week and holiday transferability and temporal instability with unobserved effects in the determinants that affect motorcyclist injury severity. Through the observed nontransferability and temporal instability, the findings provide valuable knowledge for practitioners, researchers, institutions, and decision-makers to enhance highway safety, specifically motorcyclist safety, and facilitate the development of more effective motorcycle crash injury mitigation policies.</p></div>","PeriodicalId":47520,"journal":{"name":"Analytic Methods in Accident Research","volume":"36 ","pages":"Article 100240"},"PeriodicalIF":12.9,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92016215","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Krishna Murthy Gurumurthy , Prateek Bansal , Kara M. Kockelman , Zili Li
{"title":"Modelling animal-vehicle collision counts across large networks using a Bayesian hierarchical model with time-varying parameters","authors":"Krishna Murthy Gurumurthy , Prateek Bansal , Kara M. Kockelman , Zili Li","doi":"10.1016/j.amar.2022.100231","DOIUrl":"https://doi.org/10.1016/j.amar.2022.100231","url":null,"abstract":"<div><p>Animal-vehicle collisions (AVCs) are common around the world and result in considerable loss of animal and human life, as well as significant property damage and regular insurance claims. Understanding their occurrence in relation to various contributing factors and being able to identify high-risk locations are valuable to AVC prevention, yielding economic, social, and environmental cost savings. However, many challenges exist in the study of AVC datasets. These include seasonality of animal activity, unknown exposure (i.e., the number of animal crossings), very low AVC counts across most sections of extensive roadway networks, and computational burdens that come with discrete response analysis using large datasets. To overcome these challenges, a Bayesian hierarchical model is proposed where the exposure is modeled with nonparametric Dirichlet process, and the number of segment-level AVCs is assumed to follow a binomial distribution. A Pólya-Gamma augmented Gibbs sampler is derived to estimate the proposed model. By using the AVC data of multiple years across about 85,000 segments of state-controlled highways in Texas, U.S., it is demonstrated that the model is scalable to large datasets, with a preponderance of zeros and clear monthly seasonality in counts, while identifying high-risk locations and key explanatory factors based on segment-specific factors (such as changes in speed limit). This can be done within the modelling framework, which provides useful information for policy-making purposes.</p></div>","PeriodicalId":47520,"journal":{"name":"Analytic Methods in Accident Research","volume":"36 ","pages":"Article 100231"},"PeriodicalIF":12.9,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"92019480","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A multivariate method for evaluating safety from conflict extremes in real time","authors":"Chuanyun Fu , Tarek Sayed","doi":"10.1016/j.amar.2022.100244","DOIUrl":"10.1016/j.amar.2022.100244","url":null,"abstract":"<div><p><span>Several studies have advocated the use of extreme value theory (EVT) traffic conflict models for real-time crash risk prediction using real-time safety indices such as the risk of crash (RC) and return level of a cycle (RLC). This approach provides a logical framework to estimate crash risk by extrapolating from the observed level (i.e., traffic conflict) to the unobserved level (i.e., crash). In these studies, only univariate EVT models that consider only one conflict indicator (e.g. modified time to collision, MTTC) were used which affects the models’ accuracy and precision in estimating crash risk. The use of univariate models is likely due to that existing safety analysis multivariate<span><span> EVT models have limited capability of delineating the complex dependence structure between multiple conflict indicators for application to real-time safety evaluation. This study proposes a multivariate method for evaluating real-time safety from conflict extremes which consists of novel multivariate EVT models that flexibly integrate multiple conflict indicators and several joint safety indices that comprehensively characterize the safety level of a road facility from multiple dimensions. The proposed approach has several advantages including: 1) it uses four parametric models (tilted </span>Dirichlet, pairwise beta, Husler-Reiss, and extremal-</span></span><span><math><mi>t</mi></math></span><span>) for the angular density function for fully describing the dependence level between multiple conflict extremes; and 2) it innovatively develops several important real-time safety indices (e.g., crash risk, joint return levels, and return level concomitant) from the multivariate joint distribution for multidimensionally assessing safety. A seven-step approximate likelihood-based Bayesian inference method for model development is proposed. The proposed model estimation method is applied for cycle-level real-time safety evaluation by combining several conflict indicators at four signalized intersections in the city of Surrey, British Columbia. Three conflict indicators are used: MTTC, post encroachment time (PET), and deceleration rate to avoid a crash (DRAC). Four types of multivariate EVT models were developed. Among these models, for both bivariate and trivariate framework, the Husler-Reiss model has the best goodness-of-fit as it better captures the dependence level among the three conflict indicators. The results indicate that multivariate models identify higher numbers of crash-risk cycles than their corresponding univariate models. Further, most of crash-risk cycles have at least one of joint return levels higher than the threshold (0 for both MTTC and PET, 8.5 m/s</span><sup>2</sup> for DRAC) between a conflict and a collision. For joint return levels from most cycles, one return level exceeds the threshold, while others are lower than the threshold. Under the bivariate framework, all the concomitants of positive return levels are belo","PeriodicalId":47520,"journal":{"name":"Analytic Methods in Accident Research","volume":"36 ","pages":"Article 100244"},"PeriodicalIF":12.9,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44953677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}