A Bayesian spatial random parameters Tobit model for analyzing crash rates on roadway segments

Modeling temporal correlation and heterogeneity in real-time conflict rates using Bayesian Tobit models for signalized intersections

The use of real-time traffic conflicts for safety studies provide more insight into how important dynamic signal cycle-related characteristics can affect intersection safety. However, such short-time window for data collection raises a critical issue that the observed conflicts are temporally correlated. As well, there is likely unobserved heterogeneity across different sites that exist in conflict data. The objective of this study is to develop real-time traffic conflict rates models simultaneously accommodating temporal correlation and unobserved heterogeneity across observations. Signal cycle level traffic data, including traffic conflicts, traffic and shock wave characteristics, collected from six signalized intersections were used. Three types of Tobit models: conventional Tobit model, temporal Tobit (T-Tobit) model, and temporal grouped random parameters (TGRP-Tobit) model were developed under full Bayesian framework. The results show that significant temporal correlations are found in T-Tobit models and TGRP-Tobit models, and the inclusion of temporal correlation considerably improves the goodness-of-fit of these Tobit models. The TGRP-Tobit models perform best with the lowest Deviance Information Criteria (DIC), indicating that accounting for the unobserved heterogeneity can further improve the model fit. The parameter estimates show that real-time traffic conflict rates are significantly associated with traffic volume, shock wave area, shock wave speed, queue length, and platoon ratio.

Exploring the influence of drivers' visual surroundings on speeding behavior

Despite awareness campaigns and legal consequences, speeding is a significant cause of road accidents and fatalities globally. To combat this issue, understanding the impact of a driver's visual surroundings is crucial in designing roadways that discourage speeding. This study investigates the influence of visual surroundings on drivers in 15 US cities using 3,407,253 driver view images from Lytx, covering 4,264 miles of roadways. By segmenting and analyzing these images along with vehicle-related variables, the study examines factors affecting speeding behavior. After filtering the images, to ensure an accurate representation of the driver's view, 1,340,035 driver view images were used for analysis. Statistical models, including hurdle beta and bivariate probit models with random driver effects as well as Machine Learning's eXtreme Gradient Boosting (XGBoost), were employed to estimate speeding behavior. The results indicate that factors within the driver's visual environment, weather conditions, and driver heterogeneity significantly impact speeding. Speeding behavior also varies across geographic locations, even within the same city, suggesting a connection between local context and speeding. The study highlights the importance of the driver's environment, showing that more open spaces encourage speeding, while areas with trees and buildings are associated with reduced speeding. Notably, this research differs from previous studies by utilizing real-time data from dash cameras, providing a dynamic and accurate representation of the driver's visual surroundings. This approach enhances the reliability of the findings and empowers transportation engineers and planners to make informed decisions when designing roadways and implementing interventions to address effectively excessive speeding. In addition to examining speeding behavior, the study also analyzes time-headway, a key factor affecting safety and risky driver behavior, to explore its relationship with speeding. The findings offer valuable insights into the factors influencing speeding and the driver's visual environment. These insights can inform efforts to create environments that discourage speeding (and close car following) and ultimately reduce severe accidents caused by excessive speed (and tailgating).

Investigating injury severity interaction between urban and urban-rural fringe areas: a grouped random parameters seemingly unrelated bivariate probit approach

Urban-rural integration is the critical process of urbanization, while during this process there are various corresponding problems generated, safety is the most important one, especially at urban-rural fringe areas due to mixed traffic flow and complicated land use. This study intended to investigate the injury severity interaction between urban area and urban-rural fringe area, and explore the correlation within injury severity levels and heterogeneity attributed to unobserved factors. To address the correlation and heterogeneity issues, a grouped random parameters seemingly unrelated bivariate (SUB) probit model was proposed, in which the SUB probit model addressed the correlation of residuals, while the random parameters model accommodated the heterogeneity due to unobserved factors. By comparing the pooled with random parameters models, the results showed that random parameters SUB probit model performed better than the pooled one, and the dataset collected from 2013 to 2017 in Chengdu, China was adopted to illustrate the proposed model. It is found that crash location, speed limit and age of person injured are significant for injury severity in urban and urban-rural fringe areas, but crash form plays a significant role in urban area while number of persons involved should be paid more attention due to injury severity in urban-rural fringe area. Some empirical suggestions are presented to improve the safety in urban and urban-rural fringe areas.

The impact of target speed on pedestrian, bike, and speeding crash frequencies

This research aims to investigate the influence of adopting the target speed concept on different types of crashes including pedestrian, bike, and speeding-related crashes. The Target speed is the highest speed that vehicles should operate on a roadway segment in a specific context. Based on the reviewed literature, this is the first study to investigate the relationship between target speed and crash frequency. Hence, big data including probe-vehicle data, traffic characteristics, geometric features, and land use attributes were utilized to develop crash prediction models. The main contributions of this research are to quantify the impacts of target speed on traffic safety considering context categories and to conclude the potential recommendations to lower different types of crashes. The 85th percentile speed was calculated and utilized in the developed models. Three crash prediction models were developed for pedestrian, bike, and speeding-related crashes. They were used in the analysis to quantify the impact of adopting target speed on different crash types. The results showed a significant reduction in the three crash types when using the target speed. Most of the improvements took place in three context categories: C3C: Suburban Commercial Segments, C3R: Suburban Residential Segments, and C4: Urban General Segments. Hence, this research recommends adopting target speed specifically in urban and suburban areas. Further, it suggests considering some measures to lower vulnerable road users' and speeding-related crashes. Following the recommendations of this research would help to reduce different types of crash frequency, hence, improving the mobility and safety for all users in different context classifications.

Jointly analyzing freeway primary and secondary crash severity using a copula-based approach

A copula-based model is developed in this study to jointly model the severity of freeway primary crashes and secondary crashes. The copula-based model can concurrently account for the severity levels in the crash and the correlation among primary-secondary crash pairs' severity. The model comprehensively considers a series of explanation variables, including temporal characteristics, crash characteristics, roadway characteristics and real-traffic conditions, and is estimated using traffic crash data from 2016 through 2019 for Los Angeles County, California. The proposed copula model is then contrasted with the traditional binary probit model and the results show a remarkable advantage of the copula model, which is evidenced by better fitting performance. It is found that weather, whether towed away, unsafe speed, collision type, road condition, terrain, road weaving and truck involvement have significant impact on primary crash severity propensity and collision type, road width, road condition, traffic volume and vehicle speed have significant impact on secondary crash severity propensity. In light of the findings, a number of countermeasures are proposed to mitigate freeway crashes, including emergency services, vehicle and roadway engineering, traffic law enforcement and driver education.

Bayesian spatial correlation, heterogeneity and spillover effect modeling for speed mean and variance on urban road networks

Analyzing speed mean and variance is vital to safety management in urban roadway networks. However, modeling speed mean and variance on structured roads could be influenced by the spatial effects, which are rarely addressed in the existing studies. The inadequacy may lead to biased conclusions when considering vehicle speed as a surrogate safety measure. The current study focuses on developing a Bayesian modeling approach with three types of spatial effects, i.e., spatial correlation, spatial heterogeneity, and spillover effect. To capture the spatial correlation, the study employs the intrinsic conditional autoregressive (ICAR) models, spatial lag models (SLM), and spatial error models (SEM). Spatial heterogeneity and spillover effect are considered by the random parameters approach and spatially lagged covariates (SLCs). Speed data are collected from the float cars running on 134 urban arterials in Chengdu, China. The results indicate that the random parameters ICAR model with SLCs (RPICAR-SLC) outperforms others in terms of goodness-of-fit, accuracy, and efficiency for modeling speed mean, while the random parameters ICAR model (RPICAR) is the best for modeling speed variance. Moreover, RPICAR-SLC and RPICAR models are beneficial to address spatial correlation of residuals, explaining the unobserved influence among the observations, and are less likely to cause biased or overestimated parameters. The study also discusses how traffic conditions, road characteristics, traffic management strategies, and facilities on roadway networks influence speed mean and variance. The findings highlight the importance of multi-type spatial effects on modeling speed mean and variance along the structured roadways.

An empirical analysis of factors contributing to roadway infrastructure damage from expressway accidents: A Bayesian random parameters Tobit approach

This paper presents an empirical analysis of factors contributing to roadway infrastructure damage from expressway accidents, using a Bayesian random parameters Tobit model. The accident data collected from Kaiyang Expressway, China in 2014 and 2015 are used for the empirical analysis. The results of parameter estimation in the proposed model indicate that: the effects of vehicle types are significantly heterogeneous across observations, and that the effects of horizontal curvature, time of day, vehicle registered province, and accident type are also significant but homogeneous across observations. The marginal effects of these contributing factors are calculated to explicitly quantify their impacts on road infrastructure damage. According to the analysis results, some strategies pertaining to safety education, traffic enforcement, roadway design, and intelligence transportation technology are advocated to reduce road infrastructure damage from expressway accidents.

Estimating mountainous freeway crash rate: Application of a spatial model with three-dimensional (3D) alignment parameters

The road alignment is a three-dimensional (3D) curve in nature. In this study, we quantitatively examine the effect of 3D road alignment on traffic safety on mountainous freeways. Geometric parameters of 3D curvature and torsion in mathematics are derived to characterize the 3D road curve. Based on the coordination of different horizontal and vertical elements, 3D road alignment is divided into twelve types of combined alignment. For each alignment combination, the 3D curvature and torsion are calculated according to the differential geometry theory. Regarding crash statistical modeling, the Bayesian spatial Tobit (BST) model is developed to accommodate possible spatial correlation of traffic crashes among adjacent freeway segments. The Bayesian Tobit (BT) model is also built for comparison. A 118-km mountainous freeway associated road geometric features, traffic volume with three years of crash data is used as a case study. The result from the model comparison shows the BST model outperforms the BT model in terms of goodness-of-fit. Parameter estimation result for the BST model shows that the differences of average 3D curvature (and torsion) between adjacent segments have statistically significant effects on the crash rate of the segment, indicating it is necessary to consider three-dimensional alignment parameters in estimating mountainous freeway crash rate. Moreover, by comparing the predicted crash rate calculated by the BST model and the observed crash rate, the result shows the proposed BST model can provide a reliable prediction for freeway crash rates of different combined alignments. This study provides new insight on the effect of road geometric design on traffic safety but also deepens our understanding of spatial correlations in freeway crash modeling.

Impact of Helmet-Wearing Policy on E-Bike Safety Riding Behavior: A Bivariate Ordered Probit Analysis in Ningbo, China

At present, Chinese authorities are launching a campaign to convince riders of electric bicycles (e-bikes) and scooters to wear helmets. To explore the effectiveness of this new helmet policy on e-bike cycling behavior and improve existing e-bike management, this study investigates the related statistical distribution characteristics, such as demographic information, travel information, cycling behavior information and riders’ subjective attitude information. The behavioral data of 1048 e-bike riders related to helmet policy were collected by a questionnaire survey in Ningbo, China. A bivariate ordered probit (BOP) model was employed to account for the unobserved heterogeneity. The marginal effects of contributory factors were calculated to quantify their impacts, and the results show that the BOP model can explain the common unobserved features in the helmet policy and cycling behavior of e-bike riders, and that good safety habits stem from long-term safety education and training. The BOP model results show that whether wearing a helmet, using an e-bike after 19:00, and sunny days are factors that affect the helmet wearing rate. Helmet wearing, evenings during rush hour, and picking up children are some of the factors that affect e-bike accident rates. Furthermore, there is a remarkable negative correlation between the helmet wearing rate and e-bike accident rate. Based on these results, some interventions are discussed to increase the helmet usage of e-bike riders in Ningbo, China.

Applying a Bayesian multivariate spatio-temporal interaction model based approach to rank sites with promise using severity-weighted decision parameters

Ranking sites with promise is an essential step for cost-effective engineering improvement on roadway traffic safety. This study proposes a Bayesian multivariate spatio-temporal interaction model based approach for ranking sites. The severity-weighted crash frequency and crash rate are used as the decision parameters. The posterior expected rank and posterior mean of the decision parameters are adopted as the statistical criteria. The proposed approach is applied to rank road segments on Kaiyang Freeway in China, which is conducted via programming in the freeware WinBUGS. The results of Bayesian estimation and assessment indicate that incorporating spatio-temporal correlations and interactions into the crash frequency model significantly improves the overall goodness-of-fit performance and affects the identified crash-contributing factors and the estimated safety effects for each severity level. With respect to the ranking results, significant differences are found between those generated from the proposed approach and those generated from the naïve ranking approach and a Bayesian approach based on the multivariate Poisson-lognormal model. Besides, the ranks under the posterior mean criterion are found generally consistent with those under the posterior expected rank criterion.

Analysing the main and interaction effects of commercial vehicle mix and roadway attributes on crash rates using a Bayesian random-parameter Tobit model

In previous research, the effects of commercial vehicle proportions (CVP) on overall crash propensity have been found to be significant, but the results have been varied in terms of the effect direction. In addition, the mediating or moderating effects of roadway attributes on the CVP-vs-safety relationships, have not been investigated. In addressing this gap in the literature, this study integrates databases on crashes, traffic, and inventory for Hong Kong road segments spanning 2014-2017. The classes of commercial vehicles considered are public buses, taxi, and light-, medium- and heavy-goods vehicles. Random-parameter Tobit models were estimated using the crash rates. The results suggest that the CVP of each class show credible effects on the crash rates, for the various crash severity levels. The results also suggest that the interaction between CVP and roadway attributes is credible enough to mediate the effect of CVP on crash rates, and the magnitude and direction of such mediation varies across the vehicle classes, crash severity levels, and roadway attribute type in four ways. First, the increasing effect of taxi proportion on slight-injury crash rate is magnified at road segments with high intersection density. Second, the increasing effect of light-goods vehicle proportion on slight-injury crash rate is magnified at road segments with on-street parking. Third, the association between the medium- and heavy-goods vehicle proportion and killed/severe injury (KSI) crash rate, is moderated by the roadway width (number of traffic lanes). Finally, a higher proportion of medium- and heavy-goods vehicles generally contributes to increased KSI crash rate at road segments with high intersection density. Overall, the findings of this research are expected not only to help guide commercial vehicle enforcement strategy, licensing policy, and lane control measures, but also to review existing urban roadway designs to enhance safety.

Estimating COVID-19 cases in Makkah region of Saudi Arabia: Space-time ARIMA modeling

The novel coronavirus COVID-19 is spreading across the globe. By 30 Sep 2020, the World Health Organization (WHO) announced that the number of cases worldwide had reached 34 million with more than one million deaths. The Kingdom of Saudi Arabia (KSA) registered the first case of COVID-19 on 2 Mar 2020. Since then, the number of infections has been increasing gradually on a daily basis. On 20 Sep 2020, the KSA reported 334,605 cases, with 319,154 recoveries and 4,768 deaths. The KSA has taken several measures to control the spread of COVID-19, especially during the Umrah and Hajj events of 1441, including stopping Umrah and performing this year's Hajj in reduced numbers from within the Kingdom, and imposing a curfew on the cities of the Kingdom from 23 Mar to 28 May 2020. In this article, two statistical models were used to measure the impact of the curfew on the spread of COVID-19 in KSA. The two models are Autoregressive Integrated Moving Average (ARIMA) model and Spatial Time-Autoregressive Integrated Moving Average (STARIMA) model. We used the data obtained from 31 May to 11 October 2020 to assess the model of STARIMA for the COVID-19 confirmation cases in (Makkah, Jeddah, and Taif) in KSA. The results show that STARIMA models are more reliable in forecasting future epidemics of COVID-19 than ARIMA models. We demonstrated the preference of STARIMA models over ARIMA models during the period in which the curfew was lifted.

Inference of stress-strength reliability for two-parameter of exponentiated Gumbel distribution based on lower record values

The two-parameter of exponentiated Gumbel distribution is an important lifetime distribution in survival analysis. This paper investigates the estimation of the parameters of this distribution by using lower records values. The maximum likelihood estimator (MLE) procedure of the parameters is considered, and the Fisher information matrix of the unknown parameters is used to construct asymptotic confidence intervals. Bayes estimator of the parameters and the corresponding credible intervals are obtained by using the Gibbs sampling technique. Two real data set is provided to illustrate the proposed methods.

New generalized-X family: Modeling the reliability engineering applications

As is already known, statistical models are very important for modeling data in applied fields, particularly in engineering, medicine, and many other disciplines. In this paper, we propose a new family to introduce new distributions suitable for modeling reliability engineering data. We called our proposed family a new generalized-X family of distributions. For the practical illustration, we introduced a new special sub-model, called the new generalized-Weibull distribution, to describe the new family's significance. For the proposed family, we introduced some mathematical reliability properties. The maximum likelihood estimators for the parameters of the new generalized-X distributions are derived. For assessing the performance of these estimators, a comprehensive Monte Carlo simulation study is carried out. To assess the efficiency of the proposed model, the new generalized-Weibull model is applied to the coating machine failure time data. Finally, Bayesian analysis and performance of Gibbs sampling for the coating machine failure time data are also carried out. Furthermore, the measures such as Gelman-Rubin, Geweke and Raftery-Lewis are used to track algorithm convergence.

The effect of human mobility and control measures on traffic safety during COVID-19 pandemic

As mobile device location data become increasingly available, new analyses are revealing the significant changes of mobility pattern when an unplanned event happened. With different control policies from local and state government, the COVID-19 outbreak has dramatically changed mobility behavior in affected cities. This study has been investigating the impact of COVID-19 on the number of people involved in crashes accounting for the intensity of different control measures using Negative Binomial (NB) method. Based on a comprehensive dataset of people involved in crashes aggregated in New York City during January 1, 2020 to May 24, 2020, people involved in crashes with respect to travel behavior, traffic characteristics and socio-demographic characteristics are found. The results show that the average person miles traveled on the main traffic mode per person per day, percentage of work trip have positive effect on person involved in crashes. On the contrary, unemployment rate and inflation rate have negative effects on person involved in crashes. Interestingly, different level of control policies during COVID-19 outbreak are closely associated with safety awareness, driving and travel behavior, and thus has an indirect influence on the frequency of crashes. Comparing to other three control policies including emergence declare, limits on mass gatherings, and ban on all nonessential gathering, the negative relationship between stay-at-home policy implemented in New York City from March 20, 2020 and the number of people involved crashes is found in our study.

Investigating hazardous factors affecting freeway crash injury severity incorporating real-time weather data: Using a Bayesian multinomial logit model with conditional autoregressive priors

INTRODUCTION

It has been demonstrated that weather conditions have significant impacts on freeway safety. However, when employing an econometric model to examine freeway crash injury severity, most of the existing studies tend to categorize several different adverse weather conditions such as rainy, snowy, and windy conditions into one category, "adverse weather," which might lead to a large amount of information loss and estimation bias. Hence, to overcome this issue, real-time weather data, the value of meteorological elements when crashes occurred, are incorporated into the dataset for freeway crash injury analysis in this study.

METHODS

Due to the possible existence of spatial correlations in freeway crash injury data, this study presents a new method, the spatial multinomial logit (SMNL) model, to consider the spatial effects in the framework of the multinomial logit (MNL) model. In the SMNL model, the Gaussian conditional autoregressive (CAR) prior is adopted to capture the spatial correlation. In this study, the model results of the SMNL model are compared with the model results of the traditional multinomial logit (MNL) model. In addition, Bayesian inference is adopted to estimate the parameters of these two models.

RESULT

The result of the SMNL model shows the significance of the spatial terms, which demonstrates the existence of spatial correlation. In addition, the SMNL model has a better model fitting ability than the MNL model. Through the parameter estimate results, risk factors such as vertical grade, visibility, emergency medical services (EMS) response time, and vehicle type have significant effects on freeway injury severity. Practical Application: According to the results, corresponding countermeasures for freeway roadway design, traffic management, and vehicle design are proposed to improve freeway safety. For example, steep slopes should be avoided if possible, and in-lane rumble strips should be recommended for steep down-slope segments. Besides, traffic volume proportion of large vehicles should be limited when the wind speed exceeds a certain grade.

Prediction of vehicle occupants injury at signalized intersections using real-time traffic and signal data

Intersections are among the most dangerous roadway facilities due to the existence of complex movements of traffic. Most of the previous intersection safety studies are conducted based on static and highly aggregated data such as average daily traffic and crash frequency. The aggregated data may result in unreliable findings because they are based on averages and might not necessarily represent the actual conditions at the time of the crash. This study uses real-time event-based detection records, and crash data to develop predictive models for the vehicle occupants' injury severity. The three-year (2017-2019) data were acquired from the arterial highways in the City of Tallahassee, Florida. Random Forest (RF) and eXtreme Gradient Boosting (XGBoost) classifiers were used to identify the important factors on the vehicle occupants' injury severity prediction. The performance comparison of the two classifiers revealed that the XGBoost has a higher balanced accuracy score than RF. Using the XGBoost classifier, five topmost influential factors on injury prediction were identified. The factors are the manner of the collision, through and right-turn traffic volume, arrival on red for through and right-turn traffic, split failure for through traffic, and delays for through and right-turn traffic. Moreover, the partial dependency plots of the influential variables are presented to reveal their impact on vehicle occupant injury prediction. The knowledge gained from this study will be useful in developing effective proactive countermeasures to mitigate intersection-related crash injuries in real-time.

Towards activity-based exposure measures in spatial analysis of pedestrian-motor vehicle crashes

BACKGROUND

Although numerous efforts have been devoted to exploring the effects of area-wide factors on the frequency of pedestrian crashes in neighborhoods over the past two decades, existing studies have largely failed to provide a full picture of the factors that contribute to the incidence of zonal pedestrian crashes, due to the unavailability of reliable exposure data and use of less sound analytical methods.

METHODS

Based on a crowdsourced dataset in Hong Kong, we first proposed a procedure to extract pedestrian trajectories from travel-diary survey data. We then aggregated these data to 209 neighborhoods and developed a Bayesian spatially varying coefficients model to investigate the spatially non-stationary relationships between the number of pedestrian-motor vehicle (PMV) crashes and related risk factors. To dissect the role of pedestrian exposure, the estimated coefficients of models with population, walking trips, walking time, and walking distance as the measure of pedestrian exposure were presented and compared.

RESULTS

Our results indicated substantial inconsistencies in the effects of several risk factors between the models of population and activity-based exposure measures. The model using walking trips as the measure of pedestrian exposure had the best goodness-of-fit. We also provided new insights that in addition to the unstructured variability, heterogeneity in the effects of explanatory variables on the frequency of PMV crashes could also arise from the spatially correlated effects. After adjusting for vehicle volume and pedestrian activity, road density, intersection density, bus stop density, and the number of parking lots were found to be positively associated with PMV crash frequency, whereas the percentage of motorways and median monthly income had negative associations with the risk of PMV crashes.

CONCLUSIONS

The use of population or population density as a surrogate for pedestrian exposure when modeling the frequency of zonal pedestrian crashes is expected to produce biased estimations and invalid inferences. Spatial heterogeneity should also not be negligible when modeling pedestrian crashes involving contiguous spatial units.

Severity analysis of crashes on express lane facilities using support vector machine model trained by firefly algorithm

OBJECTIVE

Express lanes (ELs) provide an alternative way for improving the capacity of the existing freeway network without considerably expanding the roadway footprint. Although much research has been done to explore factors contributing to crashes on these facilities, there is not much discussion on factors influencing their injury severity. This study explored factors influencing the injury severity of crashes on EL facilities.

METHOD

A Support Vector Machine (SVM) model trained by the Firefly Algorithm was used to identify factors influencing the injury severity of crashes on EL facilities. The analysis was based on three years of crash data (2012-2014) from four EL facilities in California, totaling 61 miles.

RESULTS

The results indicated that the following factors increased the probability of an injury or a fatality: concrete barriers, high average annual daily traffic, rolling or mountainous terrain, weekend, adverse road surface condition, and nighttime condition. Moreover, wide right and left shoulder widths decreased the probability of having an injury or a fatality.

CONCLUSIONS

The results provide insights into the influence of different geometric characteristics and crash-related factors on the severity of crashes on EL facilities. The study findings may assist agencies to better understand the impacts of factors contributing to injury and fatal crashes on EL facilities and implement strategies to reduce the severity of these crashes.

Assessing the explanatory and predictive performance of a random parameters count model with heterogeneity in means and variances

Random parameters model has been demonstrated to be an effective method to account for unobserved heterogeneity that commonly exists in highway crash data. However, the predefined single distribution for each random parameter may limit how the unobserved heterogeneity is captured. A more flexible approach is to develop a random parameters model with heterogeneity in means and variances by allowing the mean and variance of potential each random parameter to be an estimable function of explanatory variables. This burgeoning technique for modelling unobserved heterogeneity has been increasingly applied to various safety evaluation scenarios recently. However, the predictive performance of this emerging method, which determines the practicability of the model for a specific circumstance, has never been investigated as far as our knowledge. In addition, the explanatory power by including heterogeneous means and variances of random parameters need to be further investigated to confirm the potential merits of this method in crash data analysis. In this paper, a random parameters negative binomial with heterogeneity in means and variances (RPNBHMV) model, a standard random parameters negative binomial (RPNB) model and a traditional fixed parameters negative binomial (NB) model were estimated using the same dataset. The explanatory and predictive performance of the three models were thoroughly evaluated and compared. Results showed that: 1) the RPNB model fitted the data significantly better than the NB model, and the RPNBHMV model further improved the statistical fit of the RPNB model but the improvement was slight; 2) more insights into interactions of safety factors were inferred from the RPNBHMV model, which demonstrates the explanatory benefit of this model; 3) the RPNBHMV and RPNB models had both advantages (e.g., produced overall better prediction accuracy) and disadvantages (e.g., provided reduced prediction accuracy across the range of explanatory variables) when applied to in-sample observations (i.e., observations used to estimate the model); 4) the RPNBHMV and RPNB models might be less precise than the NB model when applied to out-of-sample observations. These findings indicate that the RPNBHMV model offers more insights and may be used for explanatory safety analysis for sites where reliable data can be collected. However, the simple NB model is more reliable - at least with the dataset used in this study - than its random parameters model counterparts for other sites where the data are unavailable or unreliable, which is a common safety evaluation scenario in practice.

Discovering Spatio-Temporal Clusters of Road Collisions Using the Method of Fast Bayesian Model-Based Cluster Detection

Public availability of geo-coded or geo-referenced road collisions (crashes) makes it possible to perform geovisualisation and spatio-temporal analysis of road collisions across a city. This study aims to detect spatio-temporal clusters of road collisions across Greater London between 2010 and 2014. We implemented a fast Bayesian model-based cluster detection method with no covariates and after adjusting for potential covariates respectively. As empirical evidence on the association of street connectivity measures and the occurrence of road collisions had been found, we selected street connectivity measures as the potential covariates in our cluster detection. Results of the most significant cluster and the second most significant cluster during five consecutive years are located around the central areas. Moreover, after adjusting the covariates, the most significant cluster moves from the central areas of London to its peripheral areas, while the second most significant cluster remains unchanged. Additionally, one potential covariate used in this study, length-based road density, exhibits a positive association with the number of road collisions; meanwhile count-based intersection density displays a negative association. Although the covariates (i.e., road density and intersection density) exhibit potential impact on the clusters of road collisions, they are unlikely to contribute to the majority of clusters. Furthermore, the method of fast Bayesian model-based cluster detection is developed to discover spatio-temporal clusters of serious injury collisions. Most of the areas at risk of serious injury collisions overlay those at risk of road collisions. Although not being identified as areas at risk of road collisions, some districts, e.g., City of London, are regarded as areas at risk of serious injury collisions.

Comparing Bayesian spatial models: Goodness-of-smoothing criteria for assessing under- and over-smoothing

BACKGROUND

Many methods of spatial smoothing have been developed, for both point data as well as areal data. In Bayesian spatial models, this is achieved by purposefully designed prior(s) or smoothing functions which smooth estimates towards a local or global mean. Smoothing is important for several reasons, not least of all because it increases predictive robustness and reduces uncertainty of the estimates. Despite the benefits of smoothing, this attribute is all but ignored when it comes to model selection. Traditional goodness-of-fit measures focus on model fit and model parsimony, but neglect "goodness-of-smoothing", and are therefore not necessarily good indicators of model performance. Comparing spatial models while taking into account the degree of spatial smoothing is not straightforward because smoothing and model fit can be viewed as opposing goals. Over- and under-smoothing of spatial data are genuine concerns, but have received very little attention in the literature.

METHODS

This paper demonstrates the problem with spatial model selection based solely on goodness-of-fit by proposing several methods for quantifying the degree of smoothing. Several commonly used spatial models are fit to real data, and subsequently compared using the goodness-of-fit and goodness-of-smoothing statistics.

RESULTS

The proposed goodness-of-smoothing statistics show substantial agreement in the task of model selection, and tend to avoid models that over- or under-smooth. Conversely, the traditional goodness-of-fit criteria often don't agree, and can lead to poor model choice. In particular, the well-known deviance information criterion tended to select under-smoothed models.

CONCLUSIONS

Some of the goodness-of-smoothing methods may be improved with modifications and better guidelines for their interpretation. However, these proposed goodness-of-smoothing methods offer researchers a solution to spatial model selection which is easy to implement. Moreover, they highlight the danger in relying on goodness-of-fit measures when comparing spatial models.

Investigating the Impacts of Real-Time Weather Conditions on Freeway Crash Severity: A Bayesian Spatial Analysis

This study presents an empirical investigation of the impacts of real-time weather conditions on the freeway crash severity. A Bayesian spatial generalized ordered logit model was developed for modeling the crash severity using the hourly wind speed, air temperature, precipitation, visibility, and humidity, as well as other observed factors. A total of 1424 crash records from Kaiyang Freeway, China in 2014 and 2015 were collected for the investigation. The proposed model can simultaneously accommodate the ordered nature in severity levels and spatial correlation across adjacent crashes. Its strength is demonstrated by the existence of significant spatial correlation and its better model fit and more reasonable estimation results than the counterparts of a generalized ordered logit model. The estimation results show that an increase in the precipitation is associated with decreases in the probabilities of light and severe crashes, and an increase in the probability of medium crashes. Additionally, driver type, vehicle type, vehicle registered province, crash time, crash type, response time of emergency medical service, and horizontal curvature and vertical grade of the crash location, were also found to have significant effects on the crash severity. To alleviate the severity levels of crashes on rainy days, some engineering countermeasures are suggested, in addition to the implemented strategies.

Exponentiated power generalized Weibull power series family of distributions: Properties, estimation and applications

In this paper, we introduce the exponentiated power generalized Weibull power series (EPGWPS) family of distributions, obtained by compounding the exponentiated power generalized Weibull and power series distributions. By construction, the new family contains a myriad of new flexible lifetime distributions having strong physical interpretations (lifetime system, biological studies…). We discuss the characteristics and properties of the EPGWPS family, including its probability density and hazard rate functions, quantiles, moments, incomplete moments, skewness and kurtosis. The main vocation of the EPGWPS family remains to be applied in a statistical setting, and data analysis in particular. In this regard, we explore the estimation of the model parameters by the maximum likelihood method, with accuracy supported by a detailed simulation study. Then, we apply it to two practical data sets, showing the applicability and competitiveness of the EPGWPS models in comparison to some other well-reputed models.

An improved Bayesian Modified-EWMA location chart and its applications in mechanical and sport industry

Control charts are popular tools in the statistical process control toolkit and the exponentially weighted moving average (EWMA) chart is one of its essential component for efficient process monitoring. In the present study, a new Bayesian Modified-EWMA chart is proposed for the monitoring of the location parameter in a process. Four various loss functions and a conjugate prior distribution are used in this study. The average run length is used as a performance evaluation tool for the proposed chart and its counterparts. The results advocate that the proposed chart performs very well for the monitoring of small to moderate shifts in the process and beats the existing counterparts. The significance of the proposed scheme has proved through two real-life examples: (1) For the monitoring of the reaming process which is used in the mechanical industry. (2) For the monitoring of golf ball performance in the sports industry.

Driving behavior and safety analysis at OSMS section for merged, one-way freeway based on simulated driving safety analysis of driving behaviour

In order to study driving performance at the opening section of median strip (hereafter OSMS) on the freeway capacity expansion project, this study separately controlled 9 different simulated experimental scenarios of OSMS length and freeway traffic flow. 25 participants were recruited to perform 225 simulated driving tests using the driving simulator, and the analysis of variance (ANOVA) was used to analyze the driving characteristics which can represent the safety context. The results show that the safety parameters of driving are different when the length of OSMS and the traffic flow are different. When the traffic flow is low or moderate, the OSMS length can significantly affect the speed of the vehicle and the maximum values of time to collision. The higher the traffic flow, the smaller the minimum values of time headway. As the length of the OSMS decreases, the vehicles are more generally concentrated at the end of the opening area with the minimum values of time headway. The study also found that when the traffic volume is high, the impact of the OSMS length on driving performance will be weakened. In addition, the OSMS length and the traffic flow have little impact on driving comfort. Additionally, when the traffic flow is low or moderate, the opening length can significantly affect the driving behavior and safety of the vehicle. However, when the traffic volume is high, the impact of the opening length on them will be relatively weakened to some extent. Therefore, it is advised that in the case of freeways with large traffic volume, merely extending the length of the opening section does not necessarily optimize safety. Rather, the actual traffic density of the road should be carefully considered before a design length is adopted.

Interregional inequality and road accident rates in Spain

The aim of this study was to determine whether interregional inequality in Spain had the same impact on the risks of fatality and injury across the different provinces of Spain, in the period from 1999 to 2015. This allows us to map fatality and injury rates in Spanish provinces depending on their level of economic development. Provinces were divided in two large groups according to the mean weight of their per capita GDP on the national GDP from 2000 to 2015. Using fixed effects data panel models, estimations were obtained for each group of the impact of the relationships between per capita GDP, unemployment rate and other control variables on their risks of fatality and injury. The models reveal that economic conditions and education are explanatory factors with greater significance and impact on the risks of fatality and injury in provinces with higher levels of economic development. In this group, the penalty-points driving licence was found have a greater impact, although its effectiveness is now being questioned. In contrast, to reduce the risks of fatality and injury in less developed provinces, it is imperative to invest in road infrastructure, increasing the proportion of high capacity roads and investing more in road replacement and maintenance. The geographical distribution generated in this study allows us to better identify the areas with a higher risk of fatality or injury. This, in turn, confirms the need to improve the configuration of road safety policy, taking into account the different fatality or injury rates across provinces, the origins of which lie in the specific provincial conditions.

A highway crash risk assessment method based on traffic safety state division

In order to quantitatively analyze the influence of different traffic conditions on highway crash risk, a method of crash risk assessment based on traffic safety state division is proposed in this paper. Firstly, the highway crash data and corresponding traffic data of upstream and downstream are extracted and processed by using the matched case-control method to exclude the influence of other factors on the model. Secondly, considering the weight of traffic volume, speed and occupancy, a multi-parameter fusion cluster method is applied to divide traffic safety state. In addition, the quantitative relationship between different traffic states and highway crash risk is analyzed by using Bayesian conditional logistic regression model. Finally, the results of case study show that different traffic safety conditions are in different crash risk levels. The highway traffic management department can improve the safety risk management level by focusing on the prevention and control of high-risk traffic safety conditions.

A correlated random parameters tobit model to analyze the safety effects and temporal instability of factors affecting crash rates

Numerous studies have previously used a variety of count-data models to investigate factors that affect the number of crashes over a certain period of time on roadway segments. Unlike past studies which deal with crash frequency, this study views the crash rates directly as a continuous variable left-censored at zero and explores the application of an alternate approach based on tobit regression. To thoroughly investigate the factors affecting freeway crash rates and the potentially temporal instability in the effects of crash factors involving traffic volume, freeway geometries and pavement conditions, a classic uncorrelated random parameters tobit (URPT) model and a correlated random parameters tobit (CRPT) model were estimated, along with a conventional fixed parameters tobit (FPT) model. The analysis revealed a large number of safety factors, including several appealing and interesting factors rarely studied in the past, such as the safety effects of climbing lanes and distance along composite descending grade. The results also showed that the CRPT model was not only able to reflect the heterogeneous effects of various factors, but also able to estimate the underlying interactions among unobserved characteristics, and therefore provide better statistical fit and offer more insights into factors contributing to freeway crashes than its model counterparts. Additionally, the results showed significant temporal instability in CRPT models across the studied time periods indicating that crash factors (including unobserved characteristics and the underlying interactions among them) and their effects on crash rates varied over time, and more attentions should be paid when interpreting crash data-analysis findings and making safety policies. The modeling technique in this study demonstrates the potential of CRPT model as an effective approach to gain new insights into safety factors, particularly when the heterogeneous effects of factors on safety are interactive. Additionally, findings from this study are also expected to assist in developing more effective countermeasures by better understanding the safety effects of factors associated with freeway design characteristics and pavement conditions.

The role of striking and struck vehicles in side crashes between vehicles: Bayesian bivariate probit analysis in China

OBJECTIVE

Side crashes between vehicles which usually lead to high casualties and property loss, rank first among total crashes in China. This paper aims to identify the factors associated with injury severity of side crashes at intersections and to provide suggestions for developing countermeasures to mitigate the levels of injuries.

METHOD

In order to investigate the role of striking and struck vehicles in side crashes simultaneously, bivariate probit model was proposed and Bayesian approach was employed to evaluate the model, compared to the corresponding univariate probit model.

DATA

Crash data from Beijing, China for the period 2009-2012 were used to carry out the statistical analysis. Based on the investigation with vehicles and data analysis on events, 130 intersection side crash cases were selected to form a specific dataset. Then, the influence of human, vehicles, roadway and environmental variables on crash severity was examined by means of bivariate probit regression within Bayesian framework.

RESULTS

The effects of the factors on striking vehicle drivers and struck vehicle drivers were considered separately and simultaneously to find more targeted conclusions. The statistical analysis revealed vehicle type, lane number, no non-motorized lane and speeding have the corresponding influence on the injury severity of striking vehicles, while time of day and vehicle type of struck vehicles increased the likelihood of being injured.

CONCLUSIONS

From the results it can be concluded that there indeed exists correlation between striking and struck vehicles in side crashes, although the correlation is not so strong. Importantly, Bayesian bivariate probit model can address the role of striking and struck vehicles in side crashes simultaneously and can accommodate the correlation clearly, which extends the range of univariate probit analysis. The general and empirical countermeasures are presented to improve the safety at intersections.

Ranking hospitals when performance and risk factors are correlated: A simulation-based comparison of risk adjustment approaches for binary outcomes

Background

The conceptualization of hospital quality indicators usually includes some form of risk adjustment to account for hospital differences in case mix. For binary outcome variables like in-hospital mortality, frequently utilized risk adjusted measures include the standardized mortality ratio (SMR), the risk standardized mortality rate (RSMR), and excess risk (ER). All of these measures require the estimation of expected hospital mortality, which is often based on logistic regression models. In this context, an issue that is often neglected is correlation between hospital performance (e.g. care quality) and patient-specific risk factors. The objective of this study was to investigate the impact of such correlation on the adequacy of hospital rankings based on different measures and methods.

Methods

Using Monte Carlo simulation, the impact of correlation between hospital care quality and patient-specific risk factors on the adequacy of hospital rankings was assessed for SMR/RSMR, and ER based on logistic regression and random effects logistic regression. As an alternative method, fixed effects logistic regression with Firth correction was considered. The adequacies of the resulting hospital rankings were assessed by the shares of hospitals correctly classified into quintiles according to their true (unobserved) care qualities.

Results

The performance of risk adjustment approaches based on logistic regression and random effects logistic regression declined when correlation between care quality and a risk factor was induced. In contrast, fixed-effects-based estimations proved to be more robust. This was particularly true for fixed-effects-logistic-regression-based ER. In the absence of correlation between risk factors and care quality, all approaches showed similar performance.

Conclusions

Correlation between risk factors and hospital performance may severely bias hospital rankings based on logistic regression and random effects logistic regression. ER based on fixed effects logistic regression with Firth correction should be considered as an alternative approach to assess hospital performance.

Incorporating spatial effects into temporal dynamic of road traffic fatality risks: A case study on 48 lower states of the United States, 1975-2015

The rate of road traffic fatalities has long served as a regular indicator to evaluate and compare road safety performance for different administrative divisions. This article introduces a novel method known as the Markov chain spatial model to incorporate the spatial effects into the temporal dynamic of the fatality rates. Compared to the traditional Markov chain model, the proposed spatial Markov chain model can quantify the influence of neighboring sites explicitly in the transition process. A case study using a long duration dataset, from 1975 to 2015 in the 48 lower states of the United Sates, was conducted to illustrate the proposed model. The fatality rates were measured as the number of traffic fatalities per 100 million vehicle miles or per 10,000 residents. The results show that the probability of transition for one state between different levels of traffic fatality risks depends largely on the context of its surrounding neighbors. Another important finding is that relative to the estimates of traditional Markov chain models, states surrounded by neighborhoods with relatively low fatality rates take a longer time to transform to a higher level of fatality risk in the spatial Markov chain model. On the other hand, those with high-risk neighborhoods takes less time to deteriorate. These findings confirm that it is imperative to incorporate spatial effects when modeling the temporal dynamic of safety indicators to assess and monitor the safety trends in the areas of interest.

Spatial analysis of traffic accidents near and between road intersections in a directed linear network

Although most of the literature on traffic safety analysis has been developed over areal zones, there is a growing interest in using the specific road structure of the region under investigation, which is known as a linear network in the field of spatial statistics. The use of linear networks entails several technical complications, ranging from the accurate location of traffic accidents to the definition of covariates at a spatial micro-level. Therefore, the primary goal of this study was to display a detailed analysis of a dataset of traffic accidents recorded in Valencia (Spain), which were located into a linear network representing more than 30 km of urban road structure corresponding to one district of the city. A set of traffic-related covariates was constructed at the road segment level for performing the analysis. Several issues and methodological approaches that are inherent to linear networks have been shown and discussed. In particular, the network was defined in a way that allowed the explicit investigation of traffic accidents around road intersections and the consideration of traffic flow directionality. Zero-inflated negative binomial count models accounting for spatial heterogeneity were used. Traffic safety at road intersections was specifically taken into account in the analysis by considering the higher variability and number of zeros that can be observed at these road entities and the differential contribution of the covariates depending on the proximity of a road intersection. To complement the results obtained from the count models fitted, coldspots and hotspots along the network were also detected, with explanatory objectives. The models confirmed that spatial heterogeneity, overdispersion and the close presence of road intersections explain the accident counts observed in the road network analyzed. Hotspot detection revealed that several covariates whose contribution was unclear in the modelling approaches may also be affecting accident counts at the road segment level.

Bayesian spatial-temporal model for the main and interaction effects of roadway and weather characteristics on freeway crash incidence

This study attempts to examine the main and interaction effects of roadway and weather conditions on crash incidence, using the comprehensive crash, traffic and weather data from the Kaiyang Freeway in China in 2014. The dependent variable is monthly crash count on a roadway segment (with homogeneous horizontal and vertical profiles). A Bayesian spatio-temporal model is proposed to measure the association between crash frequency and possible risk factors including traffic composition, presence of curve and slope, weather conditions, and their interactions. The proposed model can also accommodate the unstructured random effect, and spatio-temporal correlation and interactions. Results of parameter estimation indicate that the interactions between wind speed and slope, between precipitation and curve, and between visibility and slope are significantly correlated to the increase in the freeway crash risk, while the interaction between precipitation and slope is significantly correlated to the reduction in the freeway crash risk, respectively. These findings are indicative of the design and implementation of real-time traffic management and control measures, e.g. variable message sign, that could mitigate the crash risk under the adverse weather conditions.

Mapping the knowledge domain of road safety studies: A scientometric analysis

As a way of obtaining a visual expression of knowledge, mapping knowledge domain (MKD) provides a vision-based analytic approach to scientometric analysis which can be used to reveal an academic community, the structure of its networks, and the dynamic development of a discipline. This study, based on the Science Citation Index Expanded (SCIE) and Social Sciences Citation Index (SSCI) articles on road safety, employs the bibliometric tools VOSviewer and CitNetExplorer to create maps of author co-citation, document co-citation, citation networks, analyze the core authors and classic documents supporting road safety studies and show the citation context and development of such studies. It shows that road safety studies clustered mainly into four groups, whose we will refer to as "effects of driving psychology and behavior on road safety", "causation, frequency and injury severity analysis of road crashes", "epidemiology, assessment and prevention of road traffic injury", and "effects of driver risk factors on driver performance and road safety", respectively. Through our analysis, the core publications and their citation relationships were quickly located and explored, and "crash frequency modeling analysis" has been identified to be the core research topic in road safety studies, with spatial statistical analysis technique emerging as a frontier of this topic.

Using latent class analysis and mixed logit model to explore risk factors on driver injury severity in single-vehicle crashes

The single-vehicle crash has been recognized as a critical crash type due to its high fatality rate. In this study, a two-year crash dataset including all single-vehicle crashes in New Mexico is adopted to analyze the impact of contributing factors on driver injury severity. In order to capture the across-class heterogeneous effects, a latent class approach is designed to classify the whole dataset by maximizing the homogeneous effects within each cluster. The mixed logit model is subsequently developed on each cluster to account for the within-class unobserved heterogeneity and to further analyze the dataset. According to the estimation results, several variables including overturn, fixed object, and snowing, are found to be normally distributed in the observations in the overall sample, indicating there exist some heterogeneous effects in the dataset. Some fixed parameters, including rural, wet, overtaking, seatbelt used, 65 years old or older, etc., are also found to significantly influence driver injury severity. This study provides an insightful understanding of the impacts of these variables on driver injury severity in single-vehicle crashes, and a beneficial reference for developing effective countermeasures and strategies for mitigating driver injury severity.

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

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.

Analyzing freeway crash severity using a Bayesian spatial generalized ordered logit model with conditional autoregressive priors

This study develops a Bayesian spatial generalized ordered logit model with conditional autoregressive priors to examine severity of freeway crashes. Our model can simultaneously account for the ordered nature in discrete crash severity levels and the spatial correlation among adjacent crashes without fixing the thresholds between crash severity levels. The crash data from Kaiyang Freeway, China in 2014 are collected for the analysis, where crash severity levels are defined considering the combination of injury severity, financial loss, and numbers of injuries and deaths. We calibrate the proposed spatial model and compare it with a traditional generalized ordered logit model via Bayesian inference. The superiority of the spatial model is indicated by its better model fit and the statistical significance of the spatial term. Estimation results show that driver type, season, traffic volume and composition, response time for emergency medical services, and crash type have significant effects on crash severity propensity. In addition, vehicle type, season, time of day, weather condition, vertical grade, bridge, traffic volume and composition, and crash type have significant impacts on the threshold between median and severe crash levels. The average marginal effects of the contributing factors on each crash severity level are also calculated. Based on the estimation results, several countermeasures regarding driver education, traffic rule enforcement, vehicle and roadway engineering, and emergency services are proposed to mitigate freeway crash severity.

Roadway traffic crash prediction using a state-space model based support vector regression approach

Conventional traffic crash analyzing methods focus on identifying the relationship between traffic crash outcomes and impact risk factors and explaining the effects of risk factors, which ignore the changes of roadway systems and can lead to inaccurate results in traffic crash predictions. To address this issue, an innovative two-step method is proposed and a support vector regression (SVR) model is formulated into state-space model (SSM) framework for traffic crash prediction. The SSM was developed in the first step to identify the dynamic evolution process of the roadway systems that are caused by the changes of traffic flow and predict the changes of impact factors in roadway systems. Using the predicted impact factors, the SVR model was incorporated in the second step to perform the traffic crash prediction. A five-year dataset that obtained from 1152 roadway segments in Tennessee was employed to validate the model effectiveness. The proposed models result in an average prediction MAPE of 7.59%, a MAE of 0.11, and a RMSD of 0.32. For the performance comparison, a SVR model and a multivariate negative binomial (MVNB) model were developed to do the same task. The results show that the proposed model has superior performances in terms of prediction accuracy compared to the SVR and MVNB models. Compared to the SVR and MVNB models, the benefit of incorporating a state-space model to identify the changes of roadway systems is significant evident in the proposed models for all crash types, and the prediction accuracy that measured by MAPE can be improved by 4.360% and 6.445% on average, respectively. Apart from accuracy improvement, the proposed models are more robust and the predictions can retain a smoother pattern. Furthermore, the results show that the proposed model has a more precise and synchronized response behavior to the high variations of the observed data, especially for the phenomenon of extra zeros.

Time-of-day Control Double-Order Optimization of Traffic Safety and Data-Driven Intersections

This paper proposes a novel two-order optimization model of the division of time-of-day control segmented points of road intersection to address the limitations of the randomness of artificial experience, avoid the complex multi-factor division calculation, and optimize the traditional model over traffic safety and data-driven methods. For the first-order optimization-that is, deep optimization of the model input data-we first increase the dimension of traditional traffic flow data by data-driven and traffic safety methods, and develop a vector quantity to represent the size, direction, and time frequency with conflict point traffic of the total traffic flow at a certain intersection for a period by introducing a 3D vector of intersection traffic flow. Then, a time-series segmentation algorithm is used to recurse the distance amongst adjacent vectors to obtain the initial scheme of segmented points, and the segmentation points are finally divided by the combination of the preliminary scheme. For the second-order optimization-that is, model adaptability analysis-the traffic flow data at intersections are subjected to standardised processing by five-number summary. The different traffic flow characteristics of the intersection are categorised by the K central point clustering algorithm of big data, and an applicability analysis of each type of intersection is conducted by using an innovated piecewise point division model. The actual traffic flow data of 155 intersections in Yuecheng District, Shaoxing, China, in 2016 are tested. Four types of intersections in the tested range are evaluated separately by the innovated piecewise point division model and the traditional total flow segmentation model on the basis of Synchro 7 simulation software. It is shown that when the innovated double-order optimization model is used in the intersection according to the 'hump-type' traffic flow characteristic, its control is more accurate and efficient than that of the traditional total flow segmentation model. The total delay time is reduced by approximately 5.6%. In particular, the delay time in the near-peak-flow buffer period is significantly reduced by approximately 17%. At the same time, the traffic accident rate has also dropped significantly, effectively improving traffic safety at intersections.

Investigating Spatial Autocorrelation and Spillover Effects in Freeway Crash-Frequency Data

This study attempts to investigate spatial autocorrelation and spillover effects in micro traffic safety analysis. To achieve the objective, a Poisson-based count regression with consideration of these spatial effects is proposed for modeling crash frequency on freeway segments. In the proposed hybrid model, the spatial autocorrelation and the spillover effects are formulated as the conditional autoregressive (CAR) prior and the exogenous variables of adjacent segments, respectively. The proposed model is demonstrated and compared to the models with only one kind of spatial effect, using one-year crash data collected from Kaiyang Freeway, China. The results of Bayesian estimation conducted in WinBUGS show that significant spatial autocorrelation and spillover effects simultaneously exist in the freeway crash-frequency data. The lower value of deviance information criterion (DIC) and more significant exogenous variables for the hybrid model compared to the other alternatives, indicate the strength of accounting for both spatial autocorrelation and spillover effects on improving model fit and identifying crash contributing factors. Moreover, the model results highlight the importance of daily vehicle kilometers traveled, and horizontal and vertical alignments of targeted segments and adjacent segments on freeway crash occurrences.

Comparative analysis of multiple techniques for developing and transferring safety performance functions

Safety performance functions (SPFs) are crash count prediction models that are used for identifying high crash risk locations, evaluating road safety before and after countermeasure deployment and comparing the safety of alternative site designs. The traditional method of modeling crash counts is negative binomial (NB) regression. Furthermore, the Highway Safety Manual (HSM) provides analytical tools, including NB SPFs, to assess and improve road safety. Even though the HSM's SPFs are restricted to NB models, the road safety literature is rich with a variety of different modeling techniques. Researchers have calibrated the HSM's SPFs to local conditions using a calibration method prescribed by the HSM. However, studies in which SPFs are developed and transferred to other localities are uncommon. In this paper, we develop and transfer rural divided multilane highway segment SPFs of Florida, Ohio, Illinois, Minnesota, California, Washington and North Carolina to each state. For every state, NB, zero-inflated NB, Poisson lognormal (PLN), regression tree, random forest (RF), boosting and Tobit models are developed. A hybrid model that coalesces the predictions of both the Tobit and the NB model is proposed and developed as well. All SPFs are transferred to each state and their predictive performances are evaluated to discern which model type is the most transferable. According to the transferability results, there is no single superior model type. However, the Tobit, RF, tree, NB and hybrid models demonstrate better predictive performances than those of the other methods in a considerably large proportion of transferred SPFs.

Multivariate random parameter Tobit modeling of crashes involving aging drivers, passengers, bicyclists, and pedestrians: Spatiotemporal variations

The increase in 65 years and older population in the United States compels the investigation of the crashes involving all aging (65+) roadway users (drivers, passengers, bicyclists, and pedestrians) in order to ensure their safety. As such, the objective of this research is to provide a spatiotemporal comparative investigation of the crashes involving these aging roadway users in Florida via concurrently using the same set of predictors in order to obtain comparable findings among them. First, a new metric, namely Crash Rate Difference (CRD) approach is developed, which enables one to capture potential spatial and temporal (e.g., weekend and weekday) variations in crash rates of aging user-involved crashes. Second, a multivariate random parameter Tobit model is utilized to determine the factors that drive both the crash occurrence probability and the crash rate of 65+ roadway users, accounting for the unobserved heterogeneity. Findings show that there are statistically significant heterogeneous effects of predictors on the crash rates of different roadway users, which evidences the unobserved heterogeneity across observations. Results also indicate that the presence of facilities such as hospitals, religious facilities, or supermarkets is very influential on crash rates of 65+ roadway users, advocating that roadways around these facilities should be particularly scrutinized by road safety stakeholders. Interestingly, the effect of these facilities on crashes also differs significantly between weekdays and weekends. Moreover, the roadway segments with high crash rates vary temporally depending on whether it is a weekday or a weekend. These findings regarding the spatiotemporal variations clearly indicate the need to develop and design better traffic safety measures and plans addressing these specific roadway segments, which can be tailored to alleviate traffic safety problems for 65+ roadway users.

Accident severity levels and traffic signs interactions in state roads: a seemingly unrelated regression model in unbalanced panel data approach

This study intended to investigate the interactions between accident severity levels and traffic signs in state roads located in Croatia, and explore the correlation within accident severity levels and heterogeneity attributed to unobserved factors. The data from 410 state roads between 2012 and 2016 were collected from Traffic Accident Database System maintained by the Republic of Croatia Ministry of the Interior. To address the correlation and heterogeneity, a seemingly unrelated regression (SUR) model in unbalanced panel data approach was proposed, in which the seemingly unrelated model addressed the correlation of residuals, while the panel data model accommodated the heterogeneity due to unobserved factors. By comparing the pooled, fixed-effects and random-effects SUR models, the random-effects SUR model showed priority to the other two. Results revealed that (1) low visibility and the number of invalid traffic signs per km increased the accident rate of material damage, death or injured; (2) average speed limit exhibited a high accident rate of death or injured; (3) the number of mandatory signs was more likely to reduce the accident rate of material damage, while the number of warning signs was significant for accident rate of death or injured.

Impact of provincial characteristics on the number of traffic accident victims on interurban roads in Spain

This study has two aims. The first is to determine how various factors impact on the number of fatalities, serious injuries and slight injuries adjusted for the level of traffic on interurban roads in Spain. The second is to establish the number of victims per million vehicle-kilometres (veh-km) travelled on interurban roads in each province resulting from the effect of its specific characteristics. To this end, we developed six fixed effect panel data models with panel corrected standard errors for the 1999-2015 period. Our results show that while the proportion of high capacity roads, the unemployment rate and the motorization rate contribute to a reduction in the number of fatalities, serious injuries and slight injuries adjusted for level of traffic, the penalty-points licence system is effective in reducing the number of fatalities and serious injuries but not the number of slight injuries. Furthermore, the specific conditions in Ávila, Toledo, Madrid, Santa Cruz de Tenerife, Las Palmas de Gran Canaria, the Balearic Islands, Lleida and all the provinces on the Mediterranean coast cause a higher number of victims per million veh-km travelled than in the remaining provinces. Thus, greater public investment and more socially responsible behaviour are essential tools for reducing the number of traffic accident victims on Spanish interurban roads. Moreover, the provincial institutions emerge as key agents in improving road safety, due to their greater knowledge of the specific conditions and factors affecting each province.

On the existence of network Macroscopic Safety Diagrams: Theory, simulation and empirical evidence

Recent studies have proposed using well-defined relationships between network productivity and accumulation-otherwise known as Network or Macroscopic Fundamental Diagrams (network MFDs)-to model the dynamics of large-scale urban traffic networks. Network MFDs have been used to develop a variety of network-wide traffic control policies to improve a network's operational efficiency. However, the relationship between a network's MFD and its safety performance has not been well explored. This study proposes the existence of a Macroscopic Safety Diagram (MSD) that relates safety performance (e.g., likelihood of a crash occurring or number of vehicle conflicts observed) with the current network state (i.e., average density) in an urban traffic network. We theoretically posit a relationship between a network's MSD and its MFD based on the average maneuver envelop of vehicles traveling within the network. Based on this model, we show that the density associated with maximum crash propensity is always expected to be larger than the density associated with maximum network productivity. This finding suggests that congested states are not only inefficient, but they might also be associated with more crashes, which can be both more unsafe and lead to decreased network reliability. These theoretical results are validated using surrogate safety assessment metrics in microsimulation and limited field empirical data from a small arterial network in Riyadh, Kingdom of Saudi Arabia. The existence of such MSDs can be used to develop more comprehensive network-wide control policies that can ensure both safe, efficient and reliable network operations.

A cross-comparison of different techniques for modeling macro-level cyclist crashes

Despite the recognized benefits of cycling as a sustainable mode of transportation, cyclists are considered vulnerable road users and there are concerns about their safety. Therefore, it is essential to investigate the factors affecting cyclist safety. The goal of this study is to evaluate and compare different approaches of modeling macro-level cyclist safety as well as investigating factors that contribute to cyclist crashes using a comprehensive list of covariates. Data from 134 traffic analysis zones (TAZs) in the City of Vancouver were used to develop macro-level crash models (CM) incorporating variables related to actual traffic exposure, socio-economics, land use, built environment, and bike network. Four types of CMs were developed under a full Bayesian framework: Poisson lognormal model (PLN), random intercepts PLN model (RIPLN), random parameters PLN model (RPPLN), and spatial PLN model (SPLN). The SPLN model had the best goodness of fit, and the results highlighted the significant effects of spatial correlation. The models showed that the cyclist crashes were positively associated with bike and vehicle exposure measures, households, commercial area density, and signal density. On the other hand, negative associations were found between cyclist crashes and some bike network indicators such as average edge length, average zonal slope, and off-street bike links.

Analysis of stationary and dynamic factors affecting highway accident occurrence: A dynamic correlated grouped random parameters binary logit approach

Traditional accident analysis typically explores non-time-varying (stationary) factors that affect accident occurrence on roadway segments. However, the impact of time-varying (dynamic) factors is not thoroughly investigated. This paper seeks to simultaneously identify pre-crash stationary and dynamic factors of accident occurrence, while accounting for unobserved heterogeneity. Using highly disaggregate information for the potential dynamic factors, and aggregate data for the traditional stationary elements, a dynamic binary random parameters (mixed) logit framework is employed. With this approach, the dynamic nature of weather-related, and driving- and pavement-condition information is jointly investigated with traditional roadway geometric and traffic characteristics. To additionally account for the combined effect of the dynamic and stationary factors on the accident occurrence, the developed random parameters logit framework allows for possible correlations among the random parameters. The analysis is based on crash and non-crash observations between 2011 and 2013, drawn from urban and rural highway segments in the state of Washington. The findings show that the proposed methodological framework can account for both stationary and dynamic factors affecting accident occurrence probabilities, for panel effects, for unobserved heterogeneity through the use of random parameters, and for possible correlation among the latter. The comparative evaluation among the correlated grouped random parameters, the uncorrelated random parameters logit models, and their fixed parameters logit counterpart, demonstrate the potential of the random parameters modeling, in general, and the benefits of the correlated grouped random parameters approach, specifically, in terms of statistical fit and explanatory power.

Application of Fractal theory for crash rate prediction: Insights from random parameters and latent class tobit models

The repercussions from congestion and accidents on major highways can have significant negative impacts on the economy and environment. It is a primary objective of transport authorities to minimize the likelihood of these phenomena taking place, to improve safety and overall network performance. In this study, we use the Hurst Exponent metric from Fractal Theory, as a congestion indicator for crash-rate modeling. We analyze one month of traffic speed data at several monitor sites along the M4 motorway in Sydney, Australia and assess congestion patterns with the Hurst Exponent of speed (H_speed). Random Parameters and Latent Class Tobit models were estimated, to examine the effect of congestion on historical crash rates, while accounting for unobserved heterogeneity. Using a latent class modeling approach, the motorway sections were probabilistically classified into two segments, based on the presence of entry and exit ramps. This will allow transportation agencies to implement appropriate safety/traffic countermeasures when addressing accident hotspots or inadequately managed sections of motorway.