On random-parameter count models for out-of-sample crash prediction: Accounting for the variances of random-parameter distributions

Impact of speed on injury severity in single-vehicle run-off-road crashes: Insights from partially temporal constrained modeling approach

Single-vehicle run-off-road crashes accounts for approximately 35% of all the traffic fatalities in the U.S during the period of 2019-2021. This paper explores the association between driving speed and injury severity outcomes of single-vehicle run-off-road crashes. The single-vehicle run-off-road crash data from 2019 to 2021 on Interstate freeways in Florida are utilized, and categorized into periods of pre-, during-, and post-COVID-19 pandemic. The partially constrained temporal and temporal unconstrained random parameters logit models are developed considering three injury severity outcomes: no injury, minor injury and serious injury/fatality. Multiple variables in terms of driver, vehicle, roadway, environmental, crash, and temporal attributes are observed to significantly affect the injury severity. Moreover, temporal instability and transferability issues are validated through likelihood ratio test and out-of-sample prediction. In the partially constrained models, numerous variables such as indicators of new vehicle, male driver, and restraint-protected driving consistently yield identical parameter values across all periods, whereas various variables clearly illustrate the distinct differences across the three periods and three speed intervals. The marginal effects in the unconstrained models also display the obvious differences across three periods and three speed intervals. Moreover, the findings corroborate the increased risk outcomes linked to larger speed differences and the COVID-19 pandemic period. These results provide better understanding of the risk mechanisms underlying run-off-road crashes and furnish valuable direction for the formulation of effective safety interventions.

A novel framework for crash frequency prediction: Geographic support vector regression based on agent-based activity models in Greater Melbourne

The field of spatial analysis in traffic crash studies can often enhance predictive performance by addressing the inherent spatial dependence and heterogeneity in crash data. This research introduces the Geographical Support Vector Regression (GSVR) framework, which incorporates generated distance matrices, to assess spatial variations and evaluate the influence of a wide range of factors, including traffic, infrastructure, socio-demographic, travel demand, and land use, on the incidence of total and fatal-or-serious injury (FSI) crashes across Greater Melbourne's zones. Utilizing data from the Melbourne Activity-Based Model (MABM), the study examines 50 indicators related to peak hour traffic and various commuting modes, offering a detailed analysis of the multifaceted factors affecting road safety. The study shows that active transportation modes such as walking and cycling emerge as significant indicators, reflecting a disparity in safety that heightens the vulnerability of these road users. In contrast, car commuting, while a consistent factor in crash risks, has a comparatively lower impact, pointing to an inherent imbalance in the road environment. This could be interpreted as an unequal distribution of risk and safety measures among different types of road users, where the infrastructure and policies may not adequately address the needs and vulnerabilities of pedestrians and cyclists compared to those of car drivers. Public transportation generally offers safer travel, yet associated risks near train stations and tram stops in city center areas cannot be overlooked. Tram stops profoundly affect total crashes in these areas, while intersection counts more significantly impact FSI crashes in the broader metropolitan area. The study also uncovers the contrasting roles of land use mix in influencing FSI versus total crashes. The proposed framework presents an approach for dynamically extracting distance matrices of varying sizes tailored to the specific dataset, providing a fresh method to incorporate spatial impacts into the development of machine learning models. Additionally, the framework extends a feature selection technique to enhance machine learning models that typically lack comprehensive feature selection capabilities.

Multi-objective extensive hypothesis testing for the estimation of advanced crash frequency models

Analyzing crash data is a complex and labor-intensive process that requires careful consideration of multiple interdependent modeling aspects, such as functional forms, transformations, likely contributing factors, correlations, and unobserved heterogeneity. Limited time, knowledge, and experience may lead to over-simplified, over-fitted, or misspecified models overlooking important insights. This paper proposes an extensive hypothesis testing framework including a multi-objective mathematical programming formulation and solution algorithms to estimate crash frequency models considering simultaneously likely contributing factors, transformations, non-linearities, and correlated random parameters. The mathematical programming formulation minimizes both in-sample fit and out-of-sample prediction. To address the complexity and non-convexity of the mathematical program, the proposed solution framework utilizes a variety of metaheuristic solution algorithms. Specifically, Harmony Search demonstrated minimal sensitivity to hyperparameters, enabling an efficient search for solutions without being influenced by the choice of hyperparameters. The effectiveness of the framework was evaluated using two real-world datasets and one synthetic dataset. Comparative analyses were performed using the two real-world datasets and the corresponding models published in literature by independent teams. The proposed framework showed its capability to pinpoint efficient model specifications, produce accurate estimates, and provide valuable insights for both researchers and practitioners. The proposed approach allows for the discovery of numerous insights while minimizing the time spent on model development. By considering a broader set of contributing factors, models with varied qualities can be generated. For instance, when applied to crash data from Queensland, the proposed approach revealed that the inclusion of medians on sharp curved roads can effectively reduce the occurrence of crashes, when applied to crash data from Washington, the simultaneous consideration of traffic volume and road curvature resulted in a notable reduction in crash variances but an increase in crash means.

Analysis of injury severity of work zone crashes on rural and urban work zones: Accounting for out-of-sample prediction and temporal instability

This research utilizes data collected in Florida to examine the differentials in injury severities among single-vehicle drivers involved in work zone-related incidents, specifically focusing on the distinctions between rural and urban areas. The study encompasses a four-year period (2016-2019) of crash dataset. A likelihood ratio test was performed to examine model estimate's temporal consistency in datasets from rural and urban areas across several time periods throughout the year. Separate statistical models were estimated for both rural and urban datasets to understand different driver injury severity outcomes (no injury, minor injury, and severe injury) using a mixed logit approach with possible heterogeneity in mean and variance of random parameters. Out-of-sample simulations were conducted to see the effect of different parameter changes on injury severity probabilities in rural and urban work zone crashes. Over multiple years, various years in both rural and urban models have generated statistically significant random factors that effectively capture the presence of heterogeneity in means, accounting for unobservable variations within the data. Clear evidence of factors such as speed limits, work zone type, and traffic volume affecting the work zone injury severities were found to vary significantly between rural and urban work zone areas. However, despite this difference, rural and urban work zones share common safety problems and countermeasures such as driver education, improved signage, and appropriate traffic controls; combining ITS technologies and enhanced law enforcement can help mitigate crash severity in urban and rural work zone areas.

An investigation of heterogeneous impact, temporal stability, and aggregate shift in factors affecting the driver injury severity in single-vehicle rollover crashes

Single-vehicle rollover crashes have been acknowledged as a predominant highway crash type resulting in serious casualties. To investigate the heterogeneous impact of factors determining different injury severity levels in single-vehicle rollover crashes, the random parameters logit model with unobserved heterogeneity in means and variances was employed in this paper. A five-year dataset on single-vehicle rollover crashes, gathered in California from January 1, 2013, to December 31, 2017, was utilized. Driver injury severities that were determined to be outcome variables include no injury, minor injury, and severe injury. Characteristics pertaining to the crash, driver, temporal, vehicle, roadway, and environment were acknowledged as potential determinants. The results showed that the gender indicator specified to minor injury was consistently identified as a significant random parameter in four years' models and the joint five-year model, excluding the 2016 crash model where the night indicator associated with no injury was observed to produce the random effect. Additionally, two series of likelihood ratio tests were conducted to assess the year-to-year and aggregate-to-component temporal stability of model estimation results. Marginal effects of explanatory variables were also calculated and compared to analyze the temporal stability and interpret the results. The findings revealed an overall temporal instability of model specifications across individual years, while there is no significant aggregate-to-component variation. Injury severities were observed to be stably affected by several variables, including improper turn indicator, under the influence of alcohol indicator, old driver indicator, seatbelt indicator, insurance indicator, and airbag indicator. Furthermore, the year-to-year and aggregate-to-component shift was quantified and characterized by calculating the differences in probabilities between within-sample observations and out-of-sample predictions. The overall results imply that continuing to expand and refine the model to incorporate more comprehensive datasets can result in more robust and stable injury severity prediction, thus benefiting in mitigating the associated driver injury severity.

Exploring temporal instability effects on bicyclist injury severities determinants for intersection and non-intersection-related crashes

Cycling is a sustainable and healthy mode of transportation with direct links to reducing traffic congestion, lowering greenhouse gas emissions, and improving air quality. However, from a safety perspective, bicyclists represent a risky road user group with a higher likelihood of sustaining severe injuries when involved in vehicle crashes. With various determinants known to affect bicyclist injury severity and vary across locations, this study investigates the factors affecting bicyclist injury severity and temporal instability, considering the location of crashes. More specifically, the objective of this study is to understand differences in injury severities of intersection and non-intersection-related single-bicycle-vehicle crashes using four year crash data from the state of Florida. Random parameters logit models with heterogeneity in the means and variances are developed to model bicyclist injury severity outcomes (no injury, minor injury, and severe injury) for intersection and non-intersection crashes. Several variables affecting injury severities are considered in model estimation, including weather, roadway, vehicle, driver, and bicyclist characteristics. The temporal stability of the model parameters is assessed for different locations and years using a series of likelihood ratio tests. Results indicate that the determinants of bicyclist injury severities change over time and location, resulting in different injury severities of bicyclists, with non-intersection crashes consistently resulting in more severe bicyclist injuries. Using a simulation-based out-of-sample approach, predictions are made to understand the benefits of replicating driving behaviour and facilities similar to intersections for non-intersection locations, which could benefit in reducing bicyclist injury severity probabilities.

Stability of factors influencing walking-along-the-road pedestrian injury severity outcomes under different lighting conditions: A random parameters logit approach with heterogeneity in means and out-of-sample predictions

Pedestrians walking along the road's edge are more exposed and vulnerable than those on designated crosswalks. Often, they remain oblivious to the imminent perils of potential collisions with vehicles, making crashes involving these pedestrians relatively unique compared to others. While previous research has recognized that the surrounding lighting conditions influence traffic crashes, the effect of different lighting conditions on walking-along-the-road pedestrian injury severity outcomes remains unexplored. This study examines the variations in the impact of risk factors on walking-along-the-road pedestrian-involved crash injury severity across various lighting conditions. Preliminary stability tests on the walking-along-the-road pedestrian-involved crash data obtained from Ghana revealed that the effect of most risk factors on injury severity outcomes is likely to differ under each lighting condition, warranting the estimation of separate models for each lighting condition. Thus, the data were grouped based on the lighting conditions, and different models were estimated employing the random parameter logit model with heterogeneity in the means approach to capture different levels of unobserved heterogeneity in the crash data. From the results, heavy vehicles, shoulder presence, and aged drivers were found to cause fatal pedestrian walking-along-the-road severity outcomes during daylight conditions, indicators for male pedestrians and speeding were identified to have stronger associations with fatalities on roads with no light at night, and crashes occurring on Tuesdays and Wednesdays were likely to be severe on lit roads at night. From the marginal effect estimates, although some explanatory variables showed consistent effects across various lighting conditions in pedestrian walking-along-the-road crashes, such as pedestrians aged < 25 years and between 25 and 44 years exhibited significant variations in their impact across different lighting conditions, supporting the finding that the effect of risk factors are unstable. Further, the out-of-sample simulations underscored the shifts in factor effects between different lighting conditions, highlighting that enhancing visibility could play a pivotal role in significantly reducing fatalities associated with pedestrians walking along the road. Targeted engineering, education, and enforcement countermeasures are proposed from the interesting insights drawn to improve pedestrian safety locally and internationally.

Differences in single-vehicle motorcycle crashes caused by distraction and overspeed behaviors: considering temporal shifts and unobserved heterogeneity in prediction

Distraction and overspeed behaviors are acknowledged as two significant contributors to single-vehicle motorcycle crashes, injuries and fatalities resulting from which are severe and critical issues in Pakistan. To explore the temporal instability and differences in the factors determining the injury severities between single-vehicle motorcycle crashes caused by distraction and overspeed behaviors, this study estimated two groups of random parameter logit models with heterogeneity in means and variances. Single-vehicle motorcycle crash data in Rawalpindi city between 2017 and 2019 was used for model estimation, and a wide variety of explanatory variables relating to the rider, roadways, environments, and temporal attributes was simulated in the models. The current study considered three possible crash injury severity outcomes: minor injury, severe injury and fatal injury. Likelihood ratio tests were conducted to explore the temporal instability and non-transferability. Marginal effects were also calculated to further reveal temporal instability of the variables. Except for several variables, the most significant factors reported temporal instability and non-transferability, manifested as the effects varied from year to year and across different crashes. Moreover, out-of-sample prediction was also implemented to capture temporal instability and non-transferability between distraction and overspeed crash observations. The non-transferability between motorcycle crashes caused by distraction and overspeed behaviors provides insights into developing differentiated countermeasures and policies targeted at preventing and mitigating single-vehicle motorcycle crashes caused by the two risk-taking behaviors.

Further compelling evidence for safety-in-numbers: It is more than meets the eye

In the extant road safety literature, estimating safety-in-numbers is dominated by conventional cross-sectional methods in which active mode (pedestrian or cyclist) volume together with motorised traffic volume are present in regression models explaining active mode safety directly. There is "direct" evidence for safety-in-numbers when the coefficient associated with active mode volume is negative (safety improves as volume increases) or when it is smaller than one (safety decreases at a lower rate compared to the rate of increase in active mode volume). In this article we extend the concept of safety-in-numbers in the traffic safety field, introducing "indirect" safety-in-numbers, which constitutes a new form of evidence for this phenomenon. We provide empirical evidence to support this, discussing that using an approach based on heterogeneity in mean modelling-a form of random parameters (slopes) models-it is possible to reveal "indirect" safety-in-numbers effects. Therefore, such models can reveal further compelling evidence for safety-in-numbers. Accurate knowledge of safety-in-numbers effects (both direct and indirect) and their underlying mechanisms can help provide robust motives for promoting active travel and will have valuable implications for the design of road safety interventions.

Localizing safety performance functions for two-way STOP-controlled (TWST) three-leg intersections on rural two-lane two-way (TLTW) roadways in Alabama: A geospatial modeling approach with clustering analysis

Safety Performance Functions (SPFs) can be used to predict the number of crashes for highway facilities by site characteristics, including traffic exposures and other specific site factors. The traditional approach to developing SPFs relies on factors that are observed in the data and has an unstated assumption that the relationships between safety performance and observed factors are stationary. However, there might be factors that are not captured by the data but also have significant impacts on roadway safety performance. These factors can lead to significant unobserved heterogeneity in safety performance at different sites. Failure to capture such unobserved heterogeneity in developing SPFs may result in biases and decrease the predictive accuracy. Given the interactions between highway traffic and roadway environments, the unobserved heterogeneity is likely related to the geographic space of the highway network. This study employs a spatial modeling approach, namely Geographically Weighted Negative Binomial Regression (GWNBR), to incorporate spatial heterogeneity into SPF model estimation. The GWNBR model can generate a local SPF for every site instead of a global SPF for one entire jurisdiction (e.g., a state) from the traditional approach. Local SPFs (or l-SPFs) are high-resolution and may be difficult for practitioners to use. To support the implementation of l-SPFs, this study proposes a method to aggregate l-SPFs to various geographic levels. This study first uses the 2014-2018 geo-referenced crash data from Alabama to develop l-SPFs for two-way STOP-controlled (TWST) three-leg intersections on rural two-lane two-way (TLTW) roadways in the state. The results show that l-SPFs vary substantially across Alabama. For example, the coefficients of traffic volume (AADT) on major roads range from 0.126 to 1.203 across different areas of the state. Then, an aggregation method based on K-means clustering is demonstrated to aggregate l-SPFs to various geographic levels of interest. The l-SPFs and their aggregation provide geographic flexibility in developing countermeasures and allocating funds to improve traffic safety considering local conditions.

Predicting intersection crash frequency using connected vehicle data: A framework for geographical random forest

Accurate crash frequency prediction is critical for proactive safety management. The emerging connected vehicles technology provides us with a wealth of vehicular motion data, which enables a better connection between crash frequency and driving behaviors. However, appropriately dealing with the spatial dependence of crash frequency and multitudinous driving features has been a difficult but critical challenge in the prediction process. To this end, this study aims to investigate a new Artificial Intelligence technique called Geographical Random Forest (GRF) that can address spatial heterogeneity and retain all potential predictors. By harnessing more than 2.2 billion high-resolution connected vehicle Basic Safety Message (BSM) observations from the Safety Pilot Model Deployment in Ann Arbor, MI, 30 indicators of driving volatility are extracted, including speed, longitudinal and lateral acceleration, and yaw rate. The developed GRF was implemented to predict rear-end crash frequency at intersections. The results show that: 1) rear-end crashes are more likely to happen at intersections connecting minor roads compared to major roads; 2) a higher number of hard acceleration and deceleration events beyond two standard deviations in the longitudinal direction is a leading indicator of rear-end crashes; 3) the optimal GRF significantly outperforms Global Random Forest, with a 9% lower test error and a substantially better fit; and 4) geographical visualization of variable importance highlights the presence of spatial non-stationarity. The proposed framework can proactively identify at-risk intersections and alert drivers when leading indicators of driving volatility tend to worsen.

Temporal Stability Analysis of Lighting Conditions in Traffic Accidents

Different lighting conditions can result in accidents of different levels of severity. However, current studies lack the consideration of the heterogeneity and temporal stability of accident data under various lighting conditions. Therefore, three years’ worth of data were used to investigate the critical factors of accident severity. The random parameters logit model was employed to investigate the influence of different lighting conditions on temporal stability and heterogeneity. The critical factors affecting injury severity were also identified. The temporal stability and transferability of the models were investigated by a series of likelihood ratio tests. Based on different lighting conditions (daylight conditions, and night-time conditions with street lighting on), six models were established. Three kinds of accident injury severity levels were classified: property damage only (PDO), severe injury (SI), and fatal injury (FI). The estimation results showed contributing factors of accident severity were significantly different between the two kinds of lighting conditions. Additionally, accidents showed temporal instability. The proposed method can provide a guide for infrastructure construction, operation, and maintenance in traffic-safety management.

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.

A note on estimating safety performance functions with a flexible specification of traffic volume

In this note, a flexible approach to allow for variation in the impact of traffic volume in the estimation of Safety Performance Functions (SPFs) is proposed. The approach generalizes a recently proposed approach by Gayah and Donnell (2021) (GD) titled "Estimating safety performance functions for two-lane rural roads using an alternative functional form for traffic volume". GD approach proposes a multiple regime structure for AADT impact while explicitly constraining the impact at the regime threshold to be the same. While the GD approach provides a flexible structure, the framework as proposed calls for careful judgement for threshold selection and additional model estimation complexity for the AADT constraint. The current note establishes the equivalence of the proposed approach with the GD approach and subsequently presents a more flexible model structure that improves on the GD approach. Subsequently, we document the advantages of our proposed approach in terms of model estimation, parameter significance testing, flexibility to consider multiple traffic volume ranges and ease of accommodating random parameters for analysis. Finally, we present potential directions for future research.

Uncertainty matters: Bayesian modeling of bicycle crashes with incomplete exposure data

BACKGROUND

One major challenge faced by neighborhood-level bicycle safety analysis is the lack of complete and reliable exposure data for the entire area under investigation. Although the conventional travel-diary surveys, together with the emerging smartphone fitness applications and bike-sharing systems, provide straightforward and valuable opportunities to estimate territory-wide bicycle activities, the obtained ridership suffers inherently from underreporting.

METHODS

We introduced the Bayesian simultaneous-equation model as a sound methodological alternative here to address the uncertainty arising from incomplete exposure data when modeling bicycle crashes. The proposed method was successfully fitted to a crowdsourced dataset of 792 bicycle-motor vehicle (BMV) crashes aggregated from 209 neighborhoods over a 3-year period in Hong Kong.

RESULTS

Our analysis empirically demonstrated the bias due to omission of activity-based exposure measures or to the direct use of cycling distance extracted from the travel-diary survey without correcting for incompleteness. By modeling bicycle activities and the frequency of BMV crashes simultaneously, we also provided new evidence that an expansion of bicycle infrastructure was likely associated with a significant increase in cycling levels and a substantial reduction in the risk of BMV crashes, despite a slight increase in the absolute number of BMV crashes.

CONCLUSIONS

Our approach is promising in adjusting for the uncertainty in raw exposure data, extrapolating the missing exposure values, and untangling the linkage among built environment, bicycle activities, and the frequency of BMV crashes within a unified framework. To promote safer cycling, designated facilities should be provided to consecutively separate cyclists from motor vehicles.

A simulation-based empirical bayes approach: Incorporating unobserved heterogeneity in the before-after evaluation of engineering treatments

The Empirical Bayes approach for before-after evaluation methodology utilizing the negative binomial model does not account well for unobserved heterogeneity. Building on the Empirical Bayes approach, the objective of this study was to propose a framework to accommodate unobserved heterogeneity in before-after countermeasure evaluation. In particular, this study has proposed a simulation-based Empirical Bayes approach by applying the panel random parameters negative binomial model with parameterized overdispersion (PRNB-PO) to evaluate the effectiveness of engineering treatments. The proposed framework has been tested for the wide centerline treatment (WCLT) on rural two-lane two-way highways in Australia. The empirical analysis included 511 km of WCLT treated highways in a before-after evaluation within a time period of 2010 - 2018 and 430 km of reference sites in Queensland, Australia. The PRNB-PO models outperformed the traditional negative binomial models in terms of goodness-of-fit and prediction performance for total injury crashes, and fatal and serious injury (FSI) crashes. The simulation-based Empirical Bayes approach using the PRNB-PO model resulted in more precise estimates of crash modification factors than the standard Empirical Bayes approach. The WCLT is found to result in significant reductions in total injury crashes by 28.21% (95% confidence interval (CI) = 22.92 - 33.50%), FSI crashes by 13.90% (95% CI = 6.99 - 20.81%), and head-on crashes by 25.45% (95% CI = 14.87 - 36.03%). Overall, WCLT is an effective engineering treatment and should be considered a low-cost countermeasure on rural two-lane two-way highways.

Association of human mobility with road crashes for pandemic-ready safer mobility: A New York City case study

BACKGROUND

The COVID-19 pandemic has reshaped our cities in many ways. The number of motor vehicles on the road has plummeted during lockdowns, and an increasing number of people are turning to walking and biking. From a road safety perspective, the overall question is what effects the human behavior shift brings on the crash occurrence and, more importantly, how to support decision-makers on safer mobility policies?

METHOD

Based on anonymous mobile phone location and crash report data in New York City, this study attempts to provide some new insights by using survival analysis (the hazard function approach) to explore the effects of human mobility changes due to the pandemic on crashes that involve injuries and fatalities (of pedestrian, cyclist or motorist).

RESULTS

(1) the increased percentage of people staying at home improves pedestrian and cyclist safety, which adds evidence for making walking and cycling more appealing; (2) the increased percentage of people staying at home raises the likelihood of injuries for motor vehicle drivers, suggesting that it will be critical to monitor the driving behavior and establish new speed limits during the future pandemic waves and in the post-pandemic era as well; (3) non-work trips (e.g., shopping, recreation, personal business, etc.) are positively associated with crash injuries for motor vehicle drivers as well as pedestrian and cyclist; (4) human mobility factors were found not related to crash fatalities; (5) control NPIs implemented increased the motor vehicle drivers' crash risk.