Hazard-based Duration Model Research Articles

Modelling brake transition time of young alcohol-impaired drivers using hazard-based duration models

Braking performance of drivers is a crucial factor in evaluating the collision patterns and implementing road safety measures. Further, alcohol is known to impair driving control. The present study aims to examine the influence of a comprehensive range of Blood Alcohol Concentration (BAC) levels (0%, 0.03 %, 0.05 % and 0.08 %) on brake transition times of drivers. As young drivers show significantly higher crash risks compared to the experienced drivers, fifty-four young Indian drivers in the age group of 21–25 years (forty males and fourteen females) participated in the driving simulator experiments. The study adopted the framework of a within-subjects design, where each driver encountered rural and urban driving scenarios in a counterbalanced order, during experimental driving at each of the four BAC levels. Their brake transition times were estimated with respect to sudden pedestrian crossing events. Weibull Accelerated Failure Time (AFT) models with shared frailty were developed for quantifying the effects of BAC levels along with driver attributes on brake transition time. Preliminary analysis showed significant main effects of BAC (p < 0.001) and driving environment (p = 0.002) on brake transition time; however, their interaction effect was not significant (p = 0.485). The models revealed that 0.03 %, 0.05 % and 0.08 % BACs significantly reduced the brake transition times by 16 %, 28 % and 52 % in rural driving environment, and by 23 %, 37 % and 53 % in urban driving environment, compared to 0% BAC. The study outcomes may find application in assisting collision warning systems which take into account the braking behaviour of drivers.

Hazard-Based Duration Approach to Pedestrian Crossing Behavior at Signalized Intersections

With the rapid urbanization of geographical spaces worldwide, pedestrian safety is a major concern on urban roads. In developing economies like India, an unprecedented increase in accidents involving pedestrians has been observed at intersections. The present study focuses on pedestrian behavior, specifically, violation of red signals while crossing at signalized intersections. With the help of hazard-based duration models, the waiting duration of red-light violators has been analyzed. In addition, the response time of pedestrians during conflict has also been modeled with the help of a hazard-based duration approach. Four signalized intersections from Nagpur City in India were selected for the survival analysis. Kaplan–Meier survival curves have been plotted for both waiting time and response time. With the help of the semi-parametric Cox proportional hazard model, various factors have been identified to describe the survival function of the pedestrians’ crossing. However, the model results were found to be unsatisfactory since the explanatory variables failed in the proportional hazard assumption. Therefore, the parametric accelerated failure time model was utilized to determine the various covariates that affected the waiting time and the response time. The Weibull model was found to be the best fit for waiting duration analysis, while the log-logistic model was considered for the study of response time. The developed models can help understand the external factors and personal features of pedestrians in relation to the risk involved during violation crossings.

Do Larger Sample Sizes Increase the Reliability of Traffic Incident Duration Models? A Case Study of East Tennessee Incidents

Incident duration models are often developed to assist incident management and traveler information dissemination. With recent advances in data collection and management, enormous achieved incident data are now available for incident model development. However, a large volume of data may present challenges to practitioners, such as data processing and computation. Besides, data that span multiple years may have inconsistency issues because of the data collection environments and procedures. A practical question may arise in the incident modeling community—Is that much data really necessary (“all-in”) to build models? If not, then how many data are necessary? To answer these questions, this study aims to investigate the relationship between the data sample sizes and the reliability of incident duration analysis models. This study proposed and demonstrated a sample size determination framework through a case study using data of over 47,000 incidents. This study estimated handfuls of hazard-based duration models with varying sample sizes. The relationships between sample size and model performance, along with estimate outcomes (i.e., coefficients and significance levels), were examined and visualized. The results showed that the variation of estimated coefficients decreases as the sample size increases, and becomes stabilized when the sample size reaches a critical threshold value. This critical threshold value may be the recommended sample size. The case study suggested a sample size of 6,500 to be enough for a reliable incident duration model. The critical value may vary significantly with different data and model specifications. More implications are discussed in the paper.

Hazard-based duration analysis of the time between motorcyclists’ initial training and their first crash

The high fatality rates of motorcyclists relative to other motorized forms of highway transportation has been a focus of engineers and safety policies for many years. One of the most popular approaches to improve motorcycle safety has been to design training courses to improve riding competence. However, the effectiveness of these courses and the initial crash risk of motorcyclists is not well understood. The current study seeks to provide insight into motorcyclists’ initial crash risk by following the crash history of newly trained motorcyclists for up to 5 years after they complete their required motorcycle training. Specifically, attention is focused on the time until motorcyclists’ first crash. Using data from over 40,000 Florida motorcyclists, Weibull hazard-based duration models are estimated with gamma heterogeneity, and full random parameters, to determine the factors that affect the duration until motorcyclists’ first crash. The estimation results show that age and gender are driving factors in determining this duration and ultimately crash risk. In addition, estimation results show that most gender-age groups have an initial period of increasing crash risk, ranging from 30 to 96 days, where the likelihood of a crash increases the longer motorcyclists go without having a crash. After this initial period, crash risk declines over time as increasing riding experience reduces overall risk. This particular finding points to a critical motorcycle-safety opportunity in that policies and/or training can be modified to attempt to eliminate this initial high-risk period to arrive at a desirable lower initial risk and a declining risk over time as experience makes for safer and more cautious riding.

Cooperate or not? Exploring drivers’ interactions and response times to a lane-changing request in a connected environment

Lane-changing is one of the complex driving tasks that depends on the number of vehicles, objectives, and lanes. A driver often needs to respond to a lane-changing request of a lane-changer, which is a function of their personality traits and the current driving conditions. A connected environment is expected to assist during the lane-changing decision-making process by increasing situational awareness of surrounding traffic through vehicle-to-vehicle communication and vehicle-to-infrastructure communication. Although the majority of lane-changing decision-making components (e.g., gap acceptance behaviour, lane-changing execution behaviour, and drivers’ response to a heavy vehicle) in a traditional environment (an environment without driving aids) has been frequently investigated, our understanding of drivers’ interactions during the lane-changing decision-making process in a connected environment remains elusive due to the novelty of a connected environment and the scarcity of relevant data. As such, this study examines drivers’ responses to lane-changing requests in a connected environment using the CARRS-Q Advanced Driving Simulator. Seventy-eight participants responded to the lane-changing request of a lane-changer under two randomised driving conditions: baseline (traditional environment without driving aids) and connected environment (with driving aids). A segmentation-based approach is employed to extract drivers’ responses to the lane-changing request and subsequently estimate their response time from trajectory data. Additionally, drivers’ response times are modelled using a random parameter accelerated failure time (AFT) hazard-based duration model. Results reveal that drivers tend to be more cooperative in response to a lane-changing request in the connected environment compared with the baseline condition whereby they tend to accelerate to avoid the lane-changing request. The AFT model suggests that on average drivers’ response times are shorter in the connected environment, implying that drivers respond to the lane-changing request faster in the presence of driving aids. However, at the individual level, connected environment’s impact on drivers’ response times is mixed as drivers’ response times may increase or decrease in the connected environment compared to the baseline condition, for instance, we find that female drivers have lower response times in the connected environment than that of male drivers. Overall, this study finds that drivers in connected environment, on average, take less time to respond and appear to be more cooperative, and thus, are less likely to be engaged in safety–critical events.

Shifting from Private to Public Transport using Duration-Based Modeling of a School-Based Intervention

School commuting with public transportation (PT) and shifting away from private cars remains a challenge, especially for transport planners. From behavioral and cultural viewpoints, car dependence has not yet been reversed in many cities. Actions to promote the shift to PT should be multidisciplinary and multi-instrumental to increase PT adoption and achieve more sustainable mobility. There is a lack of strategic alignment between the different stakeholders involved in school commuting of children (parents, school, PT operators) and empirical studies sustaining the effectiveness of actions to shift away from the car. Moreover, PT behavioral aspects are still poorly researched from a marketing perspective. This research aims to help fill the gap by implementing actions related to the 4Ps of the marketing mix (product, place, price, promotion). Ten schools in the Lisbon Metropolitan Area were involved in those actions and then surveyed (1,760 survey participants) to evaluate the impact on their behavioral change, that is, to start going to school with PT. The study explores the impact of a set of marketing events on the time duration before children shift to PT when commuting to school, with a hazard-based duration model. Results suggest that to promote school commuting with PT, it is necessary to characterize the school community before commencing any mobility-oriented intervention, particularly concerning sociodemographic attributes and mobility patterns. These are critical information to design marketing actions better and to adapt and improve the quality of PT vehicles and services that operate to and from schools.

Impact of Cruising for Parking on Travel Time of Traffic Flow

Cruising for parking creates a moving queue of cars that are waiting for vacated parking spaces, but no one can see how many cruisers are in the queue because they are mixed in with normal cars that are actually going somewhere. In order to mitigate the influence of cruising for parking on the normal cars, the park-and-visit cruising tests with GPS and cameras was applied to collect the behavior of the cruisers, and the videotapes of traffic flows were used to measure the volume of cruising cars and the traffic status of normal cars, simultaneously. On this basis, a parking time model based on proportional hazard-based duration model was proposed, and the factors affecting cruise for parking were analyzed, including the volume, search time, speed, acceleration, lane-change frequency, and distracted time of the cruising car. The multiple linear regression model was also established to compare with proportional hazard-based duration model results. The results indicated that between 9 and 56 percent of the traffic was cruising for parking, and the average search time was about 6.03 min. The low-speed, volume, high acceleration frequency, and lane-change times of cruising cars have a negative effect on shortening travel time of the normal traffic flow. Conversely, high-speed of cruising cars has a positive effect on shortening travel time of traffic flow. Moreover, travel time changes in varying degrees due to various factors. Under postulated conditions, the model can be used to estimate the travel time. It is hoped that this study will contribute to improve the planning and management of cruising for parking.

A hazard-based model of the motorcyclists’ overtaking duration

The overtaking maneuver performed by motorcyclists is one of the primary causes of motorcycle accidents. However, few studies in the literature deal with this topic and there are no studies modeling the total overtaking duration, i.e. the time during which extreme hazards are manifest. The present paper aims to analyze the motorcyclists’ behavior during overtaking and to model the total overtaking duration. A field experiment, using instrumented motorcycles, was performed to collect data and a survival analysis was carried out to model the total overtaking duration. Twenty young motorcyclists drove their own motorcycles, which were instrumented with a camera and a global positioning system device (GPS), onto a two-lane suburban road in Rome. A total of 101 overtaking maneuvers were recorded. A methodology, based on video and GPS analyses, was developed to obtain data describing the motorcyclists’ behavior. The obtained results showed that the mean values of the main parameters of the overtaking maneuver (total overtaking duration - 6.6 s - and distance - 109.7 m - lateral distance from the passed vehicle - 1.50 m) were consistent with the few data available in the revised literature. The total overtaking duration was modelled using a hazard-based duration model. The parametric accelerated failure time duration model with a log-logistic distribution, which was the best-fitted distribution, identified the covariates which affected, in a statistically significant way, the total overtaking duration. The obtained model revealed that the overtaking duration depends on several covariates. The greater average impact was found for the initial distance and speed difference, while the initial lateral distance and final distance produced a minor impact. When performing a multiple overtaking, the duration of the maneuver tended to increase by 31 %. This research can be considered as a pilot study and a starting point for future advances on motorcyclists’ behavior during overtaking maneuver and for modeling the total overtaking duration. In addition, the findings of this study could contribute to the development of advanced rider assistance systems for the overtaking maneuver based on current driving conditions.

Is an informed driver a better decision maker? A grouped random parameters with heterogeneity-in-means approach to investigate the impact of the connected environment on driving behaviour in safety-critical situations

The motive of sharing the information in a connected environment is to assist a driver in operational, tactical, and strategic decision making and improving driving task performance. The influence of such information assistance on driver decision making and task performance during safety-critical events is not well understood. Thus, this study focusses on understanding the impact of connected environment on the acceleration noise and the response time as indicators of task performance and the decision making involved in safety-critical events. To overcome the paucity of connected environment data, an advanced driving simulator experiment is designed and conducted. Three categories of uninterrupted information are available to drivers in connected environment scenario, namely continuous information, on-time event-triggered information, and advanced event-triggered information. The safety-critical event designed in the simulator experiment is the leader’s hard braking behaviour in car-following regime. In connected environment scenario, drivers receive an advanced message for this safety-critical event. To model drivers’ decision in safety-critical situations, random parameters modelling approaches are adopted to account for the unobserved heterogeneities in drivers’ decision. Consequently, a grouped random parameters hazard-based duration model and a grouped random parameters linear regression model—both with heterogeneity in parameter means—are estimated for the response time and the acceleration noise, respectively. Results show that the acceleration noise reduces in connected environment while the response time can either increase or decrease in connected environment compared to those in the traditional environment. To better understand this mixed effect on response time, a decision tree analysis is conducted. For human factors, the results demonstrate that young drivers take more advantage of connected environment relative to the middle-aged or old drivers. Overall, drivers exhibit stable driving behaviour because they have more time to react and thus, are at low risk in safety-critical situations in connected environment.

Statistical and machine-learning methods for clearance time prediction of road incidents: A methodology review

Accurate clearance time prediction for road incident would be helpful to evaluate the incident impacting range and provide route guiding strategy according to the predicted results, and thus reduce the travel delays caused by incidents. Currently, a number of approaches have been developed for predicting incident clearance time and investigating the effects of influential factors. Statistical and machine learning methods are the two major methodological approaches. This study aims to make a methodology review for these methods by comprehensively examining their performance in incident clearance time prediction, especially, when omitted variables present significant impacts on selected variables. Specifically, we consider four widely used statistical models: Accelerated Failure Time (AFT) model, Quantile Regression (QR) model, Finite Mixture (FM) model, and Random Parameters Hazard-Based Duration (RPHD) model, and four machine learning models: K-Nearest Neighbor (KNN) model, Support Vector Machine (SVM) model, Back Propagation Neural Network (BPNN) model, and Random Forest (RF) model as candidates. Moreover, the abilities of these methods in uncovering the underlying causality (explaining the causal effects of significant influential factors on clearance time) are also investigated. Incident clearance time data was collected on freeway road sections in Seattle, Washington State from 2009 to 2011. The conclusions can be summarized as follows: 1) the RF model and RPHD model outperform the other three models in data fitting and model prediction in their respective methodological categories; 2) three “heterogeneity” methods including RPHD, FM and QR outperform machine learning methods in model prediction as measured by MAPE; 3) machine learning methods perform stably in model prediction relative to the statistical methods; 4) incident type and lane closure type present significant effects on incident clearance time in all eight selected models.

Understanding the discretionary lane-changing behaviour in the connected environment

Discretionary lane-changing (DLC) is one of the complex driving manoeuvres that requires surrounding traffic information for efficient and safe manoeuvring. The connected environment not only provides such information but also increases situational awareness, which is useful for DLC decision-making. However, the literature is devoid of any concrete evidence of such impact of the connected environment on DLC decision-making. As such, this paper analyses the effects of the connected environment on DLC behaviour. Seventy-eight participants from a diverse background performed DLCs in randomised driving conditions using the CARRS-Q advanced driving simulator. These driving conditions are: baseline (without driving messages), connected environment with perfect communication (fully functioning and uninterrupted supply of driving messages), and connected environment with communication delay (impaired communication). Various key driving behaviour indicators are analysed and compared using a linear mixed model. To analyse the effects of the connected environment on DLC decision-making, two Generalised Estimation Equation (GEE) models are developed for gap acceptance and DLC duration. In addition, a Weibull accelerated failure time hazard-based duration model is developed to investigate the impact of the connected environment on safety associated with DLC manoeuvres. We find that drivers in the connected environment have a larger spacing, larger lead and lag gaps, a longer DLC duration, and a lower acceleration noise compared to the baseline condition. The GEE model on gap acceptance reveals that drivers tend to select relatively bigger gap sizes when the connected environment offers them the subsequent gap information. Similarly, the GEE model for DLC duration suggests that the connected environment increases DLC durations by 2.22 s and 2.11 s in perfect communication and communication delay driving conditions, respectively. Finally, the hazard-based duration model provides insights into the probability of avoiding a lane-changing collision, and indicates that the probability of a lane-changing collision is less in the connected environment driving conditions than in the baseline scenario. Overall, the connected environment improves the DLC driving behaviour and enhances traffic safety.

Importance of Health Claims in the Adoption of New Breakfast Cereal Products in the UK

Regular breakfast consumption has the potential to prevent the prevalence of NCDs and to improve the nutritional profile of diets. Given consumers’ interest in improving their diets, food suppliers are interested in introducing new cereal products making different health claims to capture consumers’ attention. The purpose of this study is threefold: first, it aims to understand whether UK food suppliers are working to increase the availability of breakfast cereals with healthy and nutritious attributes; second, it explores which companies are leading the launch of these products; and third, it assesses to what extent health and nutrition claims made by breakfast cereals have an impact on their market success. The study employs an assembled database combining data from Mintel Global New Products Database (GNPD) and Kantar Worldpanel Dataset (KWDS) for the UK. A hazard-based duration model was used to analyse the success of the new products launched in the UK market in 2011 following them up to 2015. Our results reveal that UK suppliers broadened the number of breakfast cereals on offer in the period 2000 to 2018, with a particular focus on multigrain cereals, porridge and granola. Health and nutrition claims were added to 27% of these products. Although consumers welcome healthy alternatives such as muesli, the impact of positional claims on the success of newly developed breakfast cereals is claim-specific. No clear pattern regarding the impact of health and nutrition claims is identified. However, other elements such as celiac-friendly ingredients and UK origin do have a positive impact on the success of breakfast cereals.

Hazard-Based Duration Models for Predicting Actual Duration of Highway Projects Using Nonparametric and Parametric Survival Analysis

AbstractAt the preconstruction phases of project development, facility stakeholders typically seek reliable estimates of project duration. This paper shows how hazard-based duration models could be...

A hazard-based duration model to quantify the impact of connected driving environment on safety during mandatory lane-changing

Lane-changing is among the more risky of manoeuvres required of drivers, as it requires matching the speed of nearby vehicles, identifying a suitable gap in traffic, ensuring that a driver’s own movements are recognised by others, and a capable execution. The highly anticipated, future connected vehicle environment (CVE) is expected to reduce associated crash risk of lane-changing by providing driving aids, which utilise surrounding traffic information. The impact of CVE driving on safety during mandatory lane-changing, however, is unknown due to the novelty of the CVE and consequent scarcity of the data. As such, this study examines the effects of the CVE on safety during mandatory lane-changing manoeuvres. Seventy-eight participants performed mandatory lane-changing manoeuvres in a driving simulator experiment in the CARRS-Q Advanced Driving Simulator. The randomised driving conditions included baseline driving (without driving aids), CVE driving with perfect communication (on-time supply of driving aids), and CVE driving with communication delay (delayed supply of driving aids). The minimum gap time, which is a surrogate measure of safety representing time-to-collision, between the interacting vehicles during the mandatory lane-changing was modelled using a parametric accelerated failure time (AFT) hazard-based duration model. A gamma frailty specification was used to capture structured heterogeneity arising from the repeated measures design of the experiment. The AFT model reveals that the gap time during mandatory lane-changing manoeuvres is longer during CVE driving with perfect communication compared to both the baseline and CVE driving with communication delay scenarios. The gap times for young (18–26 years) and male drivers are shorter in the traditional driving environment, but longer during CVE driving with perfect communication. Overall, CVE driving assists drivers by increasing the safety and efficiency of mandatory lane-changing tasks.

Occurrence of turning point on environmental Kuznets curve in the process of (de)industrialization

Given the inverted U-shaped relationship between environmental quality and economic development, there exists a turning point which implies a transition from the state of environmental deterioration to the state of environmental improvement. We provide an investigation on the association of the occurrence of the turning point of environmental Kuznets curve (EKC) with the process of (de)industrialization. Hazard-based duration model is employed to study whether and when the turning point occurs from different perspectives of the (de)industrialization process. The results show that the speed to reach the turning point for deindustrializing countries is 1.96 times faster than that for industrializers. With regard to different types of deindustrialization, the speed to reach the turning point for countries experiencing nonpremature deindustrialization and positive deindustrialization increase by 3.57 times and 2.60 times respectively compared to the industrializers. Moreover, technological progress is positively related with the speed to reach the turning point.

Simulating pre-evacuation times using hazard-based duration models: Is waiting strategy more efficient than instant response?

In an indoor evacuation scenario, an early decision to be made by each occupant is when to initiate the (decisive) evacuation movement, a decision that determines the pre-evacuation (or pre-movement) time. We employ a class of econometric models, proportional hazard duration models, to simulate the probabilistic relation between the pre-movement times and the occupant’s proximity to exits at the onset of evacuations. This is based on the empirically-supported assumption that occupants that are relatively further from exit locations when the evacuation cue is perceived, take relatively longer times to initiate their evacuation movement. Implementing these parametric models and using extensive numerical simulations, we investigate the effects of (various degrees and forms of) pre-movement-time heterogeneity on the evacuation efficiency. This is to revisit and test the anecdotal idea that occupants’ collective instant rush hinders evacuation processes. In testing this assumption, we examined whether heterogeneity (i.e. variation) in pre-movement times can lead to better outcomes (i.e. shorter evacuation times). Our analyses included both purely-random heterogeneity as well as strategized heterogeneity, one in which occupants nearer to exits are prioritised, as a (probabilistic) waiting strategy. We observed that the instant movement of occupants led to bigger crowd jams at bottlenecks and created greater degrees of congestion which sustained for longer amounts of time. However, from a time-minimisation perspective, collective instant movement was invariably the best strategy. Neither the random nor the strategized forms of pre-movement-time heterogeneity resulted in any shorter evacuation time than when all occupants initiated their movement instantly. In fact, increasing the degree of pre-movement-time heterogeneity led monotonically to longer evacuation times, despite making the evacuation more orderly. This finding suggests that advising occupants to avoid instant rush may not be a time-optimal strategy, even though it mitigates congestion. The finding has not been tested in relation to high-rise buildings and needs further investigation in that context.

Identifying elderly travel time disparities using a correlated grouped random parameters hazard-based duration approach

Populations in countries throughout the world are ageing. Within the United States, baby boomers – those born between the years 1946 and 1964 – are living longer and are desiring more active and mobile lifestyles than prior generations. It is well established that the onset of chronic diseases and mobility impairments increase with age. Unmitigated mobility gaps threaten well-being, social interaction, and overall quality of life. As a result, transportation policy makers and planners should anticipate, identify, plan, and address transport disadvantages impacting increasingly vulnerable and possibly underserved population segments such as the elderly. Our study reveals potential mobility gaps by quantifying travel time disparities associated with the various household, traveler, travel mode, and trip purpose characteristics. In doing so, business opportunities with respect to unmet transportation needs may be uncovered.To analyze elderly trip durations, this paper extracts data from the 2009 National Household Travel Survey for the New York Consolidated Metropolitan Statistical Area. Specifically, the elderly are divided into two cohorts; those 65 through 74 years of age and those 75 and older. We apply a correlated grouped random parameters hazard-based duration model. This specification accounts for unobserved heterogeneity in the underlying hazard function and across observations, as well as unobserved effects due to the correlation between random parameters. To the authors' knowledge, this is the first study to use this statistical modeling framework to analyze travel times. Results suggest that the use of a correlated grouped random parameters provides a superior statistical fit to several established comparison models. The findings also reveal that the elderly population is not a homogeneous group and that the underlying distribution characterizing the hazard function for each age group is different. To that end, separate models are estimated for each age cohort. Furthermore, the study reveals apparent disparities in elderly travel times associated with birth nationality, ethnicity, education level, and public/private travel modes.

Analysis of E-bike Trip Duration and Frequency by Bayesian Duration and Zero-inflated Count Models

E-bike trip duration and frequency are two essential variables to identify factors affecting e-bike travel demand. This study aimed to investigate the factors affecting e-bike trip duration and frequency. The Bayesian hazard-based duration models with random effect were developed to investigate the contributing factors to the travel time of e-bike trip. The random effect was included to capture the unobserved heterogeneity. Estimation results showed that trip purpose, traffic volume, population, departure time, age and occupation are the main contributing factors to e-bike trip duration. And the factors affecting travel time of e-bike trip are distinct between males and females. The validation results indicated that the predictive performance of the developed duration models are satisfactory. The Bayesian zero-inflated count models with random effect were then used to investigate the contributing factors to the e-bike trip frequency. The zero-inflated count model assumes that the frequency of e-bike trip is generated by two states, including zero-frequency state which determines whether people use e-bikes for travel, and negative binomial state which determines e-bike trip frequency.

Improving roadside design policies for safety enhancement using hazard-based duration modeling

Roadway departure (RwD) crashes, comprising run-off-road (ROR) and cross-median/centerline head-on collisions, are one of the most lethal crash types. Nationwide, from 2014 to 2016, annual RwD crashes accounted for 53% of all motor vehicle traffic fatalities. Several factors may cause a driver leave the travel lane, including an avoidance maneuver and inattention or fatigue. Roadway and roadside geometric design features (e.g., lane widths and clear zones) play a significant role in whether human error results in a crash. In this paper, we present a hazard-based duration model to investigate the distance traveled by an errant vehicle in a run-off-road crash, the stopping hazard rates, and associated risk factors. For this study, we obtained five years' (2010–2014) of crash data related to roadway departures (i.e., overturn and fixed-object crashes) from the Federal Highway Administration's Highway Safety Information System Database. The results indicate that over 50% of the observed vehicles traveled no more than 36 ft. in a ROR crash and 25% of the observed vehicles traveled at least 78 ft. We also found that seasonal, roadway, and crash variables, along with vehicle information and driver characteristics significantly contributed to the distances traveled by errant vehicles in ROR crashes. This paper presents methodological empirical evidence that the Cox proportional-hazards model is appropriate for investigating the distances traveled by errant vehicles in ROR crashes. In addition, it also provides valuable information for traffic design and management agencies to improve roadside design policies and implementing appropriately forgiving roadsides for errant vehicles.

A hazard-based approach to modelling the effects of online shopping on intershopping duration

Despite growing prevalence of online shopping, its impacts on mobility are poorly understood. This partially results from the lack of sufficiently detailed data. In this paper we address this gap using consumer panel data, a new dataset for this context. We analyse one year long longitudinal grocery shopping purchase data from London shoppers to investigate the effects of online shopping on overall shopping activity patterns and personal trips. We characterise the temporal structure of shopping demand by means of the duration between shopping episodes using hazard-based duration models. These models have been used to study inter-shopping spells for traditional shopping in the literature, however effects of online shopping were not considered. Here, we differentiate between shopping events and shopping trips. The former refers to all types of shopping activity including both online and in-store, while the latter is restricted to physical shopping trips. Separate models were estimated for each and results suggest potential substitution effects between online and in-store in the context of grocery shopping. We find that having shopped online since the last shopping trip significantly reduces the likelihood of a physical shopping trip. We do not observe the same effect for inter-event durations. Hence, shopping online does not have a significant effect on overall shopping activity frequency, yet affects shopping trip rates. This is a key finding and suggests potential substitution between online shopping and physical trips to the store. Additional insights on which factors, including basket size and demographics, affect inter-shopping durations are also drawn.