Random Parameter Negative Binomial Model Research Articles

Investigating built environment and traffic flow impact on crash frequency in urban road networks

While numerous studies have examined the factors that influence crash occurrence, there remains a gap in understanding the intricate relationship between built environment, traffic flow, and crash occurrences across different spatial units. This study explores how built environment attributes, and dynamic traffic flow characteristics affect crash frequency by focusing on proposed traffic density-based zones (TDZs). Utilizing a comprehensive dataset from Greater Melbourne, Australia, this research emphasizes on the dynamic traffic flow variables and insights from the Macroscopic Fundamental Diagram model, considering parameters such as shockwave velocity and congestion index. The association between the potential influencing factors and crash frequency is examined using a random parameter negative binomial regression model. Results indicate that the data segmentation based on TDZs is instrumental in establishing a more refined crash model compared to traditional planning-based zones, as demonstrated by improved goodness-of-fit measures. Factors including density (e.g., employment density), network design (e.g., road density and highway density), land use diversity (e.g., job-housing balance and land use mixture), and public transit accessibility (e.g., bus route density) are significantly associated with crash occurrence. Furthermore, the unobserved heterogeneity effects of the shockwave velocity and congestion index on crashes are revealed. The study highlights the significance of incorporating dynamic traffic flow variables in understanding crash frequency variations across different spatial units. These findings can inform optimal real-time traffic monitoring, environmental design, and road safety management strategies to mitigate crash risks.

Comparative Evaluation of Crash Hotspot Identification Methods: Empirical Bayes vs. Potential for Safety Improvement Using Variants of Negative Binomial Models

The empirical Bayes (EB) method is widely acclaimed for crash hotspot identification (HSID), which integrates crash prediction model estimates and observed crash frequency to compute the expected crash frequency of a site. The traditional negative binomial (NB) models, often used to estimate crash predictive models, typically struggle with accounting for the unobserved heterogeneity in crash data. Complex extensions of the NB models are applied to overcome these shortcomings. These techniques also present new challenges, for instance, applying the EB procedures, especially for out-of-sample data. This study applies a random parameter negative binomial (RPNB) model within the EB framework for HSID using out-of-sample data, comparing its performance with a varying dispersion parameter NB model (VDPNB). The research also evaluates the potential for safety improvement (PSI) scores for both models and compares them with EB estimates using three generalised criteria: high crashes consistency test (HCCT), common sites consistency test (CSCT), and absolute rank differences test (ARDT). The results yield dual insights. Firstly, the study highlights associations between crash covariates and frequency, emphasising the significance of roadway geometric design characteristics (e.g., lane width, number of lanes, and parking type) and traffic volume. Some variables also influenced overdispersion parameters in the VDPNB model. In the RPNB model, annual average daily traffic (AADT) and lane width emerged as random parameters. Secondly, the HSID performance assessment revealed the superiority of the EB method over PSI. Notably, the RPNB model, compared to the VDPNB, demonstrates superior performance in EB estimates for HSID with out-of-sample data. This research recommends adopting the EB method with RPNB models for robust HSID.

Investigating road conditions of crash blackspots in Addis Ababa, Ethiopia: a random parameters negative binomial model

Crash blackspots significantly impact and, to some extent, determines the entire road network’s safety level. Therefore, it is imperative to identify these blackspots and investigate the contributing factors. This becomes particularly crucial for low-income countries facing financial constraints in implementing road safety measures. Methodologically multiple studies utilised random parameter negative binomial models to predict vehicle crashes due to their ability to address unobserved heterogeneity in crash data, surpassing conventional models. However, the potential of this promising method in investigating factors influencing crash blackspots remains underutilised. This study aims to identify crash blackspots and investigates the roadway factors of such segments using the random parameters negative binomial modelling method. A three-year (2017–2019) crash data collected from the Ethiopian capital, Addis Ababa, with traffic volumes and various geometric characteristics were utilised. The model estimation results demonstrate the superiority of the random parameter negative binomial model over conventional models, showcasing its ability to reveal unobserved heterogeneity associated with road condition factors in crash blackspots. The study finds that horizontal curves and access density are significant road condition-related contributors to crash blackspots, characterised as random parameters. On the other hand, fixed-parameter influence factors include average annual daily traffic, vertical gradient, vertical curve, median width, and traffic control devices. The study highlights the need to further explore horizontal curvatures and access control as potential random parameters in crash blackspot locations. The findings may assist transportation planners/agencies in prioritising road maintenance, enhancing design standards, and implementing targeted safety interventions to improve road safety effectively.

An in-depth analysis of head-on crash severity and fatalities in Ghana

Head-on collisions are often linked to more serious injuries compared to other types of crashes, due to the intense impact they cause. In low- and middle-income countries, these collisions frequently involve high occupancy public transportation vehicles, leading to higher fatality rates per crash. Given the high risk of injury and potential for multiple casualties, this study delves into the factors influencing the outcomes of head-on crashes and the number of fatalities in Ghana. The study analyzed six years of historical head-on collision data from Ghana and developed two models to address the issue. The injury-severity analysis was performed using a random parameter multinomial logit with heterogeneity in means and variances approach and aimed to identify the factors that have a significant impact on the severity of injuries sustained in head-on collisions, while the random parameters negative binomial fatality count model was designed to examine the factors that contribute to the number of fatalities in these crashes in the country. Results showed that head-on collisions with drivers over 65, buses, motorcycles, and those between 25 and 65 years of age were more likely to result in fatalities. Speeding and vehicle malfunctions were also found to be significant contributing factors to fatal head-on collisions. Head-on crashes involving minibuses and incidents where the driver was attempting to overtake another vehicle were found to be more likely to result in a higher number of fatalities. The results of this study uncover an intriguing interaction between human-related elements and socioeconomic factors, which pose obstacles to the Government's endeavor to upgrade the major highways in the country. Additionally, the increasing need for transportation has led to the presence of vehicles on the roads that may not meet safety standards. Consequently, it is no surprise that several of the study's findings align with expectations. Nevertheless, within the specific context of Ghana, these findings furnish compelling data-driven evidence supporting the adoption and implementation of the safe systems approach as a means to tackle fatal head-on collisions in the country.

How do road infrastructure investments affect Powered Two-Wheelers crash risk?

The drivers of Powered Two-Wheelers (PTWs) pertain to the collective of so-called vulnerable road users. Crashes have scarcely decreased for these roadway users in recent years, whereas among other users, e.g. cars users, they have declined considerably. Meanwhile, the use of PTWs has risen sharply worldwide. This situation adds a further concern to transportation policies and makes evident the need to explore factors involved in PTW crashes. Yet there is a lack of studies specifically about road safety for PTWs. The present study therefore aspires to advance in the knowledge of the factors affecting PTW crashes on interurban roadways, by means of analyzing the effects of some variables not considered previously in this type of studies —mainly economic resources invested in roads—while also accounting specifically for the exposure to risk of PTWs (veh-km), along with relevant variables related to road traffic, the roadway infrastructure, and socioeconomic, meteorological and legislative factors. To this end, and bearing in mind the latest advancements of incorporating unobserved heterogeneity in count data models, different configurations of random parameters negative binomial models for data panels are presented. The realm of study is the network of national roads in Spain, distributed over 43 provinces, and the time period between 2007 and 2015. The results show significant associations for 11 of the variables considered: annual and accumulated investment in construction, expense on maintenance, proportion of motorways, light and heavy vehicle traffic, per capita GDP, age, unemployment rate, price of gasoline, and modification of the demerit point system (DPS). With respect to transport policy implications, the findings provided in this study may serve to monitor the effects of economic resources allocated to road construction and maintenance —along with other measures, such as gasoline prices and DPS—on PTWs safety.

Modeling over speeding behavior of vehicles using a random parameter negative binomial approach: A case study of Mumbai, India

Over speeding is one of the most common factors contributing to road accidents leading to traffic-related injuries and deaths. Understanding determinants of over speeding behavior is an important step toward enhancing road safety and developing robust intervention strategies. Moreover, there is a need to extend this knowledge with respect to developing countries, where there is a significant variation in the operating speeds of the vehicles owing to the heterogeneous traffic conditions. The present study captured the speeding behavior of the vehicles in Mumbai, India, during the years 2017 and 2018 using roadside observational surveys along with the spatial and temporal attributes of the selected locations. This study investigates the combined effect of temporal and spatial attributes on the over speeding frequency. A random parameter negative binomial model is developed utilizing the observational data to explain the over speeding behavior of the vehicles at the selected count locations. The developed model accounts for unobserved heterogeneity across the over speeding count locations based on temporal, road geometric, and built environment attributes. The study results confirm the presence of heterogeneity in the over speeding behavior of the vehicles at the count locations. In terms of policy implications, results suggest that temporary speed calming strategies could be adopted during the non-peak hours and on weekends. Similarly, deploying speed humps, rumble strips, or adopting law enforcement strategies can circumvent over speeding behavior on arterial roads. Lastly, developing well-connected roads with frequent presence of intersections and traffic signals can be another strategy applicable for such behavior.

Investigating factors affecting rural crash frequency at marginal areas around cities in Iran: a random parameter modeling approach

ABSTRACT A significant portion of rural crashes in Iran occur in the marginal areas around cities. Exclusive crash frequency models should be developed to identify the factors affecting the occurrence of crashes in these areas. In this study, the rural crash data of highways leading to the city of Isfahan were employed to develop a negative binomial (NB) model as a constant-parameter model, along with random effects negative binomial (RENB) and random parameters negative binomial (RPNB) models as the models based on the random parameter approach. The modeling results indicated the superiority of the RPNB model over the two other models. According to the findings of this study, the traffic volume of roads and the proportion of local and non-local vehicles, the proportion of longitudinal distance-limit violation, the way of controlling access points, and the access to rest areas affected the crash frequency in the marginal areas around cities.

Examining the impact of exposure, built environment and socio-demographics on pedestrian safety: A case study of Greater London

Walking as a mode of travel alleviates congestion, pollution and concerns over physical fitness. However, safety concerns might be a barrier for some people to walking more often, so finding ways to improve pedestrian safety is important. This paper conducts a ward-level study of Greater London such that factors which are associated with pedestrian safety can be identified and interventions to improve safety can be more appropriately targeted. A wide range of factors relating to exposure, land use, built and natural environment, and socio-demographics, including markers of deprivation were considered in our analysis. We employed a multilevel random parameters negative binomial regression model with a hierarchical structure which encompassed the boroughs and wards of Greater London allowing dependency in the data and unobserved heterogeneity to be addressed more fully. The results show that BAME population, number of schools, job density and alcohol expenditure are associated with an increase in pedestrian crashes as are crime rate and children in child benefit households, which are both markers of deprivation. Also, the average number of cars per household, the proportion of green space and the percentage of adults who commute by walking have a decreasing effect on pedestrian crash frequency. This study identifies important determinates of ward-level pedestrian safety and estimates the magnitude of their association with pedestrian safety and in doing so reveals important between borough (local authority) differences in the Greater London area in terms of pedestrian safety which were not previously known or well-understood.

Evaluating the correlation between risky riding behaviour and self-reported crashes in India: Minimizing unobserved heterogeneity

Riding Behaviour is found to be the main cause of Powered Two-Wheeler (PTW) crashes in more than90% of the crash events. The high percentage of PTW crashes resulting in fatalities has sought a serious need for research to examine risky riding Behaviour. A widely used instrument for measuring the self-reported riding Behaviour of PTW riders is the Motorcycle Rider Behaviour Questionnaire (MRBQ). In this study, exploratory factor analysis of the MRBQ revealed a four-factor solution viz., traffic errors, control errors, speed violations, and stunts. Despite the popularity of MRBQ, it is capable of covering only a small fraction of the large number of elements that affect the riding Behaviour. Many other elements remain overlooked in the analysis, resulting in unobserved heterogeneity. Therefore, the present study uses a random parameter negative binomial (RPNB) model to minimize the effect of unobserved heterogeneity. It was inferred from the RPNB model that variables like gender, control error, and speed violation have a randomly distributed regression coefficient. Further, it is found that traffic errors are the most significant predictor of crash risk. Additionally, results depict that male riders are positively associated with crashes, and they are more likely to involve in crashes as compared to female riders. The finding of this paper will be valuable for policymakers and decision-makers to improve the rider training program, licensing system, and design road safety campaigns.

A Random-Parameter Negative Binomial Model for Assessing Freeway Crash Frequency by Injury Severity: Daytime versus Nighttime

This study explored the effects of contributing factors on crash frequency, by injury severity of all, daytime, and nighttime crashes that occurred on freeways. With three injury severity outcomes classified as light injury, minor injury, and severe injury, the effects of the explanatory variables affecting the crash frequency were examined in terms of the crash, traffic, speed, geometric, and sight characteristics. Regarding the model estimations, the lowest AIC and BIC values (2263.87 and 2379.22, respectively) showed the superiority of the random-parameter multivariate negative binomial (RPMNB) model in terms of the goodness-of-fit measure. Additionally, the RPMNB model indicated the highest R2 (0.25) and predictive accuracy, along with a significantly positive α parameter. Moreover, transferability tests were conducted to confirm the rationality of separating the daytime and nighttime crashes. Based on the RPMNB models, several explanatory variables were observed to exhibit relatively stable effects whereas other variables presented obvious variations. This study can be of certain value in guiding highway design and policies and developing effective safety countermeasures.

Driving Performance Evaluation of Shuttle Buses: A Case Study of Hong Kong-Zhuhai-Macau Bridge.

The risky behaviours of bus drivers are of great concern to public health and environmental sustainability, especially for the buses operated between cities. With this in mind, the present study examined the distribution of risky behaviours among bus drivers, and the contributing factors to risky performance. To achieve this, 1648 records of GPS trajectory data and 8281 records of advance warning message data from Hong Kong–Zhuhai–Macau Bridge shuttle buses were obtained. The temporal and spatial distribution of risky behaviours was analysed. A random parameters negative binomial model was developed to further investigate the relationship between speed-related factors and risky behaviours. The results indicated that the warning of safety distance, lane departure, forward collision, and distraction were more likely to occur on weekdays. The period between 14 and 16 o’clock obtained the highest frequency of safety distance and lane departure warnings. Regarding the model estimation results, indicators reflecting average speed, acceleration, and number of trips per day showed a statistically significant impact on safety distance and lane departure warnings. Also, the acceleration of bus drivers showed a mixed impact on lane departure warnings. Corresponding implications were discussed according to the findings to reduce the frequency of risky behaviours in shuttle bus operations.

A Bayesian Bivariate Random Parameters and Spatial-Temporal Negative Binomial Lindley Model for Jointly Modeling Crash Frequency by Severity: Investigation for Chinese Freeway Tunnel Safety

As hazardous locations of a road, freeway tunnels have a higher risk of casualty than open roads. Therefore, it is necessary to seek a reliable crash prediction model and propose targeted improvement measures. However, existing studies on freeway tunnel crash models mainly suffer from the following problems: 1) They ignore the correlation between different injury severity levels of crashes; 2) They ignore the impact of excess zero observations; 3) They do not consider the influence of heterogeneity between samples and the spatio-temporal correlation. To solve the above problems, this paper has compiled a dataset with freeway tunnel design features, three years of traffic conditions, pavement conditions, and traffic crash data. Then, a bivariate random parameters negative binomial Lindley model (ST-BRPNB-L) is established for jointly modeling crash counts and injury severity levels, which consider excess zero observations by introducing Lindley parameters, characterize the heterogeneity, and spatial-temporal correlation between samples by introducing random parameters and spatio-temporal parameters. The Bayesian estimation results have shown that ST-BRPNB-L has the best goodness-of-fit among a series of comparison models, which verifies the superiority of the proposed model. On this basis, the influence of the risk factors on the frequency and severity of crashes was quantitatively analyzed based on the ST-BRPNB-L model’s parameters estimation results, which provides a scientific basis for safety improvement measures of freeway tunnels.

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.

Does Displaying Safety Messages on Dynamic Message Signs have Measurable Impacts on Crash Risk?

Transportation agencies have increasingly been using dynamic message signs (DMS) to communicate safety messages in an effort to both increase awareness of important safety issues and to influence driver behavior. Despite their widespread use, evaluations as to potential impacts on driver behavior, and the resultant impacts on traffic crashes, have been very limited. This study addresses this gap in the extant literature and assesses the relationship between traffic crashes and the frequency with which various types of safety messages are displayed. Safety message data were collected from a total of 202 DMS on freeways across the state of Michigan between 2014 and 2018. These data were integrated with traffic volume, roadway geometry, and crash data for segments that were located downstream of each DMS. A series of random parameters negative binomial models were estimated to examine total, speeding-related, and nighttime crashes based on historical messaging data while controlling for other site-specific factors. The results did not show any significant differences with respect to total crashes. Marginal declines in nighttime crashes were observed at locations with more frequent messages related to impaired driving, though these differences were also not statistically significant. Finally, speeding-related crashes were significantly less frequent near DMS that showed higher numbers of messages related to speeding or tailgating. Important issues are highlighted with respect to methodological concerns that arise in the analysis of such data. Field research is warranted to investigate potential impacts on driving behavior at the level of individual drivers.

A random parameter negative binomial model for signalized intersection accidents in Seoul, Korea

A variety of statistical models were generally considered to better understand the relationship between crash occurrences and diverse factors. However, most of statistical models adapted fixed parameters which cannot incorporate time variation or sement-specific effects. To relieve this problem, this study focuses on a traffic accident frequency model using a random parameter negative binomial approach. This method allows for the consideration of unobserved heterogeneity in accident data that current popular methods such as Poisson or Negative Binomial models cannot account for. A four-year (2007-2010) continuous panel of accident histories at 95 signalized intersections in Seoul, Korea, was used to estimate the random parameter negative binomial model with traffic volumes and various geometric characteristics at intersections. Results show that the presence of a left-turn exclusive lane on a major road, the existence and length of a median barrier, and the existence of a pedestrian island on a major road are random parameters, and an additional ten variables significantly affected the safety at the intersections as fixed parameters. The fixed parameters were associated with major and minor roadway heavy vehicle volume, exclusive turn lane presence on major and minor roadway, taxiway lane presence, median barrier presence, as well as the number of lanes on major and minor roadway. The insights from this study indicate the need for broader analysis of lane channelization, lane exclusion and lane geometry effects as potential random parameters in intersection accident propensities.

Investigation of the Factors Influencing the Crash Frequency in Expressway Tunnels: Considering Excess Zero Observations and Unobserved Heterogeneity

The existing crash modeling techniques for expressway tunnels must overcome the following difficulties: 1) The collected risk factors contributing to the tunnel crashes include narrow ranges, especially the pavement conditions and weather conditions of the tunnels are rarely taken into account. 2) Most researchers ignored the estimation deviation caused by the excess zero observations of tunnel crash datasets. 3) No existing tunnel crash model can combine the random-parameters approach and spatial-temporal approach to solve the estimation deviation caused by the inter-samples and spatial-temporal heterogeneity. To address these problems, this study presents an investigation of the safety effects of risk factors of tunnel design features, traffic conditions, pavement conditions and weather conditions utilizing a 12-quarter period (3 years) of data as well as five crash frequency models: 1) a fixed parameters negative binomial model (FPNB), 2) a random parameters negative binomial model (RPNB), 3) a random parameters negative binomial Lindley model (RPNBL), 4) a spatial and random parameters negative binomial Lindley model (SP-RPNBL), and 5) a spatial-temporal and random parameters negative binomial Lindley model (ST-RPNBL). The results showed that the ST-RPNBL model solves the deviation that arises from excess zero observations by introducing the Lindley distribution and considers the unobserved heterogeneity by introducing both the random parameters and spatial-temporal parameters that provided better goodness of fit and offered more insights into the factors that contribute to tunnel safety. Furthermore, the ST-RPNBL model detected 16 variables that were significantly correlated with tunnel crash frequency, of which 12 variables were associated with a higher crash frequency and four variables were associated with a lower crash frequency. The random variables of the curvature, the steep downgrade indicator, the proportion of class 5 vehicle and the skidding resistance index (SRI) were identified, and the influence of each significant variable on the crash frequency was analyzed.

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.

Comparison and analysis of crash frequency and rate in cross-river tunnels using random-parameter models

Underground road systems are becoming popular in cites because they can overcome urban space constraints and increase capacity and accessibility for urban transport systems. In cities with rivers and seas, the construction of cross-river tunnels can preserve land resources and reduce traffic congestion without affecting navigation. However, tunnel traffic safety has become an increasing concern due to frequent and serious tunnel traffic crashes. The severity of crashes and the difficulty of rescue in tunnels are higher than those of other road sections. To improve the safety of tunnel operation, this paper analyzes the crash data of 14 river-crossing tunnels in Shanghai from 2015 to 2016. A negative binomial (NB) model is employed for crash frequency, and a tobit model is employed for crash rate. With respect to possible spatial and temporal correlations in accident data and unobserved heterogeneity across observations, random-effect (RE) and random-parameter (RP) regression models are utilized. The tunnel geometry characteristics, traffic conditions and crash location are considered as independent variables. The results of the crash frequency show that annual average daily traffic (AADT), speed limit, grade, grade differences and the ratio of the vertical grade to the curve radius (RGR) are likely to increase the crash frequency in cross-river tunnels while horizontal curve radius, vertical curve radius and long tunnel are associated with fewer crashes. This study also explored the use of crash rate instead of crash frequency as a dependent variable by using a random-parameter tobit model. The results indicate that the significance of most independent variables is consistent with the results obtained from the random-parameter negative binomial model based on crash frequency.

Roles of infrastructure and land use in bicycle crash exposure and frequency: A case study using Greater London bike sharing data

Cycling is increasingly promoted as a sustainable transport mode. However, bicyclists are more vulnerable to fatality and severe injury in road crashes, compared to vehicle occupants. It is necessary to identify the contributory factors to crashes and injuries involving bicyclists. For the prediction of motor vehicle crashes, comprehensive traffic count data, i.e. AADT and vehicle kilometer traveled (VKT), are commonly available to proxy the exposure. However, extensive bicycle count data are usually not available. In this study, revealed bicycle trip data of a public bicycle rental system in the Greater London is used to proxy the bicycle crash exposure. Random parameter negative binomial models are developed to measure the relationship between possible risk factors and bicycle crash frequency at the zonal level, based on the crash data in the Greater London in 2012−2013. Results indicate that model taking the bicycle use time as the exposure measure is superior to the other counterparts with the lowest AIC (Akaike information criterion) and BIC (Bayesian information criterion). Bicycle crash frequency is positively correlated to road density, commercial area, proportion of elderly, male and white race, and median household income. Additionally, separate bicycle crash prediction models are developed for different seasons. Effects of the presence of Cycle Superhighway and proportion of green area on bicycle crash frequency can vary across seasons. Findings of this study are indicative to the development of bicycle infrastructures, traffic management and control, and education and enforcement strategies that can enhance the safety awareness of bicyclists and reduce their crash risk in the long run.

A Correlated Random Parameters Model with Heterogeneity in Means to Account for Unobserved Heterogeneity in Crash Frequency Analysis

Unobserved heterogeneity induced by omitted variables is a major challenge in developing reliable road safety models. In recent years, the random parameters negative binomial (RPNB) model has been used frequently in crash frequency analysis to account for unobserved heterogeneity. However, the majority of past studies of the RPNB model assumed that there was no correlation between different sources of unobserved heterogeneity, which is not always true given the complex interactions of safety factors. Compared with the RPNB model, a more flexible random parameters model that is the correlated random parameters negative binomial with heterogeneity in means (CRPNBHM) model was proposed in this study. Results indicate that the CRPNBHM model could not only capture the otherwise unobserved heterogeneity, but also track the underlying correlation among different sources of unobserved heterogeneity, thus outperforming the RPNB model. In addition, new insights into the interactions of safety factors (e.g., the joint safety effects of heavy trucks and pavement rutting depth) were obtained from the CRPNBHM model and these are expected to be beneficial in developing effective safety countermeasures. Results from this study demonstrated the CRPNBHM model to be a good alternative for crash frequency analysis, particularly when unobserved heterogeneity was detected.