Methodology to develop crash modification functions for road safety treatments with fully specified and hierarchical models

Crash modification factors (CMFs) for road safety treatments are developed as multiplicative factors that are used to reflect the expected changes in safety performance associated with changes in highway design and/or the traffic control features. However, current CMFs have methodological drawbacks. For example, variability with application circumstance is not well understood, and, as important, correlation is not addressed when several CMFs are applied multiplicatively. These issues can be addressed by developing safety performance functions (SPFs) with components of crash modification functions (CM-Functions), an approach that includes all CMF related variables, along with others, while capturing quantitative and other effects of factors and accounting for cross-factor correlations. CM-Functions can capture the safety impact of factors through a continuous and quantitative approach, avoiding the problematic categorical analysis that is often used to capture CMF variability. There are two formulations to develop such SPFs with CM-Function components – fully specified models and hierarchical models. Based on sample datasets from two Canadian cities, both approaches are investigated in this paper. While both model formulations yielded promising results and reasonable CM-Functions, the hierarchical model was found to be more suitable in retaining homogeneity of first-level SPFs, while addressing CM-Functions in sub-level modeling. In addition, hierarchical models better capture the correlations between different impact factors.     

A comparative Full Bayesian before-and-after analysis and application to urban road safety countermeasures in New Jersey

This paper develops a step-by-step methodology for the application of Full Bayes (FB) approach for before-and-after analysis of road safety countermeasures. As part of this methodology, it studies the posterior prediction capability of Bayesian approaches and their use in crash reduction factor (CRF) estimation. A collection of candidate models are developed to investigate the impacts of different countermeasures on road safety when limited data are available. The candidate models include traditional, random effects, non-hierarchical and hierarchical Poisson-Gamma and Poisson-Lognormal (P-LN) distributions. The use of random effects and hierarchical model structures allows treatment of the data in a time-series cross-section panel, and deal with the spatial and temporal effects in the data. Next, the proposed FB estimation methodology is applied to urban roads in New Jersey to investigate the impacts of different treatment measures on the safety of “urban collectors and arterial roads” with speed limits less than 45 mph. The treatment types include (1) increase in lane width, (2) installation of median barriers, (3) vertical and horizontal improvements in the road alignment; and (4) installation of guide rails. The safety performance functions developed via different model structures show that random effects hierarchical P-LN models with informative hyper-priors perform better compared with other model structures for each treatment type. The individual CRF values are also found to be consistent across the road sections, with all showing a decrease in crash rates after the specific treatment except guide rail installation treatment. The highest decrease in the crash rate is observed after the improvement in vertical and horizontal alignment followed by increase in lane width and installation of median barriers. Overall statistical analyses of the results obtained from different candidate models show that when limited data are available, P-LN model structure combined with higher levels of hierarchy and informative priors may reduce the biases in model parameters resulting in more robust estimates.     

Exploring a Bayesian hierarchical approach for developing safety performance functions for a mountainous freeway

While rural freeways generally have lower crash rates, interactions between driver behavior, traffic and geometric characteristics, and adverse weather conditions may increase the crash risk along some freeway sections. This paper examines the safety effects of roadway geometrics on crash occurrence along a freeway section that features mountainous terrain and adverse weather. Starting from preliminary exploration using Poisson models, Bayesian hierarchical models with spatial and random effects were developed to efficiently model the crash frequencies on road segments on the 20-mile freeway section of study. Crash data for 6 years (2000–2005), roadway geometry, traffic characteristics and weather information in addition to the effect of steep slopes and adverse weather of snow and dry seasons, were used in the investigation. Estimation of the model coefficients indicates that roadway geometry is significantly associated with crash risk; segments with steep downgrades were found to drastically increase the crash risk. Moreover, this crash risk could be significantly increased during snow season compared to dry season as a confounding effect between grades and pavement condition. Moreover, sites with higher degree of curvature, wider medians and an increase of the number of lanes appear to be associated with lower crash rate. Finally, a Bayesian ranking technique was implemented to rank the hazard levels of the roadway segments; the results confirmed that segments with steep downgrades are more crash prone along the study section.     

Using hierarchical Bayesian binary probit models to analyze crash injury severity on high speed facilities with real-time traffic data

Severe crashes are causing serious social and economic loss, and because of this, reducing crash injury severity has become one of the key objectives of the high speed facilities’ (freeway and expressway) management. Traditional crash injury severity analysis utilized data mainly from crash reports concerning the crash occurrence information, drivers’ characteristics and roadway geometric related variables. In this study, real-time traffic and weather data were introduced to analyze the crash injury severity. The space mean speeds captured by the Automatic Vehicle Identification (AVI) system on the two roadways were used as explanatory variables in this study; and data from a mountainous freeway (I-70 in Colorado) and an urban expressway (State Road 408 in Orlando) have been used to identify the analysis result's consistence. Binary probit (BP) models were estimated to classify the non-severe (property damage only) crashes and severe (injury and fatality) crashes. Firstly, Bayesian BP models’ results were compared to the results from Maximum Likelihood Estimation BP models and it was concluded that Bayesian inference was superior with more significant variables. Then different levels of hierarchical Bayesian BP models were developed with random effects accounting for the unobserved heterogeneity at segment level and crash individual level, respectively. Modeling results from both studied locations demonstrate that large variations of speed prior to the crash occurrence would increase the likelihood of severe crash occurrence. Moreover, with considering unobserved heterogeneity in the Bayesian BP models, the model goodness-of-fit has improved substantially. Finally, possible future applications of the model results and the hierarchical Bayesian probit models were discussed.     

Corridor-level signalized intersection safety analysis in Shanghai,China using Bayesian hierarchical models

Most traffic crashes in Chinese cities occur at signalized intersections. Research on the intersection safety problem in China is still in its early stage. The recent development of an advanced traffic information system in Shanghai enables in-depth intersection safety analyses using road design, traffic operation, and crash data. In Shanghai, the road network density is relatively high and the distance between signalized intersections is small, averaging about 200 m. Adjacent signalized intersections located along the same corridor share similar traffic flows, and signals are usually coordinated. Therefore, when studying intersection safety in Shanghai, it is essential to account for intersection correlations within corridors. In this study, data for 195 signalized intersections along 22 corridors in the urban areas of Shanghai were collected. Mean speeds and speed variances of corridors were acquired from taxis equipped with Global Positioning Systems (GPS). Bayesian hierarchical models were applied to identify crash risk factors at both the intersection and the corridor levels. Results showed that intersections along corridors with lower mean speeds were associated with fewer crashes than those with higher speeds, and those intersections along two-way roads, under elevated roads, and in close proximity to each other, tended to have higher crash frequencies.     

Bayesian random effect models incorporating real-time weather and traffic data to investigate mountainous freeway hazardous factors

Freeway crash occurrences are highly influenced by geometric characteristics, traffic status, weather conditions and drivers’ behavior. For a mountainous freeway which suffers from adverse weather conditions, it is critical to incorporate real-time weather information and traffic data in the crash frequency study. In this paper, a Bayesian inference method was employed to model one year's crash data on I-70 in the state of Colorado. Real-time weather and traffic variables, along with geometric characteristics variables were evaluated in the models. Two scenarios were considered in this study, one seasonal and one crash type based case. For the methodology part, the Poisson model and two random effect models with a Bayesian inference method were employed and compared in this study. Deviance Information Criterion (DIC) was utilized as a comparison factor. The correlated random effect models outperformed the others. The results indicate that the weather condition variables, especially precipitation, play a key role in the crash occurrence models. The conclusions imply that different active traffic management strategies should be designed based on seasons, and single-vehicle crashes have different crash mechanism compared to multi-vehicle crashes.     

Assessment of safety effects for widening urban roadways in developing crash modification functions using nonlinearizing link functions

Since a crash modification factor (CMF) represents the overall safety performance of specific treatments in a single fixed value, there is a need to explore the variation of CMFs with different roadway characteristics among treated sites over time. Therefore, in this study, we (1) evaluate the safety performance of a sample of urban four-lane roadway segments that have been widened with one through lane in each direction and (2) determine the relationship between the safety effects and different roadway characteristics over time. Observational before–after analysis with the empirical Bayes (EB) method was assessed in this study to evaluate the safety effects of widening urban four-lane roadways to six-lanes. Moreover, the nonlinearizing link functions were utilized to achieve better performance of crash modification functions (CMFunctions). The CMFunctions were developed using a Bayesian regression method including the estimated nonlinearizing link function to incorporate the changes in safety effects of the treatment over time. Data was collected for urban arterials in Florida, and the Florida-specific full SPFs were developed and used for EB estimation.     

Developing crash modification functions to assess safety effects of adding bike lanes for urban arterials with different roadway and socio-economic characteristics

Although many researchers have estimated crash modification factors (CMFs) for specific treatments (or countermeasures), there is a lack of studies that explored the heterogeneous effects of roadway characteristics on crash frequency among treated sites. Generally, the CMF estimated by before–after studies represents overall safety effects of the treatment in a fixed value. However, as each treated site has different roadway characteristics, there is a need to assess the variation of CMFs among the treated sites with different roadway characteristics through crash modification functions (CMFunctions). The main objective of this research is to determine relationships between the safety effects of adding a bike lane and the roadway characteristics through (1) evaluation of CMFs for adding a bike lane using observational before–after with empirical Bayes (EB) and cross-sectional methods, and (2) development of simple and full CMFunctions which are describe the CMF in a function of roadway characteristics of the sites. Data was collected for urban arterials in Florida, and the Florida-specific full SPFs were developed. Moreover, socio-economic parameters were collected and included in CMFunctions and SPFs (1) to capture the effects of the variables that represent volume of bicyclists and (2) to identify general relationship between the CMFs and these characteristics. In order to achieve better performance of CMFunctions, data mining techniques were used.