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.     

Support vector machine in crash prediction at the level of traffic analysis zones: Assessing the spatial proximity effects

In zone-level crash prediction, accounting for spatial dependence has become an extensively studied topic. This study proposes Support Vector Machine (SVM) model to address complex, large and multi-dimensional spatial data in crash prediction. Correlation-based Feature Selector (CFS) was applied to evaluate candidate factors possibly related to zonal crash frequency in handling high-dimension spatial data. To demonstrate the proposed approaches and to compare them with the Bayesian spatial model with conditional autoregressive prior (i.e., CAR), a dataset in Hillsborough county of Florida was employed. The results showed that SVM models accounting for spatial proximity outperform the non-spatial model in terms of model fitting and predictive performance, which indicates the reasonableness of considering cross-zonal spatial correlations. The best model predictive capability, relatively, is associated with the model considering proximity of the centroid distance by choosing the RBF kernel and setting the 10% of the whole dataset as the testing data, which further exhibits SVM models’ capacity for addressing comparatively complex spatial data in regional crash prediction modeling. Moreover, SVM models exhibit the better goodness-of-fit compared with CAR models when utilizing the whole dataset as the samples. A sensitivity analysis of the centroid-distance-based spatial SVM models was conducted to capture the impacts of explanatory variables on the mean predicted probabilities for crash occurrence. While the results conform to the coefficient estimation in the CAR models, which supports the employment of the SVM model as an alternative in regional safety modeling.     

Investigating driver injury severity patterns in rollover crashes using support vector machine models

Rollover crash is one of the major types of traffic crashes that induce fatal injuries. It is important to investigate the factors that affect rollover crashes and their influence on driver injury severity outcomes. This study employs support vector machine (SVM) models to investigate driver injury severity patterns in rollover crashes based on two-year crash data gathered in New Mexico. The impacts of various explanatory variables are examined in terms of crash and environmental information, vehicle features, and driver demographics and behavior characteristics. A classification and regression tree (CART) model is utilized to identify significant variables and SVM models with polynomial and Gaussian radius basis function (RBF) kernels are used for model performance evaluation. It is shown that the SVM models produce reasonable prediction performance and the polynomial kernel outperforms the Gaussian RBF kernel. Variable impact analysis reveals that factors including comfortable driving environment conditions, driver alcohol or drug involvement, seatbelt use, number of travel lanes, driver demographic features, maximum vehicle damages in crashes, crash time, and crash location are significantly associated with driver incapacitating injuries and fatalities. These findings provide insights for better understanding rollover crash causes and the impacts of various explanatory factors on driver injury severity patterns.     

Crash risk analysis for Shanghai urban expressways: A Bayesian semi-parametric modeling approach

Urban expressway systems have been developed rapidly in recent years in China; it has become one key part of the city roadway networks as carrying large traffic volume and providing high traveling speed. Along with the increase of traffic volume, traffic safety has become a major issue for Chinese urban expressways due to the frequent crash occurrence and the non-recurrent congestions caused by them. For the purpose of unveiling crash occurrence mechanisms and further developing Active Traffic Management (ATM) control strategies to improve traffic safety, this study developed disaggregate crash risk analysis models with loop detector traffic data and historical crash data. Bayesian random effects logistic regression models were utilized as it can account for the unobserved heterogeneity among crashes. However, previous crash risk analysis studies formulated random effects distributions in a parametric approach, which assigned them to follow normal distributions. Due to the limited information known about random effects distributions, subjective parametric setting may be incorrect. In order to construct more flexible and robust random effects to capture the unobserved heterogeneity, Bayesian semi-parametric inference technique was introduced to crash risk analysis in this study. Models with both inference techniques were developed for total crashes; semi-parametric models were proved to provide substantial better model goodness-of-fit, while the two models shared consistent coefficient estimations. Later on, Bayesian semi-parametric random effects logistic regression models were developed for weekday peak hour crashes, weekday non-peak hour crashes, and weekend non-peak hour crashes to investigate different crash occurrence scenarios. Significant factors that affect crash risk have been revealed and crash mechanisms have been concluded.     

Multi-level Bayesian analyses for single- and multi-vehicle freeway crashes

This study presents multi-level analyses for single- and multi-vehicle crashes on a mountainous freeway. Data from a 15-mile mountainous freeway section on I-70 were investigated. Both aggregate and disaggregate models for the two crash conditions were developed. Five years of crash data were used in the aggregate investigation, while the disaggregate models utilized one year of crash data along with real-time traffic and weather data. For the aggregate analyses, safety performance functions were developed for the purpose of revealing the contributing factors for each crash type. Two methodologies, a Bayesian bivariate Poisson-lognormal model and a Bayesian hierarchical Poisson model with correlated random effects, were estimated to simultaneously analyze the two crash conditions with consideration of possible correlations. Except for the factors related to geometric characteristics, two exposure parameters (annual average daily traffic and segment length) were included. Two different sets of significant explanatory and exposure variables were identified for the single-vehicle (SV) and multi-vehicle (MV) crashes. It was found that the Bayesian bivariate Poisson-lognormal model is superior to the Bayesian hierarchical Poisson model, the former with a substantially lower DIC and more significant variables. In addition to the aggregate analyses, microscopic real-time crash risk evaluation models were developed for the two crash conditions. Multi-level Bayesian logistic regression models were estimated with the random parameters accounting for seasonal variations, crash-unit-level diversity and segment-level random effects capturing unobserved heterogeneity caused by the geometric characteristics. The model results indicate that the effects of the selected variables on crash occurrence vary across seasons and crash units; and that geometric characteristic variables contribute to the segment variations: the more unobserved heterogeneity have been accounted, the better classification ability. Potential applications of the modeling results from both analysis approaches are discussed.     

A joint-probability approach to crash prediction models

Many road safety researchers have used crash prediction models, such as Poisson and negative binomial regression models, to investigate the associations between crash occurrence and explanatory factors. Typically, they have attempted to separately model the crash frequencies of different severity levels. However, this method may suffer from serious correlations between the model estimates among different levels of crash severity. Despite efforts to improve the statistical fit of crash prediction models by modifying the data structure and model estimation method, little work has addressed the appropriate interpretation of the effects of explanatory factors on crash occurrence among different levels of crash severity. In this paper, a joint probability model is developed to integrate the predictions of both crash occurrence and crash severity into a single framework. For instance, the Markov chain Monte Carlo (MCMC) approach full Bayesian method is applied to estimate the effects of explanatory factors. As an illustration of the appropriateness of the proposed joint probability model, a case study is conducted on crash risk at signalized intersections in Hong Kong. The results of the case study indicate that the proposed model demonstrates a good statistical fit and provides an appropriate analysis of the influences of explanatory factors.     

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.     

Development of crash-severity-index models for the measurement of work zone risk levels

Highway work zones interrupt regular traffic flows and create safety problems. Improving safety without sacrificing the main function of highways is a challenging task that traffic engineers and researchers have to confront. In this study, the concept of using crash severity index (CSI) for work zone safety evaluation was proposed and a set of CSI models were developed through the modeling of work zone crash severity outcomes. A CSI is a numerical value between zero and one that is estimated from given work zone variables. It is interpreted as the likelihood of having fatality/fatalities when a severe crash occurs in a given work zone. The CSI models were developed using a three-step approach. First, a wide range of crash variables were examined in a comprehensive manner and the significant risk factors that had impact on crash severity were selected. Second, the CSI models were developed using logistic regression technique by incorporating the selected risk factors. Finally, the developed models were validated using the recent crash data and their ability in assessing work zone risk levels were analyzed. Results of this study showed that CSI models can provide straightforward measurements of work zone risk levels.     

A Bayesian ridge regression analysis of congestion's impact on urban expressway safety

With the rapid growth of traffic in urban areas, concerns about congestion and traffic safety have been heightened. This study leveraged both Automatic Vehicle Identification (AVI) system and Microwave Vehicle Detection System (MVDS) installed on an expressway in Central Florida to explore how congestion impacts the crash occurrence in urban areas. Multiple congestion measures from the two systems were developed. To ensure more precise estimates of the congestion's effects, the traffic data were aggregated into peak and non-peak hours. Multicollinearity among traffic parameters was examined. The results showed the presence of multicollinearity especially during peak hours. As a response, ridge regression was introduced to cope with this issue. Poisson models with uncorrelated random effects, correlated random effects, and both correlated random effects and random parameters were constructed within the Bayesian framework. It was proven that correlated random effects could significantly enhance model performance. The random parameters model has similar goodness-of-fit compared with the model with only correlated random effects. However, by accounting for the unobserved heterogeneity, more variables were found to be significantly related to crash frequency. The models indicated that congestion increased crash frequency during peak hours while during non-peak hours it was not a major crash contributing factor. Using the random parameter model, the three congestion measures were compared. It was found that all congestion indicators had similar effects while Congestion Index (CI) derived from MVDS data was a better congestion indicator for safety analysis. Also, analyses showed that the segments with higher congestion intensity could not only increase property damage only (PDO) crashes, but also more severe crashes. In addition, the issues regarding the necessity to incorporate specific congestion indicator for congestion's effects on safety and to take care of the multicollinearity between explanatory variables were also discussed. By including a specific congestion indicator, the model performance significantly improved. When comparing models with and without ridge regression, the magnitude of the coefficients was altered in the existence of multicollinearity. These conclusions suggest that the use of appropriate congestion measure and consideration of multicolilnearity among the variables would improve the models and our understanding about the effects of congestion on traffic safety.     

The estimated effect of mass or footprint reduction in recent light-duty vehicles on U.S. societal fatality risk per vehicle mile traveled

The National Highway Traffic Safety Administration (NHTSA) recently updated its 2003 and 2010 logistic regression analyses of the effect of a reduction in light-duty vehicle mass on US societal fatality risk per vehicle mile traveled (VMT; Kahane, 2012). Societal fatality risk includes the risk to both the occupants of the case vehicle as well as any crash partner or pedestrians. The current analysis is the most thorough investigation of this issue to date. This paper replicates the Kahane analysis and extends it by testing the sensitivity of his results to changes in the definition of risk, and the data and control variables used in the regression models. An assessment by Lawrence Berkeley National Laboratory (LBNL) indicates that the estimated effect of mass reduction on risk is smaller than in Kahane's previous studies, and is statistically non-significant for all but the lightest cars (Wenzel, 2012a). The estimated effects of a reduction in mass or footprint (i.e. wheelbase times track width) are small relative to other vehicle, driver, and crash variables used in the regression models. The recent historical correlation between mass and footprint is not so large to prohibit including both variables in the same regression model; excluding footprint from the model, i.e. allowing footprint to decrease with mass, increases the estimated detrimental effect of mass reduction on risk in cars and crossover utility vehicles (CUVs)/minivans, but has virtually no effect on light trucks. Analysis by footprint deciles indicates that risk does not consistently increase with reduced mass for vehicles of similar footprint. Finally, the estimated effects of mass and footprint reduction are sensitive to the measure of exposure used (fatalities per induced exposure crash, rather than per VMT), as well as other changes in the data or control variables used. It appears that the safety penalty from lower mass can be mitigated with careful vehicle design, and that manufacturers can reduce mass as a strategy to increase their vehicles’ fuel economy and reduce greenhouse gas emissions without necessarily compromising societal safety.     

A note on modeling road accident frequency: A flexible elasticity model

Count data models and their variants have been widely applied in accident modeling. The traditional log-linear function is used to represent the relationship between explanatory variables and the dependent variable (accident frequency). However, this function assumes constant elasticity for the estimation parameters, which is a limitation in the analysis of the effects of explanatory variables on accident risk. Although interaction effects between explanatory variables have been studied in the road safety context (where they are normally assessed by logistic regression), no one has yet examined the possibility of using a flexible function form allowing non-constant elasticity values. This paper seeks to explore the use of the translog function usually used in the economics context to allow the elasticity to vary with the values of other explanatory variables. Therefore, the objective of this study was to evaluate the application of the translog function to accident modeling and to compare the results with those of the traditional log-linear function negative binomial (NB) model. The results show that, in terms of goodness-of-fit statistics and residual analysis, the NB model with the translog function performs better than the traditional NB model. Additional evaluations in terms of predictive performance, hotspot identification and uncertainty associated with the estimated values were taken into account. Although this study is exploratory in nature, it suggests that the translog function has considerable potential for modeling accident observations. It is hoped that this novel accident modeling methodology will open the door to the reliable interpretation and evaluation of the influence of explanatory variables on accident frequency.     

A note on modeling road accident frequency: a flexible elasticity model

Count data models and their variants have been widely applied in accident modeling. The traditional log-linear function is used to represent the relationship between explanatory variables and the dependent variable (accident frequency). However, this function assumes constant elasticity for the estimation parameters, which is a limitation in the analysis of the effects of explanatory variables on accident risk. Although interaction effects between explanatory variables have been studied in the road safety context (where they are normally assessed by logistic regression), no one has yet examined the possibility of using a flexible function form allowing non-constant elasticity values. This paper seeks to explore the use of the translog function usually used in the economics context to allow the elasticity to vary with the values of other explanatory variables. Therefore, the objective of this study was to evaluate the application of the translog function to accident modeling and to compare the results with those of the traditional log-linear function negative binomial (NB) model. The results show that, in terms of goodness-of-fit statistics and residual analysis, the NB model with the translog function performs better than the traditional NB model. Additional evaluations in terms of predictive performance, hotspot identification and uncertainty associated with the estimated values were taken into account. Although this study is exploratory in nature, it suggests that the translog function has considerable potential for modeling accident observations. It is hoped that this novel accident modeling methodology will open the door to the reliable interpretation and evaluation of the influence of explanatory variables on accident frequency.     

Predicting crash risk and identifying crash precursors on Korean expressways using loop detector data

In order to improve traffic safety on expressways, it is important to develop proactive safety management strategies with consideration for segment types and traffic flow states because crash mechanisms have some differences by each condition. The primary objective of this study is to develop real-time crash risk prediction models for different segment types and traffic flow states on expressways. The mainline of expressways is divided into basic segment and ramp vicinity, and the traffic flow states are classified into uncongested and congested conditions. Also, Korean expressways have irregular intervals between loop detector stations. Therefore, we investigated on the effect and application of the detector stations at irregular intervals for the crash risk prediction on expressways. The most significant traffic variables were selected by conditional logistic regression analysis which could control confounding factors. Based on the selected traffic variables, separate models to predict crash risk were developed using genetic programming technique. The model estimation results showed that the traffic flow characteristics leading to crashes are differed by segment type and traffic flow state. Especially, the variables related to the intervals between detector stations had a significant influence on crash risk prediction under the uncongested condition. Finally, compared with the single model for all crashes and the logistic models used in previous studies, the proposed models showed higher prediction performance. The results of this study can be applied to develop more effective proactive safety management strategies for different segment types and traffic flow states on expressways with loop detector stations at irregular intervals.     

Analysis of injury severity of drivers involved in single- and two-vehicle crashes on highways in Ontario

This study analyzes driver's injury severity in single- and two-vehicle crashes and compares the effects of explanatory variables among various types of crashes. The study identified factors affecting injury severity and their effects on severity levels using 5-year crash records for provincial highways in Ontario, Canada. Considering heteroscedasticity in the effects of explanatory variables on injury severity, the heteroscedastic ordered logit (HOL) models were developed for single- and two-vehicle crashes separately. The results of the models show that there exists heteroscedasticity for young drivers (≤30), safety equipment and ejection in the single-vehicle crash model, and female drivers, safety equipment and head-on collision in the two-vehicle crash models. The results also show that young car drivers have opposite effects between single-car and car–car crashes, and sideswipe crashes have opposite effects between car–car and truck–truck crashes. The study demonstrates that separate HOL models for single-vehicle and different types of two-vehicle crashes can identify differential effects of factors on driver's injury severity.     

Real-time assessment of fog-related crashes using airport weather data: A feasibility analysis

The effect of reduction of visibility on crash occurrence has recently been a major concern. Although visibility detection systems can help to mitigate the increased hazard of limited-visibility, such systems are not widely implemented and many locations with no systems are experiencing considerable number of fatal crashes due to reduction in visibility caused by fog and inclement weather. On the other hand, airports’ weather stations continuously monitor all climate parameters in real-time, and the gathered data may be utilized to mitigate the increased risk for the adjacent roadways. This study aims to examine the viability of using airport weather information in real-time road crash risk assessment in locations with recurrent fog problems. Bayesian logistic regression was utilized to link six years (2005–2010) of historical crash data to real-time weather information collected from eight airports in the State of Florida, roadway characteristics and aggregate traffic parameters. The results from this research indicate that real-time weather data collected from adjacent airports are good predictors to assess increased risk on highways.     

A multinomial logit model-Bayesian network hybrid approach for driver injury severity analyses in rear-end crashes

Rear-end crash is one of the most common types of traffic crashes in the U.S. A good understanding of its characteristics and contributing factors is of practical importance. Previously, both multinomial Logit models and Bayesian network methods have been used in crash modeling and analysis, respectively, although each of them has its own application restrictions and limitations. In this study, a hybrid approach is developed to combine multinomial logit models and Bayesian network methods for comprehensively analyzing driver injury severities in rear-end crashes based on state-wide crash data collected in New Mexico from 2010 to 2011. A multinomial logit model is developed to investigate and identify significant contributing factors for rear-end crash driver injury severities classified into three categories: no injury, injury, and fatality. Then, the identified significant factors are utilized to establish a Bayesian network to explicitly formulate statistical associations between injury severity outcomes and explanatory attributes, including driver behavior, demographic features, vehicle factors, geometric and environmental characteristics, etc. The test results demonstrate that the proposed hybrid approach performs reasonably well. The Bayesian network reference analyses indicate that the factors including truck-involvement, inferior lighting conditions, windy weather conditions, the number of vehicles involved, etc. could significantly increase driver injury severities in rear-end crashes. The developed methodology and estimation results provide insights for developing effective countermeasures to reduce rear-end crash injury severities and improve traffic system safety performance.     

Differences in passenger car and large truck involved crash frequencies at urban signalized intersections: An exploratory analysis

The influence of intersection features on safety has been examined extensively because intersections experience a relatively large proportion of motor vehicle conflicts and crashes. Although there are distinct differences between passenger cars and large trucks-size, operating characteristics, dimensions, and weight-modeling crash counts across vehicle types is rarely addressed. This paper develops and presents a multivariate regression model of crash frequencies by collision vehicle type using crash data for urban signalized intersections in Tennessee. In addition, the performance of univariate Poisson-lognormal (UVPLN), multivariate Poisson (MVP), and multivariate Poisson-lognormal (MVPLN) regression models in establishing the relationship between crashes, traffic factors, and geometric design of roadway intersections is investigated. Bayesian methods are used to estimate the unknown parameters of these models. The evaluation results suggest that the MVPLN model possesses most of the desirable statistical properties in developing the relationships. Compared to the UVPLN and MVP models, the MVPLN model better identifies significant factors and predicts crash frequencies. The findings suggest that traffic volume, truck percentage, lighting condition, and intersection angle significantly affect intersection safety. Important differences in car, car–truck, and truck crash frequencies with respect to various risk factors were found to exist between models. The paper provides some new or more comprehensive observations that have not been covered in previous studies.     

Individual driver risk assessment using naturalistic driving data

Driving risk varies substantially among drivers. Identifying and predicting high-risk drivers will greatly benefit the development of proactive driver education programs and safety countermeasures. The objective of this study is twofold: (1) to identify factors associated with individual driver risk and (2) predict high-risk drivers using demographic, personality, and driving characteristic data. The 100-Car Naturalistic Driving Study was used for methodology development and application. A negative binomial regression model was adopted to identify significant risk factors. The results indicated that the driver's age, personality, and critical incident rate had significant impacts on crash and near-crash risk. For the second objective, drivers were classified into three risk groups based on crash and near-crash rate using a K-mean cluster method. The cluster analysis identified approximately 6% of drivers as high-risk drivers, with average crash and near-crash (CNC) rate of 3.95 per 1000 miles traveled, 12% of drivers as moderate-risk drivers (average CNC rate = 1.75), and 84% of drivers as low-risk drivers (average CNC rate = 0.39). Two logistic models were developed to predict the high- and moderate-risk drivers. Both models showed high predictive powers with area under the curve values of 0.938 and 0.930 for the receiver operating characteristic curves. This study concluded that crash and near-crash risk for individual drivers is associated with critical incident rate, demographic, and personality characteristics. Furthermore, the critical incident rate is an effective predictor for high-risk drivers.     

On the nature of over-dispersion in motor vehicle crash prediction models

Statistical modeling of traffic crashes has been of interest to researchers for decades. Over the most recent decade many crash models have accounted for extra-variation in crash counts--variation over and above that accounted for by the Poisson density. The extra--variation--or dispersion--is theorized to capture unaccounted for variation in crashes across sites. The majority of studies have assumed fixed dispersion parameters in over-dispersed crash models--tantamount to assuming that unaccounted for variation is proportional to the expected crash count. Miaou and Lord [Miaou, S.P., Lord, D., 2003. Modeling traffic crash-flow relationships for intersections: dispersion parameter, functional form, and Bayes versus empirical Bayes methods. Transport. Res. Rec. 1840, 31-40] challenged the fixed dispersion parameter assumption, and examined various dispersion parameter relationships when modeling urban signalized intersection accidents in Toronto. They suggested that further work is needed to determine the appropriateness of the findings for rural as well as other intersection types, to corroborate their findings, and to explore alternative dispersion functions. This study builds upon the work of Miaou and Lord, with exploration of additional dispersion functions, the use of an independent data set, and presents an opportunity to corroborate their findings. Data from Georgia are used in this study. A Bayesian modeling approach with non-informative priors is adopted, using sampling-based estimation via Markov Chain Monte Carlo (MCMC) and the Gibbs sampler. A total of eight model specifications were developed; four of them employed traffic flows as explanatory factors in mean structure while the remainder of them included geometric factors in addition to major and minor road traffic flows. The models were compared and contrasted using the significance of coefficients, standard deviance, chi-square goodness-of-fit, and deviance information criteria (DIC) statistics. The findings indicate that the modeling of the dispersion parameter, which essentially explains the extra-variance structure, depends greatly on how the mean structure is modeled. In the presence of a well-defined mean function, the extra-variance structure generally becomes insignificant, i.e. the variance structure is a simple function of the mean. It appears that extra-variation is a function of covariates when the mean structure (expected crash count) is poorly specified and suffers from omitted variables. In contrast, when sufficient explanatory variables are used to model the mean (expected crash count), extra-Poisson variation is not significantly related to these variables. If these results are generalizable, they suggest that model specification may be improved by testing extra-variation functions for significance. They also suggest that known influences of expected crash counts are likely to be different than factors that might help to explain unaccounted for variation in crashes across sites.     

Application of Poisson random effect models for highway network screening

In recent years, Bayesian random effect models that account for the temporal and spatial correlations of crash data became popular in traffic safety research. This study employs random effect Poisson Log-Normal models for crash risk hotspot identification. Both the temporal and spatial correlations of crash data were considered. Potential for Safety Improvement (PSI) were adopted as a measure of the crash risk. Using the fatal and injury crashes that occurred on urban 4-lane divided arterials from 2006 to 2009 in the Central Florida area, the random effect approaches were compared to the traditional Empirical Bayesian (EB) method and the conventional Bayesian Poisson Log-Normal model. A series of method examination tests were conducted to evaluate the performance of different approaches. These tests include the previously developed site consistence test, method consistence test, total rank difference test, and the modified total score test, as well as the newly proposed total safety performance measure difference test. Results show that the Bayesian Poisson model accounting for both temporal and spatial random effects (PTSRE) outperforms the model that with only temporal random effect, and both are superior to the conventional Poisson Log-Normal model (PLN) and the EB model in the fitting of crash data. Additionally, the method evaluation tests indicate that the PTSRE model is significantly superior to the PLN model and the EB model in consistently identifying hotspots during successive time periods. The results suggest that the PTSRE model is a superior alternative for road site crash risk hotspot identification.