Karim El-Basyouny

Collision prediction models using multivariate Poisson-lognormal regression

This paper advocates the use of multivariate Poisson-lognormal (MVPLN) regression to develop models for collision count data. The MVPLN approach presents an opportunity to incorporate the correlations across collision severity levels and their influence on safety analyses. The paper introduces a new multivariate hazardous location identification technique, which generalizes the univariate posterior probability of excess that has been commonly proposed and applied in the literature. In addition, the paper presents an alternative approach for quantifying the effect of the multivariate structure on the precision of expected collision frequency. The MVPLN approach is compared with the independent (separate) univariate Poisson-lognormal (PLN) models with respect to model inference, goodness-of-fit, identification of hot spots and precision of expected collision frequency. The MVPLN is modeled using the WinBUGS platform which facilitates computation of posterior distributions as well as providing a goodness-of-fit measure for model comparisons. The results indicate that the estimates of the extra Poisson variation parameters were considerably smaller under MVPLN leading to higher precision. The improvement in precision is due mainly to the fact that MVPLN accounts for the correlation between the latent variables representing property damage only (PDO) and injuries plus fatalities (I+F). This correlation was estimated at 0.758, which is highly significant, suggesting that higher PDO rates are associated with higher I+F rates, as the collision likelihood for both types is likely to rise due to similar deficiencies in roadway design and/or other unobserved factors. In terms of goodness-of-fit, the MVPLN model provided a superior fit than the independent univariate models. The multivariate hazardous location identification results demonstrated that some hazardous locations could be overlooked if the analysis was restricted to the univariate models.

Accident prediction models with random corridor parameters.

Recent research advocates the use of count models with random parameters as an alternative method for analyzing accident frequencies. In this paper a dataset composed of urban arterials in Vancouver, British Columbia, is considered where the 392 segments were clustered into 58 corridors. The main objective is to assess the corridor effects with alternate specifications. The proposed models were estimated in a Full Bayes context via Markov Chain Monte Carlo (MCMC) simulation and were compared in terms of their goodness of fit and inference. A variety of covariates were found to significantly influence accident frequencies. However, these covariates resulted in random parameters and thereby their effects on accident frequency were found to vary significantly across corridors. Further, a Poisson-lognormal (PLN) model with random parameters for each corridor provided the best fit. Apart from the improvement in goodness of fit, such an approach is useful in gaining new insights into how accident frequencies are influenced by the covariates, and in accounting for heterogeneity due to unobserved road geometrics, traffic characteristics, environmental factors and driver behavior. The inclusion of corridor effects in the mean function could also explain enough variation that some of the model covariates would be rendered non-significant and thereby affecting model inference.

Comparison of Two Negative Binomial Regression Techniques in Developing Accident Prediction Models

There are several regression techniques to develop accident prediction models. Model development and subsequently the results are affected by the choice of regression technique. The objective of this paper is to compare two types of regression techniques: the traditional negative binomial (TNB) and the modified negative binomial (MNB). The TNB approach assumes that the shape parameter of the negative binomial distribution is fixed for all locations, while the MNB approach assumes that this shape parameter varies with the locations characteristics. The difference between the two approaches in terms of their goodness of fit and the identification and ranking of accident-prone locations is investigated. The study makes use of a sample of accident, volume, and geometric data corresponding to 392 arterial segments in British Columbia, Canada. Both models appear to fit the data well. However, the MNB approach provides a statistically significant improvement in model fit over the TNB approach. A total of 100 locations were identified as accident-prone by both approaches. A comparison between the ranks showed a close agreement in the general trend of ranking between the two models. While the MNB approach appears to fit the data better than the TNB approach, there was little difference in the results of the identification and ranking of accident-prone locations. This is likely due to the nature of the application and the data set used. The difference in results will depend on the extent to which deviant sites exist in the data set.

A full Bayes multivariate intervention model with random parameters among matched pairs for before-after safety evaluation.

The objective of this study is to evaluate the safety performance of a sample of intersections that have been improved with the implementation of certain safety countermeasures in the Greater Vancouver area. A full Bayes approach is utilized to determine the effectiveness of the improvements using a before-after design with matched (yoked) comparison groups. A multivariate Poisson-lognormal intervention model is used for the analysis of crash counts by severity levels. The model is extended to incorporate random parameters to account for the correlation between sites within comparison-treatment pairs. The full Bayes analysis revealed that incorporating such design features as matched comparison groups in the specification of safety performance functions can significantly improve the fit, while reducing the estimates of the extra-Poisson variation. As well, such extended models can be used to account for heterogeneity due to unobserved road geometrics, traffic characteristics, environmental factors and driver behavior. The results showed that the overall odds ratios for injuries and fatalities (I+F) and property damage only (PDO) imply significant reductions in predicted crash counts of 23% and 15%, respectively. The corresponding credible intervals were (12%, 33%) and (6%, 24%) at the 0.95 confidence level. The majority of the site-level odds ratio exhibited reductions in both I+F and PDO predicted crash counts. However, only some of these reductions were significant. As well, the effectiveness of the treatment seems to vary by severity level from one location to another. For I+F, the crash reduction factors were 29%, 15% and 21% for improving signal visibility, left turn phase improvement and left turn lane installation, respectively. The corresponding crash reduction factors for PDO were 21%, 4% and 20%, respectively.

Urban Arterial Accident Prediction Models with Spatial Effects

This paper investigates the inclusion of spatial effects in accident prediction models. Two types of spatial modeling techniques–-the Gaussian conditional autoregressive (CAR) and the multiple membership (MM) models–-were compared with the traditional Poisson–lognormal model. A variation of the MM model (extended MM or EMM) was also investigated to study the effect of clustering segments within the same corridor on spatial correlation. Full Bayes estimation was used by means of the Markov chain Monte Carlo methodology to estimate the parameters. The study made use of 281 urban road segments in Vancouver, British Columbia, Canada. Various traffic and geometric variables were included in the accident prediction models. The models were compared in terms of their goodness of fit and inference. For the data set under consideration, the results showed that annual average daily traffic, business land use, the number of lanes between signals, and the density of unsignalized intersections have significant positive impact on the number of accidents. The fitted CAR and MM models had significant estimates for both heterogeneity and spatial correlation parameters. The best-fit model was EMM, followed by CAR. Furthermore, a significant portion of the total variability was explained by the spatial correlation. A significant correlation was also found between the heterogeneity and spatial effects. This may be because neighboring road segments typically have similar environmental and geographic characteristics and thereby form a cluster with similar accident occurrence. The results also showed that corridor variation was a major component of total variability and that the spatial effects have been considerably alleviated by clustering segments within the same corridor.

Investigation of time and weather effects on crash types using full Bayesian multivariate Poisson lognormal models

Previous research shows that various weather elements have significant effects on crash occurrence and risk; however, little is known about how these elements affect different crash types. Consequently, this study investigates the impact of weather elements and sudden extreme snow or rain weather changes on crash type. Multivariate models were used for seven crash types using five years of daily weather and crash data collected for the entire City of Edmonton. In addition, the yearly trend and random variation of parameters across the years were analyzed by using four different modeling formulations. The proposed models were estimated in a full Bayesian context via Markov Chain Monte Carlo simulation. The multivariate Poisson lognormal model with yearly varying coefficients provided the best fit for the data according to Deviance Information Criteria. Overall, results showed that temperature and snowfall were statistically significant with intuitive signs (crashes decrease with increasing temperature; crashes increase as snowfall intensity increases) for all crash types, while rainfall was mostly insignificant. Previous snow showed mixed results, being statistically significant and positively related to certain crash types, while negatively related or insignificant in other cases. Maximum wind gust speed was found mostly insignificant with a few exceptions that were positively related to crash type. Major snow or rain events following a dry weather condition were highly significant and positively related to three crash types: Follow-Too-Close, Stop-Sign-Violation, and Ran-Off-Road crashes. The day-of-the-week dummy variables were statistically significant, indicating a possible weekly variation in exposure. Transportation authorities might use the above results to improve road safety by providing drivers with information regarding the risk of certain crash types for a particular weather condition.

Full Bayes Approach to Before-and-After Safety Evaluation with Matched Comparisons: Case Study of Stop-Sign In-Fill Program

The full Bayes (FB) approach has recently been proposed for evaluating road safety treatments in before-and-after studies. In recognition of the advantages of the FB method and because of the lack of sufficient data to develop the safety performance function necessary to conduct an empirical Bayes study, the FB approach is used to determine the effectiveness of the Stop-Sign In-Fill (SSIF) program of the Canadian Insurance Corporation of British Columbia. The SSIF program funds the conversion from uncontrolled residential intersections to two-way stop-controlled intersections in an alternating pattern. This alternating pattern provides consistency in the application of stop signs within a residential neighborhood. Different modeling formulations for the before-and-after evaluation were investigated, and the results were compared with those of the traditional approach. No postprocessing of the results is required to achieve the odds ratio. The FB analysis revealed an overall significant reduction in predicted collision frequency of 51.1% with the credible interval (36.8%, 62.3%) at the 0.95 confidence level. It was also found that incorporating such design features as matched yoked comparison groups in collision prediction models may significantly improve the fit, while reducing the need to account for overdispersion. The results of the traditional technique were compatible with those of the FB approach at the overall level. It seems that the random selection of sites, which reduces the regression-to-the-mean effect, is the reason that both approaches gave relatively similar overall level results. However, the two methods produced quite different results at the zone (site) level.

Assessing Mobility and Safety Impacts of a Variable Speed Limit Control Strategy

With the recent advances in active transportation and demand management, variable speed limits (VSLs) have been identified as an active traffic management strategy for improving freeway mobility and safety. Several heuristic VSL strategies have been proposed and evaluated. This paper proposes a model predictive VSL control strategy and evaluates its safety and mobility impacts. The strategy uses second-order traffic flow models to predict the traffic state and to provide a speed for optimizing corridor operational performance. A sensitivity analysis of the VSL update frequency and the safety constraints for the VSL strategy was performed to determine the best scenario in terms of safety and mobility. A stretch of Whitemud Drive, an urban freeway corridor in Edmonton, Alberta, Canada, was selected as the study area. The proposed VSL strategy was implemented in the microsimulation platform with a special software module. A real-time collision prediction model was developed for the same study area by using a matched case-control logistic regression technique to estimate the collision probability for each scenario. The results indicated that the proposed VSL control strategy can improve safety by approximately 50% and mobility by approximately 30%. A VSL update frequency of 5 min and a maximum speed difference of 10 km/h between successive time steps yielded the best performances. This finding can be useful for field implementation of VSL control.

A method to account for outliers in the development of safety performance functions

Accident data sets can include some unusual data points that are not typical of the rest of the data. The presence of these data points (usually termed outliers) can have a significant impact on the estimates of the parameters of safety performance functions (SPFs). Few studies have considered outliers analysis in the development of SPFs. In these studies, the practice has been to identify and then exclude outliers from further analysis. This paper introduces alternative mixture models based on the multivariate Poisson lognormal (MVPLN) regression. The proposed approach presents outlier resistance modeling techniques that provide robust safety inferences by down-weighting the outlying observations rather than rejecting them. The first proposed model is a scale-mixture model that is obtained by replacing the normal distribution in the Poisson-lognormal hierarchy by the Student t distribution, which has heavier tails. The second model is a two-component mixture (contaminated normal model) where it is assumed that most of the observations come from a basic distribution, whereas the remaining few outliers arise from an alternative distribution that has a larger variance. The results indicate that the estimates of the extra-Poisson variation parameters were considerably smaller under the mixture models leading to higher precision. Also, both mixture models have identified the same set of outliers. In terms of goodness-of-fit, both mixture models have outperformed the MVPLN. The outlier rejecting MVPLN model provided a superior fit in terms of a much smaller DIC and standard deviations for the parameter estimates. However, this approach tends to underestimate uncertainty by producing too small standard deviations for the parameter estimates, which may lead to incorrect conclusions. It is recommended that the proposed outlier resistance modeling techniques be used unless the exclusion of the outlying observations can be justified because of data related reasons (e.g., data collection errors).

Depth-based hotspot identification and multivariate ranking using the full Bayes approach.

Although the multivariate structure of traffic accidents has been recognized in the safety literature for over a decade now, univariate identification and ranking of hotspots is still dominant. The present paper advocates the use of multivariate identification and ranking of hotspots based on statistical depth functions, which are useful tools for non-parametric multivariate analysis as they provide center-out ordering of multivariate data. Thus, a depth-based multivariate method is proposed for the identification and ranking of hotspots using the full Bayes (FB) approach. The proposed method is applied to a sample of 236 signalized intersections in the Greater Vancouver Area. Various multivariate Poisson log-normal (MVPLN) models were used for data analysis. For each model, the FB posterior estimates were obtained using the Markov Chains Monte Carlo (MCMC) techniques and several goodness-of-fit measures were used for model selection. Using a depth threshold of 0.025, the proposed method identified 26 intersections (11%) as potential hotspots. The choice of a depth threshold is a delicate decision and it is suggested to determine the threshold according to the amount of funding available for safety improvement, which is the usual practice in univariate hotspot identification (HSID). Also, the results show that the performance of the proposed multivariate depth-based FB HSID method is superior to that of an analogous method based on the depths of accident frequency (AF) in terms of sensitivity, specificity and the sum of norms (lengths) of Poisson mean vectors.