Lingtao Wu

Comparison of Sichel and Negative Binomial Models in Hot Spot Identification

Identification of crash hot spots is the critical component of the highway safety management process. Errors in hot spot identification (HSID) may result in the inefficient use of resources for safety improvements. One HSID method that is based on the empirical Bayesian (EB) method has been widely used as an effective approach for identifying crash-prone sites. For the EB method, the negative binomial (NB) model is usually needed to obtain the EB estimates. Recently, some studies have shown that the Sichel (SI) model can be easily used in the EB modeling framework and potentially yield better EB estimates. The objective of this study was to compare the performance of the two crash prediction (SI and NB) models in identifying hot spots with the EB method. To accomplish the objective of this study, empirical crash data collected at highway segments in Texas were used to generate simulated crash counts. Three commonly used HSID methods (simple ranking, confidence interval, and EB) were applied with the use of simulated data. False positives, false negatives, and false identifications were calculated and compared across the methods. The simulation results in this study suggested that the SI-based EB method could consistently provide a better HSID result than the NB-based EB method. Moreover, EB methods yielded the lowest error percentage of the three HSID methods. This study confirmed that the EB technique was an effective method for identifying hazardous sites. On the basis of the findings in this study, it is recommended that transportation safety researchers consider the SI model as an alternative crash prediction model when the EB approach is used.

Validation of crash modification factors derived from cross-sectional studies with regression models

Crash modification factors (CMFs) can be used to capture the safety effects of countermeasures and play a significant role in traffic safety management. As an alternative to the before-and-after study, the regression model method has been widely used for estimating CMFs. Although before-and-after studies are considered to be superior, the use of regression models for estimating CMFs has never been fully investigated. Consequently, the conditions in which regression models could be used for such a purpose were examined. CMFs for three variables—lane width, curve density, and pavement friction—were assumed and used for generating random crash counts. Then CMFs were derived from regression models by using the simulated crash data for three different scenarios. The results were then compared with the assumed true values. The study results showed that (a) when all factors affecting traffic safety are identical in all segments except those of interest, CMFs derived from regression models should be unbiased; (b) if some factors having minor safety effects are omitted from the models, the accuracy of estimated CMFs can still be acceptable; and (c) if some factors already known to have significant effects on crash risk are omitted, CMFs derived from the regression models are generally unreliable. Thus, depending on missing variables not included in the model, the transportation safety analyst can decide whether CMFs developed from regression models should be used for highway safety applications.

Finite mixture modeling approach for developing crash modification factors in highway safety analysis

This study aimed to investigate the relative performance of two models (negative binomial (NB) model and two-component finite mixture of negative binomial models (FMNB-2)) in terms of developing crash modification factors (CMFs). Crash data on rural multilane divided highways in California and Texas were modeled with the two models, and crash modification functions (CMFunctions) were derived. The resultant CMFunction estimated from the FMNB-2 model showed several good properties over that from the NB model. First, the safety effect of a covariate was better reflected by the CMFunction developed using the FMNB-2 model, since the model takes into account the differential responsiveness of crash frequency to the covariate. Second, the CMFunction derived from the FMNB-2 model is able to capture nonlinear relationships between covariate and safety. Finally, following the same concept as those for NB models, the combined CMFs of multiple treatments were estimated using the FMNB-2 model. The results indicated that they are not the simple multiplicative of single ones (i.e., their safety effects are not independent under FMNB-2 models). Adjustment Factors (AFs) were then developed. It is revealed that current Highway Safety Manuals method could over- or under-estimate the combined CMFs under particular combination of covariates. Safety analysts are encouraged to consider using the FMNB-2 models for developing CMFs and AFs.

Examining the influence of link function misspecification in conventional regression models for developing crash modification factors

This study further examined the use of regression models for developing crash modification factors (CMFs), specifically focusing on the misspecification in the link function. The primary objectives were to validate the accuracy of CMFs derived from the commonly used regression models (i.e., generalized linear models or GLMs with additive linear link functions) when some of the variables have nonlinear relationships and quantify the amount of bias as a function of the nonlinearity. Using the concept of artificial realistic data, various linear and nonlinear crash modification functions (CM-Functions) were assumed for three variables. Crash counts were randomly generated based on these CM-Functions. CMFs were then derived from regression models for three different scenarios. The results were compared with the assumed true values. The main findings are summarized as follows: (1) when some variables have nonlinear relationships with crash risk, the CMFs for these variables derived from the commonly used GLMs are all biased, especially around areas away from the baseline conditions (e.g., boundary areas); (2) with the increase in nonlinearity (i.e., nonlinear relationship becomes stronger), the bias becomes more significant; (3) the quality of CMFs for other variables having linear relationships can be influenced when mixed with those having nonlinear relationships, but the accuracy may still be acceptable; and (4) the misuse of the link function for one or more variables can also lead to biased estimates for other parameters. This study raised the importance of the link function when using regression models for developing CMFs.

Empirical Bayes estimates of finite mixture of negative binomial regression models and its application to highway safety

ABSTRACT The empirical Bayes (EB) method is commonly used by transportation safety analysts for conducting different types of safety analyses, such as before–after studies and hotspot analyses. To date, most implementations of the EB method have been applied using a negative binomial (NB) model, as it can easily accommodate the overdispersion commonly observed in crash data. Recent studies have shown that a generalized finite mixture of NB models with K mixture components (GFMNB-K) can also be used to model crash data subjected to overdispersion and generally offers better statistical performance than the traditional NB model. So far, nobody has developed how the EB method could be used with finite mixtures of NB models. The main objective of this study is therefore to use a GFMNB-K model in the calculation of EB estimates. Specifically, GFMNB-K models with varying weight parameters are developed to analyze crash data from Indiana and Texas. The main finding shows that the rankings produced by the NB and GFMNB-2 models for hotspot identification are often quite different, and this was especially noticeable with the Texas dataset. Finally, a simulation study designed to examine which model formulation can better identify the hotspot is recommended as our future research.

Developing Crash Modification Factors for Horizontal Curves on Rural Two-Lane Undivided Highways Using a Cross-Sectional Study

Horizontal curves have been identified as experiencing more crashes than tangent sections on roadways, especially on rural two-lane highways. The first edition of the Highway Safety Manual provides crash modification functions (CM functions) for curves on rural two-lane highways. The CM functions proposed in the manual may suffer from both outdated data and analysis technique. Before-and-after studies are usually the preferred method for estimating the safety effects of treatments. Unfortunately, this method is not feasible for curves. Previous studies have frequently used regression models for developing CM functions for horizontal curves. As recently documented in the literature, some potential problems exist with using regression models to develop crash modification factors. This research utilized a cross-sectional study to develop curvature CM functions. Curves located on Texas rural two-lane undivided highways were divided into a number of bins based on the curve radius. Safety was predicted with the assumption that these curves had been tangents. The observed number of crashes that occurred on the curves was compared with the dummy tangents and for different bins. The results showed that the horizontal curve radius has a significant role in the risk of a crash. From these results, a new CM function was developed. The prediction performance of the Highway Safety Manual CM function was compared with the new CM function in this study and another function that was recently proposed in the literature. It was found that the new CM function documented in this study outperformed both.

Application of the Empirical Bayes Method with the Finite Mixture Model for Identifying Accident-Prone Spots

Hotspot identification (HSID) is an important component of the highway safety management process. A number of methods have been proposed to identify hotspots. Among these methods, previous studies have indicated that the empirical Bayes (EB) method can outperform other methods for identifying hotspots, since the EB method combines the historical crash records of the site and expected number of crashes obtained from a safety performance function (SPF) for similar sites. However, the SPFs are usually developed based on a large number of sites, which may contain heterogeneity in traffic characteristic. As a result, the hotspot identification accuracy of EB methods can possibly be affected by SPFs, when heterogeneity is present in crash data. Thus, it is necessary to consider the heterogeneity and homogeneity of roadway segments when using EB methods. To address this problem, this paper proposed three different classification-based EB methods to identify hotspots. Rural highway crash data collected in Texas were analyzed and classified into different groups using the proposed methods. Based on the modeling results for Texas crash dataset, it is found that one proposed classification-based EB method performs better than the standard EB method as well as other HSID methods.

Evaluating the Impact of Rumble Strips on Fatal and Injury Freeway Crashes

Rumble strips are known to be one of the most cost-effective treatments for preventing roadway departure crashes. However, in recent years some studies have found controversial results indicating that rumble strips may in fact increase the number of more severe crashes. Although these effects are estimated to be very small, highway safety agencies deploy these treatments with an expectation that they will reduce all crash types. In this paper, the authors have conducted a statistical evaluation to determine the impact of rumble strip presence on fatal and injury crashes at freeway locations. For this purpose, the authors acquired an existing database used for one of the aforementioned studies and evaluated the variables using alternative assessment methods. The results of the current study suggest that rumble strips do in fact improve the safety outcomes in rural freeways. These findings are observed to also apply to urban freeways, but the effects are not statistically significant for the study database.

Safety Evaluation of Alternative Audible Lane Departure Warning Treatments in Reducing Traffic Crashes: An Empirical Bayes Observational Before–After Study

Roadway departure crashes are a major contributor to traffic fatalities and injury. Rumble strips have been shown to be an effective countermeasure in reducing roadway departure crashes. However, some roadway situations, for instance, inadequate shoulder width or roadway surface depth, have limited the application of conventional milled or rolled in rumble strips. Alternative audible lane departure warning systems, including profile (audible) pavement markings and preformed rumble bars, are increasingly used to overcome the limitations that exist with the milled rumble strips. So far, the safety effectiveness of these alternative audible lane departure warning systems has not been extensively assessed. The main purpose of this paper is to examine the safety effect of installing profile pavement markings and preformed rumble bars. Specifically, this study developed crash modification factors for these treatments that quantify the effectiveness in reducing single-vehicle-run-off-road (SVROR) and opposite-direction (OD) crashes. Traffic, roadway, and crash data at the treated sites on 189 miles of rural two-lane highways in Texas were analyzed using an empirical Bayes (EB) before–after analysis method. Safety performance functions from the Highway Safety Manual and Texas Highway Safety Design Workbook were used in the EB analysis. The results revealed a 21.3% reduction in all SVROR and OD crashes, and 32.5% to 39.9% reduction in fatal and injury SVROR and OD crashes after installing profile pavement marking and preformed rumble bars.