Crash modification factors for high friction surface treatment on horizontal curves of two-lane highways: A combined propensity scores matching and empirical Bayes before-after approach.

Horizontal curves are locations that, as a result of the changing alignment, may be a contributing factor in roadway departure crashes. One low-cost countermeasure to mitigate crashes at these locations is the installation of the high friction surface treatment (HFST), which increases roadway friction and is intended to help keep drivers on the roadway when traversing a horizontal curve. This treatment has been implemented at numerous curves in Pennsylvania, but the overall safety effectiveness is not known. The purpose of this study is to estimate a suite of Crash Modification Factors (CMFs) for HFST applied to curve sections of undivided two-lane roadways. A novel combination of the empirical Bayes observational before-after study design and propensity score matching was used to estimate CMFs for multiple crash types, crash severities, and roadway settings (urban and rural). Propensity score matching was implemented to identify the most appropriate reference group to use within the empirical Bayes methodology. The results indicate that the installation of HFST is associated with a statistically significant decrease in all crash types and severities considered.

Estimation of crash type frequency accounting for misclassification in crash data.

Crash misclassification (MC) - e.g., a crash of one type or severity being mistakenly miscategorized as another - is a relatively common problem in transportation safety. Crash frequency models for individual crash categories estimated using datasets with MC errors could result in biased parameter estimates and thus lead to ineffective countermeasure planning. This study proposes a novel methodological formulation to directly account for this MC error and incorporates it into the two most common count data models used for crash frequency prediction: Poisson and Negative Binomial (NB) regression. The proposed framework introduces probabilistic MC rates among different crash types and modifies the likelihood function of the count models accordingly. The paper also demonstrates how this approach can be integrated into reformulated models that express each count model as a discrete choice model. The capability of the proposed models to estimate true parameters, given the existence of MC error, is examined via simulation analysis. Then, the proposed models are applied to empirical data to examine the presence of MC in crash data and further examine the robustness of the proposed models. Although the MC rates are found to be very low in the empirical data, the fit of proposed models are found to be better compared to the models that ignore MC error and thus likely provide more reliable parameter estimates.

Copula-based bivariate count data regression models for simultaneous estimation of crash counts based on severity and number of vehicles.

Statistical models of crash frequency typically apply univariate regression models to estimate total crash frequency or crash counts by various categories. However, a possible correlation between the dependent variables or unobserved variables associated with the dependent variables is not considered when univariate models are used to estimate categorized crash counts-such as different severity levels or numbers of vehicles involved. This may lead to inefficient parameter estimates compared to multivariate models that directly consider these correlations. This paper compares the results obtained from univariate negative binomial regression models of property-damage only (PDO) and fatal plus injury (FI) crash frequencies to models using traditional bivariate and copula-based bivariate negative binomial regression models. A similar comparison was made using models for the expected crash frequency of single- (SV) and multi-vehicle (MV) crashes. The models were estimated using two-lane, two-way rural highway segment-level data from an engineering district in Pennsylvania. The results show that all bivariate negative binomial models (with or without copulas) outperformed the corresponding univariate negative binomial models for PDO and FI, as well as SV and MV, crashes. Second, the statistical association of various traffic and roadway/roadside features with PDO and FI, as well as SV and MV crashes, were not the same relative to their corresponding relationships in the univariate models. The bivariate negative binomial model with normal copula outperformed all other models based on the goodness-of-fit statistics. The results suggest that copula-based bivariate negative binomial regression models may be a valuable alternative for univariate models when simultaneously modeling two disaggregate levels of crash counts.

A note on estimating safety performance functions with a flexible specification of traffic volume.

In this note, a flexible approach to allow for variation in the impact of traffic volume in the estimation of Safety Performance Functions (SPFs) is proposed. The approach generalizes a recently proposed approach by Gayah and Donnell (2021) (GD) titled "Estimating safety performance functions for two-lane rural roads using an alternative functional form for traffic volume". GD approach proposes a multiple regime structure for AADT impact while explicitly constraining the impact at the regime threshold to be the same. While the GD approach provides a flexible structure, the framework as proposed calls for careful judgement for threshold selection and additional model estimation complexity for the AADT constraint. The current note establishes the equivalence of the proposed approach with the GD approach and subsequently presents a more flexible model structure that improves on the GD approach. Subsequently, we document the advantages of our proposed approach in terms of model estimation, parameter significance testing, flexibility to consider multiple traffic volume ranges and ease of accommodating random parameters for analysis. Finally, we present potential directions for future research.

Estimation of crash type frequencies on individual collector roadway segments.

Individual collision types have different underlying causes and thus the relationships between roadway/traffic characteristics and crash frequency are likely to differ across unique collision types. One way these different influences have been studied is by developing separate statistical models for each collision type. While this is the most straightforward approach, developing collision-specific models can be very tedious and can produce unreliable estimates for collision types that are less frequently observed. Moreover, ignoring correlations between different collision types may result in biased and inefficient parameter estimation. To overcome these limitations, researchers have adopted a multivariate approach that explicitly accounts for the correlation among individual collision types. As an alternative to multivariate approach, two-stage approaches have been proposed in which one model is estimated to predict total crash frequency and its prediction is combined with another model, used to predict the proportions of different collision types. More efficient one-stage joint models, in which both the frequency and proportion models are estimated simultaneously and predictions are provided more directly, have also been proposed for macro-level analysis. This study investigates the performance of this joint model paradigm in analyzing unique collision type frequencies on individual road segments. For this, a joint negative binomial-multinomial fractional split (NB-MFS) model is used. Moreover, this study also proposes the use of a multinomial logit (MNL) model to estimate the proportion of different collision types. As total crash frequency NB model and MNL model utilize different datasets, a two-stage estimation process is required, which leads to the two-stage NB-MNL model proposed here. The performance of proposed model is compared with that of collision-specific NB models, multivariate negative binomial (MVNB) model, and NB-MFS model in predicting crash frequency by collision type on two-way two-lane urban-suburban collector roadway segments in Pennsylvania. The goodness of fit statistics show that the NB-MNL model performs better than collision-specific NB models, MVNB model and joint NB-MFS model and is thus a promising approach in predicting crash frequency by collision type.

Examining the impacts of crash data aggregation on SPF estimation.

The American Association of State Highway and Transportation Officials' Highway Safety Manual (HSM) includes a collection of safety performance functions (SPFs) or statistical models to estimate the expected crash frequency of roadway segments, intersections, and interchanges. These models are applied in several steps of the safety management process, including to screen the road network for opportunities to improve safety and to evaluate the performance of safety countermeasure deployments. The SPFs in the HSM are generally estimated using negative binomial regression modeling. In some instances, they are estimated using annual crash frequency and site-specific (e.g., traffic volume) data, while in other instances they are estimated using aggregate crash frequency and site-specific data. This paper explores the differences that result from estimating SPFs using aggregate versus disaggregate data using the same methods as those used to estimate the SPFs in the HSM. A synthetic dataset was first used to conduct these comparisons - these data were generated in a manner that is consistent with the properties of the negative binomial distribution. Then, an observational dataset from Pennsylvania was used to compare the SPFs from both aggregate and disaggregate data. The results show that SPFs estimated using the panel (disaggregate) data and aggregated data provide similar model coefficients, although some differences may sometimes arise. However, the overdispersion parameter obtained using each dataset can differ significantly. These differences result in systematic biases in calculations of expected crash frequency when Empirical Bayes adjustments are applied, which - as the paper demonstrates - could lead to different outcomes in a network screening exercise. Overall, these results reveal that aggregating crash data might result in biased SPF outputs and lead to inconsistent Empirical Bayes adjustments.

Estimating safety performance functions for two-lane rural roads using an alternative functional form for traffic volume.

Statistical models of expected crash frequency are referred to as Safety Performance Functions (SPFs) in the first edition of the American Association of State Highway and Transportation Officials' Highway Safety Manual (HSM). The SPFs in the HSM specify expected annual crash frequencies as a function of various roadway and roadside features, with the most important predictor variable being traffic volume, which serves as a measure of vehicle exposure to crashes. Traffic volumes are typically measured using the average annual daily traffic and are incorporated into the SPFs using a natural logarithm transformation. This specification suggests that the relationship between expected crash frequency and traffic volume increases non-linearly with a constant elasticity over the range of observed values. While researchers concur that the relationship between expected crash frequencies and traffic volume is non-linear, further exploration of the functional form of this relationship may offer additional insights concerning the association between safety performance and vehicle exposure. This paper proposes an alternative functional form for the traffic volume variable in SPFs that allows for different elasticities between traffic volume and expected crash frequency within different traffic volume ranges, while preserving the same general non-linear relationship in existing HSM SPFs. Although other forms-like the Hoerl function-have been proposed in the literature, the proposed model allows for natural breakpoints in the traffic volume for which roadway or geometric features might have varying effects on low- or high-volume roads. The proposed functional form was applied to SPFs developed for two-lane rural roadways in Pennsylvania. Comparisons with SPFs developed using the traditional and Hoerl functional forms suggest that this proposed functional form offers an improved fit and predictive performance, and thus might be considered for the development of future SPFs.

Crash modification factors for adaptive traffic signal control: An Empirical Bayes before-after study.

Adaptive traffic signal control (ATSC) is a novel traffic management system that is often deployed at high-volume intersections in order to mitigate traffic congestion and improve travel time reliability. While past studies have demonstrated its operational effectiveness, relatively few have focused on safety performance. Those that have tend to suffer from limitations including small sample sizes, insufficient study designs, or the lack of consideration of potential temporal and corridor effects after ATSC installation. Furthermore, results from previous studies are mixed: while many studies point to a safety improvement, more recent studies seem to indicate that ATSC systems might increase crash frequency. In light of this, a comprehensive Empirical Bayes (EB) before-after observational study was conducted using ATSC data collected throughout Pennsylvania. Crash modification factors (CMFs) were estimated based on the following different case scenarios: crash severity levels and crash types (total, fatal and injury, rear-end, and angle crashes); intersection locations (all intersections and intersections along corridors only); and, intersection configurations (3-leg and 4-leg). Temporal trends for intersection-level CMFs were examined using annual crash data in the after period. Corridor-level CMFs were also developed to quantify changes in safety performance along corridors with ATSC installed. The results suggest that ATSC is associated with a nominal increase in total and angle crashes, and an expected decrease in fatal plus injury crashes and rear-end crashes. However, the results were not statistically significant. The safety effect estimates are similar when considering intersection locations and configurations. In addition, the temporal trend analysis indicates that the safety effectiveness does not vary annually in the after period, suggesting no obvious novelty effect associated with ATSC. Finally, the magnitude of the corridor-level CMFs are slightly lower than the intersection-level CMFs, except for rear-end crashes.

Evaluating the predictive power of an SPF for two-lane rural roads with random parameters on out-of-sample observations.

Negative binomial (NB) regression is among the most common statistical modeling methods used to model crash frequencies due to its simple functional form and ability to handle over-dispersion commonly found in crash data. However, a drawback of this approach is that regression parameters are assumed to be the same across observations, which could contribute to biased parameter estimates. To alleviate this concern, the random parameters negative binomial (RPNB) model was recently proposed, which allows regression parameters to differ across observations following some known distribution. The resulting coefficients should be less biased, and thus the RPNB approach is believed to provide a more accurate relationship between independent variables and expected crash frequency. However, the prediction accuracy of the RPNB model relative to the standard NB model has not been thoroughly evaluated, particularly with respect to out-of-sample observations for which unique random parameters cannot be estimated. In this paper, the predictive power of the RPNB and NB models are examined using two-lane rural highway data from three engineering Districts in Pennsylvania. Multiple evaluation metrics are applied-root-mean-square error (RMSE) and mean absolute error (MAE), coefficients from calibration functions and cumulative residual (CURE) plots-to assess each model type. The results show that the RPNB model outperforms the NB model when applied to within sample observations (i.e., those used to estimate the model) by making use of the observation-specific coefficients. However, the predictive power of the RPNB model appears to be similar to or slightly less precise than the traditional NB model when applied to out-of-sample observations. Since the RPNB model is estimated using a simulation-based approach, sensitivity tests were also performed to see how the parameter estimates change with the number of Halton draws used to perform the simulation. For the sample sizes used in this paper, the estimates were fairly insensitive when more than 50 Halton draws were used. The findings suggest that the RPNB model is more reliable when applied to the same set of sites that were used to estimate the model but might not be as robust as the traditional NB model when applied to other sites.

Safety and operational impacts of setting speed limits below engineering recommendations.

This study quantifies the operational and safety impacts of setting posted speed limits below engineering recommendations using field data from rural roads in Montana. Vehicle operating speeds and historical crash data were collected at multiple sites with posted speed limits set equal to engineering recommendations and sites with posted speed limits set lower than engineering recommendations. Linear, quantile and logistic regression models were estimated to predict mean operating speed, 85th percentile operating speed and speed limit compliance, respectively, as a function of various roadway characteristics and level of speed enforcement. The Empirical-Bayes before-after approach was also used to develop crash modification factors (CMFs) that describe the expected change in total and fatal + injury crash frequency when setting posted speed limits lower than engineering recommendations. Because safety data were collected over a long time period, temporal adjustments were incorporated to account for yearly changes in crash reporting, traffic characteristics and other variables. The results revealed that speed limit compliance worsened as the difference between the engineering recommended and posted speed limits increased. The presence of verified heavy police enforcement reduced both mean and 85th-percentile operating speeds by approximately 4 mph and increased speed limit compliance. The safety analysis found a statistically significant reduction in total, fatal + injury, and property damage only (PDO) crash frequency at locations with posted speed limits set 5 mph lower than engineering recommendations. Locations with posted speed limits set 10 mph lower than engineering recommendations experienced a decrease in total and PDO crash frequency, but an increase in fatal + injury crash frequency. The safety effects of setting speed limits 15 to 25 mph lower than engineering recommendations were less clear, as the results were not statistically significant, likely due to the small sample of sites included in the evaluation. Overall, the results suggest that setting posted speed limits 5 mph lower than the engineering recommended practice may result in operating speeds that are more consistent with the posted speed limits and overall safety benefits.

Safety performance functions for horizontal curves and tangents on two lane, two way rural roads.

Horizontal curves on two-way, two-lane rural roads pose critical safety concerns. Accurate prediction of safety performance at these locations is vital to properly allocate resources as a part of any safety management process. The current method of predicting safety performance on horizontal curves relies on the application of a safety performance function (SPF) developed using only tangent sections and adjusting this value using a crash modification factor (CMF). However, this process inherently assumes that safety performance on curves and tangent sections share the same general functional relationships with variables included in the SPF, notably traffic volumes and segment length, even though research suggests otherwise. In light of this, the goal of this paper is to systematically study the relationship between safety performance and traffic volumes on horizontal curves of two-lane, two-way rural roads and to compare this to the safety performance of tangent sections. The propensity scores-potential outcomes framework is used to help ensure similarity between tangent and curve sections considered in the study, while mixed-effects negative binomial regression is used to quantify safety performance. The results reveal that safety performance on horizontal curves differs significantly from that on tangent sections with respect to both traffic volumes and segment length. Significant differences were also found between the safety performance on tangents and curves relative to other roadway features. These results suggest that curve-specific SPFs should be considered in the next edition of the Highway Safety Manual.

On the existence of network Macroscopic Safety Diagrams: Theory, simulation and empirical evidence.

Recent studies have proposed using well-defined relationships between network productivity and accumulation-otherwise known as Network or Macroscopic Fundamental Diagrams (network MFDs)-to model the dynamics of large-scale urban traffic networks. Network MFDs have been used to develop a variety of network-wide traffic control policies to improve a network's operational efficiency. However, the relationship between a network's MFD and its safety performance has not been well explored. This study proposes the existence of a Macroscopic Safety Diagram (MSD) that relates safety performance (e.g., likelihood of a crash occurring or number of vehicle conflicts observed) with the current network state (i.e., average density) in an urban traffic network. We theoretically posit a relationship between a network's MSD and its MFD based on the average maneuver envelop of vehicles traveling within the network. Based on this model, we show that the density associated with maximum crash propensity is always expected to be larger than the density associated with maximum network productivity. This finding suggests that congested states are not only inefficient, but they might also be associated with more crashes, which can be both more unsafe and lead to decreased network reliability. These theoretical results are validated using surrogate safety assessment metrics in microsimulation and limited field empirical data from a small arterial network in Riyadh, Kingdom of Saudi Arabia. The existence of such MSDs can be used to develop more comprehensive network-wide control policies that can ensure both safe, efficient and reliable network operations.

Development of regionalized SPFs for two-lane rural roads in Pennsylvania.

The American Association of State Highway and Transportation Officials' Highway Safety Manual (HSM) contains safety performance functions (SPFs) to predict annual crash frequencies for several roadway types. When applying these SPFs in a jurisdiction whose data were not used to develop the SPF, a calibration factor can be applied to adjust the expected crash frequency estimate to statewide or local conditions. Alternatively, the HSM suggests that transportation agencies may develop their own SPFs in lieu of applying the calibration factor to the HSM SPFs. However, the HSM does not provide guidance on the appropriate level of regionalization that should be adopted for either method, even though safety performance may vary considerably within a state. In light of this, the present study considers the development of local or regionalized SPFs for two-lane rural highways within the Commonwealth of Pennsylvania. Three regionalization levels were considered: statewide, engineering district and individual counties. The expected crash frequency for each level of regionalization was compared to the reported crash frequency over an eight-year analysis period. The results indicate that district-level SPFs with county-level adjustment factors provide better predictive accuracy than the development of a statewide SPF or application of the HSM-calibrated SPF. The findings suggest that there are significant differences in safety performance across engineering districts within Pennsylvania. As such, other state transportation agencies developing SPFs or using calibration factors may also consider how variations across jurisdictions will affect predicted crash frequencies.

Quantifying the safety effects of horizontal curves on two-way, two-lane rural roads.

The objective of this study is to quantify the safety performance of horizontal curves on two-way, two-lane rural roads relative to tangent segments. Past research is limited by small samples sizes, outdated statistical evaluation methods, and unreported standard errors. This study overcomes these drawbacks by using the propensity scores-potential outcomes framework. The impact of adjacent curves on horizontal curve safety is also explored using a cross-sectional regression model of only horizontal curves. The models estimated in the present study used eight years of crash data (2005-2012) obtained from over 10,000 miles of state-owned two-lane rural roads in Pennsylvania. These data included information on roadway geometry (e.g., horizontal curvature, lane width, and shoulder width), traffic volume, roadside hazard rating, and the presence of various low-cost safety countermeasures (e.g., centerline and shoulder rumble strips, curve and intersection warning pavement markings, and aggressive driving pavement dots). Crash prediction is performed by means of mixed effects negative binomial regression using the explanatory variables noted previously, as well as attributes of adjacent horizontal curves. The results indicate that both the presence of a horizontal curve and its degree of curvature must be considered when predicting the frequency of total crashes on horizontal curves. Both are associated with an increase in crash frequency, which is consistent with previous findings in the literature. Mixed effects negative binomial regression models for total crash frequency on horizontal curves indicate that the distance to adjacent curves is not statistically significant. However, the degree of curvature of adjacent curves in close proximity (within 0.75 miles) was found to be statistically significant and negatively correlated with crash frequency on the subject curve. This is logical, as drivers exiting a sharp curve are likely to be driving slower and with more awareness as they approach the next horizontal curve.

Examining the link between public transit use and active commuting.

BACKGROUND: An established relationship exists between public transportation (PT) use and physical activity. However, there is limited literature that examines the link between PT use and active commuting (AC) behavior. This study examines this link to determine if PT users commute more by active modes. METHODS: A volunteer, convenience sample of adults (n = 748) completed an online survey about AC/PT patterns, demographic, psychosocial, community and environmental factors. t-test compared differences between PT riders and non-PT riders. Binary logistic regression analyses examined the effect of multiple factors on AC and a full logistic regression model was conducted to examine AC. RESULTS: Non-PT riders (n = 596) reported less AC than PT riders. There were several significant relationships with AC for demographic, interpersonal, worksite, community and environmental factors when considering PT use. The logistic multivariate analysis for included age, number of children and perceived distance to work as negative predictors and PT use, feelings of bad weather and lack of on-street bike lanes as a barrier to AC, perceived behavioral control and spouse AC were positive predictors. CONCLUSIONS: This study revealed the complex relationship between AC and PT use. Further research should investigate how AC and public transit use are related.