Sample-size guidelines for recalibrating crash prediction models: Recommendations for the highway safety manual

Assessing the Negative Binomial-Lindley model for crash hotspot identification: Insights from Monte Carlo simulation analysis

Identifying hazardous crash sites (or hotspots) is a crucial step in highway safety management. The Negative Binomial (NB) model is the most common model used in safety analyses and evaluations - including hotspot identification. The NB model, however, is not without limitations. In fact, this model does not perform well when data are highly dispersed, include excess zero observations, or have a long tail. Recently, the Negative Binomial-Lindley (NB-L) model has been proposed as an alternative to the NB. The NB-L model overcomes several limitations related to the NB, such as addressing the issue of excess zero observations in highly dispersed data. However, it is not clear how the NB-L model performs regarding the hotspot identification. In this paper, an innovative Monte Carlo simulation protocol was designed to generate a wide range of simulated data characterized by different means, dispersions, and percentage of zeros. Next, the NB-L model was written as a Full-Bayes hierarchical model and compared with the Full-Bayes NB model for hotspot identification using extensive simulation scenarios. Most previous studies focused on statistical fit, and showed that the NB-L model fits the data better than the NB. In this research, however, we investigated the performance of the NB-L model in identifying the hazardous sites. We showed that there is a trade-off between the NB-L and NB when it comes to hotspot identification. Multiple performance metrics were used for the assessment. Among those, the results show that the NB-L model provides a better specificity in identifying hotspots, while the NB model provides a better sensitivity, especially for highly dispersed data. In other words, while the NB model performs better in identifying hazardous sites, the NB-L model performs better, when budget is limited, by not selecting non-hazardous sites as hazardous.

Alternative approaches to modeling heterogeneity to analyze injury severity sustained by motorcyclists in two-vehicle crashes

The presence of unobserved factors in the motorcycle involved two-vehicle crashes (MV) data could lead to heterogenous associations between observed factors and injury severity sustained by motorcyclists. Capturing such heterogeneities necessitates distinct methodological approaches, of which random and scale heterogeneity models are paramount. Herein, we undertake an empirical evaluation of random and scale heterogeneity models, exploring their efficacy in delineating the influence of external determinants on the degree of injury severity in crashes. Within the effects of scale heterogeneity, this study delves into two dominant models: the scaled multinomial logit model (S-MNL) and its generalized counterpart, the G-MNL, which encompasses both the S-MNL and the random parameters multinomial logit model (RPL). While the random heterogeneity domain is represented by the random parameters multinomial logit and an upgraded variant - the random parameters multinomial logit model with heterogeneity in means and variances (RPLHMV). Motorcycle involved two-vehicle crashes data were extracted from the UK STATS19 dataset from 2016 to 2020. Likelihood ratio tests are computed to assess the temporal variability of the significant factors. The test result demonstrates the temporal variations over a five-year study period. Some very important differences started to show up across the years based on the model estimation results: that the RPLHMV model statistically outperforms the G-MNL model in the 2016, 2018, and 2019 models, while the S-MNL model is statistically superior in the 2017 and 2020 years. These important findings suggest that the origin of heterogeneity in explaining factor weights can be captured by scale effects, not just random heterogeneity. In addition, the model results further show that motorcyclists' injury severities are significantly affected by motorcycle-related characteristics; there is the added factor of external influences, such as non-motorcycle drivers (males, young drivers, and elderly drivers) and vehicles (the moving status, age, and types of vehicles) that collide with motorcycles. The results of this paper are anticipated to help policymakers develop effective strategies to mitigate motorcycle involved two-vehicle crashes by implementing appropriate measures.

Bivariate joint analysis of injury severity of drivers in truck-car crashes accommodating multilayer unobserved heterogeneity

Truck-involved crashes, especially truck-car crashes, are associated with serious and even fatal injuries, thus necessitating an in-depth analysis. Prior research focused solely on examining the injury severity of truck drivers or developed separate performance models for truck and car drivers. However, the severity of injuries to both drivers in the same truck-car crash may be interrelated, and influencing factors of injury severities sustained by the two parties may differ. To address these concerns, a random parameter bivariate probit model with heterogeneity in means (RPBPHM) is applied to examine factors affecting the injury severity of both drivers in the same truck-car crash and how these factors change over the years. Using truck-car crash data from 2017 to 2019 in the UK, the dependent variable is defined as slight injury and serious injury or fatality. Factors such as driver, vehicle, road, and environmental characteristics are statistically analyzed in this study. According to the findings, the RPBPHM model demonstrated a remarkable statistical fit, and a positive correlation was observed between the two drivers' injury severity in truck-car crashes. More importantly, the effects of the explanatory factors showing relatively temporal stability vary across different types of vehicle crashes. For example, car driver improper actions and lane changing by trucks, have a significant interactive effect on the severity of injuries sustained by drivers involved collisions between trucks and cars. Male truck drivers, young truck drivers, older truck drivers, and truck drivers' improper actions, elevate the estimated odds of only truck drivers; while older car and unsignalized crossing increase the possibility of injury severity of only car drivers. Finally, due to shared unobserved crash-specific factors, the 30-mph speed limit, dark no lights, and head-on collision, significantly affect the severity of injuries sustained by drivers involved in collisions between trucks and cars. The modeling approach provides a novel framework for jointly analyzing truck-involved crash injury severities. The findings will help policymakers take the necessary actions to reduce truck-car crashes by implementing appropriate and accurate safety countermeasures.

Finite mixture Negative Binomial-Lindley for modeling heterogeneous crash data with many zero observations

Crash data are often highly dispersed; it may also include a large amount of zero observations or have a long tail. The traditional Negative Binomial (NB) model cannot model these data properly. To overcome this issue, the Negative Binomial-Lindley (NB-L) model has been proposed as an alternative to the NB to analyze data with these characteristics. Research studies have shown that the NB-L model provides a superior performance compared to the NB when data include numerous zero observations or have a long tail. In addition, crash data are often collected from sites with different spatial or temporal characteristics. Therefore, it is not unusual to assume that crash data are drawn from multiple subpopulations. Finite mixture models are powerful tools that can be used to account for underlying subpopulations and capture the population heterogeneity. This research documents the derivations and characteristics of the Finite mixture NB-L model (FMNB-L) to analyze data generated from heterogeneous subpopulations with many zero observations and a long tail. We demonstrated the application of the model to identify subpopulations with a simulation study. We then used the FMNB-L model to estimate statistical models for Texas four-lane freeway crashes. These data have unique characteristics; it is highly dispersed, have many locations with very large number of crashes, as well as significant number of locations with zero crash. We used multiple goodness-of-fit metrics to compare the FMNB-L model with the NB, NB-L, and the finite mixture NB models. The FMNB-L identified two subpopulations in datasets. The results show a significantly better fit by the FMNB-L compared to other analyzed models.

Developing Bicycle-Vehicle Crash-Specific Safety Performance Functions in Alabama Using Different Techniques

This study develops bicycle-vehicle safety performance functions (SPFs) for five facilities in the Highway Safety Manual (HSM). These are urban two-lane undivided segments (U2U), urban four-lane divided/undivided segments (U4DU), rural two-lane undivided segments (R2U), urban four-leg and three-leg signalized intersections (USG), and urban four-leg and three-leg stop-controlled intersections (UST). Two modeling techniques were explored, the Conway-Maxwell-Poisson (COM-Poisson) model (to accommodate bicycle-vehicle crash under-dispersion) and a machine learning technique, the multivariate adaptive regression splines (MARS). MARS is a non-black-box model and can effectively handle non-linear crash predictors and interactions. A total of 1,311 bicycle-vehicle crashes from 2011 through 2015 in Alabama were collected and their respective police reports were reviewed in details. Results from the SPFs for roadway segments using COM-Poisson showed that bicycle-vehicle crash frequencies were reduced along curved and downgrade/upgrade stretches and when having heavy traffic flow (along U2U segments). For urban signalized (USG) intersections, the absence of right-turn lanes on minor roads, the presence of bus stops, and the increase in the major road annual average daily traffic (AADT) were significant factors contributing to the increase in the number of bicycle-vehicle crashes. However, the presence of divided medians on major approaches was found to reduce bicycle-vehicle crashes at USG and UST intersections. MARS outperformed the corresponding COM-Poisson models for all five facilities based on mean absolute deviance (MAD), mean square prediction error (MSPE), and generalized R-square. MARS is recommended as a promising technique for effectively predicting bicycle-vehicle crashes on segments and intersections.

Calibration of highway safety manual predictive models for Kansas freeway segments

The Safety Performance Functions (SPFs) in the Highway Safety Manual (HSM) are statistical formulas developed based on limited data gathered from selected few states. Therefore, the HSM recommends calibrating the HSM-default SPFs to local conditions or developing local SPFs to enhance the accuracy of crash prediction. This paper demonstrates the HSM calibration procedure for freeway segments and the quality assessment of the calibration process using Kansas freeway geometric and crash data. A minimum sample size of 446 freeway segments was calculated corresponding to 95% confidence level and 5% error; consequently, data for 521 freeway segments were collected and utilized in this freeway calibration. Results indicated that the HSM methodology overpredicts fatal and injury crashes and underpredicts property damage only crashes for freeway segments in Kansas. Results of quality assessment of the calibration process showed that estimated calibration factors were satisfactory for all freeway types considered in this study.

Development of Macro-Level Safety Performance Functions in the City of Naples

This paper presents macro-level safety performance functions and aims to provide empirical tools for planners and engineers to conduct proactive analyses, promote more sustainable development patterns, and reduce road crashes. In the past decade, several studies have been conducted for crash modeling at a macro-level, yet in Italy, macro-level safety performance functions have neither been calibrated nor used, until now. Therefore, for Italy to be able to fully benefit from applying these models, it is necessary to calibrate the models to local conditions. Generalized linear modelling techniques were used to fit the models, and a negative binomial distribution error structure was assumed. The study used a sample of 15,254 crashes which occurred in the period of 2009–2011 in Naples, Italy. Four traffic analysis zones (TAZ) levels were used, as one of the aims of this paper is to check the extent to which these zoning levels help in addressing the issue. The models were developed by the stepwise forward procedure using explanatory Socio-Demographic (S-D), Transportation Demand Management (TDM), and Exposure variables. The most significant variables were: children and young people placed in re-education projects, population, population aged 65 and above, population aged 25 to 44, male population, total vehicle kilometers traveled, average congestion level, average speed, number of trips originating in the TAZ, number of trips ending in the TAZ, number of total trips and, number of bus stops served per hour. An important result of the study is that children and young people placed in re-education projects negatively affects the frequency of crashes, i.e., it has a positive safety effect. This demonstrates the effectiveness of education projects, especially on children from disadvantaged neighbourhoods.

A new approach for calibrating safety performance functions

Safety performance functions (SPFs) are statistical regression models used for estimating crash counts by roadway facility classification. They are required for identifying high crash risk locations, assessing the effectiveness of safety countermeasures and comparing road designs in terms of safety. Roadway agencies may opt to develop local SPFs or adopt them from elsewhere such as the national Highway Safety Manual (HSM), provided by the American Association of State Highway and Transportation Officials. The HSM offers a simple technique to calibrate its SPFs to conditions of specific jurisdictions. A more recent calibration technique, also known as the calibration function, is similar to that of the HSM. In this research, we develop SPFs of total crashes for rural divided multilane highway segments in four states. The states are Florida, Ohio, California and Washington. We also calibrate each SPF to each state using the HSM calibration method and the calibration function. Furthermore, we propose the use of the K nearest neighbor data mining method for calibrating SPFs. According to the goodness of fit (GOF) results, our proposed calibration method performs better than the other two methods.

Do safety performance functions used for predicting crash frequency vary across space? Applying geographically weighted regressions to account for spatial heterogeneity

Safety Performance Functions (SPFs) provide a basis for identifying locations where countermeasures can be effective. While SPFs in the Highway Safety Manual (HSM) were calibrated based on data from select states, calibration factors can be developed to localize SPFs to other states. Calibration factors typically provide a coarse adjustment-time and space stationarity of associations between crash frequencies and various factors is still assumed, implying that the SPF functional form is transferable. However, with increasing availability of statewide geo-referenced safety data, new spatial analysis methods, and increasing computational power, it is possible to relax the stationarity assumption. Specifically, to address spatial heterogeneity in SPFs, this study proposes relaxing SPFs (referring to them as Localized SPFs (L-SPFs)) that can be developed by using sophisticated geo-spatial modeling techniques that allow correlates of crash frequencies to vary in space. For demonstration, a 2013 geo-referenced freeway crash and traffic database from Virginia is used. As a potential methodological alternative, crash frequencies are predicted by estimating Geographically Weighted Negative Binomial Regressions. This model significantly outperforms the traditional negative binomial model in terms of model goodness-of-fit, providing a better and fuller understanding of spatial variations in modeled relationships. Our study results uncover significant spatial variations in parameter estimates for Annual Average Daily Traffic (AADT) and segment length. Ignoring such variations can result in prediction errors. The results indicate low transferability of a single statewide SPF highlighting the importance of developing L-SPFs. From a practical standpoint, L-SPFs can better predict crash frequencies and support prioritizing safety improvements in specific locations.

A methodology to design heuristics for model selection based on the characteristics of data: Application to investigate when the Negative Binomial Lindley (NB-L) is preferred over the Negative Binomial (NB)

Safety analysts usually use post-modeling methods, such as the Goodness-of-Fit statistics or the Likelihood Ratio Test, to decide between two or more competitive distributions or models. Such metrics require all competitive distributions to be fitted to the data before any comparisons can be accomplished. Given the continuous growth in introducing new statistical distributions, choosing the best one using such post-modeling methods is not a trivial task, in addition to all theoretical or numerical issues the analyst may face during the analysis. Furthermore, and most importantly, these measures or tests do not provide any intuitions into why a specific distribution (or model) is preferred over another (Goodness-of-Logic). This paper ponders into these issues by proposing a methodology to design heuristics for Model Selection based on the characteristics of data, in terms of descriptive summary statistics, before fitting the models. The proposed methodology employs two analytic tools: (1) Monte-Carlo Simulations and (2) Machine Learning Classifiers, to design easy heuristics to predict the label of the 'most-likely-true' distribution for analyzing data. The proposed methodology was applied to investigate when the recently introduced Negative Binomial Lindley (NB-L) distribution is preferred over the Negative Binomial (NB) distribution. Heuristics were designed to select the 'most-likely-true' distribution between these two distributions, given a set of prescribed summary statistics of data. The proposed heuristics were successfully compared against classical tests for several real or observed datasets. Not only they are easy to use and do not need any post-modeling inputs, but also, using these heuristics, the analyst can attain useful information about why the NB-L is preferred over the NB - or vice versa- when modeling data.

A Monte-Carlo simulation analysis for evaluating the severity distribution functions (SDFs) calibration methodology and determining the minimum sample-size requirements

Severity distribution functions (SDFs) are used in highway safety to estimate the severity of crashes and conduct different types of safety evaluations and analyses. Developing a new SDF is a difficult task and demands significant time and resources. To simplify the process, the Highway Safety Manual (HSM) has started to document SDF models for different types of facilities. As such, SDF models have recently been introduced for freeway and ramps in HSM addendum. However, since these functions or models are fitted and validated using data from a few selected number of states, they are required to be calibrated to the local conditions when applied to a new jurisdiction. The HSM provides a methodology to calibrate the models through a scalar calibration factor. However, the proposed methodology to calibrate SDFs was never validated through research. Furthermore, there are no concrete guidelines to select a reliable sample size. Using extensive simulation, this paper documents an analysis that examined the bias between the 'true' and 'estimated' calibration factors. It was indicated that as the value of the true calibration factor deviates further away from '1', more bias is observed between the 'true' and 'estimated' calibration factors. In addition, simulation studies were performed to determine the calibration sample size for various conditions. It was found that, as the average of the coefficient of variation (CV) of the 'KAB' and 'C' crashes increases, the analyst needs to collect a larger sample size to calibrate SDF models. Taking this observation into account, sample-size guidelines are proposed based on the average CV of crash severities that are used for the calibration process.