Development of safety performance functions for empirical Bayes estimation of crash reduction factors

Crash reduction factors (CRFs) are used to estimate the potential number of traffic crashes expected to be prevented from investment in safety improvement projects. The method used to develop CRFs in Florida has been based on the commonly used before-and-after approach. This approach suffers from a widely recognized problem known as regression-to-the-mean (RTM). The Empirical Bayes (EB) method has been introduced as a means to addressing the RTM problem. This method requires the information from both the treatment and reference sites in order to predict the expected number of crashes had the safety improvement projects at the treatment sites not been implemented. The information from the reference sites is estimated from a safety performance function (SPF), which is a mathematical relationship that links crashes to traffic exposure. The objective of this dissertation was to develop the SPFs for different functional classes of the Florida State Highway System. Crash data from years 2001 through 2003 along with traffic and geometric data were used in the SPF model development. SPFs for both rural and urban roadway categories were developed. The modeling data used were based on one-mile segments that contain homogeneous traffic and geometric conditions within each segment. Segments involving intersections were excluded. The scatter plots of data show that the relationships between crashes and traffic exposure are nonlinear, that crashes increase with traffic exposure in an increasing rate. Four regression models, namely, Poisson (PRM), Negative Binomial (NBRM), zero-inflated Poisson (ZIP), and zero-inflated Negative Binomial (ZINB), were fitted to the one-mile segment records for individual roadway categories. The best model was selected for each category based on a combination of the Likelihood Ratio test, the Vuong statistical test, and the Akaike's Information Criterion (AIC). The NBRM model was found to be appropriate for only one category and the ZINB model was found to be more appropriate for six other categories. The overall results show that the Negative Binomial distribution model generally provides a better fit for the data than the Poisson distribution model. In addition, the ZINB model was found to give the best fit when the count data exhibit excess zeros and over-dispersion for most of the roadway categories. While model validation shows that most data points fall within the 95% prediction intervals of the models developed, the Pearson goodness-of-fit measure does not show statistical significance. This is expected as traffic volume is only one of the many factors contributing to the overall crash experience, and that the SPFs are to be applied in conjunction with Accident Modification Factors (AMFs) to further account for the safety impacts of major geometric features before arriving at the final crash prediction. However, with improved traffic and crash data quality, the crash prediction power of SPF models may be further improved.

Effects of roadway geometric features on run-off road crashes on the Florida State Highway System

Run-off-road (ROR) crashes have increasingly become a serious concern for transportation officials in the State of Florida. These types of crashes have increased proportionally in recent years statewide and have been the focus of the Florida Department of Transportation. The goal of this research was to develop statistical models that can be used to investigate the possible causal relationships between roadway geometric features and ROR crashes on Florida's rural and urban principal arterials. ^ In this research, Zero-Inflated Poisson (ZIP) and Zero-Inflated Negative Binomial (ZINB) Regression models were used to better model the excessive number of roadway segments with no ROR crashes. Since Florida covers a diverse area and since there are sixty-seven counties, it was divided into four geographical regions to minimize possible unobserved heterogeneity. Three years of crash data (2000–2002) encompassing those for principal arterials on the Florida State Highway System were used. Several statistical models based on the ZIP and ZINB regression methods were fitted to predict the expected number of ROR crashes on urban and rural roads for each region. Each region was further divided into urban and rural areas, resulting in a total of eight crash models. A best-fit predictive model was identified for each of these eight models in terms of AIC values. The ZINB regression was found to be appropriate for seven of the eight models and the ZIP regression was found to be more appropriate for the remaining model. To achieve model convergence, some explanatory variables that were not statistically significant were included. Therefore, strong conclusions cannot be derived from some of these models. ^ Given the complex nature of crashes, recommendations for additional research are made. The interaction of weather and human condition would be quite valuable in discerning additional causal relationships for these types of crashes. Additionally, roadside data should be considered and incorporated into future research of ROR crashes. ^

Development of safety performance functions for SafetyAnalyst applications in Florida

In 2010, the American Association of State Highway and Transportation Officials (AASHTO) released a safety analysis software system known as SafetyAnalyst. SafetyAnalyst implements the empirical Bayes (EB) method, which requires the use of Safety Performance Functions (SPFs). The system is equipped with a set of national default SPFs, and the software calibrates the default SPFs to represent the agency's safety performance. However, it is recommended that agencies generate agency-specific SPFs whenever possible. Many investigators support the view that the agency-specific SPFs represent the agency data better than the national default SPFs calibrated to agency data. Furthermore, it is believed that the crash trends in Florida are different from the states whose data were used to develop the national default SPFs. In this dissertation, Florida-specific SPFs were developed using the 2008 Roadway Characteristics Inventory (RCI) data and crash and traffic data from 2007-2010 for both total and fatal and injury (FI) crashes. The data were randomly divided into two sets, one for calibration (70% of the data) and another for validation (30% of the data). The negative binomial (NB) model was used to develop the Florida-specific SPFs for each of the subtypes of roadway segments, intersections and ramps, using the calibration data. Statistical goodness-of-fit tests were performed on the calibrated models, which were then validated using the validation data set. The results were compared in order to assess the transferability of the Florida-specific SPF models. The default SafetyAnalyst SPFs were calibrated to Florida data by adjusting the national default SPFs with local calibration factors. The performance of the Florida-specific SPFs and SafetyAnalyst default SPFs calibrated to Florida data were then compared using a number of methods, including visual plots and statistical goodness-of-fit tests. The plots of SPFs against the observed crash data were used to compare the prediction performance of the two models. Three goodness-of-fit tests, represented by the mean absolute deviance (MAD), the mean square prediction error (MSPE), and Freeman-Tukey R2 (R2FT), were also used for comparison in order to identify the better-fitting model. The results showed that Florida-specific SPFs yielded better prediction performance than the national default SPFs calibrated to Florida data. The performance of Florida-specific SPFs was further compared with that of the full SPFs, which include both traffic and geometric variables, in two major applications of SPFs, i.e., crash prediction and identification of high crash locations. The results showed that both SPF models yielded very similar performance in both applications. These empirical results support the use of the flow-only SPF models adopted in SafetyAnalyst, which require much less effort to develop compared to full SPFs.

Improved Criteria for Estimating Calibration Factors for Highway Safety Manual (HSM) Applications

The Highway Safety Manual (HSM) estimates roadway safety performance based on predictive models that were calibrated using national data. Calibration factors are then used to adjust these predictive models to local conditions for local applications. The HSM recommends that local calibration factors be estimated using 30 to 50 randomly selected sites that experienced at least a total of 100 crashes per year. It also recommends that the factors be updated every two to three years, preferably on an annual basis. However, these recommendations are primarily based on expert opinions rather than data-driven research findings. Furthermore, most agencies do not have data for many of the input variables recommended in the HSM. This dissertation is aimed at determining the best way to meet three major data needs affecting the estimation of calibration factors: (1) the required minimum sample sizes for different roadway facilities, (2) the required frequency for calibration factor updates, and (3) the influential variables affecting calibration factors. In this dissertation, statewide segment and intersection data were first collected for most of the HSM recommended calibration variables using a Google Maps application. In addition, eight years (2005-2012) of traffic and crash data were retrieved from existing databases from the Florida Department of Transportation. With these data, the effect of sample size criterion on calibration factor estimates was first studied using a sensitivity analysis. The results showed that the minimum sample sizes not only vary across different roadway facilities, but they are also significantly higher than those recommended in the HSM. In addition, results from paired sample t-tests showed that calibration factors in Florida need to be updated annually. To identify influential variables affecting the calibration factors for roadway segments, the variables were prioritized by combining the results from three different methods: negative binomial regression, random forests, and boosted regression trees. Only a few variables were found to explain most of the variation in the crash data. Traffic volume was consistently found to be the most influential. In addition, roadside object density, major and minor commercial driveway densities, and minor residential driveway density were also identified as influential variables.

Development of Safety Performance Functions for SafetyAnalyst Applications in Florida

In 2010, the American Association of State Highway and Transportation Officials (AASHTO) released a safety analysis software system known as SafetyAnalyst. SafetyAnalyst implements the empirical Bayes (EB) method, which requires the use of Safety Performance Functions (SPFs). The system is equipped with a set of national default SPFs, and the software calibrates the default SPFs to represent the agency’s safety performance. However, it is recommended that agencies generate agency-specific SPFs whenever possible. Many investigators support the view that the agency-specific SPFs represent the agency data better than the national default SPFs calibrated to agency data. Furthermore, it is believed that the crash trends in Florida are different from the states whose data were used to develop the national default SPFs. In this dissertation, Florida-specific SPFs were developed using the 2008 Roadway Characteristics Inventory (RCI) data and crash and traffic data from 2007-2010 for both total and fatal and injury (FI) crashes. The data were randomly divided into two sets, one for calibration (70% of the data) and another for validation (30% of the data). The negative binomial (NB) model was used to develop the Florida-specific SPFs for each of the subtypes of roadway segments, intersections and ramps, using the calibration data. Statistical goodness-of-fit tests were performed on the calibrated models, which were then validated using the validation data set. The results were compared in order to assess the transferability of the Florida-specific SPF models. The default SafetyAnalyst SPFs were calibrated to Florida data by adjusting the national default SPFs with local calibration factors. The performance of the Florida-specific SPFs and SafetyAnalyst default SPFs calibrated to Florida data were then compared using a number of methods, including visual plots and statistical goodness-of-fit tests. The plots of SPFs against the observed crash data were used to compare the prediction performance of the two models. Three goodness-of-fit tests, represented by the mean absolute deviance (MAD), the mean square prediction error (MSPE), and Freeman-Tukey R2 (R2FT), were also used for comparison in order to identify the better-fitting model. The results showed that Florida-specific SPFs yielded better prediction performance than the national default SPFs calibrated to Florida data. The performance of Florida-specific SPFs was further compared with that of the full SPFs, which include both traffic and geometric variables, in two major applications of SPFs, i.e., crash prediction and identification of high crash locations. The results showed that both SPF models yielded very similar performance in both applications. These empirical results support the use of the flow-only SPF models adopted in SafetyAnalyst, which require much less effort to develop compared to full SPFs.