Investigating Differences in the Performance of Safety Performance Functions Estimated for Total Crash Count and for Crash Count by Crash Type

In recent years the development and use of crash prediction models for roadway safety analyses have received substantial attention. These models, also known as Safety Performance Functions (SPFs), relate the expected crash frequency of roadway elements (intersections, road segments, on-ramps) to traffic volumes and other geometric and operational characteristics. A commonly practiced approach for applying intersection SPFs is to assume that crash types occur in fixed proportions, e.g., rear-end crashes make up 20% of crashes, angle-crashes 35%, etc., and then apply these fixed proportions to crash totals to estimate crash frequencies by type. As demonstrated in this paper, this practice makes questionable assumptions and results in considerable error in estimating crash proportions. Using rudimentary safety performance functions based solely on major and minor road AADTs, the homogeneity-in-proportions assumption is shown to not hold across AADT, because crash proportions vary as a function of both major and minor road AADT. For example, with minor road AADT of 400 vpd, the proportion of intersecting direction crashes decreases from about 50% with 2000 major road AADT to about 15% with 82,000 AADT. Same direction crashes increase from about 15% to 55% over this same comparison. The homogeneity-in-proportions assumption should be abandoned and crash type models should be used to predict crash frequency by crash type. SPFs using additional geometric variables would only exacerbate the problem quantified here. Comparing models for different crash types using additional geometric variables remains the subject of future research. MOTIVATION AND OBJECTIVES In recent years, the development and use of crash prediction models for roadway safety analyses has made substantial progress. These models, also known as Safety Performance Functions (SPFs), relate the expected crash frequency of a roadway element such as an intersection or road segment to the traffic volume and other characteristics of that element. Typically, traffic volumes account for the majority of the variability in crash frequencies. In addition, models with AADT as only predictor variable are often used by transportation safety analysts (1) (2). They are generally considered for use over models that include several covariates because they can be easily re-calibrated when they are developed in one jurisdiction and applied to another (3) (4). In fact, this type of model is likely to be the kind of model used for estimating the safety performance of rural and urban highways as well as for intersections in the forthcoming Highway Safety Manual (HSM) (5). Although such models will suffer from an omitted variables bias (because many non-flow related factors are known to affect the frequency of crashes) and the possibility of being subjected to a structured variance (6) (7), the empirical assessment carried out in this work still provides valuable insight into the comparison analysis, particularly when models are built for use at national level and across a number of states. SPFs are normally developed for different types of facilities, e.g., separate models for four-legged signalized intersections, three-legged stop controlled intersections, two-lane rural road segments, etc. However, for any facility, the purpose of the model would usually be to predict the total number of crashes, ignoring the fact that the severity distributions differ by crash type and the mechanism and dynamics of how the severity distribution arises (8), e.g., a rear-end crash involves two vehicles traveling in the same direction and generally only results in slight injuries, while an angle crash can only occur when there is intersecting traffic and its consequences (i.e., occupant deceleration and compartmental intrusion) are often more severe than that of the rear-end crash (9). An unresolved issue in the development and use of SPFs is whether it is more compelling statistically to develop models for total crashes or separately for specific crash types. There are at least three important and defensible reasons for estimating models separately by crash type (10). One is to identify sites with high risk for specific crash types, but with fairly typical total crash counts. A second is to learn more about how various crash types are associated with road geometry, the environment, and traffic variables differently from one another. Finally, different crash types typically are associated with different distributions of crash severity due to the relative speed and dynamics of the colliding vehicles. Predicting crashes by crash type can promote advancement in knowledge about road safety in all three of these ways. While considerable research has concentrated on the estimation of crash prediction models at intersections (see (10) for a more complete review of this literature), limited effort has been devoted to investigating the safety effects of roadway geometric, traffic, and environmental factors on different crash types. An early study by Hauer et al. (11) developed crash type prediction models for 15 different crash patterns at urban and suburban signalized intersections in Toronto, Canada. The inclusion of turning movements significantly improved the predictive ability of these models. Another study on Canadian roads (12) developed two levels of models based on data inputs. The Level 2 models were similar to the model developed by Hauer et al., while the Level 1 models developed ‘aggregate’ prediction models for crash types rear-end, right-angle, and turning movement crashes. Another study by Shankar et al. (13) focused on identifying the safety effects of environmental variables on crash types rather than identifying the safety effects of roadway geometric variables, and concluded that allowing coefficient estimates to vary by the type of crash has the potential for providing greater explanatory power relative to a single overall frequency model. Kim et al. (10) describes an estimation of crash prediction models for angle, head-on, rear-end, sideswipe (same direction and opposite direction) and pedestrian-involved crash types, and compared their results with a model estimated for total crashes. They found that the best fitting model covariates are related to crash types in varying capacities, suggesting that crash types are associated with different pre-crash conditions and that modeling total crash frequency may not be helpful for identifying specific countermeasures. Kononov and Allery (14) acknowledge this fact noting that some, but not all, normative parameters (including crash types percentage) within the same SPF change with AADT. For instance, in general, the severity of accidents gradually decreases and distribution of accidents by type changes with AADT. Consequently, to build upon this body of research this paper demonstrates the value of predicting crashes by crash type by comparing results for SPFs developed for the total number of crashes and crash specific models for threeand four-legged unsignalized intersections on rural multilane roadways. The paper presents two comparisons. The objective of the first comparison was to evaluate two approaches to estimating the total number of crashes. The first approach was to use a single model for all crash types; for the second approach, predictions from models for four crash types were summed type by type to represent the total number of crashes. The objective of the second comparison was to assess two approaches for estimating the number of crashes for each specific crash type. The predictions from the crash type models were compared to predictions obtained by applying the proportion of each crash type of interest to the predictions from a model for total crash count. This latter approach has been proposed for inclusion in the predictive methodology of the forthcoming HSM (15). The four crash types used for the crash type models were single-vehicle crashes (SV), opposite direction crashes (OD), same direction crashes (SD) and intersecting direction crashes (ID), as designated by Jonsson et al. (9) The models used for the comparisons have been developed for threeand four-legged stop controlled intersections on multilane rural highways in California. Only the minor road in the intersection was stop controlled, the major road had the right of way. COMPARISON METHOD How well a model fits the data can be assessed using a variety of goodness of fit (GOF) measures. For this exercise, primarily the Cumulative Residual (CURE) plots (16) were used, in which the cumulative residuals (the difference between the observed and predicted crash frequencies for each site) are plotted in increasing order for a key covariate. The plot shows how well the model fits the data with respect to each individual covariate, in this case only AADT, and has been used by Persaud et al. (3) to assess model transferability. The indication is that the fit is very good for the covariate if the cumulative residuals oscillate around the value of zero. An additional measure used is the Maximum CURE Plot Deviation which is defined as the maximum absolute value that the CURE plot deviates from 0. The other GOF measures used were the mean prediction bias, mean absolute deviation and mean squared prediction error. These measures are defined below. Mean Prediction Bias (MPB) The mean prediction bias (MPB) is the sum of observed crash frequencies minus predicted crash frequencies divided by the number of data points. This statistic provides a measure of the magnitude and direction of the average prediction error. The smaller the average prediction error, the better the model is at predicting observed data. The MPB can be positive or negative, and is given by: