Development of Roundabout Crash Prediction Models and Methods (2019)

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5 Literature Review Approach and Findings This chapter presents the findings from the literature review; the findings helped inform the data collection and modeling approach. For example, findings from other research con- ducted in the United States and abroad were used to identify candidate crash prediction modeling techniques, geometric features for data collection, definition of a roundabout-related crash, and database formation. Outreach to public agencies was also conducted as a means to identify specific roundabout sites and roundabout inventory databases as well as under- stand the issues or concerns at the forefront of public agencies with respect to roundabout design and implementation. The literature review is organized into the following sections: • Critical Review of Literature—Documents potential crash modeling techniques and approaches, roundabout features found in previous studies to influence crash fre- quency or severity, and specific crash modification factors (CMFs) and safety performance factors (SPFs) from previ- ous research. • Outreach to Public Agencies with Roundabouts— Summarizes the agencies contacted and those with inven- tories of roundabout locations as well as the ability to help supply data to the research effort. Also summarizes questions or concerns expressed by the public agencies and informa- tion regarding driver learning curve at roundabouts. • Candidate Roundabout Configurations—Presents the ini- tial candidate configurations for which the team explored developing crash prediction models. Identified based on findings from the literature review. • Alternative Statistical Modeling Approaches—Presents more detailed discussion of potential types of crash pre- diction modeling techniques. • Roundabout-Related Crash Definitions—Presents the definition of roundabout-related crashes found in the lit- erature and the definition used for this research project. • Model Development Literature Review—At the time of model development activities, the research team revisited and evaluated the literature review findings in greater detail to inform and compare as new models were produced. 2.1 Critical Review of Literature 2.1.1 Overview of Crash Modeling Techniques and Approaches This section summarizes the modeling approaches applied in developing SPFs and CMFs for similar research projects. 2.1.1.1 Safety Performance Functions An SPF is a crash prediction equation that predicts crash frequency (dependent variable) based on site character- istics (independent variables). Generally speaking, SPFs are developed through multiple regression techniques based on crash data collected over a number of years at sites with similar characteristics and covering a wide range of annual average daily traffic (AADT) [Highway Safety Manual (HSM)] (AASHTO, 2010). Among different models, the most popular model for crash events is the negative binomial regression model. All of the SPFs developed in the HSM 2010 were determined by assuming that crash frequencies follow a negative binomial distribution. For crash data, the variance typically exceeds the mean; this condition is called overdispersion (AASHTO, 2010). The negative binomial regression model accounts for the over- dispersion of crash counts as well. This is the reason that the negative binomial regression has become the dominating sta- tistical modeling technique to develop SPFs. In the negative C H A P T E R 2

6 binomial regression model, the variance of number of crashes per year can be written as follows: VAR y E y k E y Equation 2-12[ ]( ) ( ) ( )= + × where VAR(y) = the variance of number of crashes per year; E(y) = the expected number of crashes per year; and k = the overdispersion parameter. If k is zero, this negative binomial regression model becomes a Poisson regression model. This form or similar forms of the negative binomial regres- sion model has been applied in different studies [e.g., Cameron and Trivedi (1998) and Hauer et al. (2002)]. When the variance is less than the mean, the condition is called underdispersion. Crash data rarely exhibit this condi- tion. When it occurs, the use of a negative binomial distri- bution to develop a regression model will lead to incorrect parameter coefficients (Lord and Mannering, 2010). A count distribution that can accommodate underdispersed data is typically used when underdispersion is detected in the data. Example distributions include Conway-Maxwell-Poisson, Double-Poisson, and weighted Poisson. The overdispersion parameter, k, is an important param- eter in the negative binomial regression model. It can be used in the empirical Bayes (EB) method to adjust expected crash frequencies as determined by an SPF by considering observed crash counts as well. The EB method is used in vari- ous instances, including the development of CMFs through before–after studies. When proceeding with the EB method, the expected crashes are calculated as a weighted average of the expected crashes predicted by the SPF and the observed crashes. The weight involved in the calculation can be deter- mined based on the overdispersion parameter: 1 1 Equation 2-2w k n SPF = + × × where SPF denotes the dependent variable of the SP function (crashes per year), and n is the number of years of observed crash data to be used in the EB method. The common practice is to assume the overdispersion parameter as a constant. However, several studies suggested that the overdispersion parameter should be modeled as a function of site characteristics when roadway segments are modeled [Hauer (2001), Cafiso et al. (2010), Miaou and Lord (2003), Mitra and Washington (2007)]. Although these studies did not focus on roundabouts, their findings that the over dispersion parameter may vary as some function of site characteristics should be considered for roundabout modeling. Srinivasan and Bauer (2013) discussed several statisti- cal issues associated with the development of SPFs. These include • Correlation among variables. Correlation is a statistical measure that indicates the extent to which two or more vari- ables fluctuate together. If strong correlation exists between variables, these variables are not independent to each other. Therefore, it will be difficult to obtain reliable estimation of the effects of a variable. This is critical if these effects are used to infer crash modification factors. • Overfitting. If too many parameters are incorporated into the SPF development, overfitting will occur. The overfitting will result in poor predictive models and will introduce correlation into the model. • Outliers. The presence of outliers can significantly impact the model development and result in incorrect predictions. Chapter 5 provides more-detailed review of SPF estimation methods and statistical issues. 2.1.1.2 Crash Modification Factors CMFs represent the relative change in crash frequency due to a change in one specific condition, when all other conditions and site characteristics remain constant (AASHTO, 2010). Therefore, a CMF serves as a multiplicative factor to estimate the number of crashes if a change were made at the study site. Several statistical methods have been used to develop CMFs; these are discussed below. The before–after method and cross-sectional studies are the two most frequently used methods in developing CMFs. Gen- erally speaking, before–after methods are preferred to cross- sectional if before–after data are available and provide a large enough sample size. Within before–after methods, before– after with empirical Bayes is widely used to develop the CMFs [e.g., HSM 2010, NCHRP Report 672 (Rodegerdts et al., 2010), and NCHRP Report 705 (Srinivasan et al., 2011)]. A detailed review of CMF estimation methods and statisti- cal issues is provided in Chapter 5. 2.1.1.3 Summary of Crash Modeling Techniques and Approaches Safety Performance Functions • Negative binomial regression model. As the most frequently used method to develop the SPFs, negative binomial regres- sion model is the preferred choice for this project. The nega- tive binomial regression model is an appropriate model for rare events (such as crashes) during which large variance relative to the low mean value results in overdispersion. The negative binomial model also provides the estimated

7 overdispersion parameter that is required to apply the EB method in the HSM. Moreover, the extensive experience of negative binomial regression modeling from previous safety studies facilitated the model development in this project. Crash Modification Factors • Before–after with EB. Before–after EB methods are pre- ferred to cross-sectional if before–after data are available and the sample size is big enough. Compared with other methods, the before–after EB method is a statis- tically robust method that can effectively account for the regression-to-the-mean, traffic volume changes over time, and non–treatment-related time trends. Because round abouts are fairly new in the United States, and any individual changes made in geometry or traffic control are rarely done in isolation, the opportunity to conduct before– after studies to isolate a CMF for an individual geometric or traffic control change is limited. • Cross-sectional. When there are not enough before–after data for the before–after EB method, the cross-sectional method can be used. The cross-sectional method has been proven as a feasible statistical method to develop CMF and CMF functions when very limited before–after data are available. Results should be confirmed with limited before–after data if possible. 2.1.2 Roundabout Features Influencing Crash Frequency and Severity A range of U.S.–based and international research has iden- tified roundabout features—characteristics related to geom- etry, volume, and speed—that influence crash frequency and severity. In some instances, previous research has been able to quantify with some level of confidence the effects on crashes, and in other studies the relationship was found to exist but was difficult to quantify. 2.1.2.1 U.S.-Based Crash Evaluation and Prediction at Roundabouts Many of the U.S.-based research studies found in the litera- ture focused solely on evaluating the effectiveness of convert- ing existing intersections to roundabouts and were not able to (or were not intended to or scoped to) develop crash predic- tion models that quantified the effect of geometric or opera- tional features of roundabouts on crash frequency and severity. For example, Persaud et al. (2001) and Eisenman et al. (2004) were two of the earliest research projects that evaluated the safety effectiveness of converting stop- and signal-controlled intersections to roundabouts. These studies provided the initial findings regarding the safety effectiveness of roundabouts for subsequent studies such as Rodegerdts et al. (2007) to build on. Since Rodegerdts et al. (2007), Srinivasan et al. (2011) eval- uated the safety effectiveness of converting signalized inter- sections to roundabouts using data from six states. Bagdade et al. (2011) evaluated the safety effectiveness of intersection conversion to roundabouts specific to Michigan. Qin et al. (2013) evaluated the safety effectiveness of intersection conver- sion to roundabouts specific to 24 roundabouts in Wisconsin. Persaud et al. (2001) found the safety effect of roundabout conversions in the United States to be 40% reduction in total crashes and 80% reduction in injury crashes; this was based on a dataset of 23 intersections across seven states. Rodegerdts et al. (2007) considered 55 intersections and found a 35.4% reduction in total crashes and 75.8% reduction in injury crashes. These research efforts have been valuable in identifying contexts in which converting existing stop- and signal- controlled intersections to roundabouts result in reduced crash frequency and severity. These trends include • Control type before roundabout installation. Consistent safety benefits are realized when converting two-way, stop-controlled and many signal-controlled intersections to roundabouts (single-lane and double-lane). Benefits are larger for injury crashes than total crashes. Conver- sion from all-way stop-controlled (AWSC) intersections to roundabouts found no apparent safety effect. • Number of lanes. The safety benefit is larger for single- lane roundabouts than multilane roundabouts. Research for U.S. multilane roundabouts with more than two cir- culating lanes is limited to Bagdade et al. (2011), which did not find consistent safety benefits relative to previous intersection control. • Setting (land use). Safety benefits for rural intersections converted to single-lane roundabouts tend to be larger than for urban and suburban single-lane roundabouts. There were not enough rural multilane roundabouts to draw comparisons between urban/suburban and rural. • AADT. Safety benefits appear to decrease with increas- ing AADT, irrespective of control type before conversion, number of lanes, and setting (Rodegerdts et al., 2007). This was substantiated by Srinivasan et al. (2011) for signal- controlled intersections. Using cross-sectional data, Srinivasan et al. (2011) found that as AADT increased total crashes may become higher with the roundabout control than signal control. Based on these evaluations of intersection conversion to roundabouts, features influencing the safety effectiveness of roundabouts include number of circulatory lanes, setting (or attributes reflected in the setting, such as high-speed or low- speed approaches), and AADT.

8 Of the U.S.-based research found in the literature, Rodegerdts et al. (2007), Bagdade et al. (2011), and Dixon and Zheng (2013) were the studies that developed safety performance functions (i.e., crash prediction models) to use for crash prediction at roundabout intersections. Rodegerdts et al. (2007) developed intersection-level crash prediction models and leg-level crash prediction models. The intersection-level models are used for network screening and planning-level assessment of potential safety performance of a single-lane or multilane roundabout at an intersection. These were developed from a dataset of 90 roundabouts from across the United States; the majority of the round- abouts were single-lane roundabouts in urban or suburban environments. The leg-level models are intended to be used to inform design decisions. These were developed from a subset of approaches in the intersection-level model dataset; 139 approaches at 39 roundabouts were used. Rodegerdts et al. (2007) used a generalized linear modeling approach assuming a negative binomial error distribution for the intersection-level and leg-level crash prediction models. The preferred intersection-level crash models include AADT, number of approaches, and number of circulating lanes as the significant variables. Separate intersection-level crash prediction models were developed for single-lane, multi- lane lane with two lanes, and multilane with three or four lanes for total crashes and injury crash prediction. The leg-level models considered a wide range of variables, including entry radius, entry width, central island diame- ter, approach half-width, circulating width, and others. The leg-level models were developed for specific crash types: entering-circulating, exiting-circulating, and approaching crashes. The preferred crash prediction models for these crash types included a mix of AADT, entry width, angle to next approach, inscribed circle diameter, circulating width, and approach width. These are discussed in more detail in Section 2.3, where the U.S.-based leg-level crash prediction models are compared to crash prediction models developed in other countries. Section 2.4 presents the preferred inter- section-level and leg-level crash prediction models devel- oped by Rodegerdts et al. (2007). Bagdade et al. (2011) developed intersection-level crash prediction models for roundabouts in Michigan. The dataset for the crash prediction model development consisted of 36 roundabouts with two or fewer circulating lanes. Bagdade et al. (2011) used a generalized linear modeling approach assuming a negative binomial error distribution. The model development considered total entering AADT, number of cir- culating lanes, number of approaches, environment (urban vs. rural), and whether or not the intersection was a ramp terminal intersection. The preferred crash prediction model included total entering AADT, number of circulating lanes, and if the intersection was a ramp terminal intersection. Crash prediction models were developed for total crashes and a combined fatal-and-injury crash prediction. Dixon and Zheng (2013) used a dataset from Oregon focused on single-lane roundabouts with four approaches. Given the similar volume and geometric characteristics represented in their data of 21 roundabouts, they devel- oped a base SPF. The base SPF is an intersection-level crash prediction model; the only input into the SPF is the total entering AADT. 2.1.2.2 International Crash Prediction at Roundabouts The international literature had more research studies that included crash prediction model development with a focus of identifying roundabout features that influence crash fre- quency. The literature was limited in connecting roundabout features to crash severity. Studies appear to have focused on predicting specific crash types to better understand how roundabout design features influence crash occurrence. From those crash types, one could draw connections to potential severities (e.g., sideswipe crashes tend to be less severe than other crash types). The international literature review included studies from the United Kingdom, Australia, Sweden, the United States, and New Zealand. The team considered hallmark studies from Maycock and Hall (1984), Arndt (1994 and 1998), and Brude and Larsson (2000) that were previously reviewed as part of Rodegerdts et al. (2007). Findings from Rodegerdts et al. (2007) were added to this international review to be able to compare side-by-side crash prediction models from other countries with those from the United States that considered leg-level geometric characteristics. Also reviewed were two studies from New Zealand—one by Harper and Dunn (2005) and another by Turner et al. (2009)—and one study from India (Anjana and Anjaneyulu, 2014). Table 2-1 summarizes characteristics regarding sample size and models developed of the studies included in the review. Table 2-2 summarizes the geometric, operational, and other characteristics found to affect crash frequency and/or sever- ity in the international studies noted in Table 2-1. Table 2-2 is an expansion and update to Rodegerdts et al. (2007) Table 2 Summary of geometric, traffic, and other characteristics affect- ing safety. Findings from the research projects summarized in Table 2-2 indicate the international trends discussed below. Volume Characteristics. Vehicle volumes are a consis- tently strong characteristic influencing crash frequency at roundabouts. More-recent research categorizes volume as entering AADT and circulating AADT (Harper and Dunn, 2005; Rodegerdts et al., 2007; and Turner et al. 2009), when

9 possible, to disaggregate it from the total entering AADT at the intersection. When available, pedestrian, bicycle, and motorcycle volume information are useful data for predicting crash types unique to those modes as well as more severe crashes. This is consistent with findings from TOPR 34 Accelerating Roundabout Implementation in the United States (Steyn et al., 2015), which found that motorcyclists are more likely to crash at roundabouts than other road users and that they have been involved in 34% of fatal crashes that have occurred at roundabouts. Basic Configuration Characteristics. The approaching or entering number of lanes at a roundabout was one of the more prominent basic roundabout configurations found to be associated with crashes. Several studies found that crashes increase as the number of these lanes increases (Arndt, 1994 and 1998; Brude and Larsson, 2000; Turner et al., 2009). Arndt (1994 and 1998) and Brude and Larsson (2000) also found that crashes increase as the number of circulating lanes increases. When considering width in the aggregate, Maycock and Hall (1984) found that increasing the entry width tends to be associated with an increase in the number of crashes occurring between entering vehicles and circulating vehicles. Geometric Characteristics. There is a wide range of detailed geometric characteristics that various studies, most notably Maycock and Hall (1984), have included and quanti- fied in crash prediction models for roundabouts. No single geometric measure is seen consistently across the interna- tional literature. This may reflect the range of information available to researchers when undertaking their respective studies as well as the variation in roundabout designs across different countries. Specific to the United States, Rodegerdts et al. (2007) found that increasing the dimensions of the following roundabout characteristics is associated with the following changes in crashes: • Entry width increases entering/circulating collisions; • Central island diameter decreases entering/circulating collisions; • The angle between approach legs decreases entering/ circulating collisions; • Inscribed circle diameter increases exiting/circulating collisions; • Central island diameter increases exiting/circulating collisions; • Circulating width increases exiting/circulating crashes; and • Lane width increases approach crashes. Speed-Related Characteristics. Turner et al. (2009) found significant relationships between different measures of speed and crash frequency of different crash types. Free mean speed (i.e., average free-flow speed) of circulating vehicles is a significant variable in the entering-circulating and entering- bicycling preferred crash prediction models. Higher entering vehicle speeds were also found to be associated with increases in total, rear-end, entering-circulating, and loss-of-control crashes. Entering vehicle speed was not a variable in the pre- ferred crash prediction models for those crashes types, but research by Turner et al. (2009) did find a distinct relation- ship between entering speed and crash occurrence. Similarly, Arndt (1994 and 1998) found 85th percentile speed entering the roundabout and reduction in 85th percen- tile speed as a driver travels through the roundabout to influ- ence certain crash types at a roundabout. Arndt (1994 and 1998) found that an increase in the 85th percentile speeds entering the roundabout was associated with an increase in each of the crash types explored in that research, except for Corresponding Author Sample Size Models Developed United Kingdom: Maycock and Hall (1984) 84 Total crashes/roundabout Total crashes/crash type Total crashes/approach and by crash type Australia: Arndt (1994 and 1998) 100 Total crashes/approach and by crash type Sweden: Brude and Larsson (2000) 650 Crashes per million entering vehicles United States: Rodegerdts et al. (2007) 90: Intersection-level 39: Leg-level (139 approaches) Total crashes/roundabout Injury crashes/roundabout Total crashes/approach and by crash type New Zealand: Harper and Dunn (2005) 95 Total crashes/approach and by crash type New Zealand: Turner et al. (2009) 104 Total crashes/approach and by crash type India: Anjana and Anjaneyulu (2014) 75 approaches at 20 roundabouts Total crashes/approach Injury crashes/approach Property damage–only (PDO) crashes/approach Note: Table 2-1 is an expansion and update to Rodegerdts et al. (2007) Table 1 Summary of safety models. Table 2-1. Summary of crash model characteristics.

Table 2-2. Summary of volume, geometrics, speed, and other characteristics affecting crashes [Table 2-2 is an expansion and update to Rodegerdts et al. (2007) Table 2]. Measures United Kingdom (Maycock and Hall, 1984) Australia (Arndt, 1994, 1998) Sweden (Brude and Larsson, 2000) United States (Rodegerdts et al., 2007) New Zealand (Harper and Dunn, 2005) New Zealand (Turner et al., 2009) India (Anjana and Anjaneyulu, 2014) SV APP Ent/C Other Ped SV RE Ent/C Ext/C SS All Bike Ped APP Ent/ C Ext/C All Ent/C Ped All AllH RE Ent/C LoC Other Ped Ent/ Bike Other Bike All Injury PDO AADT and/or vehicle volumes + + + + + + + + + + + + + + + + + + + + + + + + + + + + Pedestrian volumes + + + Bicycle volumes + + Percentage of motorcycles + + Number of approaching/ entering lanes + + + + + I I + I Number of circulating lanes + + + + – Three legs instead of four legs – Presence of bicycle crossings – Radius (or diameter) of central island – + 1 – D + + Radius of vehicle path – – – – + + Approach curvature or delection – – – Angle to next leg * – – – Road width at entry */+ */– +/– + Approach half-width + Inscribed circle diameter + Circulating width + + – – Gradient +/+ % +/– % I/– % –% Pedestrian crossing distance + Weaving length between splitter islands – * + + Average lare length * Length of vehicle path +

Splitter island type +/- Posted speed limit * + + Free mean speed of circulating vehicles + + Entering vehicle speed I I I I Variation in vehicle speed I I + 85th percentile speed + + + + Reduction in 85th percentile speed + Sight distance + + I I + Distance to irst sight of roundabout * Potential side friction + NOTES: SV = single vehicle; APP = approaching; Ent/C = crashes between an entering vehicle and a circulating vehicle; Other = other nonpedestrian crashes; Ped = pedestrian crashes; RE = rear-end crashes on approach; Ext/C = crashes between an exiting vehicle and a circulating vehicle at multilane roundabouts; SS = sideswipe crashes on two-lane segments; AllH = total crashes at roundabouts with approaches posted speed greater than 70 km/h; LoC = loss-of-control crashes; Ent/Bike = crashes between a vehicle entering and a bicyclist circulating the roundabout; + = an increase in this measure increases crash frequency; – = an increase in this measure decreases crash frequency; * = the measure had a signiŠicant relationship with crash frequency, but the relationship was not speciŠied; I = an increase in this measure increases crash frequency; relationship was not quantiŠied in the preferred model; D = an increase in this measure decreases crash frequency; relationship was not quantiŠied in the preferred model; and 1Optimum 10 m (32.8 ft) to 25 m (82.0 ft).

12 sideswipe crashes. Higher reductions in 85th percentile speed (i.e., the more a driver would need to reduce his/her speed to travel through the roundabout) were found to be associated with an increase in single-vehicle crashes. Anjana and Anjaneyulu (2014) found that an increase in the relative difference between approach and circulating speeds was associated with an increase in all PDO crashes at an approach. Finally, Rodegerdts et al. (2007) also explored the contribu- tion of vehicle speeds to crash frequency at roundabouts. The research explored the effects of absolute vehicle speeds (e.g., free mean entering vehicle speed) and relative speeds (e.g., speed consistency or variation). They developed models using AADT and observed speeds measured at four different points through the roundabout. The speed-related models were deemed inadequate based on the weak effects found with the speed variables. However, further exploring of vehicle speeds as a predictor of crash frequency at roundabouts was found to be promising, particularly with an expanded data set. Other Characteristics. Increasing sight distance (from the perspective of approach driver) was previously quanti- fied by Maycock and Hall (1984) as being associated with an increase in single-vehicle crashes and crashes on roundabout approaches. More-recent research by Turner et al. (2009) confirmed this initial finding and found increasing sight distance to be associated with an increase in loss-of-control, rear-end, and entering-circulating crashes. The relationship of sight distance to rear-end and entering-circulating crashes was not included in the preferred crash model for those crash types, but this relationship was found to be significant in alternate models that did not fit the data as well as the pre- ferred model. U.S.-based research of 26 single-lane round- abouts by Angelastro (2010) also found sight distance to be a statistically significant variable in predicting entry rear-end, loss-of-control, and total crashes as well as a statistically sig- nificant variable in predicting 85th percentile approach and entry vehicle speeds. U.S. Use of International Roundabout Crash Prediction Models As part of the research effort by Rodegerdts et al. (2007), the research team evaluated the feasibility of using non-U.S. models to represent U.S. crash frequency at roundabouts and found this approach to be undesirable. Researchers calibrated the models developed from sites and data in other coun- tries to U.S. data and then used them to predict crashes at U.S. roundabouts. Statistical goodness-of-fit tests were used to evaluate the how well the internationally developed, U.S.-calibrated models predicted crash performance at U.S. roundabouts. Rodegerdts et al. (2007) found the intersection- level models from Sweden, the United Kingdom, and France did not fit U.S. data very well. The models also included other limitations such as limited number of approaches and inherent assumption of linear relationship between volume and crashes. The leg-level models from the United Kingdom were calibrated and evaluated. A similarly poor fit was found with U.S. data. Rodegerdts et al. (2007) concluded that it was undesirable to use international roundabout crash prediction models at the intersection or leg levels. Bicycle and Pedestrian Crash Evaluation and Prediction at Roundabouts Four of the international research studies developed crash prediction models specific to bicycle and/or pedestrian crashes. The four studies that developed pedestrian crash predic- tion models consistently included vehicle and/or pedes- trian volume data as statistically significant input variables indicating that as each increases the number of pedestrian crashes also increases. Brude and Larsson (2000) also found that increasing entry lanes and circulating lanes was associ- ated with an increase in pedestrian crashes. This was substan- tiated by a Turner et al. (2009) finding related to increasing the number of entering lanes. Turner et al. (2009) also found increasing variation in vehicle speed to be associated with an increase in pedestrian crashes. Harper and Dunn (2005) found increasing pedestrian crossing distance, which is directly related to the number of entering vehicle lanes, to be associated with an increase in pedestrian crashes. Two of the studies discussed above developed crash pre- diction for bicycle crashes. Brude and Larsson (2000) found increasing entering lanes and increasing circulating lanes to be associated with an increase in bicycle crashes. They also found that increasing bicycle crossings and increasing the radius of the central island were associated with a decrease in bicycle crashes. Turner et al. (2009) found that collisions between entering vehicles and circulating bicyclists increased as vehicle and bicycle volumes increased, and as free mean speed of vehi- cles increased. Turner et al. (2009) also found an increase in entering vehicle–circulating bicyclists collisions as the down- grade approach to the roundabout increased. In addition to the above bicycle and pedestrian research at roundabouts, several other relatively recent studies in the literature have considered bicycle and pedestrian safety at roundabouts. Cummings (2012), in an Australian study, found that during 2005–2009 nearly 50% of crashes at roundabouts involved bicyclists in Melbourne and 24% in Victoria. “Entering-circulating” crashes accounted for 48% of total crashes at roundabouts in Victoria and 82% of total vehicle– bicycle crashes. This indicates that the primary conflict point at roundabouts at which vehicle–bicycle crashes occur is the entering vehicle to circulating bicyclist conflict. Daniels et al. (2009) considered the influence of bicy- cle facilities at roundabouts on safety for roundabouts in

13 Belgium. Findings from the study indicated that round- abouts with bicycle lanes adjacent to the circulating vehicle lane experienced a 93% increase in bicycle injury crashes. This is likely due to the right-hook conflict between a vehicle exiting the roundabout and the bicyclist continuing to circu- late around the roundabout. The same study indicated that the increase in bicycle injury crashes may be negated if a separated bicycle lane is provided and designed such that motor vehi- cles must yield to bicyclists (Daniels et al., 2009). Daniels et al. (2010) evaluated 90 roundabouts in Belgium in a cross-sectional study that created risk models for various users based on traffic and geometric features. In general, Daniels et al. (2010) found that bicyclists and pedestrians are overrepresented in crashes at the roundabouts evaluated. For bicyclists, increasing motor vehicle volumes, increas- ing bicycle volumes, increasing moped volumes, and the presence of a bicycle lane were correlated with an increase in bicycle crash frequency. For pedestrians, volume metrics and the presence of sidewalk and Zebra crossings were tested and found to be significant, but multicollinearity issues (i.e., their presence tends to correspond with increasing pedestrian volumes) led Daniels et al. (2010) to leave these variables out of the final models. There is limited U.S.-based research specific to bicycle and pedestrian safety at roundabouts. Increasing attention in the United States has been given to access needs for users with dis- abilities (e.g., visually impaired pedestrians) at roundabouts. Less focus has been given to the general bicycle and pedes- trian population. Rodegerdts et al. (2007) gathered data spe- cific to bicycle and pedestrian behavior at roundabouts. The data were used to develop design guidance ultimately incor- porated into NCHRP Report 672: Roundabouts: An Informa- tional Guide, 2nd Edition. These data were also used by Harkey and Carter (2006), who analyzed the interactions between motorists and pedestrians or bicyclists at roundabouts. This research did not find any substantial safety problems for non- motorists at roundabouts based on conflicts or collisions, but the research highlighted some aspects of roundabout design that require additional care to ensure safe access for pedestrians and bicyclists, for example, in designing exit legs to ensure proper sight lines and motor vehicle speeds and in designing the junction of the circulatory lane and exit lane. Harkey and Carter (2006) also suggested that multilane roundabouts may require additional traffic control measures to enhance pedestrian safety. Other recent U.S.-based research specific to bicycle and pedestrian safety at roundabouts includes Arnold et al. (2010) and Hourdos et al. (2012). Arnold et al. (2010) conducted a study of three multilane roundabouts for the California Department of Transpor- tation [(DOT) Caltrans]. The study used video analysis and in-person observations and surveys to identify factors that contribute to crashes involving bicyclists and pedes- trians at multilane roundabouts. Crash data were analyzed for two roundabouts, and video data were analyzed at three roundabouts. The study identified the following qualitative findings: • Bicyclists are more likely than pedestrians to perceive multi- lane roundabouts as being uncomfortable to travel through (53% of bicyclists surveyed said they were comfortable, compared to 60% of pedestrians surveyed); • Drivers were more likely to yield to pedestrians at locations with higher pedestrian volumes; • Bicyclists must take a lane in the roundabout to avoid right-hook collisions; and • Bicyclists must be able to judge whether there is enough of a gap to enter and take a lane, which can be difficult with higher circulating speeds. Hourdos et al. (2012) evaluated pedestrian and bicycle risk at roundabout crossings in Minnesota. The study was con- ducted for the Minnesota DOT in response to public concerns about being able to safely cross at roundabouts. Hourdos et al. (2012) conducted an observational study between pedestri- ans and/or bicyclists and vehicles at two urban roundabouts in Minneapolis and St. Paul. Findings from the study focused on road user behavior as opposed to the impact on frequency or severity of crashes. Researchers found drivers entering the roundabout were more likely to yield to pedestrians than drivers exiting the roundabout. Summary of Roundabout Features Influencing Crash Frequency and Severity The roundabout geometric and operational features con- sistently found to influence crash frequency and severity that have the potential to be explored further in NCHRP 17-70 are listed below. • Volume Characteristics – Vehicle AADT (disaggregated by entering, circulating, and exiting movements provides additional value); and – Pedestrian, bicycle, and motorcycle volume data (particu- larly useful for predicting crashes by mode). • Basic Configuration Characteristics – Number of approaching or entering lanes and – Number of circulating lanes. • Geometric Characteristics – Entry width, – Central island diameter, – Angle between approach legs, – Inscribed circle diameter, – Circulating width, and – Approach lane width. • Speed-Related Characteristics – Entering, exiting, and circulating vehicle speed (e.g., free mean speed, 85th percentile speed), and

14 – Variation in vehicle speed (e.g., between vehicles, for one vehicle as traveling through the roundabout). • Other Characteristics – Sight distance (from perspective of approaching vehicle). The degree to which this project was able to consider the above characteristics (or slight variations thereof) depended on data availability for the roundabouts identified as part of the project evaluation. This will be discussed further in Chapter 4. From past research, it is recognized that data such as pedes- trian, bicycle, and motorcycle volume data are valuable for the crash prediction models but also difficult to obtain. Similarly, information about vehicle speed and available sight distance are also challenging to obtain. Research by Arndt (1994 and 1998) and Turner et al. (2009) used a combination of spot speed measurements and calculated theoretical speeds based on roundabout geometric features to be able to explore vehicle speed as a factor for roundabout crashes. Rodegerdts et al. (2007) used solely in-field spot speed measurements to develop speed-based crash prediction models but found the resulting dataset to be too small to result in adequate crash prediction models. Sight distance information was gathered in Turner et al. (2009) with in-field measurements at three locations (at the yield line, 10 m back from the yield line, and 40 m back from the yield line). These types of data collection considerations and challenges are discussed in Chapter 4. 2.1.3 Crash Modification Factors and Safety Performance Functions Potentially Applicable to NCHRP Project 17-70 This section presents SPFs and CMFs potentially transferra- ble to this project. SPFs and CMFs are the basic building blocks for crash prediction models. There are two basic approaches to using SPFs and CMFs for crash prediction purposes: • Develop SPFs with AADT-only variables that are associated with a base condition and provide CMFs that are multiplied to the results of the SPF prediction when a practitioner analysis scenario differs from the base condition. For exam- ple, an SPF for a signal-controlled intersection could be set to have no exclusive left turns present. If a practitioner is evaluating a scenario with a left-turn lane present, he or she would apply the CMF for a left-turn lane. The current crash prediction models in the HSM follow this approach. • Develop fully specified SPFs that include input variables for each geometric and operational attribute found to be significant. Practitioners input the variables as reflected in their analysis scenario directly into the SPF. CMFs are not generated or provided to use with the SPF. Recent research developing crash prediction models for roundabouts fol- low this approach (e.g., Rodegerdts et al., 2007; Turner et al., 2009; Bagdade et al., 2011). The intent of this section is to identify which previous research efforts produced crash modeling building blocks (SPFs and CMFs) that this project may be able to use or work from. This section focuses on U.S.-based research given that past attempts to calibrate non-U.S.-based research to U.S. data found that such an approach was undesirable (Rodegerdts et al., 2007). 2.1.3.1 Safety Performance Functions Potentially Transferable to NCHRP 17-70 Rodegerdts et al. (2007) provided crash prediction models estimated from a national U.S. database and, in this regard, held the most promise for this project to review more closely and potentially build from. Given that Bagdade et al. (2011) and Dixon and Zheng (2013) focused exclusively on round- abouts in Michigan and Oregon, respectively, the specific crash prediction models developed were less immediately transfer- able to this project. However, the data used for the crash predic- tion models developed by Bagdade et al. (2011) and Dixon and Zheng (2013) served as source of potential additional data to include in this project’s crash prediction model development. As discussed, the crash prediction models developed by Rodegerdts et al. (2007) are fully specified SPFs with only number of legs, number of lanes, and entering AADT as explanatory variables for intersection-level SPFs, thus assum- ing average conditions for any other variables. For approach- level SPFs, further geometric variables were considered. Therefore, the safety effects of the geometric and operational elements are incorporated into the SPF rather than quanti- fied separately as CMFs. The models can be converted into a form where there is a base SPF accompanied by CMFs, similar to the current approach used in the HSM. The intersection-level and leg-level crash prediction mod- els from Rodegerdts et al. (2007) are presented below. Intersection-Level Crash Prediction Models. The inter- section-level crash prediction models follow the general form below: Crashes/year AADT . . . Equation 2-3 11exp intercept exp X Xb n( ) ( )= × + + where AADT = average annual daily traffic entering the intersection, X1 + . . . + Xn = independent variables other than AADT in the model equation, and b1 = calibration parameter. Table 2-3 presents the preferred intersection-level crash pre- diction models for total crashes; Table 2-4 presents the preferred intersection-level crash prediction models for injury crashes.

15 Approach-Level Crash Prediction Models. The leg- level crash prediction models follow the general form below: Crashes/year AADT . . . AADT . . . Equation 2-4 1 1 1 1 exp intercept exp c X c X b m bm n n ( ) ( ) = × × + + where AADT1 . . . AADTm = average annual daily traffic, X1 . . . Xn = independent variables other than AADT in the model equation, and b1 . . . bm, c1 . . . cn = calibration parameters. The approach-level models were developed for specific crash types: entering-circulating, exiting-circulating, and approaching. The models predict total crashes only due to the relatively small number of crashes in the dataset. Table 2-5 presents the preferred crash prediction models per crash type. 2.1.3.2 Crash Modification Factors Potentially Transferable to NCHRP 17-70 Much of the U.S.-based research that has developed roundabout-related CMFs has focused on the effective- ness of converting stop- and signal-controlled intersections Number of Circulating Lanes Safety Performance Functions (Validity Ranges) 3 Legs 4 Legs 5 Legs 1 0.0011(AADT)0.7490 [4,000 to 31,000 AADT] 0.0023(AADT)0.7490 [4,000 to 37,000 AADT] 0.0049(AADT)0.7490 [4,000 to 18,000 AADT] 2 0.0018(AADT)0.7490 [3,000 to 20,000 AADT] 0.0038(AADT)0.7490 [2,000 to 35,000 AADT] 0.0073(AADT)0.7490 [2,000 to 52,000 AADT] 3 or 4 Not in dataset 0.0126(AADT)0.7490 [25,000 to 59,000 AADT] Not in dataset Dispersion factor, k = 0.8986 Table 2-3. Rodegerdts et al. (2007) intersection-level safety prediction model for total crashes. Number of Circulating Lanes Safety Performance Functions (Validity Ranges) 3 Legs 4 Legs 5 Legs 1 or 2 0.0008(AADT)0.5923 [3,000 to 31,000 AADT] 0.0013(AADT)0.5923 [2,000 to 37,000 AADT] 0.0029(AADT)0.5923 [2,000 to 52,000 AADT] 3 or 4 Not in dataset 0.0119(AADT)0.5923 [25,000 to 59,000 AADT] Not in dataset Dispersion factor, k = 0.9459 Table 2-4. Rodegerdts et al. (2007) intersection-level safety prediction model for injury crashes. Preferred Model Characteristics Entering-Circulating Crashes Exiting-Circulating Crashes Approach Crashes Dispersion 1.080 2.769 1.289 Intercept -7.2158 -11.6805 -5.1527 Entering AADT 0.7018 0.2801 0.4613 Circulating AADT 0.1321 0.2530 n/a Entry width (ft) 0.0511 n/a n/a Angle to next leg (degrees) -0.0276 n/a n/a Inscribed circle diameter (ft) n/a 0.0222 n/a Circulating width (ft) n/a 0.1107 n/a Approach half-width (ft) n/a n/a 0.0301 NOTES: Table 2-5 was developed from Rodegerdts et al. (2007) Tables 21, 22, and 23. “n/a” indicates not applicable. The attribute is not in the preferred model for that speciŠic crash type; the attribute is included in the preferred model for one of the other crash types modeled. Table 2-5. Rodegerdts et al. (2007) crash prediction models by crash type.

16 to roundabouts (e.g., Persaud et al., 2001; Eisenman et al., 2004). The Kansas Roundabout Guide (Kansas DOT, 2014) summarized the most-recent CMFs related to intersection conversions to roundabouts; these are summarized in Table 2-6. It may be feasible to use some of the CMFs from the effec- tiveness evaluations to create CMFs that indicate the degree to which crashes change relative to single and multilane roundabouts or roundabouts with three to four approaches. However, with the more robust analysis by Rodegerdts et al. (2007) such evaluation may not be as valuable to this project. Other sources of potential CMFs applicable to this project are the fully specified SPFs from Rodegerdts et al. (2007) and potentially Bagdade et al. (2011). Table 2-7 is an example of how the fully specified SPFs from Rodegerdts et al. (2007) could be converted to CMFs that would be accompanied by a base SPF (i.e., consistent with the current HSM crash pre- diction modeling approach). In the table, the variable coeffi- cients have been converted to a CMF as exp(coefficient) reflecting the log-linear model form. The CMF is applied for each unit change in the variable. Treatment Setting Crash Type Source All Injury TWSC to single-lane roundabout Rural 0.29 0.13 HSM 2010 Suburban 0.22 0.22 HSM 2010 Urban 0.61 0.22 HSM 2010 TWSC to two-lane roundabout Suburban 0.81 0.32 HSM 2010 Urban 0.88 – HSM 2010 TWSC to single-lane or two-lane roundabout Suburban 0.68 0.29 HSM 2010 Urban 0.71 0.19 HSM 2010 All 0.56 0.18 HSM 2010 AWSC to single-lane or two-lane roundabout All 1.03 – HSM 2010 Signal to single-lane roundabout All 0.74 0.45 Gross et al. 2010 Signal to two-lane roundabout Suburban 0.33 – HSM 2010 All 0.81 0.29 Gross et al. 2010 Signal to single-lane or two-lane roundabout Suburban 0.58 0.26 Gross et al. 2010 Urban 0.99 0.40 HSM 2010 Urban 1.15 0.45 Gross et al. 2010 3-approach 1.07 0.37 Gross et al. 2010 4-approach 0.76 0.34 Gross et al. 2010 All 0.52 0.22 HSM 2010 All 0.79 0.34 Gross et al. 2010 NOTES: TWSC = two-way stop-controlled; AWSC = all-way stop-controlled. Table 2-6. CMFs for conversion of stop-control and signalized intersections to a roundabout. Variables from Preferred Models Entering-Circulating Crashes Exiting-Circulating Crashes Approach Crashes Entry width (ft) 1.0524 n/a n/a Angle to next leg (degrees) 0.9728 n/a n/a Inscribed circle diameter (ft) n/a 1.0224 n/a Circulating width (ft) n/a 1.1171 n/a Approach half-width (ft) n/a n/a 1.0306 NOTES: Table 2-7 was developed from Rodegerdts et al. (2007) Table 24 CMFs implied from candidate leg-level models for unit change in variable. “n/a” indicates not applicable. The attribute is not in the preferred model for that speci‘ic crash type; the attribute is included in the preferred model for one of the other crash types modeled. Table 2-7. CMFs implied in Rodegerdts et al. (2007) leg-level models for unit change in variable.

17 2.2 Outreach to Public Agencies with Roundabouts As part of the literature review activities, the research team reached out to 17 public agencies with roundabouts. The purpose of these outreach activities was to identify • Existing databases and data sources that could be used in this project, • Potential focus sites for roundabouts that had been modi- fied in the past, • Information that could be used to understand or evaluate driver learning curve, and • General information related to each agency’s experiences with roundabouts that could be informative to this project. The following subsections present the agencies contacted, the specific information the research team found related to driver learning curve, and a summary of key findings from the outreach. 2.2.1 Agencies Contacted The public agencies that were contacted focused on U.S. state DOTs and local agencies with roundabouts. In total, 17 agencies were contacted: three cities and 14 state DOTs. Table 2-8 summarizes the agencies contacted. 2.2.2 Driver Learning Curve Each agency indicated they generally have observed or anec- dotally knew that when roundabouts are initially built, espe- cially in areas without a roundabout, there is typically a period of time where drivers tend to make more mistakes, are more hesitant in decision-making at roundabouts, or both. None of the agencies had completed a formal study regarding driver learning curve. Recognizing that one of the objectives of this project is to learn more about driver learning curve at roundabouts, the research team searched the general literature for studies completed regarding this subject specific to U.S. drivers. The research team Agency Estimated No. of Roundabouts Maintain an Inventory? Received Response? Georgia DOT 99 Yes Yes Wisconsin DOT 266 Yes Yes Florida DOT 258 Yes Yes Pennsylvania DOT 20 Yes Yes Alaska DOT and Public Facilities 14 Does not have one. Yes Colorado DOT 154 — No Kansas DOT 103 Yes Yes Washington State DOT 212 Yes Yes Maryland SHA 92 — No Caltrans 166 Does not have one. Yes Iowa DOT 36 Yes Yes Arizona DOT 58 Does not have one. Yes City of Carmel, IN 55 Yes Yes City of Bend, OR 28 — No New York State DOT 110 Yes Yes City of Columbia, MO 30 Yes Yes North Carolina DOT 223 Yes Yes Notes: “—“ indicates unknown. “Yes” indicates the research team has interviewed one or more agency representatives and obtained available roundabout-related information from the agency. “No” indicates the research team has attempted to contact one or more persons at agency via email and telephone and has not received a response. Table 2-8. Summary of agencies contacted.

18 found two relevant studies. One study, Hanscom (2010), focused on driver understanding of signing and pavement markings at multilane roundabouts related to lane use. The second study, Joerger (2007), focused on driver learning curve at the first multilane roundabout constructed in Springfield, Oregon. 2.2.2.1 Hanscom (2010): Pavement Markings and Guide Signs at Multilane Roundabouts Hanscom (2010) documents the approach and findings from a study that investigated drivers’ understanding of fishhook pavement markings and curved-stem guide sign arrows at multilane roundabouts. Twenty-eight combina- tions of guide signs and pavement markings were tested in a laboratory setting using a study methodology used by the Federal Highway Administration (FHWA) to determine the design of diagrammatic guide signs. The study had 117 par- ticipants. Specific to multilane roundabout pavement mark- ings and guide signs, the study evaluated the following: • Pavement Markings – Fishhook; – Turn and through-lane arrows, both entry lanes; – Left-turn-only arrow, left lane; right-turn and through- lane arrows, right lane; – Through-lane use arrow, left lane; turn and through- lane arrows, right lane; and – No pavement markings. • Guide Signs – Conventional arrows; and – Curved-stem arrows. The study found the combination of the curved-stem advance sign and the fishhook pavement marking was associ- ated with the highest percentage of correct lane choice from study participants. The study also found that conventional advanced signing for typical roundabout situations works well; therefore, it concluded that the curved-stem arrow advance sign should be reserved for situations in which drivers may need more direction for correct left-turn path guidance. 2.2.2.2 Joerger (2007): Driver Learning Curve at Multilane Roundabout in Springfield, Oregon Joerger (2007) evaluated driver learning curve at the first multilane roundabout in Springfield, Oregon, which opened in 2006. Joerger (2007) evaluated driver behavior at the round- about over the first 6 months of its operation. The multilane roundabout has five approaches; two of the approaches have right-turn yield-controlled bypass lanes. Four of the five approaches also have two entry lanes into the circulating roadway. Upon initial opening of the roundabout, Joerger (2007) observed two entries to the roundabout at which drivers were not choosing the correct lane, resulting in behavior such as lane changes within the circulatory roadway or abrupt lane changes at the roundabout entry. Eight, 24-hour data observa- tions were conducted over the first 6 months. One entry had a through/left-turn lane and a through/ right-turn lane. Joerger (2007) observed drivers making an abrupt lane change in the circulatory roadway from the through/right-turn lane to the inside lane to be able to stay in the roundabout (to presumably take the third exit). Initially, 40% of the drivers observed made the abrupt lane change noted above. After 6 months, 3.3% of drivers observed made the same abrupt lane change maneuver. The other entry had a through/left-turn lane adjacent to a through lane, which was separated from a right-turn bypass lane. Joerger (2007) observed drivers making a late lane change from the through/left-turn lane to the through lane on approach to the roundabout. Initially, following the opening of the roundabout approximately 20% of drivers observed made the late lane change. After 6 months, 5% of drivers observed made the late lane change. For both roundabout entries, Joerger (2007) fit the 6-month period of observations to a logarithmic “learning curve.” 2.2.3 Summary of Findings from Outreach with Public Agencies The following information summarizes the outreach with public agencies with roundabouts. • Existing Databases or Inventories: There were 11 agencies that were willing and able to share roundabout inventory and other available data. The ultimate number of agencies involved in providing data is documented in Chapter 4, Data Collection Approach and Findings. This information helped prioritize sites that were feasible to use in developing crash prediction models and sites included in the project database. • Modified Roundabouts: There were 15 roundabouts that have been modified since their initial construction. These modifications varied by site. As a result, the sample was too small to be able to definitively quantify the safety effects of those modifications. • Driver Learning Curve: Driver learning curve at roundabouts in the United States had not been thoroughly researched. Initial findings indicated that driver error or hesitancy at multilane roundabouts dissipated relatively quickly over the first 6 months of operation. • Challenges Designing and Implementing Roundabouts: Some of the common challenges agencies encounter specific to roundabouts included multilane roundabout design, signing and pavement markings, perception of heavy vehi- cles at roundabouts, high-speed approaches, and design of compact urban roundabouts.

19 • Driver Education: Driver education across agencies included project-based informational campaigns, information in driver manuals, and an increasing number of agencies with larger general public information campaigns regarding how to drive and use a roundabout. • Coordination with Law Enforcement and Crash Report- ing: Coordination activities with law enforcement agencies showed to be relatively minimal, with some focus on project- based outreach. Crash reporting at roundabouts currently is completed as it would be at any other intersection form. The input gathered above directly informed the candidate roundabout configurations, the roundabout crash defini- tions, and the project data collection plan. 2.3 Candidate Roundabout Configurations A primary goal of this project is to help practitioners make informed roundabout design decisions based on the crash potential of alternative configurations. To accomplish this, the roundabout crash prediction models address common round- about configurations, including those that present key chal- lenges to practitioners. The ability to develop crash prediction models for the desired set of configurations is based on data of sufficient depth and breadth being available. The discus- sion below presents the range of potential configurations and attributes. The discussion also identifies data that are available based on the literature review and feedback from state and local agencies. The project data collection plan further explored data availability and presented an approach for filling in data gaps. The intersection-level roundabout configurations are • Urban/suburban single-lane roundabouts (for posted speed limits less than 45 mph and greater than or equal to 45 mph); • Rural single-lane roundabouts (for posted speed limits less than 45 mph and greater than or equal to 45 mph); • Urban/suburban multilane roundabouts (for posted speed limits less than 45 mph and greater than or equal to 45 mph); and • Rural multilane roundabouts (for posted speed limits less than 45 mph and greater than or equal to 45 mph). The leg-level roundabout configurations are • Single-lane roundabout approaches (with and without right-turn bypass lanes); and • Multilane roundabouts with differing approaching lane configurations: – Two-lane entry versus a single circulating lane; – Two-lane entry versus two circulating lanes; and – Single-lane entry versus two circulating lanes. Sufficient data were not available to be able to evaluate roundabouts with more than two entering, exiting, or cir- culating lanes. Chapter 4, Data Collection Approach and Findings, presents the final set of attributes and the range of values in the database used to develop the final crash predic- tion models. 2.4 Alternative Statistical Modeling Approaches This section presents the range of possible alternative crash prediction modeling approaches based on research completed prior to this project. Chapter 5, Crash Predic- tion Model Development Approach, describes the approach used in this project to develop the crash prediction models and findings. 2.4.1 Evolution of Modeling for the Highway Safety Manual Predictive Algorithm The modeling for the HSM predictive chapters began with the work of Vogt and Bared (1998), who estimated models for intersections and segments on two-lane rural roads and intersection models for certain intersection types on rural multilane roads. Negative binomial models were estimated for crash rates for road segments, assuming (as has since been shown to be invalid) that crash frequency is proportional to traffic volume. Additional covariates were included in the model when the direction of the implied effect was found to be in accord with intuition. The Vogt and Bared models formed the basis of the pre- dictive algorithm proposed by Harwood et al. (2000) that is currently prescribed in the HSM predictive chapters. In this, CMFs are applied to a base model prediction to adjust for conditions different from those assumed in the base model. The base models for the two-lane, rural highways chapter were derived by substituting base condition values in the multi covariate models estimated by Vogt and Bared (1998). For example, for four-legged, stop-controlled intersections on two-lane rural roads, the multicovariate crash model is Crashes/year 9.34 0.60 Major Road ADT 0.61 Minor Road ADT 0.13 ND 0.0054 Equation 2-5 exp ln ln SKEW [ ] ( ) ( ) ( ) = − + + + − where ND = the number of driveways within 76 m of the inter- section on the major road and SKEW = the intersection skew angle (= 0 for right angle intersections).

20 The base condition is no driveways, adequate sight dis- tance, no turn lanes, and no skew. For this condition, the base model is then derived as Crashes/year 9.34 0.60 Major Road ADT 0.61 Minor Road ADT Equation 2-6 exp ln ln [ ] ( ) ( ) = − + + Crash-type models were not estimated. Rather the HSM approach specified crash-type proportions that could be applied to the model predictions for total crashes. Washington et al. (2005) proposed and used an alterna- tive approach to developing base models in a validation of the Bared and Vogt models. In this they estimated some base models directly from subsets of data meeting base conditions. The multilane rural roads chapter presented both estimated base models and multiple covariate models. The former, like Washington et al. (2005), were estimated directly from the subset of data that met base conditions, while the latter were also used for estimating a few CMFs. All models were esti- mated with a negative binomial error structure, allowing the estimation of a dispersion parameter used for EB prediction in the HSM. SPFs were directly estimated for total crashes of all types and severities as well as KAB-only crashes. KABCO models were estimated from various crash types. The urban and suburban arterials chapter presented esti- mated models for average conditions of variables and specified these as base models to which CMFs externally determined. The approach estimated separate models for single- and multiple-vehicle crashes but specified crash-type proportions to be applied to model predictions for total crashes to esti- mate crashes by type. A safety prediction model for freeways was developed for the next edition of the HSM. The predictive models were based on multicovariate models. The covariates in the regression model were represented as CMFs. The base conditions were specified in the model when it was calibrated, with the values defined by the researchers based on typical conditions. Sepa- rate models were developed for single- and multiple-vehicle crashes. Crash-type proportions are used with the predictive model to estimate the crash frequency for individual crash types. The researchers also developed a severity distribution function (SDF) to be used with the predictive model to esti- mate crash frequency for various severity categories. The SDF includes variables that define the influence of a change in the dimension of key geometric elements to a change in the pro- portion of crashes in each severity category. 2.4.2 Crash Prediction Models for Roundabouts For NCHRP Report 572, generalized linear modeling was used to estimate model coefficients assuming a negative binomial error distribution, consistent with the state of research in developing these models. Models were developed at the intersection level (using AADT and number of lanes and legs) for total and injury crashes and at the approach level for approaching, entering-circulating, and exiting-circulating crashes. For the latter, alternative models were estimated with different combinations of geometric variables. These models were used to imply some CMFs. The report also reviewed models calibrated by others, find- ing that the approach to calibration of the better models was similar to that adopted in NCHRP Report 572. 2.4.3 Modeling Approaches and Issues Some content for the first two subsections is taken mainly from a recent series of papers that provide an excellent review of modeling approaches and issues (Lord and Mannering, 2010; Savolainen et al., 2011). Some content is also based on a recent NCHRP Project 17-62 white paper that outlined the proposed methods for estimation of crash type and severity models under that project for the three predictive chapters currently in the HSM. 2.4.3.1 Crash Frequency Modeling Lord and Mannering (2010) provide an excellent review of the advantages and disadvantages of methods for mod- eling crash frequency data. This is reproduced below as Figure 2-1. The authors also discuss what they term as formidable problems in terms of data characteristics, namely overdisper- sion, underdispersion, time-varying explanatory variables, low sample-means and size, crash-type correlation, underre- porting of crashes, omitted-variables bias, and issues related to functional form and fixed parameters. They identify some innovative methodological approaches to resolve these issues, including random-parameter models, finite mixture models, and Markov switching models. 2.4.3.2 Crash Severity Modeling The approaches used for the HSM prediction methodol- ogy run the gamut from specifying severity proportions to be applied to model predictions for total crashes, to directly estimating SPFs for KAB and KABC crashes, to probability models used to estimate severity distribution functions in the freeways chapter. The “proportions” method is now regarded as obsolete, while the issues with the approach of estimating SPFs directly are the same as those for crash frequency models in general. The probabilistic approach was preferred by the NCHRP 17-62 team for re-estimating severity models for the existing HSM predictive chapters, so the following review will

21 focus on that, with some content taken from a white paper developed by the NCHRP 17-62 project team. The probabilistic approach estimates the probability of an injury of a given severity, given that a crash has occurred, as a function of roadway and traffic characteristics and, potentially, crash and person-related variables. From these, SDFs can be derived by estimating frequencies of crashes of given severities as a function of model variables. The NCHRP 17-45 project report (Bonneson et al., 2012) outlines the SDF estimation procedure in detail. The probability models can be ordered or unordered. Ordered models reflect the ordinal nature of injury severity data, but some studies, according to the NCHRP 17-62 white paper, show that unobserved effects among adjacent injury categories can bias the parameter estimation (Savolainen and Mannering, 2007; Paleti et al., 2011; Savolainen et al., 2011). On the other hand, using unordered models to fit ordered data may result in a loss of efficiency (Amemiya, 1985). More details about limitations or these models are in Washington et al. (2011) and Savolainen et al. (2011). Probability model formulations can be logit or probit. The error term of the probit model is normally distributed across observations, while the error term of the logit model is logisti- cally distributed. Also, the link function of the probit and logit models is different for each. In probit models, the link func- tion is the inverse normal cumulative distribution function, but in the logit model, the link function is the logit transform. However, there is usually no significant difference between the SOURCE: Lord and Mannering, 2010. Figure 2-1. Pros and cons of methods for modeling crash frequency data.

22 fitting results when the model uses either logit or probit func- tions (Chambers and Cox, 1967). The partial proportional odds model (Mooradian et al., 2013) is a mixed version of ordered and multinomial logit. This preserves the ordered nature of the dependent variable but allows some covariates to have different slopes for each boundary. Savolainen et al. (2011) provide an excellent review of the many variations of the probability models for injury severity and discuss many of the data issues associated with this type of modeling. The approaches reviewed are listed below; the more popular ones (with five or more relevant publications) are identified in boldface. • Artificial neural networks, • Bayesian hierarchical binomial logit, • Bayesian ordered probit, • Binary logit and binary probit, • Bivariate binary probit, • Bivariate ordered probit, • Classification and regression tree, • Generalized ordered logit, • Heterogeneous outcome model, • Heteroskedastic ordered logit/probit, • Log-linear model, • Markov switching multinomial logit, • Mixed generalized ordered logit, • Mixed joint binary logit-ordered logit, • Multinomial logit (MNL), • Multivariate probit, • Nested logit, • Ordered logit and ordered probit, • Partial proportional odds model, • Random parameters (mixed) logit, • Random parameters (mixed), • Ordered logit, • Random parameters ordered probit, • Sequential binary logit, • Sequential binary probit, • Sequential logit, and • Simultaneous binary logit. Researchers for NCHRP Project 17-45, “Enhanced Safety Prediction Methodology and Analysis Tool for Freeways and Interchanges” (Bonneson at al., 2012) selected the standard MNL model as the basis for SDF development. Nested logit models were also developed to evaluate the independence of irrelevant alternatives (IIA) limitation of the MNL. A test com- paring the two models showed that the nested logit model is not different from the standard MNL model. A linear function was used to relate the crash severity with the geometric design features, traffic control features, and traffic characteristics. 2.4.3.3 Modeling for CMF Estimation This section presents methods and statistical issues in CMF estimation, followed by a review of methods actually used or proposed for estimating CMFs for the HSM. Methods and Statistical Issues. Gross et al. (2010) sum- marized the different methods available for CMF develop- ment; these are shown in Table 2-9. Statistical issues associated with developing CMFs include the following: • Sample size. The sample size may significantly impact the accuracy of CMF development. Generally, the standard error decreases as the sample size increases. Hauer (1997) provides a method for estimating required sample sizes assuming a comparison-group study is being conducted. • Potential bias. Besides the countermeasure of interest, the observed change in the safety performance may be due to other factors, such as regression-to-the-mean, traffic vol- ume changes, and secular changes in reported crash experi- ence. Without accounting for the impacts of these factors, the CMFs derived from these data are usually unreliable. For cross-sectional studies the true relationship between a vari- able and crash risk may be misinterpreted by omitting impor- tant variables, correlation between explanatory variables, and selecting an inappropriate functional form for the model. • Development of multiple CMFs. Instead of assuming inde- pendence between individual CMFs, a CMF for a combi- nation treatment should be developed directly from an appropriate method [Gross et al. (2010)]. Otherwise, if there is correlation between the effects of different treat- ments, the prediction based on the product of individual CMFs may be invalid. • Estimation context. If the CMF was developed based on the data collected from a site with relatively high crash frequency, applying this CMF to other sites may result in incorrect pre- diction. For example, the CMF (0.764) for total crashes for the application of skid treatment was derived from the data collected at the road segments with a high frequency of wet weather crashes and low skid numbers. Therefore, Gross et al. (2010) suggested that it should not be expected that the same CMF will apply for resurfacing any road segment. In fact, Lyon and Persaud (2008) suggested that resurfacing can increase crashes at some locations. CMF Estimation for the HSM Chapters. CMFs have been estimated using three basic approaches, as were con- sidered in NCHRP Project 17-29, “Prediction Methodology for Rural Multilane Roads.” The review below is taken mainly from that project report (Lord et al., 2008). The first approach is based on the before–after study frame- work. This method consists of estimating the safety effects of

23 Method Applications Strengths Weaknesses Before–after with comparison group Treatment is similar among treatment sites. Simple Dificult to account for regression-to-the-mean. Before and after data are available for both treated and untreated sites. Accounts for non– treatment-related time trends and changes in trafic volume. Before–after with empirical Bayes Treatment is similar among treatment sites. Accounts for regression-to-the-mean. Relatively complex. Before and after data are available for both treated sites and an untreated reference group. Traf ic volume changes over time. Cannot consider spatial correlation. Non–treatment-related time trends. Full Bayes Useful for before–after or cross-section studies when May require smaller sample sizes. Can include prior knowledge, spatial correlation, and complex model forms in the evaluation process. Implementation requires a high degree of training. 1. There is a need to consider spatial correlation among sites. 2. Complex model forms are required. 3. Previous model estimates or CMF estimates are to be introduced in the modeling. Cross-sectional Useful when limited before–after data are available. Requires suficient sites that are similar except for the treatment of interest. Possible to develop crash modiication functions. Allows estimation of CMFs when conversions are rare. Useful for predicting crashes. CMFs may be inaccurate for a number of reasons: 1. Inappropriate functional form. 2. Omitted variable bias. 3. Correlation among variables. Case-control Assess whether exposure to a potential treatment is disproportionately distributed between sites with and without the target crash. Useful for studying rare events because the number of cases and controls is predetermined. Can only investigate one outcome per sample. Indicates the likelihood of an actual treatment through the odds ratio. Can investigate multiple treatments per sample. Does not differentiate between locations with one crash or multiple crashes. Cannot demonstrate causality. Cohort Used to estimate relative risk, which indicates the expected percent change in the probability of an outcome given a unit change in the treatment. Useful for studying rare treatments because the sample is selected based on treatment status. Only analyzes the time to the irst crash. Can demonstrate causality. Large samples are often required. Meta-analysis Combines knowledge on CMFs from multiple previous studies while considering the study quality in a systematic and quantitative way. Can be used to develop CMFs when data are not available for recent installations and it is not feasible to install the strategy and collect data. Can combine knowledge from several jurisdictions and studies. Requires the identiication of previous studies for a particular strategy. Requires a formal statistical process. All studies included should be similar in terms of data used, outcome measure, and study methodology. Table 2-9. Summary of methods for CMF development. (continued on next page)

24 changes in geometric design features, traffic operations, or other characteristics by examining the increase or reduction in crash counts between the before and after periods. Three techniques have been proposed for this kind of study: (1) the simple or naive before–after study, (2) the before–after study with a control group, and (3) the before–after study using the EB method (Hauer 1997), which is considered state of the art. These techniques, including the limitations that apply mainly to the first two, have been well documented by others. A key resource is the FHWA Guidebook (Gross et al. 2010). The second approach consists of estimating CMFs using the coefficients of multicovariate regression models. This method provides a simple way to estimate the effects of changes in geometric design features. However, although the variables are assumed to be independent, they may be corre- lated, which could affect the coefficients of the model, some- times resulting in counterintuitive effects. This method was used as the basis for several CMFs in the HSM. Two CMFs for rural multilane roads were produced from the data used for NCHRP 17-29. NCHRP Report 572 also provides some CMFs estimated on this basis for approach-level models. The third approach estimates CMFs using baseline mod- els and applying them to data that do not meet the baseline conditions. This method has been proposed by Washington et al. (2005), who thusly estimated some intersection-related CMFs. For this method, the baseline model is first applied to sites not meeting all of the baseline conditions; then, the predicted and observed values per year are compared, and a linear relationship between these two values is estimated via a regression model to determine whether or not CMFs could be produced from its coefficients. A variation of the second approach was applied for esti- mating some CMFs for the HSM freeways chapter (Bonneson et al., 2012). The researchers used a combination of previously estimated CMFs along with new CMFs estimated as part of the predictive SPFs, thereby taking advantage of existing road safety knowledge (contained in previously estimated CMFs) while adding the information contained in the esti- mation data. 2.4.4 Using Surrogates to Predict Crashes Several researchers have attempted to analyze roundabout safety through surrogate measures. For the purpose of this review these efforts have been categorized as Speed-based, Simulation-Conflict-based or Other-Conflict-based. The simulation-conflict approach has made use of the FHWA Surrogate Safety Assessment Model (SSAM) software to extract conflict data from the outputs of microsimulation software. Other-Conflict-based approaches have used video data to extract various conflict types. The use of observed speeds (where available) or predicted speeds holds promise for exploring the use of speed as a sur- rogate in crash prediction models. Although simulation- and video-based methods can be powerful tools, the effort required for this type of approach is outside the scope of the project. Such methods are promising avenues to pursue in future research. The validation of accurately predicting con- flicts and establishing the relationship between conflicts and real-world crashes are key to their success. 2.4.4.1 Speed-Based Prediction Approaches Rodegerdts et al. (2007) documents an attempt to estab- lish a speed-based, leg-level safety SPF using measured mean vehicle speeds with the following structure: exp intercept exp cXbCrashes/year AADT Equation 2-7 ( ) ( )= × × where AADT = average annual daily traffic, X = independent speed-related variable, and intercept, b, c = calibration parameters. Method Applications Strengths Weaknesses SOURCE: Gross et al. (2010) Expert panel Expert panels are assembled to critically evaluate the indings of published and unpublished research. A CMF recommendation is made based on agreement among panel members. Can be used to develop CMFs when data are not available for recent installations and it is not feasible to install the strategy and collect data. Can combine knowledge from several jurisdictions and studies. Does not require a formal statistical process. Traditional expert panels do not systematically derive precision estimates of a CMF. Possible complications may arise from interactions and group dynamics. Possible forecasting bias. Table 2-9. (Continued).

25 The regression model was deemed inadequate on the basis of the weak effects of the speed variables, so no speed-based SPF was recommended for use. In addition to the attempt to model a speed-based SPF, the research documented in Rodegerdts et al. (2007) showed that SPFs for roundabouts typically do not include many geometric variables that would allow a designer to assess the safety implications of decisions in designing a roundabout. This is perhaps not surprising given that such functions are in fact difficult to estimate, given that roundabouts tend to have very few crashes and design features with little variation. An approach for addressing this void was explored by Chen et al. (2011). The premise behind this research is that if the safety performance of a roundabout can be related to vehicle speeds, and speed can be better estimated from traffic and geometric variables than crash experience can, then speed can be used indirectly as a surrogate in evaluating the safety implications of decisions in designing or redesigning a roundabout. In their work, four SPFs for predicting crashes were developed and compared based on the same sample of U.S. roundabouts used in Rodegerdts et al. (2007). The sample included data for the 33 individual approaches at 14 round- abouts that had measured average vehicle speeds. The four SPFs were (1) approach-level, speed-based; (2) approach- level, non–speed-based (3) roundabout-level, speed-based; and (4) roundabout-level, non–speed-based. In developing the SPFs, the average approach, entry, circulating, and exiting speeds were considered. For the speed-based SPFs the best speed measure found for predicting crashes was the inside average speed (IAS), which averages the entry, upstream circulating, and upstream exiting speeds for a given round- about approach. For the roundabout-level SPFs, the average of the IAS of each leg was used as the predictor speed variable. It was found that the SPFs including the IAS speed measures were superior to the SPFs lacking this variable in predicting crashes. The speed-based SPFs developed are shown below. Speed-Based, Approach-Level Model Y exp exp12.8046 AADT 0.3388 IAS Equation 2-8 0.8075( )( ) ( )= − × where Y = total crash frequency for specific approach per year; AADT = entering AADT on approach; and IAS = average of the entry, upstream circulating, and upstream exiting mean speeds in miles per hour. Speed-Based, Roundabout-Level (i.e., Intersection- Level) Model Y exp exp15.0165 AADT 0.3260 IASavg Equation 2-9 1.0745 ( )( )( )= − × where Y = total crash frequency for entire roundabout; AADT = entering AADT for entire roundabout; and IASavg = average of the IAS for each approach. The research further developed models for predicting roundabout speeds as a function of design features, with a view to using the speeds estimated from these models, along with the speed-based SPFs, to assess roundabout safety per- formance. With this approach, speed is used as a surrogate safety measure. The model developed is IAS 0.0253 ICD 0.1848 EW 9.51 Equation 2-10 ( ) ( )= × + × + where ICD = inscribed circle diameter in feet and EW = entry width in feet. Building on the Chen et al. (2011) work, Chen et al. (2013) developed geometric-based models for predict- ing average vehicle speeds and then used these estimates to develop SPFs for roundabout approaches using a larger database of sites without in-field speed measurements. To develop the speed prediction models, the researchers used the same U.S. data as the previous study with additional data for roundabouts in Italy. The speed prediction model applied the IAS variable found in the earlier research to be the best pre- dictor of roundabout crashes. The speed prediction model developed was = − × + × × IAS 13.015958 3.088964 Cntry 0.034074 Dav + 0.142936 Wav Equation 2-11 where Cntry = 1 for U.S. site, 0 for Italian site; Dav = average of the inscribed circle and central island diameters in feet; and Wav = average of the entry, and circulating and exiting width in feet. The speed prediction model was then applied to a larger database of 139 U.S. roundabout approaches to predict the IAS for each approach. The predicted speeds were then used to develop a speed-based SPF as shown below. expCrashes/year 16.3755 AADT IAS 4.3314 Equation 2-12 0.5094( )( ) ( )= − × The authors concluded that the developed SPF suggests that the predicted speed approach seems to be promising for indirectly estimating roundabout safety performance. This approach is conceptually more preferable than conventional

26 observed speed-based models for the advantage of expand- ing accessible sample size. The applicable sample size of the United States, for example, would be 33 if observed speed were applied to develop SPF. On the contrary, for predicted speed-based modeling, sample size was 138. Turner et al. (2009) developed a number of crash predic- tion models for urban roundabouts in New Zealand focusing on the relationship between crashes, speed, traffic volume, and sight distance for various approach and circulating movements. Separate models were developed for the following crash types: • Total crashes and • Types at urban roundabouts: – Entering versus circulating vehicles, – Rear-end, – Loss of control, – Other motor vehicles, – Pedestrian, – Entering versus circulating cyclist, and – Other cyclist. Speed measures used were calculated from free-flowing vehicles. Variables used in the models included mean speed of vehicles on the circulating path, entering vehicle speed, and the variation in entering vehicle speed. Results indicated that increased speeds and speed variance are associated with a high crash risk. Also developed were models predicting vehicle entering speed using sight distance from 10 m behind the entry point to an upstream circulating vehicle and the inscribed circle diameter as explanatory variables. Entering speeds are associated with a larger diameter and larger visibility distance. Zirekel et al. (2013) explored the relationship between crashes, operating speed, and sight distance at low-volume single-lane roundabouts in the United States. Data for 72 round- about approaches were collected and split into two groups, one with a posted speed limit of 40 km/h or greater and the other less than 40 km/h. In general it was observed that once a required sight distance is met, larger sight distances were associated with larger speed differentials between conflicting vehicles and also with total and rear-end entry crashes. Crash prediction models using AADT and upstream approach sight distance explained more variation in crash counts than a model with AADT as the only explanatory variable. Given the observed relationship between sight distance and speed, it is reasonable to assume that vehicle speeds would also have been a good predictor of crashes. 2.4.4.2 S imulation-Conflict–Based Prediction Approach In a paper submitted for the 2015 Transportation Research Board annual meeting (Saulino et al., 2015), the microsimu- lation software VISSIM combined with the Surrogate Safety Assessment Model (SSAM) software was used to estimate the number of peak-hour conflicts for roundabout approaches. Conflicts defined by time-to-collision (1.5 s) and post- encroachment time (5 s) were considered. Conflict predic- tion models and approach-level crash prediction models were calibrated, suggesting that simulated conflicts can be applied for predicting crashes at roundabouts. The explana- tory variables for the conflict models include peak-hour vehicle volumes and either observed or predicted speeds with speed being the average of entering, exiting, and circulating at the approach. The crash prediction models using the pre- dicted number of conflicts as the explanatory variable proved to be a better predictor of multiple-vehicle crashes than mod- els using AADT as the explanatory variable. Vasconcelos et al. (2014) also used the SSAM software to calculate surrogate measures of safety using trajectory files generated by microscopic simulation for a four-leg single- lane roundabout and a five-leg two-lane roundabout. The time-to-collision was used for defining conflicts (less than 1.5 s being a conflict) and the relative speed at the time of minimum time-to-collision between vehicles as a proxy for crash severity. The generated conflicts at various levels of assumed AADT were compared to the predicted num- ber of injury crashes from various available crash predic- tion models for the single-lane roundabout. A satisfactory correlation between generated conflicts and predicted roundabout crashes was observed. At both the single- and two-lane roundabouts, the generated conflicts were com- pared to observed conflicts. It was found that the simula- tion predicted entering-circulating and weaving conflicts where they were observed in the field, but underpredicted the number of conflicts observed. However, if a larger value of time-to-collision had been used, more conflicts would have been generated. In the field, a conflict was recorded whenever a driver had to change their behavior as a result of another vehicle’s action. Al-Ghandour et al. (2011), using the VISSIM simulation and SSAM software, analyzed conflict patterns at single-lane roundabouts with and without slip lanes for various scenarios of traffic movements. Three different slip-lane exit-control sce- narios were also considered (yield, stop, and free-flow merge). Conflict models were then developed using a Poisson log-linear regression model. Conflicts in various zones in the roundabout and slip lane were modeled as a function of approach entry, circulating, and slip-lane traffic flows and were found to be sensitive to the slip-lane exit type. The addition of slip lanes was found to reduce overall conflicts. A time-to-collision threshold of less than 1.5 s was used to define conflicts. Predicted conflicts were used to predict crashes using the relationship established from FHWA (2008): Crashes/year 0.119 conflicts/h Equation 2-131.419( )=

27 The predicted crashes correlated well to some of the exist- ing crash prediction models. Observed data from 10 single- lane roundabouts in Indiana were then used to model con- flicts in VISSIM and SSAM and a model calibrated to predict observed crashes from the estimated conflict frequencies: Crashes/year 0.796 exp 0.0486 conflicts/h Equation 2-14 ( )= × × 2.4.4.3 Other-Conflict–Based Surrogate Approaches Richfield et al. (2014) collected 216 hours of video before and after changes were made to striping and signage along with an accompanying education campaign and traffic enforce- ment at a two-lane roundabout that had been experiencing a high number of crashes. The video was used to record driver violations including incorrect turns (turning movement is not allowed from the lane in which a vehicle is driving) or failing to yield (not yielding to a circulating vehicle upon entering) and lane change violations (changing lanes within the circulat- ing roadway). Other measured violations included wrong-way violations, stop violations, and incorrect entrance lane choice. Video was collected for 6 days each for three distinct periods: before, immediately after, and 1 year after the changes were made. Traffic volumes were also recorded in order to normal- ize the violation data with respect to exposure by dividing the violation count by the traffic volume. Lasting improvements in most violation types were observed following the changes. St.-Aubin et al. (2014) used video data to extract road user trajectories and then predicted conflicts defined by time-to- collision. The observed road user trajectories were used to build models that predict the probability of a road user’s location at any time based on its previous position, speed, and travel lane, as well as the road type and other observable variables. These probabilities were then used to predict the probability of a conflict at all points within the area of the roundabout being modeled. Zheng et al. (2013) examined the relationship between driver behavior and crash patterns using video data from two multilane roundabouts and quantifying 12 types of improper movements. Field videos were reviewed to identify instances of improper maneuvers at one quadrant of each roundabout. A conflict rate was determined by dividing the count of the improper movements in the observed time interval by the volume of vehicles in that time interval that enter the quad- rant from the same lane where the undesired movement started. The rates were then used to derive expected crash percentages of crash types and compared to the observed crash data at one of the roundabouts studied. The results did not pass a statistical test of significance to accept the hypothesis that the expected crash pattern predicted by exposure rates could predict the actual crash pattern; how- ever, the results for some crash types were accurate. Guido et al. (2011) used data obtained by video record- ing the operations at an urban roundabout in Italy focusing on rear-end conflicts. Five measures of safety were recorded: maximum deceleration rate to avoid a crash (DRAC), time-to- collision (TTC), proportion of stopping distance (PSD), time integrated TTC, and crash potential index (CPI). A vehicle was considered in conflict if the value of DRAC exceeds a given limit, 3.35 m/s2 in this paper. For TTC the measure assumed a lead vehicle maintains a constant speed, and a conflict for TTC is assumed to be the minimum perception or reaction time of 1.5 s. The PSD was measured as the distance remaining until the point of collision divided by the minimum acceptable stopping distance, which was based on the maximum deceleration rate. The time integrated TTC measured the difference between the TTC and the time interval where a collision would be unavoid- able and was integrated over the period it takes a vehicle to pass a given road segment. The CPI measured the proportion of time that the DRAC exceeds the braking capability for a given vehicle and road conditions. The video was analyzed for seven different vehicle paths through the roundabout. The authors concluded that safety performance was very dependent on how it was measured and that different measures may highlight different geometric or operational characteristics of a round- about as being of a safety concern. 2.5 Roundabout-Related Crash Definitions One of the key objectives of this research was to connect how geometric and operational features influence crashes at roundabouts. Therefore, the research team established clear definitions for crashes at roundabouts. This included two key considerations: (1) identifying which crashes occur as a result of the presence of a roundabout and (2) defining crash types for the roundabout intersection. The research team identified two alternative approaches for defining crash types at roundabouts that achieve the above objective. One approach uses the crash-type definitions traditionally reflected in crash databases within the United States (e.g., rear-end, sideswipe). The second approach uses crash-type definitions unique to circular intersections (e.g., entering-circulating, exiting-circulating). These two approaches are discussed in the following sections. 2.5.1 Traditional Crash-Type Definitions Traditional crash-type definitions reported in most crash databases include crash types such as rear-end, turning, angle, single-vehicle, fixed object, sideswipe, and others

28 that describe the type of collision without reference to where it occurred on the roadway segment or within the intersection. The advantages of using these crash-type definitions in this project include requiring less time to assemble databases and develop crash prediction models; creating an easier way for practitioners to apply the crash prediction models at existing roundabouts and apply the EB method (i.e., integrate round- about crash history into the crash prediction to improve its predictive power); and helping to create and maintain con- sistency for practitioners evaluating and comparing multiple intersections with different types of traffic control. The potential disadvantages of this approach include the possibility that deviating from international research and pre- vious U.S.-based research may make it more difficult to com- pare this project’s crash prediction models to previous work, and there might be less of a clear connection between crash type and the location of those crashes within the roundabout (e.g., rear-end crashes could occur on approach to or at the entry of the roundabout versus entering-circulating crashes, which clearly occur at the roundabout entry). 2.5.2 Specific Crash Types Roundabout-specific crash types have been used in pre- vious research in an attempt to more clearly tie geometric and operational features of a roundabout to crash frequency. Potential roundabout-specific crash types considered in this project are listed below. • Entering-circulating: Crashes occurring between an enter- ing vehicle and a circulating vehicle. • Exiting-circulating: Crashes occurring between an exiting vehicle and a circulating vehicle. • Rear-end on approach lanes: A rear-end crash involving vehicles on the approach to the roundabout. • Loss of control: A single-vehicle crash on approach to the roundabout or in the circulatory roadway. • Pedestrian: A crash involving a pedestrian. • Bicyclist: A crash involving a bicyclist. The advantages of the above crash-type definitions include the following: (1) They capture the unique aspects of round- abouts in a way that traditional crash types do not, thereby helping to connect geometric and operational features of the roundabout to crashes. (2) They allow for relatively easy comparison to previously developed U.S.-based roundabout crash prediction models and international roundabout crash prediction models. The potential disadvantages of using the above crash defi- nitions include the following: (1) More time is required to develop the crash prediction models as a result of each crash needing to be redefined to fit the above categories. (2) It is more time-intensive for practitioners to apply the crash pre- diction models at existing roundabouts because they would need to redefine historic crashes to fit the above categories in order to apply the EB method. (3) The crash types might be inconsistent with those used at other intersection forms and relative to those used in the HSM. Of these potential dis advantages, 1 and 2 are the most concerning. Rodegerdts et al. (2007) used roundabout-specific crash-type definitions similar to those noted above. The effort to redefine and recode each crash for each roundabout site would limit (more than if the traditional crash-type definitions were used) the total sample size the research team could use in developing the crash prediction models. When less data are used to develop and validate the models, the inherent risk is that the final crash prediction models are of lower quality with less applica- bility than if larger sample sizes are used. Similarly, the effort to redefine and recode roundabout crashes by practitioners for use of the models is also a concern with respect to developing readily applicable prediction tools. 2.5.3 Summary With respect to identifying crashes that are roundabout- related crashes (i.e., more generally intersection-related crashes), this project used criteria similar to the HSM and crash reporting practices in most jurisdictions. Therefore, for this project roundabout crashes are defined as those that occurred at the intersection proper and coded by the respond- ing police officer as intersection-related, and crashes that occurred within approximately 250 feet of the yield line. With respect to crash-type definitions, previous interna- tional and U.S.-based roundabout crash prediction research has used crash-type definitions specific to roundabout or cir- cular intersection forms. These crash types include entering- circulating, exiting-circulating, and other similar categories based on movement at or on approach to the roundabout. U.S. crash databases use the same crash-type definitions across different types of intersections, which means crashes at roundabout intersections within the United States are coded as crash types like rear-end, sideswipe, and other traditional crash categories. The final crash prediction models developed by this proj- ect used the following crash types: • Intersection-level crash prediction models—Use traditional crash-type definitions and • Leg-level crash prediction models—Use roundabout- specific crashes types. The specifics of the models are presented in Chapter 6, Research Findings.

29 2.6 Model Development Literature Review This subsection describes the findings from a review of the literature related to the topic of roundabout safety predic- tion. It extends the review documented in Section 2.1.3. The purpose of this review is to inform the model development process, which is discussed in Chapter 5. Separate subsections are provided for roundabout-related SPFs and CMFs. 2.6.1 Safety Performance Functions Several SPFs for roundabouts were identified in the litera- ture. These SPFs are shown in Figure 2-2. The figure parts show the trend in predicted crash frequency as a function of average annual daily entering traffic volume. This volume represents the number of vehicles entering the roundabout on the average day. For a given roundabout leg serving two- way flow, the entering volume is often estimated as being equal to one-half of the AADT volume for that leg. There is a general trend in Figure 2-2 for the predicted crash frequency to increase with an increase in entering vol- ume. A comparison of Figure 2-2a and Figure 2-2c indicates that a roundabout with two circulating lanes tends to have a higher total crash frequency (for a given entering volume) than a roundabout with one circulating lane. A compari- son of the trend lines attributed to Rodegerdts et al. (2007) suggests that roundabouts with two circulating lanes have about 65% more crashes than roundabouts with one circu- lating lane. In contrast, a similar comparison of the trend lines shown in Figure 2-2b and Figure 2-2d suggests that the number of circulating lanes does not have a significant influence on fatal-and-injury (FI) crash frequency. Together, these findings suggest that the number of circulating lanes primarily influences PDO crash frequency. The SPFs in Figure 2-2 that are attributed to Rodegerdts, et al. (2007) are based on data from approximately 60 round- abouts with one circulating lane and 30 roundabouts with two or more circulating lanes. The roundabouts are collectively a. One circulating lane, total crashes. b. One circulating lane, FI crashes. c. Two circulating lanes, total crashes. d. Two circulating lanes, FI crashes. Figure 2-2. Roundabout SPFs based on circulating lanes and crash severity.

30 located in several states. For total crashes, Rodegerdts et al. (2007) developed four SPFs: one SPF for each combination of number of circulating lanes (one or two) and number of legs (three or four). For KAB crashes, they developed two SPFS: one SPF for three legs (with either one or two circu- lating lanes) and one for four legs (with either one or two circulating lanes). To facilitate a comparison of the KAB SPFs to those of other researchers (which are based on KABC crashes), the values obtained from the KAB SPFs developed by Rodegerdts et al. (2007) were inflated by the ratio of KABC to KAB crashes found in the project database (as described in Sec- tion 4.5). This ratio was computed to be 2.4. The SPFs developed by Rodegerdts et al. (2007) indicate that crash frequency is influenced by the number of round- about legs. These SPFs indicate that, for a given entering vol- ume, three-leg roundabouts experience about one-half the number of crashes that four-leg roundabouts experience. Bagdade et al. (2011) developed SPFs using 30 roundabouts with one circulating lane and 18 roundabouts with two or more circulating lanes. All of the roundabouts are located in Michigan. The SPFs include variables for the number of circulating lanes and whether the roundabout was located in an interchange. There are separate SPFs for total crashes and FI crashes (i.e., KABC crashes). The SPFs do not address the number of legs; however, the roundabouts in the database have three or four legs. Figure 2-2 shows the SPF predictions for noninterchange roundabouts. Dixon and Zheng (2013) developed SPFs for single-lane roundabouts using data for 21 roundabouts in Oregon. Their dataset included only roundabouts with four legs. The SPFs they developed predict total crash frequency (all severities) and FI crash frequency. These SPFs are shown in Figure 2-2a and Figure 2-2b. Isebrands (2011) developed SPFs using data for 18 rural single-lane roundabouts. The dataset included roundabouts with three and four legs. There are separate SPFs for predict- ing total crash frequency and FI crash frequency. These SPFs are shown in Figure 2-2a and Figure 2-2b. 2.6.2 Crash Modification Factors Rodegerdts et al. (2007) developed approach-level crash prediction models using regression analysis of cross-section data (in this report these models are called leg-level crash prediction models). These models predict the frequency of crashes occurring on (or in the circulating lanes conflicting with) a given roundabout leg. The researchers considered developing one model for each crash type listed in Table 2-10. The names of the first four crash types listed Table 2-10 describe the movements of the involved vehicles just prior to the crash. Based on sample size considerations, the researchers ultimately developed models for only the following three crash types: entering-circulating, exiting-circulating, and approaching. The coefficients in the three crash prediction models developed by Rodegerdts et al. (2007) were used to infer sev- eral CMFs. These inferred CMFs are listed in Table 24 of the report by Rodegerdts et al. (2007). Each CMF corresponds to one geometric design element dimension. These CMFs are identified in the following list by the name of the associated design element. Each of these CMFs is applicable to total crashes (all severities). • CMFs applicable to entering-circulating crashes: – Entry radius, – Entry width, – Central island diameter, and – Angle to next leg. • CMFs applicable to exiting-circulating crashes: – Inscribed circle diameter (ICD), – Central island diameter, and – Circulating width. • CMFs applicable to approaching crashes: – Approach half-width. As indicated by the list, each of the CMFs developed by Rodegerdts et al. (2007) applies to a specific crash type. The CMF values were converted to a value that reflects the aggregated treatment effect on total crashes (all crash types) to facilitate a comparison of these CMFs with the trends found Crash Type Incidence Percentage Entering-circulating 141 23 Exiting-circulating 187 31 Rear-end on approach lanes 187 31 Loss of control on approach lanes 77 13 Vehicle-pedestrian 5 1 Vehicle-bicycle 8 1 Total: 605 100 SOURCE: Rodegerdts et al. (2007), Table 13. Table 2-10. Roundabout crash-type distribution.

31 in the data (the findings from this comparison are provided in Section 5.2.3.3). The converted value was computed using the following equation. CMF P P CMFi agg j j j i1.0 Equation 2-15, ,( )= − + where CMFi,agg = aggregated CMF for design element i; Pi = proportion of crashes associated with crash type j ( j = en-cir: entering-circulating; ex-cir: exiting-circulating; app: approaching); and CMFj,i = crash modification factor for design element i and crash type j. Equation 2-15 is based on the assumption that the design element does not have an effect on the other crash types. This assumption is reasonable given that disaggregated CMFs are inferred to capture the treatment’s main effects and that they are used here only to facilitate the aforementioned compari- son. The proportion used in this equation was computed using the percentages in the last column of Table 2-10 (i.e., Pj = percentage in Table 2-10/100). Four CMFs included in the bullet list within this sec- tion correspond to design elements whose dimension was included in the project database. These CMFs include entry width, angle to the next leg, ICD, and circulating width. They are described more fully in the following paragraphs. The entry width CMF developed by Rodegerdts et al. (2007) describes the relationship between entry width and total crash frequency (all severities). Entry width is the width of the approaching lanes (plus shoulders, if provided) on the subject leg, as measured at the yield line. As developed, the CMF is applicable to entering-circulating crashes on a specified round- about leg. However, this CMF was converted to an equivalent CMF aggregated for all crash types using Equation 2-1 and a base entry width of 25 feet. The relationship between the aggregate CMF value and entry width is shown in Figure 2-3. The CMF indicates that leg crash frequency increases as entry width is increased. Angle to next leg, another CMF developed by Rodegerdts et al. (2007), describes the relationship between the angle to the next leg and the total crash frequency (all severities). This angle is measured between the subject leg and the next leg going in a counterclockwise direction (i.e., in the direction of travel within the roundabout). As developed, the CMF is applicable to entering-circulating crashes on a specified roundabout leg. This CMF was converted to an equivalent CMF aggregated for all crash types using Equation 2-1 and a base angle of 90 degrees. The relationship between the aggre- gate CMF value and angle is shown in Figure 2-4. The CMF indicates that leg crash frequency decreases as the angle is increased. The ICD CMF developed by Rodegerdts et al. (2007) describes the relationship between ICD and total crash fre- quency (all severities). This diameter describes the circle that best fits the outside edge of the circulating lanes. As developed, the CMF is applicable to exiting-circulating crashes on a speci- fied roundabout leg. This CMF was converted to an equivalent CMF aggregated for all crash types using Equation 2-1 and a base diameter of 125 ft. The relationship between the aggregate CMF value and ICD is shown in Figure 2-5. The CMF indicates that leg crash frequency increases as the ICD is increased. Another CMF developed by Rodegerdts et al. (2007), cir- culating width, describes the relationship between circulating width and total crash frequency (all severities). This width rep- resents the total width of the circulating lane (or lanes) con- flicting with the subject leg, including any shoulders that may be present. As developed, the CMF is applicable to exiting- circulating crashes on a specified roundabout leg. This CMF Figure 2-3. Relationship between CMF value and entry width. Figure 2-4. Relationship between CMF value and angle to next leg.

32 was converted to an equivalent CMF aggregated for all crash types using Equation 2-1 and a circulating width of 25 ft. The relationship between the aggregate CMF value and circulating width is shown in Figure 2-6. The CMF indicates that leg crash frequency increases as the circulating width is increased. Chapter 14 of the HSM (2010) includes the intersection lighting CMF for the addition of lighting at an intersection. This CMF is recommended in the HSM for use at rural and urban intersections. It is applicable to injury crashes. How- ever, it is implemented in HSM Chapters 10, 11, and 12 and offered as being applicable to total crashes (all severities). The reported CMF value of 0.62 is applicable to nighttime crashes. It is used in Equation 2-1, with the proportion of crashes that occur at night, to estimate the aggregate CMF value applicable to total crashes (all crash types and all times of day). The proportion of nighttime crashes in the project database is 0.185. Using this proportion in Equation 2-1 with a nighttime CMF value 0.62 yields an aggregate CMF value of 0.93. Thus, this CMF suggests that the addition of lighting at a roundabout may reduce overall crashes by 7%. Chapter 19 of the HSM includes the number of access points CMF for the presence of unsignalized access points (e.g., drive- way) on the crossroad within 250 ft of the crossroad-ramp ter- minal. This CMF increases the predicted crash frequency for the crossroad-ramp terminal when access points are present. One version of this CMF applies to signalized crossroad-ramp terminals. The CMF values computed using this CMF are listed in Table 2-11. 2.7 References and Bibliography Aguero-Valverde, J., and P. Jovanis. 2008. Analysis of Road Crash Fre- quency with Spatial Models. Transportation Research Record, Journal of the Transportation Research Board, No. 2061, pp. 55–63. Al-Ghandour, M. N., B. J. Schroeder, B. M. Williams, and W. J. Rasdorf. 2011. Conflict Models for Single-Lane Roundabout Slip Lanes from Microsimulation: Development and Validation. Transporta- tion Research Record, Journal of the Transportation Research Board, No. 2236. Amemiya, T. 1985. Advanced Econometrics. Cambridge, Mass.: Harvard University Press. American Association of State Highway and Transportation Officials (AASHTO). 2010. Highway Safety Manual, First Edition. AASHTO, Washington, D.C. Angelastro, M. 2010. The Influence of Driver Sight Distance on Crash Rates and Driver Speed at Modern Roundabouts in the United States. Institute of Transportation Engineers Journal, July. Anjana, S., and M. V. L. R. Anjaneyulu. 2014. Development of Safety Performance Measures for Urban Roundabouts in India. Journal of Transportation Engineering, July. Arndt, O. K. 1994. Relationship Between Roundabout Geometry and Accident Rates. ME thesis. Queensland University of Technology, Brisbane, Queensland, Australia. Figure 2-5. Relationship between CMF value and ICD. Figure 2-6. Relationship between CMF value and circulating width. Number of Unsignalized Access Points CMF Value for FI Crashes 0 1.00 1 1.17 2 1.37 3 1.61 4 1.88 Table 2-11. Relationship between CMF value and number of access points.

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