Roundabouts in the United States (2007)

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23 This chapter describes a number of safety modeling and evaluation tasks. First, the results of the investigation of the ability of non-U.S. prediction models to represent U.S. data are presented—separately for intersection-level and approach-level models. Next are presented the results of the efforts to develop intersection- and approach-level models for U.S. data collected for this project. The last two sections present the results for the modeling of safety as a function of speed and the results of the before-after study. Ability of Existing Non-U.S. Models to Represent U.S. Data To test the feasibility of international models, the models were calibrated and used to predict crashes at the U.S. round- abouts in the database. Statistical goodness-of-fit tests were then performed. Appendix E contains a summary of the goodness-of-fit measures and statistical assessments used in this analysis. Ability of Non-U.S. Intersection-Level Accident Prediction Models to Represent U.S. Data The general purpose of the intersection-level models is to predict the expected crash performance of an intersection during the planning level of analysis. These models are intended for comparing roundabouts with other forms of intersections and intersection control. As a result, the vari- ables selected for use in the models are deliberately set to be the most basic variables, such as AADT, the number of legs, and the number of circulating lanes. Existing models were tested with the U.S. data to assess their goodness of fit. The eight intersection-level models came from four sources: four models were based on data from Sweden, three from the United Kingdom, and one from France. These models are designated as follows: • SWED-TOT1 and SWED-INJ1 (Equations A-10a and A-11a in Appendix A). • SWED-INJ2 and SWED-INJ3 (Equations A-12a through A-12d in Appendix A). • UK-INJ1, UK-INJ2, and UK-INJ3 (Equations A-1c through A-1f in Appendix A). The constant parameter for the semi-urban (30–40 mph, or 48–64 km/h) and rural (50–70 mph, or 80–112 km/h) models has been averaged where applicable. • FR-INJ1 (Equation A-9 in Appendix A). (Details on these models, including equations, are given in Appendix A.) Only the first study from Sweden provides a model that predicts total crashes, and the UK models apply only to four-leg roundabouts. For the SWED-TOT1 model, both 70-km/h (44-mph) and 50-km/h (31-mph) speed limits were tested. With the use of a speed limit of 70 km/h [44 mph], testing determined that the model underpredicts crashes (see Table 12). Further testing with the 50-km/h [31-mph] speed limit revealed further underprediction of crashes. The results of the statistical goodness-of-fit tests, which are also shown in Table 12, indicate that the mean prediction bias per site-year (MPB/site-yr) and mean absolute deviation per site-year (MAD/site-yr) are roughly of the same magnitude, if not greater, than the number of crashes per site-year. This statistic indicates that none of the models fit the data very well. The existing models include other limitations: • No model exists for roundabouts with more than four legs or more than two circulating lanes. • Only one model predicts total crashes, and, by predicting a crash rate independent of traffic volume, it inherently assumes a linear relationship between traffic volumes and crashes. C H A P T E R 3 Safety Findings

24 In light of these limitations and the poor goodness of fit to the U.S. data, the use of existing models to represent the U.S. data is an undesirable option for developing intersection- level prediction models for use in the United States. On this basis, the research team determined that new intersection- level models based on U.S. data needed to be calibrated to have models available for both total crashes and injury crashes at the various site types found in the United States. Ability of Existing Non-U.S. Approach-Level and Other Disaggregate Safety Prediction Models to Represent U.S. Data Similarly, to test the possibility of using the UK approach- level models directly on the U.S. database, U.S. data were applied to the existing approach-level and other disaggregate models from the UK to assess their goodness of fit. The UK model form is described in Appendix A. Initially, the U.S. data developed for this project and crash data used to develop the UK models were compared (Table 13). As shown in the table, • The U.S. data have a much higher percentage of exiting- circulating crashes; • The UK data have a much higher percentage of crashes involving loss of control, although this percentage includes crashes in the circulating part of the roundabout, which the U.S. data does not; and • The U.S. data have a much smaller proportion of pedes- trian crashes. Before testing the UK models, the research team removed from the model any variables for which the necessary data were unavailable by evaluating the estimated parameters at their mean values and adding this value as a multiplicative factor. Table 14 shows the full UK models (for each crash type) and the mean value of each variable removed. Note that the U.S. data were applied to the more general form of the May- cock and Hall model (4). In the final Maycock and Hall model, some variables were omitted (e.g., sight distance and gradient category), and some coefficients were rounded com- pared to those used here. Next, the full UK models were recalibrated against the U.S. data by testing them as specified, and then calculating a recal- ibration term defined as the ratio of observed crashes to pre- dicted crashes. This recalibration term is simply added to the original model as a multiplicative factor. Table 15 describes which UK model was tested against which set of U.S. data for recalibration. Table 16 provides goodness-of-fit statistics for the UK models tested against the U.S. data for entering- circulating, approaching, and single-vehicle crashes. In light of the limitations imposed by the differences in crash categories between the UK models and the U.S. data, the calibration of the UK models on only fatal and injury SWED- TOT1 SWED -INJ1 SWED- INJ2 SWED -INJ3 UK- INJ1 UK- INJ2 UK-INJ3 FR-INJ1 Model Total Injury Injury Injury Injury Injury Injury Injury No. Sites 78 78 78 78 20 20 61 85 MPB –3.45 0.49 0.03 0.44 2.77 2.81 2.86 –0.28 MPB/site-yr –1.18 0.17 0.01 0.15 1.01 1.02 1.00 –0.10 MAD 5.49 1.34 1.09 1.30 3.15 3.17 3.17 1.84 MAD/site-yr 1.88 0.46 0.37 0.44 1.14 1.15 1.11 0.64 MSPE 71.65 4.06 2.83 3.58 23.05 24.85 22.29 13.60 MSPE/site-yr2 0.11 0.01 <0.01 0.01 0.15 0.16 0.04 0.02 AADT average (range) 15,539 (2,668– 37,564) 15,539 (2,668– 37,564) 15,539 (2,668– 37,564) 15,539 (2,668– 37,564) 21,050 (5,322– 36,770) 21,050 (5,322– 36,770) 16,434 (3,870– 37,564) 15,908 (3,870– 37,564) Crashes/site-yr 2.63 0.24 0.24 0.24 0.29 0.29 0.36 0.41 Notes Only applicable to urban roundabouts Only applicable to four-leg roundabouts and where major and minor AADTs known separately Only applicable to four-leg roundabouts Applicable where entering AADT between 32,000 and 40,000 Legend: MPB = mean prediction bias; MAD = mean absolute deviation; MSPE = mean square prediction error; AADT = average annual daily traffic; yr = year Table 12. Goodness-of-fit tests of existing intersection-level models to U.S. data.

25 Crash Type Model Term Parameter Value Mean Value Term at Mean Value Entering-Circulating Crashes (Crashes involving an entering and a circulating vehicle) L(constant) Lk -3.09 L(entering flow) LQe 0.65 L(circulating flow) LQc 0.36 Entry path curvature Ce -40.3 Entry width e 0.16 Approach width correction ev -0.009 Ratio factor RF -1.0 Percentage of motorcycles Pm 0.21 2.24 1.60 Angle to next leg A -0.008 Gradient category g 0.09 -0.11 0.99 Approaching Crashes (Crashes between vehicles approaching the roundabout—mostly rear-ends) L(constant) Lk -4.71 L(entering flow) LQe 1.76 Entry path curvature Ce 20.7 Reciprocal sight distance 1/Vr -43.9 0.015 0.52 Entry width e -0.093 Gradient category g -0.13 -0.11 1.01 Single-Vehicle Crashes (Crashes involving single vehicle anywhere in intersection) L(constant) Lk -4.71 L(entering flow) LQe 0.82 Approach half-width v 0.21 Entry path curvature Ce 23.7 Approach curvature category Ca -0.17 0.05 0.99 Reciprocal sight distance 1/Vr -33.0 Other (non-pedestrian) Crashes (includes exiting-circulating, exiting-exiting, circulating, etc.) L(constant) Lk -5.69 L(entering × circulating flow) LQec 0.73 Percentage of motorcycles Pm 0.21 2.24 1.60 Pedestrian Crashes L(constant) Lk -3.59 L((entering + exiting vehicle flow) × pedestrian flow) LQexp 0.53 Source: Maycock and Hall (4) U.S. Data Crash Type Incidence Percentage Percentage in UK1 Notes Entering- circulating 141 23% 43.3% Exiting-circulating 187 31% 14.5% (Defined as “other” in the UK) Other crashes include exiting-circulating, circulating-circulating, etc. Rear-end on approach lanes 187 31% 17.0% (Defined as “approach” in the UK) Most approaching crashes in UK are rear-ends. Loss of control on approach lanes 77 13% 20.1% In UK, this type includes single-vehicle crashes on circulating part of roadway. Pedestrian 5 1% 5.1% Bicyclist 8 1% – Total 605 100% 100% 1Only fatal plus injury crashes Table 13. Comparison of disaggregated crash data in the U.S. and UK databases. Table 14. Approach-level models by crash type at UK roundabouts showing mean values for variables not in the U.S. data.

26 crashes, and the relatively poor goodness of fit to the U.S. data as evidenced by the relatively high values of MAD/site- year (compared to the crashes/site-year) and the relatively high calibration factors, using the existing models to repre- sent the U.S. data is not a desirable option for developing approach-level prediction models for use in the United States. On this basis, new approach-level models need to be calibrated based on U.S. data. Models Calibrated for U.S. Data This section presents the development of U.S. intersection- level and approach-level models. These new models are directly calibrated using the data assembled for this project and model forms that others have found successful for round- about and general intersection modeling. See Appendix E for definitions of statistical terms. Intersection-Level Prediction Models Intersection-level safety prediction models were calibrated for total and injury crashes; the latter includes fatal and defi- nite injury crashes and excludes possible injury and property damage only (PDO) crashes. To develop the models, a variety of variable sets were tested: • AADT entering the intersection only • AADT, number of legs, and number of lanes • AADT, number of legs, number of lanes, and the ratio of central island diameter to inscribed circle diameter • AADT, number of legs, number of lanes, and inscribed circle diameter • AADT, number of legs, number of lanes, and central island diameter Generalized linear modeling was used to estimate model coefficients using the software package SAS and an assumed negative binomial error distribution, all consistent with the state of research in developing these models. Consistent with common practice, the models calibrated are of the following very general and flexible form: where AADT = average annual daily traffic entering the inter- section X1LXn = independent variables other than AADT in the model equation b1 = calibration parameter Crashes year Intercept AADT Xb/ exp( ) exp(= ⋅ + +1 1 L Xn) ( )3-1 UK Model Based on Fatal and Injury Crashes U.S. Crashes Applied to Model Entering-circulating: Crashes involving an entering and a circulating vehicle. Entering-circulating: Crashes involving an entering and a circulating vehicle. Approaching: Crashes between vehicles on the approach. Mostly rear-ends. Rear-ends on approach lanes Single Vehicle: Crashes involving single vehicle anywhere in junction. Loss of control on approach lanes Other (non-pedestrian): Crashes include exiting- circulating, exiting-exiting, circulating, etc. Not attempted because this category is not compatible with U.S. data collected Pedestrian Not attempted because pedestrian flows unknown and only 5 total pedestrian crashes in database Bicyclist – No UK Model No model Crash Type Entering-Circulating Approaching Single Vehicle Measure UK UK UK Number of legs 81 110 107 Calibration factor (observed/predicted) 1.82 3.83 1.29 MAD/site-yr 0.14 0.36 0.16 MSPE/site-yr2 0.0004 0.0035 0.0006 Crashes/site-yr 0.32 0.57 0.55 Legend: MAD = mean absolute deviation; MSPE = mean square prediction error Notes: The number of legs is the number of roundabout legs the data were recalibrated against. The calibration factor is the recalibration factor for the UK models calculated by dividing the sum of observed crashes by the sum of predicted crashes. Table 15. UK models matched with U.S. data for recalibration of approach-level and other disaggregate models. Table 16. Goodness-of-fit tests of the ability of UK entering- circulating, approaching, and single-vehicle models to represent U.S. data.

27 In selecting the recommended intersection-level models for total and injury crashes, the research team looked for low val- ues of the dispersion parameter and statistical significance of the estimated variable coefficients. Tables 17 and 18 summarize these major considerations. The recommended models are the ones that achieve the lowest dispersion parameter values while having all variables significant at a level of at least 10 percent. The analyses indicate that a model including AADT, num- ber of legs, and number of lanes has the best fit to the data available for calibration. The research team also believes that, at the planning level, the inclusion of central island diameter and inscribed circle diameter was not appropriate, as a prac- titioner assuming values for these dimensions may introduce artificial error in the prediction. The final calibrated models are shown in Tables 19 and 20. SAS output including detailed statistics, such as standard errors of the estimated parameters, are presented in Appendix F. It is important to reiterate that these models have been calibrated to the data available to this project. When using the models for a particular jurisdiction, they should be recalibrated using data for a sample of roundabouts in the jurisdiction. To do this, the local jurisdiction dataset is applied to the model provided in Equation 3-1. A calibra- tion factor is calculated as the ratio of the sum of crashes actually recorded in the sample to the sum of the model pre- dictions for individual roundabouts in the sample. The indi- vidual local jurisdiction calibration factor is then applied to Equation 3-1. At a minimum, data for at least 10 round- abouts with at least 60 crashes are needed to complete this calibration. Approach-Level Crash Prediction Models The general purpose of the approach-level models is to understand the impacts of geometric design decisions on various crash types. For example, as the designer evaluates different design options (e.g. entry width, entry radius, or central island diameter), he/she can assess the direction, if not the magnitude, of the safety consequence of the selection. These models are not intended as predictive models in the same sense that the intersection-level models are. However, if they are used for this purpose, it is stressed that a multiplier should be calibrated, as for the intersection-level models, to reflect local conditions. Model Variables Significance of Variable Coefficients (10% level) Dispersion Parameter 1 AADT AADT significant. 1.4986 2 AADT, number of legs and number of lanes All variables significant. 0.8986 3 AADT, number of legs, number of lanes, and ratio of central island diameter to inscribed circle diameter Central island diameter/ inscribed circle diameter ratio is not significant; other variables are. 0.8348 4 AADT, number of legs, number of lanes, and inscribed circle diameter Inscribed circle diameter is not significant; other variables are. 0.7792 5 AADT, number of legs, number of lanes, and central island diameter Central island diameter is not significant; other variables are. 0.8408 Model Variables Significance of Variable Coefficients (10% level) Dispersion Parameter 1 AADT AADT significant. 1.7262 2 AADT, number of legs, and number of lanes All variables significant. 0.9459 3 AADT, number of legs, number of lanes, and ratio of central island diameter to inscribed circle diameter AADT and central island diameter/inscribed circle diameter ratio are not significant; other variables are. 0.8714 4 AADT, number of legs, number of lanes, and inscribed circle diameter AADT and inscribed circle diameter are not significant; other variables are. 0.6891 5 AADT, number of legs, number of lanes, and central island diameter AADT and central island diameter are not significant; other variables are. 0.8894 Table 17. Comparison of intersection-level model results for total crashes. Table 18. Comparison of intersection-level model results for fatal and injury crashes.

28 The approach-level safety performance functions (SPFs) were developed for specific crash types: entering-circulating, exiting-circulating, and approaching. Due to the relatively small number of crashes being modeled, the SPFs were developed for total crashes only. Generalized linear model- ing was applied to estimate model coefficients using the software package SAS and an assumed negative binomial error distribution, all consistent with the state of research in developing these models. These models are of the following form: where AADT1LAADTm = average annual daily traffic X1LXn = independent variables other than AADT in the model equation b1Lbm, c1Lcn = calibration parameters Crashes year Intercept AADT AADb/ exp( )= ⋅ ⋅⋅⋅⋅⋅1 1 T c X c X m bm n n⋅ + +exp( ) ( )1 1 L 3-2 The variables tested include entry radius, entry width, cen- tral island diameter, approach half-width (referred to as approach width on Figure 9), circulating width, and others. Tables 21, 22, and 23 present the candidate models for entering-circulating, exiting-circulating, and approaching crashes, respectively. These tables can be interpreted by apply- ing the values in the tables to the model form given above. For example, Model 6 in Table 21 has the following equation form: where AADTE = entering AADT for the subject entry AADTC = circulating AADT conflicting with the subject entry e = entry width (ft) θ = angle to next leg (degrees) Crashes year AADT AAE/ exp( . ) ( ) ( . = − ⋅ ⋅7 2158 0 7018 DT e C ) exp( . . ) ( ) .0 1321 0 0511 0 0276⋅ − θ 3-3 Safety Performance Functions [Validity Ranges] Number of Circulating Lanes 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 Safety Performance Functions [Validity Ranges] Number of Circulating Lanes 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 M od el N o. D isp er sio n In te rc ep t En te ri ng A A D T C ir cu la tin g A A D T En tr y R ad iu s (ft ) En tr y W id th (ft ) C en tr a l Is la n d D ia m et er (f t) A ng le to N ex t Le g (d eg . ) 1/ En tr y Pa th R ad iu s (1/ ft) 1 1.665 -13.2495 1.0585 0.3672 2 1.664 -13.0434 0.9771 0.3088 0.0099 3 1.495 -12.2601 0.9217 0.2900 0.0582 -0.0076 4 1.514 -13.0579 1.0048 0.3142 0.0103 -0.0046 5 1.302 -8.7613 0.9499 0.2687 0.0105 -0.0425 6* 1.080 -7.2158 0.7018 0.1321 0.0511 -0.0276 7 2.032 -8.9686 0.8322 0.1370 -138.096 *Recommended model Table 19. Intersection-level safety prediction model for total crashes. Table 20. Intersection-level safety prediction model for injury crashes. Table 21. Entering-circulating crash candidate models for total crashes.

29 Because of correlations among the variables in the individual candidate models and the small sample size of crashes, calibration of a model with more than a few vari- ables was not possible. The candidate models presented for each crash type are quite close statistically. They all tend to contain logical variables with estimated effects in the expected direction. Appendix H contains the SAS output for each of these models. To recommend the models with the best predictive power, the research team looked for the models with the lowest dis- persion parameters while ensuring that the variables in the selected models and the direction of the indicated effects were logical. These recommended models are marked with an asterisk and shaded in Tables 21 through 23. On the basis of the dispersion parameter, models with AADT as the only explanatory variable, clearly, do not have the predictive power of models that contain at least one geometric variable. These AADT-only models are nevertheless presented in Tables 21 through 23 because they are intended for consideration for Highway Safety Manual (HSM)-type predictions that are dis- cussed in Chapter 6. The recommended models do not incorporate the wide array of geometric design features that engineers will be working with as the roundabout design is being developed. However, consistent with current prototype HSM proce- dures, the analysis does allow for the estimated coefficients for geometric features in recommended and other models to be considered in developing crash modification factors (CMFs) for use in the HSM. For example, the designer can use the AADT- only models (Model No. 1 given in Tables 21 through 23) and then identify the effect of a design change by applying the appropriate CMF (shown in Table 24). For example, to deter- mine the effect of a unit change in entry width on entering- circulating crashes, the designer would first determine a base level of entering-circulating crashes using Model No. 1 given in Table 21 as follows: The designer would then apply the implied CMF from Table 24 that relates a unit change in entry width to entering- circulating crashes: 1.0524. Caution is advised, however, because many of the variables are correlated, resulting in model-implied effects that may not reflect reality. Therefore, the correlations should be considered when determining which CMFs might be used in the HSM. To this end, a cor- relation matrix is provided as Table 25. Although the number of entering-circulating, exiting- circulating, and approaching crashes predicted with the approach-level models can be added together to estimate the total number of crashes at a roundabout, the designer is advised to use the intersection-level model for the purposes of estimating the number of crashes at a roundabout. The intersection-level model is better for this purpose because (1) recalibrating the approach-level models for local conditions is more difficult than recalibrating the intersection-level models, and (2) the intersection-level models were developed specifically for such prediction while the approach-level models were developed to assess designs. Development of Speed-Based Prediction Models Using U.S. Data The concept of a speed-based model that relates safety performance to absolute speeds and/or relative speeds (speed consistency) was pursued with the hope of providing an intermediate link to both safety and operational per- formance. The rationale is that speed profiles are a manifes- tation of the driver’s response to a design. Speed profiles are Crashes year AADT AADTE/ exp( . ) . = − ⋅ ⋅13 2495 1 0585 C 0 3672. ( )3-4 M od el N o. D isp er sio n In te rc ep t Ex iti ng A A D T C ir cu la tin g A A D T In sc ri be d C ir cl e D ia m et er (f t) C en tr a l Is la n d D ia m et er (f t) C ir cu la tin g W id th (f t) 1/ C ir cu la tin g Pa th R ad iu s (1/ ft) 1/ Ex it Pa th R ad iu s (1/ ft) 1 6.131 -7.7145 0.3413 0.5172 2* 2.769 -11.6805 0.2801 0.2530 0.0222 0.1107 3 3.015 -11.2447 0.3227 0.3242 0.0137 0.1458 4 3.317 -3.8095 0.2413 0.5626 372.8710 5 4.430 -9.8334 0.6005 0.7471 -387.729 *Recommended model Model No. Dispersion Intercept Entering AADT Approach Half-Width (ft) 1 1.330 -5.6561 0.6036 2* 1.289 -5.1527 0.4613 0.0301 *Recommended model Table 22. Exiting-circulating crash candidate models for total crashes. Table 23. Approaching crash candidate models for total crashes.

30 Variable Entering-Circulating Exiting-Circulating Approaching Entry Radius (ft) 0.9901 to 0.9896 – – Entry Width (ft) 1.0524 * – – Approach Half-Width (ft) – – 1.0306 * Inscribed Circle Diameter (ft) – 1.0224 * – Central Island Diameter (ft) 0.9924 to 0.9954 1.0138 – Circulating Width (ft) – 1.1171 * – Angle to Next Leg (deg.) 0.9728 * – – *CMF was derived from the recommended model. Parameter Statistic In sc ri be d ci rc le di am et er En tr y w id th A pp ro a ch ha lf- w id th En tr y ra di us C irc u la tin g w id th C en tr al is la nd di am et er A ng le to n ex t le g En te ri ng A A D T C irc u la tin g A A D T Ex iti ng A A D T Pearson Correlation 1.000 0.653 0.611 0.399 0.689 0.946 -0.169 0.245 0.131 0.085 Sig. (2-tailed) . 0.000 0.000 0.000 0.000 0.000 0.050 0.005 0.193 0.394 Inscribed circle diameter N 139 138 132 131 138 134 135 130 100 102 Pearson Correlation 0.653 1.000 0.818 0.455 0.827 0.629 -0.219 0.416 0.136 0.300 Sig. (2-tailed) 0.000 . 0.000 0.000 0.000 0.000 0.011 0.000 0.178 0.002 Entry width N 138 138 131 130 138 133 134 129 100 102 Pearson Correlation 0.611 0.818 1.000 0.187 0.698 0.597 -0.213 0.392 0.186 0.185 Sig. (2-tailed) 0.000 0.000 . 0.037 0.000 0.000 0.014 0.000 0.073 0.073 Approach half-width N 132 131 132 125 131 127 132 123 93 95 Pearson Correlation 0.399 0.455 0.187 1.000 0.327 0.336 0.150 -0.004 0.023 0.023 Sig. (2-tailed) 0.000 0.000 0.037 . 0.000 0.000 0.093 0.969 0.821 0.821 Entry radius N 131 130 125 131 130 126 127 122 97 99 Pearson Correlation 0.689 0.827 0.698 0.327 1.000 0.658 -0.194 0.599 0.203 0.281 Sig. (2-tailed) 0.000 0.000 0.000 0.000 . 0.000 0.025 0.000 0.042 0.004 Circulating width N 138 138 131 130 138 133 134 129 100 102 Pearson Correlation 0.946 0.629 0.597 0.336 0.658 1.000 -0.234 0.310 0.072 0.021 Sig. (2-tailed) 0.000 0.000 0.000 0.000 0.000 . 0.007 0.000 0.477 0.833 Central island diameter N 134 133 127 126 133 134 130 125 100 102 Pearson Correlation -0.169 -0.219 -0.213 0.150 -0.194 -0.234 1.000 -0.316 -0.124 -0.001 Sig. (2-tailed) 0.050 0.011 0.014 0.093 0.025 0.007 . 0.000 0.228 0.991 Angle to next leg N 135 134 132 127 134 130 135 126 96 98 Pearson Correlation 0.245 0.416 0.392 -0.004 0.599 0.310 -0.316 1.000 0.647 0.596 Sig. (2-tailed) 0.005 0.000 0.000 0.969 0.000 0.000 0.000 . 0.000 0.000 Entering AADT N 130 129 123 122 129 125 126 130 98 98 Pearson Correlation 0.131 0.136 0.186 0.023 0.203 0.072 -0.124 0.647 1.000 0.220 Sig. (2-tailed) 0.193 0.178 0.073 0.821 0.042 0.477 0.228 0.000 . 0.028 Circulating AADT N 100 100 93 97 100 100 96 98 100 100 Pearson Correlation 0.085 0.300 0.185 0.023 0.281 0.021 -0.001 0.596 0.220 1.000 Sig. (2-tailed) 0.394 0.002 0.073 0.821 0.004 0.833 0.991 0.000 0.028 . Exiting AADT N 102 102 95 99 102 102 98 98 100 102 Table 24. CMFs implied from candidate approach-level models for unit change in variable. Table 25. Correlation analysis of approach-level independent variables.

31 especially relevant to roundabouts for which it is widely believed that speed management is the key to how safe a roundabout is. The models are of the following form: where AADT = average annual daily traffic X = independent speed-related variable b, c = calibration parameters Crashes were modeled with AADT and the observed speeds at various locations through the roundabout as independent variables. Speeds were measured upstream of the entry, at the entry point, at the exit point, and in front of the splitter islands at the entry and exit points. With the available data, only models for crashes between vehicles approaching the roundabout showed any distinct relation- ship to speed. Thirty-six legs had speed data and volume data suitable to calibrating a model for approaching crashes. Table 26 shows the results of this analysis. Appen- dix I presents the statistical results of the various models that were tested. The models, on the whole, were deemed inadequate on the basis of the weak effects of the speed variables. However, the Australian experience (5, 6) and the one relatively successful model shown here indicate that a speed-based model approach is promising and that, with a more elaborate dataset, more can be made of it. At the moment, however, this approach is not recommended. Before-After Analysis The objective of the before-after analysis was to conduct a statistically defensible before-after study to estimate the safety benefits of installing roundabouts. While such studies have previously been done using U.S. data (9, 10), the goal was to build on those studies using a database that was richer in num- ber of intersections and number of years of data, thus provid- ing the ability to further disaggregate the results. In so doing, the hope was that insights could be gained into conditions that Crashes year Intercept AADT cXb/ exp( ) exp( ) (= ⋅ ⋅ 3-5) favor roundabout installation from a safety perspective by examining how the safety effect estimates vary with the fol- lowing factors: • Traffic volumes • Type of control before (signal or stop) • Crash history • Number of legs • Single-lane or multilane designs • Setting (urban versus rural) The empirical Bayes before-after procedure (31) was employed to properly account for regression-to-the-mean while normalizing, where possible, for differences in traffic volume between the before and after periods. The change in safety at a converted intersection for a given crash type is given by where B = the expected number of crashes that would have occurred in the after period without the conversion A = the number of reported crashes in the after period B was estimated using the empirical Bayes procedure in which an SPF for the intersection type before roundabout conversion is used to first estimate the annual number of crashes (P) that would be expected at intersections with traffic volumes and other characteristics similar to the one being evaluated. The SPF crash estimate is then combined with the count of crashes (x) in the n years before conver- sion to obtain a site-specific estimate of the expected annual number of crashes (m) at the intersection before conversion. This estimate of m uses weights estimated from the mean and variance of the regression estimate as follows: where m = expected site-specific annual number of crashes before conversion m w x w P= +1 2 ( )3-7 Change in safety 3-6= −B A ( ) Model No. Overdispersion parameter Intercept Entering AADT Speed Differential (mph) Approach Speed (mph) 1 1.3683 -9.0059 0.8255 0.0622 2* 1.3346 -9.9951 0.8609 0.0521 Legend: Speed Differential = difference between the speed of vehicles approaching the roundabout and the speed of entering vehicles *Recommended model Table 26. Speed-based approach candidate models.

32 x = count of crashes in the n years before conversion P = prediction of annual number of crashes using SPF for intersection with similar characteristics k = dispersion parameter for a given model, esti- mated from the SPF calibration process with the use of a maximum likelihood procedure Factors then are applied to account for the length of the after period and differences in traffic volumes between the before and after periods. The result is an estimate of B. The procedure also produces an estimate of the variance of B. The significance of the difference (BA) is established from this estimate of the variance of B and assuming, based on a Poisson distribution of counts, that In the estimation of changes in crashes, the estimate of B is summed over all intersections in the converted group of interest (to obtain Bsum) and compared with the count of crashes during the after period in that group (Asum). The vari- ance of B is also summed over all conversions. The variance of the after period counts, A, assuming that these are Poisson distributed, is equal to the sum of the counts. The estimate of safety effect, the Index of Effectiveness (θ), is estimated as The percentage change in crashes is equal to 100(1 – θ); thus, a value of θ  0.70 indicates a 30% reduction in crashes. The variance of θ is given by Table 27 lists the base SPFs used as described previously. These data were taken from a variety of reliable sources because data were not collected for this purpose in this project. These base SPFs were recalibrated for use in the spe- cific jurisdictions using data for the sample of roundabout Var Var A A Var B B Var sum sum sum sum( ) ( ) ( ) θ θ= + + 2 2 2 1 ( ) ( ) B B sum sum 2 2⎛ ⎝⎜ ⎞⎠⎟ 3-10 θ = + A B Var B B sum sum sum sum / ( )/ ( ) 1 2 3-9 Var A A( ) ( )= 3-8 w k k nP 2 1 1 = + w P k nP 1 1 = + conversions for the period immediately before conversion. Only the data in the 1 year immediately prior to roundabout construction were used for this purpose to guard against the possibility that a randomly high crash count in earlier years may have prompted the decision to install the roundabout and therefore provide functions that would overestimate safety performance. Examination of annual crash trends in the before periods indicated that this decision was justified. The composite results are shown in Table 28, both in terms of percentage reduction in crashes and the index of effectiveness, θ. Injury crashes are defined as those involv- ing definite injury or fatality. In other words, PDOs and possible injury are excluded. Results are shown separately for various logical groups for which sample sizes were large enough to facilitate a disaggregate analysis. The aggregate results for all sites are reasonably consistent with those from the IIHS and NYSDOT studies. The following conclusions can be drawn: • Control type before. There are large and highly significant safety benefits of converting signalized and two-way- stop–controlled intersections to roundabouts. The benefits are larger for injury crashes than for all crash types com- bined. For the conversions from all-way-stop–controlled intersections, there was no apparent safety effect. • Number of lanes. Disaggregation by number of lanes was possible for urban and suburban roundabouts that were controlled by two-way stops before conversion. The safety benefit was larger for single-lane roundabouts than for two-lane designs, for both urban and suburban settings. All rural roundabouts were single lane. • Setting. The safety benefits for rural installations, which were all single lane, were larger than for urban and subur- ban single-lane roundabouts. • Additional insights. Further disaggregate analysis pro- vided the following insights: – The safety benefits appear to decrease with increasing AADT, irrespective of control type before conversion, number of lanes, and setting. – For various combinations of settings, control type before conversion, and number of lanes for which there were sufficiently large samples, there was no apparent relationship to inscribed or central island diameter. Conclusion The safety analysis described in this chapter results in a set of intersection-level prediction tools, approach-level prediction tools, and the most extensive disaggregation to date of U.S. crash performance before and after conversion to a roundabout. Further discussion of the significance and applicability of these findings can be found in Chapter 6.

Setting Previous Control Number of Legs Source of SPF Data Model Urban Signal 4 Howard and Montgomery Counties, MD Acc/yr = exp(-9.00)(AADT)1.029, k = 0.20 InjAcc/yr = exp(-10.43)(AADT)1.029, k = 0.20 Urban Two-way stop 4 Howard and Montgomery Counties, MD Acc/yr = exp(-1.62)(AADT)0.220, k = 0.45 InjAcc/yr = exp(-3.04)(AADT)0.220, k = 0.45 Urban All-way stop 4 Minnesota – rural sites used due to lack of urban data Acc/yr = exp(-12.972)(AADT)1.465, k = 0.50 InjAcc/yr = exp(-15.032)(AADT)1.493, k=1.67 Urban Signal 3 California Acc/yr = exp(-5.24)(AADT) 0.580 , k = 0.18 InjAcc/yr = exp(-6.51)(AADT)0.580, k = 0.18 Urban Two-way stop 3 Howard and Montgomery Counties, MD Acc/yr = exp(-2.22)(AADT)0.254, k = 0.36 InjAcc/yr = exp(-3.69)(AADT)0.254, k = 0.36 Urban All-way stop 3 Minnesota – rural sites used due to lack of urban data Acc/yr = exp(-12.972)(AADT)1.465, k = 0.50 InjAcc/yr = exp(-15.032)(AADT)1.493, k=1.67 Rural Two-way stop 4 Minnesota Acc/yr = exp(-8.6267)(AADT)0.952, k = 0.77 InjAcc/yr = exp(-8.733)(AADT)0.795, k = 1.25 Rural All-way stop 4 Minnesota Acc/yr = exp(-12.972)(AADT)1.465, k = 0.50 InjAcc/yr = exp(-15.032)(AADT)1.493, k=1.67 Legend: SPF = safety performance function; Acc/yr = total crashes per year; InjAcc/yr = fatal and injury crashes per year); AADT = average annual daily traffic entering the intersection; k = dispersion factor Crashes recorded in after period EB estimate of crashes expected without roundabouts Index of Effectiveness (standard error) & Point Estimate of the Percentage Reduction in Crashes Control Before Sites Setting Lanes All Injury All Injury All Injury All Sites 55 All All 726 72 1122.0 296.1 0.646 (0.034) 35.4% 0.242 (0.032) 75.8% 9 All All 215 16 410.0 70.0 0.522 (0.049) 47.8% 0.223 (0.060) 77.7% 4 Suburban 2 98 2 292.2 Too few 0.333 (0.044) 66.7% Too few to estimate Signalized 5 Urban All 117 14 117.8 34.6 0.986 (0.120) 1.4% 0.399 (0.116) 60.1% All-Way Stop 10 All All 93 17 89.2 12.6 1.033 (0.146) -3.3% 1.282 (0.406) -28.2% 36 All All 418 39 747.6 213.2 0.558 (0.038) 44.2% 0.182 (0.032) 81.8% 9 Rural 1 71 16 247.7 124.7 0.285 (0.040) 71.5% 0.127 (0.034) 87.3% 17 All 102 6 142.7 31.6 0.710 (0.090) 29.0% 0.188 (0.079) 81.2% 12 1 58 5 93.7 22.5 0.612 (0.101) 39.8% 0.217 (0.100) 80.3% 5 Urban 2 44 1 48.9 Too few 0.884 (0.174) 11.6% Too few to estimate 10 All 245 17 357.2 57.0 0.682 (0.067) 31.8% 0.290 (0.083) 71.0% 4 1 17 5 77.1 21.8 0.218 (0.057) 78.2% 0.224 (0.104) 77.6% 6 Suburban 2 228 12 280.1 35.2 0.807 (0.091) 19.3% 0.320 (0.116) 68.0% 27 All 347 23 499.9 88.6 0.692 (0.055) 30.8% 0.256 (0.060) 74.4% 16 1 75 10 162.8 44.3 0.437 (0.060) 56.3% 0.223 (0.074) 77.7% Two-Way Stop 11 Urban/ Suburban 2 272 13 329.0 44.3 0.821 (0.082) 17.9% 0.282 (0.093) 71.8% Table 27. Base safety performance functions used in the empirical Bayes before-after analysis. Table 28. Results for before-after analysis by logical group.