Development of Roundabout Crash Prediction Models and Methods (2019) / Chapter Skim
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From page 53... ...
53 Crash Prediction Model Development Approach This chapter describes the approach taken, including specific considerations, in developing the crash prediction models. The following sections present the specifics of how the planning-level, intersection-level, and leg-level crash prediction models were developed, including the modeling framework, data used, and specific statistical approach.
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54 characteristics under consideration for the planning and network screening level models as well as the crash characteristics in terms of crashes per million entering vehicles (MEV)
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Area Type Circulating Lanes Number of Legs Number of Sites Inscribed Circle Diameter, ft. Sites at a Ramp Terminal Major Road Speed Limit Minor Road Speed Limit Major Road AADT Minor Road AADT Average Stdev Average Stdev Average Stdev Average Stdev Average Stdev Rural 1 3 19 120.0 21.1 0 36.3 9.7 32.9 10.8 8,128 4,033 4,017 2,658 4 58 134.1 27.1 5 44.4 8.7 39.8 10.3 6,988 3,414 3,101 2,027 2 3 7 173.3 39.8 0 47.5 4.2 37.9 9.8 13,110 7,196 5,391 5,198 4 21 172.7 30.7 3 46.5 7.3 39.9 6.5 13,123 6,358 6,298 3,808 Urban 1 3 50 118.5 20.7 1 33.9 8.2 31.4 8.0 7,267 4,100 4,348 2,917 4 108 118.7 25.5 6 34.9 31.7 31.7 8.1 7,882 3,892 3,890 2,455 2 3 28 178.2 54.1 1 37.8 9.0 34.8 8.2 10,531 5,672 5,228 3,914 4 64 184.4 58.7 14 36.6 7.7 31.7 6.6 1,2229 5,835 5,992 4,417 Table 5-1.
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56 • Number of circulating lanes, • Number of legs, • Number of entering lanes per leg, • Number of exiting lanes per leg, • Posted speed limit, and • Inscribed circle diameter. The development of the models is discussed in detail in the following subsections.
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57 STATE term to assess the impact on model accuracy. In the tables, the column, STATE, indicates whether or not the variable was included in the model.
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58 The results in Table 5-7 show little difference between the models estimated with or without the STATE variable. The calibrated overdispersion parameters are larger than for the original models for total and PDO crashes but are a reasonable size.
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59 The AIC measure reflects the overall fit of the model and penalizes for the addition of parameters, and thus selects a model that fits well but has a minimum number of parameters. AIC is not typically used as a goodness-of-fit measure but can be used to compare the relative fit of alternate models.
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60 validation took the model form below. No other independent variables were successfully included in any of the models attempted.
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61 with a maximum cure deviation of 25%, which would be 5 of the 20 observations. The overall assessment of the validation of the urban single- lane roundabout models is that the model form selected for the validation models is performing reasonably well, although some bias is evidenced across the AADT and posted speed variables.
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62 Model Name Variable Name Max Absolute CURE Deviation % CURE Deviation TOT1 [MAJSPD]
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63 Table 5-17 presents the parameter estimates and standard errors (in brackets) for the models developed for each crash type, as well as the negative binomial overdispersion parameters, k.
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64 The results in Table 5-22 indicate that for PDO crashes the model with STATE performs slightly better, while for total and FI crashes the models, with and without STATE perform similarly with no consistency in which performs better across the different variables tested. There is some bias evident in the models with a maximum cure deviation of 35% for MAJAADT with the FI models, which would be 7 of the 20 observations.
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65 Model Name Variable Name Max Absolute CURE Deviation % CURE Deviation TOT1 [MAJSPD]
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66 where N = predicted average crash frequency, crashes/yr; MAJAADT = total entering AADT on major road; MINAADT = total entering AADT on minor road; and NUMBERLEGS = 1 if a 3-leg roundabout; 0 if 4 legs. Table 5-24 presents the parameter estimates and standard errors (in brackets)
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67 of models was calibrated to predict PDO crash frequency. This approach for modeling FI crash frequency is in contrast to that used by some researchers who developed models for other severity combinations, such as the models developed by Rodegerdts et al.
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68 developed to predict vehicle–bicycle crash frequency. However, the frequency of vehicle–pedestrian and vehicle–bicycle crashes at roundabouts is typically very small.
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69 115 roundabouts identified as two circulating lanes actually have some combination of one and two circulating lanes within the roundabout. The inscribed circle diameter describes the circle that best fits the outside edge of the circulating lanes.
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70 this case, the one-way outbound lane corresponded to an entrance ramp for the freeway. A total of 44 roundabouts have a right-turn bypass lane on one or more legs.
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71 (= 1 entering lane + 1 bypass lane) to obtain a more accurate estimate of the actual entry width.
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72 State Number of Legs Number of Sites Total Years FI Crashes PDO Crashes Total MEV Crash Rate, cr/MEV FI PDO Total CA 1 3 1 7.0 2 2 17 0.12 0.12 0.24 2 4 3 21.0 49 163 161 0.30 1.01 1.32 FL 1 3 15 120.0 38 64 494 0.08 0.13 0.21 4 30 259.1 115 249 1,318 0.09 0.19 0.28 2 3 5 43.0 17 20 211 0.08 0.09 0.18 4 13 86.0 79 157 541 0.15 0.29 0.44 KS 2 3 1 7.0 0 5 24 0.00 0.21 0.21 4 5 33.0 9 129 144 0.06 0.90 0.96 MI 1 3 5 13.0 1 16 23 0.04 0.68 0.73 4 20 87.0 22 205 358 0.06 0.57 0.63 2 3 7 26.0 10 92 114 0.09 0.81 0.90 4 10 37.0 19 161 191 0.10 0.84 0.94 MN 1 3 3 21.0 1 5 33 0.03 0.15 0.18 4 13 85.0 23 80 276 0.08 0.29 0.37 2 3 5 28.0 5 17 85 0.06 0.20 0.26 4 6 39.0 21 126 280 0.08 0.45 0.53 NC 1 3 10 70.0 5 20 226 0.02 0.09 0.11 4 16 141.0 29 121 475 0.06 0.25 0.32 2 4 1 10.0 2 21 55 0.04 0.38 0.42 NY 1 3 5 37.0 7 27 202 0.03 0.13 0.17 4 8 62.0 17 85 289 0.06 0.29 0.35 2 3 1 7.0 6 46 58 0.10 0.79 0.90 4 5 41.0 97 439 453 0.21 0.97 1.18 ON 2 3 4 20.0 27 147 177 0.15 0.83 0.99 4 3 15.0 25 283 142 0.18 2.00 2.17 PA 1 3 3 21.0 0 5 54 0.00 0.09 0.09 4 6 38.0 11 31 191 0.06 0.16 0.22 WA 1 3 16 145.1 25 115 588 0.04 0.20 0.24 4 24 232.1 71 315 1,000 0.07 0.31 0.39 2 3 5 41.0 16 60 173 0.09 0.35 0.44 4 12 96.0 168 961 699 0.24 1.37 1.61 WI 1 3 3 18.0 2 13 35 0.06 0.37 0.42 4 34 201.1 90 412 813 0.11 0.51 0.62 2 3 6 34.0 10 63 139 0.07 0.45 0.53 4 23 109.0 92 469 644 0.14 0.73 0.87 Grand Total 327 2,250.6 1,111 5,124 10,681 0.10 0.48 0.58 Circulating Lanes Table 5-29. Crash data summary by state.
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73 crash rates also varies within each jurisdiction. This variation may be the result of differences among enforcement agencies within the jurisdiction with regard to the degree to which they adhere to their jurisdiction's legal reporting threshold.
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74 width is increased. Further examination of the data indicated that there is negligible correlation between entry width and traffic volume.
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75 This trend is consistent with the CMF value for angle to the next leg shown in Figure 2-4. Figure 5-3b shows the relationship between angle to the next leg and crash rate when the data are regrouped according to the number of legs and number of circulating lanes.
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76 where Dk = deviation for leg k, degrees; and Ak = angle to the next leg for leg k, degrees. Representative values for deviation are listed in Table 5-31.
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77 in urban and suburban areas are shown. The trends in this figure suggest that crash rate increases with an increase in the number of circulating lanes and is not likely correlated with circulating width per lane.
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78 a. Combined data.
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79 effect of lighting presence at traditional intersection configurations, as discussed in Section 2.6.2. As shown in Table 5-26, almost all roundabouts included in the assembled database have some lighting.
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80 with an increase in the proportion of total leg AADT associated with legs having a right-turn bypass lane. 5.2.4 Crash Frequency Prediction Model Development This section describes the activities undertaken to develop the models for predicting crash frequency (excluding vehicle– pedestrian and vehicle–bicycle crashes)
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81 where Np = predicted average crash frequency, crashes/yr; C = local calibration factor; NSPF = predicted average crash frequency for base conditions on all legs, crashes/yr; pj = proportion of crashes associated with roundabout leg j (j = 1 to m) ; CMFj,i = CMF for traffic characteristic, geometric element, or traffic control feature i on leg j (i = 1 to n; j = 1 to m)
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82 If the magnitude, direction, and significance were acceptable, then the variable was retained in the model. At the conclusion of the first stage, the calibrated regression model included only variables whose coefficients were considered acceptable.
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83 variables (e.g., entry width) and the variables have the same value at a three-leg roundabout and at a four-leg roundabout, then the CMF value is the same for both roundabouts.
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84 history. Yet this high level of similarity is not evident in the original inverse dispersion parameter values for the PDO crash history at the same three-leg sites (2.07, 0.98)
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85 Comparison of the values in columns 3 and 4 show that the inverse dispersion parameter values are biased to be much larger than the true value for the smaller sample sizes. The adjusted values are shown to be nearer to the true value than the original value for any given sample size.
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86 where X – is the average crash frequency for all n observations, crashes, and all other variables are as previously defined. The last measure of model fit is the dispersion parameter– based coefficient of determination Rk 2.
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87 CMFICD = CMF for inscribed circle diameter at urban roundabouts; EntAADTm = entering AADT for roundabout with m legs (m = 3, 4) , veh/d; Irural = area type indicator variable (= 1.0 if area is rural, 0.0 otherwise)
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88 out the possibility that these factors have an influence on roundabout safety. It is possible that their effect is sufficiently small that it would require either a larger database (with more observations and a wider range in variable values)
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89 on FI crash frequency. The Pearson c2 statistic for the model is 163, and the degrees of freedom are 159 (= n − p = 169 −10)
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90 The calibrated CMFs used with this SPF are described in Section 6.1.2. The fit of the calibrated model is shown in Figure 5-11.
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91 data. The individual site observations were used for model calibration.
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92 This section consists of four subsections. The first subsection describes the structure of the safety predictive models as used in the regression analysis.
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93 where Ica = indicator variable for California (= 1.0 if site is in California, 0.0 otherwise) , and all other variables as previously defined.
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94 on FI crash frequency. The Pearson c2 statistic for the model is 88.7, and the degrees of freedom are 82 (= n − p = 92 −10)
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95 These fit statistics are listed in the top row of Table 5-41. The Pearson c2 statistic for the combined model (= 39.0)
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96 presented in Table 5-44. Calibration of this model focused on FI crash frequency.
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97 these models are applicable only to roundabouts having one circulating lane conflicting with each leg. They are not applicable to roundabouts that have two circulating lanes conflicting with one or more legs.
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98 Equation 5-67 1 1 2 2 3 3CMF p CMF p CMF p CMFlegs ( )
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99 nap,j = number of driveways or unsignalized access points on leg j ( j = 1 to m) (within 250 ft of yield line)
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100 and its transferability to roundabouts not represented in the calibration sites. The validation activity entailed the application of the calibrated model to the sites not included in the calibration database.
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101 As this statistic is less than c20.05, 57 (= 75.6) , the hypothesis that the model fits the data cannot be rejected.
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102 is 148, and the degrees of freedom are 145 (= n − p = 151 − 6)
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103 three- and four-leg roundabouts in urban and rural areas. The generalized form shows all the CMFs in the model.
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104 Wew,b,j = base entry width on leg j (= 20 if one entering lane, 29 if two entering lanes) , ft; CMFcl,j = CMF for number of circulating lanes conflicting with leg j (j = 1 to m)
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105 Model Validation. This subsection describes the findings from a model validation activity.
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106 the model fits the data cannot be rejected. The R2 for the model is 0.17.
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107 points shown in the figure and, thereby, to facilitate an examination of trends in the data. The individual site observations were used for model calibration.
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108 the sites in the database. The second subsection presents the findings from an exploratory analysis of trends in the data.
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109 A total of 42 roundabouts have a right-turn bypass lane on one or more legs. About 75% of these roundabouts are located in urban or suburban areas.
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110 categorized by state, number of circulating lanes, and number of legs. There are 321 roundabout study sites collectively representing nine states.
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111 The values in columns 2 through 6 of Table 5-59 are used to compute the proportions shown in the last four columns. The proportion of K crashes is 0.014 in rural areas and 0.005 in urban areas.
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112 example, the row associated with three legs represents the sum of the crash frequencies for 93 roundabouts. The proportions shown in Table 5-61 indicate that roundabouts with three legs tend to have a larger proportion of K, A, and B crashes, relative to those roundabouts with four legs.
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113 had the same speed limit on the opposing legs (the north and south legs oppose; the east and west legs oppose)
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114 used to predict the proportion of K (fatal) , A (incapacitating- injury)
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115 5.2.6.2 Modeling Approach This section describes several elements of the modeling approach. It consists of four subsections.
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116 Option A Each Year of Data Has Equal Weight.
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117 and 1 Equation 5-102, , , , , , , ,P P P PC q m K q m A q m B q m( ) = − + + with A
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118 variables and other equations. The first step is to evaluate the null model.
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119 Model Development. This subsection describes the proposed prediction model and the methods used to calibrate it.
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120 4 Equation 5-128, , ,4 ,0 , ,S exp b b q bK b q K KA cl KA lg[ ] = + × + × 4 Equation 5-129, , ,4 ,0 , ,S exp b b q bA b q A KA cl KA lg[ ]
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121 to compute the corresponding distribution scores for each severity category. Similarly, the coefficients were combined with Equations 5-128 to 5-130 to obtain the calibrated base distribution score equations for four-leg roundabouts.
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122 State Circulating Lanes Number of Legs Number of Sites Total Years Multiple-Vehicle Crash Count by Crash Type Single-Vehicle Crash Count by Crash Type Unknown Type Total Crashes Head On Right Angle Rear End Sideswipe, Same Dir. Other Animal Fixed Object Other Object Parked Vehicle Other CA 1 3 1 7.0 0 0 1 0 0 0 0 0 0 1 0 2 2 4 3 21.0 2 11 24 0 5 0 3 0 0 4 0 49 FL 1 3 18 134.0 0 5 16 3 8 0 4 0 0 8 1 45 4 37 309.1 4 22 25 5 14 0 31 0 1 22 4 128 2 3 5 43.0 0 1 0 4 3 0 4 0 0 5 0 17 4 13 93.0 0 8 10 7 8 0 11 0 0 18 0 62 KS 2 3 1 7.0 0 0 0 0 0 0 0 0 0 0 0 0 4 1 7.0 0 0 0 0 0 0 0 0 0 0 0 0 MI 1 3 6 16.0 0 2 1 0 0 0 0 0 0 0 0 3 4 20 87.0 0 1 11 1 0 0 8 0 0 1 0 22 2 3 7 26.0 0 0 3 0 1 0 4 0 0 2 0 10 4 11 38.0 0 4 4 2 3 0 5 0 0 1 0 19 MN 1 3 6 45.0 1 1 1 0 0 0 1 0 0 0 0 4 4 19 140.0 0 1 12 2 4 0 7 0 0 3 0 29 2 3 5 28.0 0 1 0 1 0 0 2 0 0 1 0 5 4 6 39.0 0 9 2 7 1 0 1 0 0 1 0 21 NC 1 3 10 70.0 0 0 4 1 0 0 0 0 0 0 0 5 4 16 141.0 0 3 11 1 5 0 0 0 0 9 0 29 2 4 1 10.0 0 1 1 0 0 0 0 0 0 0 0 2 PA 1 3 3 21.0 0 0 0 0 0 0 0 0 0 0 0 0 4 6 38.0 0 5 4 1 0 0 0 0 0 1 0 11 WA 1 3 16 145.1 0 0 12 0 8 0 5 0 0 0 0 25 4 24 232.1 1 0 28 2 8 0 25 0 0 7 0 71 2 3 5 41.0 0 0 4 0 5 0 5 0 0 2 0 16 4 12 96.0 1 0 48 21 60 0 29 0 0 9 0 168 WI 1 3 4 23.0 0 0 0 0 0 0 2 0 0 4 0 6 4 35 205.1 0 11 29 11 1 0 17 0 0 25 0 94 2 3 6 34.0 0 2 1 3 0 0 1 0 0 3 0 10 4 24 118.0 0 17 31 29 3 0 6 0 0 15 0 101 Grand Total 321 2214.6 9 105 283 101 137 0 171 0 1 142 5 954 Table 5-66.
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123 5.2.7.2 PDO Crash Characteristics The database assembled for the project includes 355 roundabouts. However, data for nine roundabouts were removed from the database for various reasons.
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124 State Circulating Lanes Number of Legs Number of Sites Total Years Multiple-Vehicle Crash Count by Crash Type Single-Vehicle Crash Count by Crash Type Unknown Type Total Crashes Head On Right Angle Rear End Sideswipe, Same Dir. Other Animal Fixed Object Other Object Parked Vehicle Other CA 1 3 1 7.0 0 1 0 0 0 0 1 0 0 0 0 2 2 4 3 21.0 1 28 49 0 62 0 22 0 0 1 0 163 FL 1 3 18 134.0 1 16 19 4 14 2 11 0 0 10 6 83 4 38 317.1 14 74 74 3 42 3 28 2 7 37 42 326 2 3 5 43.0 0 1 3 5 3 0 5 0 0 3 0 20 4 14 95.0 11 32 33 28 15 0 9 0 0 14 17 159 KS 2 3 1 7.0 0 1 3 1 0 0 0 0 0 0 0 5 4 5 33.0 2 52 16 48 1 0 7 1 0 2 0 129 MI 1 3 6 16.0 0 3 8 1 0 1 3 0 0 1 0 17 4 20 87.0 1 33 92 15 16 8 33 0 2 5 0 205 2 3 7 26.0 0 14 26 18 13 2 15 0 0 4 0 92 4 11 38.0 0 35 50 38 13 7 21 0 0 1 0 165 MN 1 3 6 45.0 0 0 4 0 0 0 4 0 0 1 0 9 4 19 140.0 0 10 33 6 16 0 40 1 0 4 0 110 2 3 5 28.0 0 2 5 5 0 0 4 0 0 1 0 17 4 6 39.0 0 21 19 45 17 0 23 1 0 0 0 126 NC 1 3 10 70.0 1 5 5 1 2 0 1 1 0 4 0 20 4 16 141.0 0 20 24 10 41 1 15 0 0 10 0 121 2 4 1 10.0 0 13 1 5 1 0 0 0 0 1 0 21 PA 1 3 3 21.0 0 0 0 1 0 0 4 0 0 0 0 5 4 6 38.0 0 7 3 2 0 0 17 0 1 1 0 31 WA 1 3 16 145.1 0 0 24 18 51 0 22 0 0 0 0 115 4 24 232.1 0 0 57 29 146 0 78 0 1 4 0 315 2 3 5 41.0 1 0 6 13 30 0 10 0 0 0 0 60 4 12 96.0 0 0 140 134 525 0 155 2 0 5 0 961 WI 1 3 4 23.0 0 1 1 0 0 0 18 0 0 3 0 23 4 35 205.1 1 106 94 85 2 0 92 0 0 37 1 418 2 3 6 34.0 0 4 10 10 0 0 19 0 0 20 0 63 4 24 118.0 3 94 73 244 10 0 62 0 0 31 0 517 NY 1 3 5 37.0 0 0 3 0 12 0 4 0 0 2 6 27 4 8 62.0 0 18 32 0 16 0 12 0 0 4 3 85 2 3 1 7.0 0 3 16 0 18 0 7 0 0 0 2 46 4 5 41.0 0 95 114 2 162 0 4 0 0 11 51 439 Grand Total 346 2397.7 36 689 1037 771 1228 24 746 8 11 217 128 4895 Table 5-68.
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125 computed using the average crash frequency (in crashes per year) for each site.
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126 where sp,ct = standard error of the proportion p for crash type ct (ct = head on, right angle, or .
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127 to predict the average frequency of crashes associated with a specific roundabout leg, disaggregated by specific crash type. The crash types studied include the following: • Entering-circulating, • Exiting-circulating, • Rear-end on approach, • Single-vehicle on approach, • Circulating-circulating, • Single-vehicle circulating, and • Total.
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128 The database assembled for the leg-level models included 150 roundabouts. From these, only legs with all of entering, exiting, and circulating AADTs available were kept.
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Circulating Lanes Entering Lanes Area Type Number of Legs Inscribed Circle Diameter, ft. Number of Legs with … Average Std.
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130 Circulating Lanes Entering Lanes Area Type Number of Legs Entering AADT Exiting AADT Circulating AADT Average Std.
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131 Alternative model forms were considered with a focus on developing CMFs for roundabout geometry-related variables. Those models were not successful and, therefore, were not adopted.
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132 Equation 5-145 EntCirc exp EntAADT CircAADT exp a b c d ICD e Angle g CircWidth h TwoEnteringLanes = ( ) × + × + × + × Equation 5-147 EntCirc exp EntAADT CircAADT exp a b c e Angle f COS Angle g CircWidth = ( )
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133 Equation 5-148 EntCirc exp EntAADT CircAADT exp a b c d ICD e Angle f COS Angle g CircWidth h TwoEnteringLanes i EntrywidAvg = ( )
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134 Equation 5-149 EntCirc exp EntAADT CircAADT exp a b c d ICD e Angle f COS Angle h TwoEnteringLanes = ( )
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135 For legs with one circulating and either one or two exiting lanes, the parameter estimate for circulating AADT has a large standard error. For legs with two circulating and one exiting lanes, two models were estimated, one with and one without circulating width.
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136 Equation 5-154 RearEnd Approach exp ApprAADT CircAADT exp a b c d NumberAccess e Luminaires = ( ) × + × Equation 5-155 SV Approach exp ApprAADT expa b c PostedSpeed d AreaType+e State= ( )
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137 5.3.3.6 Single-Vehicle Circulating Plus Single-Vehicle Approach Crash Models No models were successfully estimated for single-vehicle circulating crashes. These were combined with single-vehicle approach crashes to estimate a new model.
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138 Equation 5-159 Total exp ApprAADT CircAADT exp a b c d AreaType e TwoExitingLanes f TwoExitingLanes = ( ) × + × + × • Benefit–cost analysis: Design exceptions and funding decisions are often made on the basis of a benefit–cost analysis, so being able to better quantify roundabout design features would help make more informed decisions during different stages of project planning and design.
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139 thesis tested is that at new roundabouts driver behavior may improve with familiarity. This would be seen in a reduction in the frequency and/or severity of crashes over time.
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140 5.5.2 Data Summary for Driver Learning Curve Analysis This section identifies the data used for model estimation. Table 5-95 provides general summary statistics of the data available for investigating a driver learning curve.
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141 Years in Service Total Crashes per MEV KABC Crashes per MEV PDO Crashes per MEV 1 0.721 0.084 0.636 2 0.793 0.096 0.697 3 0.672 0.125 0.546 4 0.763 0.102 0.660 5 0.770 0.121 0.649 6 0.643 0.086 0.557 7 0.606 0.105 0.501 8 0.668 0.120 0.549 9 0.624 0.095 0.529 10 0.483 0.109 0.374 11 0.613 0.104 0.510 12 0.571 0.125 0.446 13 1.423 0.097 1.326 14 1.449 0.505 0.944 Table 5-97. Average crashes per MEV by years in service.
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142 Bagdade, J., B Persaud, K
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