Application of Crash Modification Factors for Access Management, Volume 2: Research Overview (2021)

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81   Introduction This chapter presents the analysis results for intersections and segments with the respective access management strategies. Results are presented and discussed for each access manage- ment strategy, including goodness-of-fit measures, CURE plots, assessment tables, and CMFs to adjust the existing SPFs where applicable. Refer to Appendix C for guidance on inter- preting goodness-of-fit measures, CURE plots, and assessment tables. Note: in all CURE plots, “Series1” includes the cumulative residuals, and “Series2” and “Series3” include the upper and lower 95th percentile limits, respectively. Intersections Distance to Ramp Terminal To consider distance to ramp terminal using the Ohio data, each crash prediction model (3ST, 4ST, 3SG, 4SG) was first calibrated using all available sites. Then all sites without a distance to ramp terminal measurement were removed. This left a small number of locations, so 3ST and 4ST were combined, as were 3SG and 4SG sites. Using these remaining sites, prediction biases were investigated for the calibrated prediction and distance to ramp terminal. Table 67 shows the CURE plot summary results for the Ohio sites, and the CURE plots follow. The CURE plots, shown in Figures 27 through 30, indicated that some bias exists across predicted values for the stop-controlled crash prediction models. For distance to ramp terminal, the CURE plots did not show substantial bias, although the CURE plot does indicate that for distances under 1,500 ft, there may be an under-prediction of crashes. That indicates that a CMF greater than 1.0 may be appropriate for sites where a ramp terminal is within 1,500 ft. For signalized intersections, the CURE plots indicated that the crash prediction models are predicting very well across the range of predicted values and distance to ramp terminal. Even so, CMFs were explored for signalized sites using the same 1,500-ft criteria as for unsignalized sites. The results for the crash-type models are not shown but agree with the results for total crashes in that no substantial bias was seen for either stop- or signal-controlled intersections for single-vehicle, same-direction, opposite-direction, or intersecting-direction crashes. CMFs for distance to ramp terminal were developed using a categorical variable for less than or equal to 1,500 ft. The GLM approach was also applied using the same categorical variable and as a continuous variable but the latter use was unsuccessful. The base condition is a ramp terminal that is more than 1,500 ft away from the intersection. C H A P T E R 7 Analysis Results

82 Application of Crash Modification Factors for Access Management -60 -40 -20 0 20 40 60 0 2 4 6 8 10 12 14 16 18 Cu m ul ati ve R es id ua ls Highway Safety Manual (1st Edition) Calibrated Prediction Series1 Series2 Series3 Figure 27. CURE plot of 3ST and 4ST fitted values. Site Types Number of Sites Number of Crashes Plotted Variable Factor MAX DEV % CURE >2 S.D. 3ST and 4ST 42 218 Fitted value 50.25 26 3ST and 4ST 42 218 Distance to ramp terminal 29.30 2 3SG and 4SG 26 529 Fitted value 47.02 4 3SG and 4SG 26 529 Distance to ramp terminal 50.15 4 MAX DEV = maximum deviation, S.D. = standard deviation. Table 67. CURE plot measures for distance to ramp terminal (Ohio). -50 -40 -30 -20 -10 0 10 20 30 40 50 0 500 1000 1500 2000 2500 3000 Cu m ul ati ve R es id ua ls Distance to Ramp Terminal Series1 Series2 Series3 Figure 28. CURE plot of 3ST and 4ST distance to ramp terminal.

Analysis Results 83   -80 -60 -40 -20 0 20 40 60 80 0 5 10 15 20 25 30 35 40 45 Cu m ul ati ve R es id ua ls Highway Safety Manual (1st Edition) Calibrated Prediction Series1 Series2 Series3 Figure 29. CURE plot of 3SG and 4SG fitted values. -100 -80 -60 -40 -20 0 20 40 60 80 100 0 500 1000 1500 2000 2500 3000 Cu m ul ati ve R es id ua ls Distance to Ramp Terminal Series1 Series2 Series3 Figure 30. CURE plot of 3SG and 4SG distance to ramp terminal.

84 Application of Crash Modification Factors for Access Management Table 68 shows the estimated CMFs, and Table 69 shows the details of the GLM models. For stop-controlled sites, the results logically indicate more crashes when ramp terminals are 1,500 ft or less away. For signalized intersections, the opposite is true, which is counterintuitive. For both sets of results, the magnitude of the standard errors is large, making the results far from statistically significant at the 95 percent confidence level. A validation of the results using the data collected from North Carolina could not be under- taken because only five sites, all 4SG, included a distance to ramp terminal measurement and all were under 1,500 ft. Channelized Right-Turn Lanes To consider channelized right-turn lanes, each crash prediction model (3ST, 4ST, 3SG, 4SG) was calibrated to sites with at least one right-turn lane. Since the Highway Safety Manual (1st Edition) (AASHTO 2010) already has a CMF for the presence of right-turn lanes, the interest here is if the right-turn lanes are channelized. In the analysis, it was assumed that if one right-turn lane was channelized, then all right-turn lanes present were channelized. This was the case for nearly all 38 sites where there was a channelized right-turn lane. Only five of these sites had another right-turn lane that was not channelized. Prediction biases were assessed for the calibrated prediction and presence or absence of channelization for right-turn lanes. For developing the CMF, the base condition is the presence of a right-turn lane with no channelization. Table 70 shows the calibration factors for sites with and without channelization of right- turn lanes. The derived CMFs from these calibration factors are provided as well as the CMFs derived from the GLM models presented in Table 71. The results indicate fewer total crashes with channelization, with the exception of 4SG sites, where the opposite is true. For the GLM models and derived CMFs, only the results for 3SG sites were statistically significant. CMFs by crash type were not explored because there are no Highway Safety Manual (1st Edition) CMFs for right-turn lane presence by crash type. Validation of the results was conducted by comparing the Ohio results to the North Carolina results, with the exception of 4ST sites because none of these was channelized in North Carolina. Site Type Calibration Factor <= 1,500 ft Calibration Factor > 1,500 ft CMF for Distance to Ramp Terminal <= 1,500 ft Using Calibration Factors CMF for Distance to Ramp Terminal < 1,500 ft Using GLM 3ST and 4ST 1.14 0.60 1.90 (1.14) 2.12 (0.91) 3SG and 4SG 0.97 1.04 0.93 (0.46) 0.82 (0.24) Table 68. CMFs for distance to ramp terminal (Ohio). 3ST and 4ST −0.3925 (0.4277) −0.2992 (0.3689) 0.7523 (0.4181) 0.9237 (0.2594) 3SG and 4SG 0.4987 (0.2200) n/a −0.1939 (0.2789) 0.4176 (0.1262) Ramp category = 1 if distance to ramp terminal is less than or equal to 1,500 ft, 0 otherwise. 3ST term used if site is a three-legged intersection, 0 otherwise. se = standard error, a = model coefficient for predictor variable. Table 69. GLM results for distance to ramp terminal (Ohio).

Analysis Results 85   Table 72 shows the estimated CMFs and Table 73 shows the details of the GLM models. As shown in Table 72, the North Carolina results for 4SG and 3SG disagree with the Ohio results. The results of the two states for 3ST agree, and the CMFs are roughly the same magnitude. Since the Ohio results for 3ST agree with the North Carolina results, the data were combined to estimate a CMF. Table 74 shows the details of the combined GLM model. The implied CMF from the GLM model is 0.72 [i.e., exp(–0.3340)] with a standard error of 0.25 [i.e., exp(0.1666)]. Site Type Number of Sites Number of Crashes Calibration Factor for No Right-Turn Channelization Calibration Factor for Right-Turn Channelization CMF for Channelized Right-Turn Using Calibration Factors CMF for Channelized Right-Turn from GLM 4ST 36 190 1.08 0.85 0.79 (0.28) 0.96 (0.36) 4SG 58 1,119 0.95 1.48 1.56 (1.26) 1.27 (0.51) 3ST 62 204 1.07 0.80 0.75 (0.35) 0.69 (0.28) 3SG 38 322 1.09 0.45 0.41 (0.24) 0.42 (0.19) Table 70. CMFs for right-turn lane channelization (Ohio). Site Type Number of Sites Number of Crashes Calibration Factor for No Right-Turn Channelization Calibration Factor for Right-Turn Channelization CMF for Channelized Right-Turn Using Calibration Factors CMF for Channelized Right-Turn from GLM 4ST 5 51 -- -- -- -- 4SG 77 5,195 1.01 0.97 0.96 (0.14) 0.89 (0.18) 3ST 9 55 1.05 0.86 0.82 (0.05) 0.75 (0.32) 3SG 18 529 1.00 1.03 1.03 (0.31) 1.27 (0.64) -- indicates no channelized intersections in the sample. Table 72. CMFs for right-turn lane channelization (North Carolina). Table 71. GLM results for right-turn lane channelization (Ohio). 4ST −0.0519 (0.2082) −0.0393 (0.3668) 0.8291 (0.2528) 4SG 0.4408 (0.1264) 0.2393 (0.3885) 0.7616 (0.1477) 3ST −0.1395 (0.1892) −0.3732 (0.3942) 1.3012 (0.3025) 3SG 0.2265 (0.1485) −0.8614 (0.4438) 0.5963 (0.1789) Channelized right-turn lane = 1 if right-turn lane is channelized, 0 otherwise. se = standard error, a = model coefficient for predictor variable. Table 73. GLM results for right-turn lane channelization (North Carolina). 4ST -- -- -- 4SG 1.3265 (0.1123) −0.1168 (0.2017) 0.6462 (0.1038) 3ST 0.1588 (0.2325) −0.2924 (0.4197) 0.1555 (0.1561) 3SG 0.7779 (0.1600) 0.2383 (0.4843) 0.3681 (0.1382) Channelized right-turn lane = 1 if right-turn lane is channelized, 0 otherwise. --indicates no channelized intersections in the sample. se = standard error, a = model coefficient for predictor variable.

86 Application of Crash Modification Factors for Access Management Segments Median Opening Density Median opening density, defined as median openings per mile, is only relevant for 4D sites. Table 75 presents the goodness-of-fit measures from the CURE plots. There is no evidence in the CURE plots of substantial prediction bias for median opening density. Table 76 shows the details of the GLM model. The estimated GLM model shows crashes decreasing with higher median opening density, the opposite of what would be expected, but the model parameters are not statistically significant at any reasonable level of significance. The results for the crash-type models are not shown but agree with the results for total crashes in that no substantial bias was seen in the CURE plots for rear-end, single-vehicle, sideswipe- same-direction, multivehicle-non-driveway, or nighttime crashes. GLM models for these crash types, shown in Figures 31 and 32, showed no improvement in model fit with the addition of median opening density. A validation of the results was conducted by comparing the Ohio results to the Minnesota results. Table 77 presents the goodness-of-fit measures for the CURE plots shown in Fig- ures 33 and 34. Contrary to Ohio, there is some evidence of prediction bias against the median opening density variable because the % CURE >2 S.D. is greater than 5 percent. Table 78 shows the details of the GLM model. The estimated GLM model indicates a statistically sig- nificant and positive parameter for median opening density, indicating that more crashes are expected with more median openings per mile, which is intuitive but contrary to the Ohio results. Table 74. Combined GLM results for right-turn lane channelization (Ohio and North Carolina). 3ST −0.0989 (0.1666) −0.3340 (0.3377) 1.1280 (0.2504) Channelized right-turn lane = 1 if right-turn lane is channelized, 0 otherwise. se = standard error, a = model coefficient for predictor variable. Table 75. Goodness-of-fit measures for median opening density (Ohio). Site Types Number of Sites Number of Crashes Plotted Variable Factor MAX DEV % CURE >2 S.D. 4D 387 3,247 Fitted Value 111.04 7 4D 387 3,247 Median Opening Density 183.68 5 MAX DEV = maximum deviation, S.D. = standard deviation. Table 76. GLM results for median opening density (Ohio). 4D −0.1319 (0.0654) −0.0025 (0.0076) 0.8943 (0.0938) Median opening density is defined as the number of median openings per mile. se = standard error, a = model coefficient for predictor variable.

Analysis Results 87   -250 -200 -150 -100 -50 0 50 100 150 200 250 0 20 40 60 80 100 120 140 160 Cu m ul ati ve R es id ua ls Highway Safety Manual (1st Edition) Calibrated Prediction Series1 Series2 Series3 Figure 31. CURE plot of 4D fitted values (Ohio). -250 -200 -150 -100 -50 0 50 100 150 200 250 0 10 20 30 40 50 60 70 80 Cu m ul ati ve R es id ua ls Median Opening Density Series1 Series2 Series3 Figure 32. CURE plot of 4D median opening density (Ohio). Site Types Number of Sites Number of Crashes Plotted Variable Factor MAX DEV % CURE >2 S.D. 4D 133 600 Fitted Value 62.64 1 4D 133 600 Median Opening Density 72.92 14 MAX DEV = maximum deviation, S.D. = standard deviation. Table 77. Goodness-of-fit measures for median opening density (Minnesota).

88 Application of Crash Modification Factors for Access Management -80 -60 -40 -20 0 20 40 60 80 0 5 10 15 20 25 Cu m ul ati ve R es id ua ls Highway Safety Manual (1st Edition) Calibrated Prediction Series1 Series2 Series3 Figure 33. CURE plot of 4D fitted values (Minnesota). -100 -80 -60 -40 -20 0 20 40 60 80 0 2 4 6 8 10 12 14 16 18 Cu m ul ati ve R es id ua ls Median Opening Density Series1 Series2 Series3 Figure 34. CURE plot of 4D median opening density (Minnesota). Table 78. GLM results for median opening density (Minnesota). 4D 0.0540 (0.1088) 0.0457 (0.0244) 0.7524 (0.1390) Median opening density is defined as the number of median openings per mile. se = standard error, a = model coefficient for predictor variable.

Analysis Results 89   Median Opening Spacing Median opening spacing is only relevant for 4D segments. To consider median opening spacing, the analysis included only segments with at least one median opening spacing measurement. The two median opening spacing variables considered were the maximum and minimum spacing. Table 79 presents the goodness-of-fit measures for the CURE plots. There is no evidence in the CURE plots of bias for the fitted value or the maximum or minimum median spacing variables. Table 80 shows the details for the GLM models. The estimated GLM models indicate fewer crashes are expected as spacing increases, which is logical, but the standard errors are high, and improvement in model fit was minimal compared to a model with only an intercept term. The results for the crash-type models are not shown but agree with the results for total crashes in that no substantial bias was seen in the CURE plots (shown in Figures 35 and 36), for rear-end, single-vehicle, sideswipe-same-direction, multivehicle-non-driveway, or nighttime crashes. GLM models for these crash types showed no substantial improvement in model fit with the addition of either median opening spacing variable. Validation with the Minnesota data was not possible because only five sites had a measure- ment for median opening spacing. Number of Median Openings by Type The number of median openings is only relevant for 4D segments. To consider the number of median openings by type, all 4D segments were included. Table 81 presents the goodness-of-fit measures for the CURE plots. The CURE plots, shown in Figures 37 through 42, do not show significant bias for full median openings. Some bias is seen when looking at directional median openings or those with left-turn lanes. There is some indication that the crash prediction model over-predicts for larger numbers of median open- ings, indicating that the number of crashes is expected to be lower as the number of median openings increases. This is true for all openings and openings by type. That is contrary to expectations since median openings create more potential conflict points in the segment. Site Types Number of Sites Number of Crashes Plotted Variable Factor MAX DEV % CURE >2 S.D. 4D 214 2,135 Fitted Value 119.31 3 4D 214 2,135 Maximum Median Opening Spacing 85.33 3 4D 214 2,135 Minimum Median Opening Spacing 87.96 0 MAX DEV = maximum deviation, S.D. = standard deviation.. Table 79. Goodness-of-fit measures for median opening spacing (Ohio). Table 80. GLM results for median opening spacing (Ohio). 4D −0.1223 (0.0997) -- −0.1161 (0.1116) 0.7734 (0.1094) 4D −0.0932 (0.1164) −0.0677 (0.0612) -- 0.7719 (0.1093) Maximum median opening spacing is defined as the longest distance between two median-crossing points (i.e., median openings and intersections) within a segment. Minimum median opening spacing is defined as the shortest distance between two median-crossing points (i.e., median openings and intersections) within a segment. -- indicates not applicable. se = standard error, a = model coefficient for predictor variable.

90 Application of Crash Modification Factors for Access Management -200 -150 -100 -50 0 50 100 150 200 0 2000 4000 6000 8000 10000 12000 Cu m ul ati ve R es id ua ls Maximum Median Opening Spacing Series1 Series2 Series3 Figure 35. CURE plot of 4D maximum median opening spacing (Minnesota). -200 -150 -100 -50 0 50 100 150 200 0 2000 4000 6000 8000 10000 12000 Cu m ul ati ve R es id ua ls Minimum Median Opening Spacing Series1 Series2 Series3 Figure 36. CURE plot of 4D minimum median opening spacing (Minnesota).

Analysis Results 91   Site Types Number of Sites Number of Crashes Plotted Variable Factor MAX DEV % CURE >2 S.D. 4D 387 3,247 Fitted Value 111.04 7 4D 387 3,247 Number of Full Median Openings 169.52 3 4D 387 3,247 Number of 1-Direction Median Openings 169.52 7 4D 387 3,247 Number of 2-Direction Median Openings 183.68 9 4D 387 3,247 Number of Full Median Openings with Left-Turn Lane 183.68 6 4D 387 3,247 Number of 1-Direction Median Openings with Left-Turn Lane 184.69 13 4D 387 3,247 Number of 2-Direction Median Openings with Left-Turn Lane 184.69 9 MAX DEV = maximum deviation, S.D. = standard deviation. Table 81. Goodness-of-fit measures for median openings by type (Ohio). -250 -200 -150 -100 -50 0 50 100 150 200 250 0 5 10 15 20 25 30 35 40 Cu m ul ati ve R es id ua ls Number of Full Median Openings Series1 Series2 Series3 Figure 37. CURE plot of 4D number of full median openings (Minnesota).

92 Application of Crash Modification Factors for Access Management -250 -200 -150 -100 -50 0 50 100 150 200 250 0 2 4 6 8 10 Cu m ul ati ve R es id ua ls Number of Two-Directional Median Openings Series1 Series2 Series3 Figure 39. CURE plot of 4D number of two-directional median openings (Minnesota). -250 -200 -150 -100 -50 0 50 100 150 200 250 0 2 4 6 8 10 12 Cu m ul ati ve R es id ua ls Number of One-Directional Median Openings Series1 Series2 Series3 Figure 38. CURE plot of 4D number of one-directional median openings (Minnesota).

Analysis Results 93   -250 -200 -150 -100 -50 0 50 100 150 200 250 0 2 4 6 8 10 Cu m ul ati ve R es id ua ls Number of Full Median Openings with Left-Turn Lane Series1 Series2 Series3 Figure 40. CURE plot of 4D number of full median openings with left-turn lane (Minnesota). -250 -200 -150 -100 -50 0 50 100 150 200 250 0 2 4 6 8 10 12 Cu m ul ati ve R es id ua ls Number of One-Directional Median Openings with Left-Turn Lane Series1 Series2 Series3 Figure 41. CURE plot of 4D number of one-directional median openings with left-turn lane (Minnesota).

94 Application of Crash Modification Factors for Access Management Tables 82 and 83 show the details for the GLM models based on two different model forms. For the GLM models, the parameter estimates also indicate the same trend with a few excep- tions. However, the standard errors are typically high, and improvement in model fit over a model with only an intercept term is marginal. In estimating the GLM models, only sites with zero median openings or the median type of interest were included, thus the base condition would be no median openings. Two model forms were attempted. In Model Form 1, the impact of median openings is multiplicative. In Model Form 2, the impact of median openings is additive. Where no parameter estimates are provided, the models did not converge. The results for the crash-type models are not shown but no bias was found in the estimates for rear-end, single-vehicle, sideswipe-same-direction, multivehicle-non-driveway, or nighttime crashes. Validation of the results was done by comparing the Ohio results to the Minnesota -250 -200 -150 -100 -50 0 50 100 150 200 250 0 1 2 3 4 5 6 7 8 9 Cu m ul ati ve R es id ua ls Number of Two-Directional Median Openings with Left-Turn Lane Series1 Series2 Series3 Figure 42. CURE plot of 4D number of two-directional median openings with left-turn lanes (Minnesota). Table 82. GLM results for median openings by type—Model Form 1 (Ohio). 4D Full Median Openings −0.1116 (0.0682) −0.0009 (0.0177) 0.9663 (0.1103) 4D 1-Direction Median Openings -- -- -- 4D 2-Direction Median Openings (all have left-turn lanes) −0.0901 (0.0902) −1.5687 (1.1415) 1.0449 (0.1677) 4D Full Median Openings with Left-Turn Lane −0.1119 (0.0886) 0.0235 (0.0950) 1.0957 (0.1624) 4D 1-Direction Median Openings with Left-Turn Lane -- -- -- 4D 2-Direction Median Openings with Left-Turn Lane −0.0901 (0.0902) −1.5687 (1.1415) 1.0449 (0.1677) Number of median openings is the total number of median openings for each type within the segment. -- indicates model did not converge. se = standard error, a = model coefficient for predictor variable.

Analysis Results 95   results. In the Minnesota data, most segments have zero median openings. Of those segments that do have median openings, most have only one, and the maximum number is two; therefore, the CURE plots are not very useful, and only the summary numbers are provided. Table 84 presents the goodness-of-fit measures for the CURE plots. There is some evidence of prediction bias against the number of median opening variables where the % CURE >2 S.D. is greater than 5 percent. Tables 85 and 86 show the details for the GLM models based on two different model forms. For the GLM models, the small sample size only allowed for the isolation of results for full median openings. The results indicate that more crashes are expected with an increase in median openings. However, it must be kept in mind that the data are limited to a maximum of two median openings per segment, so the results may not be applicable in all scenarios. The estimated parameters are approaching statistical significance for Model Form 1 but not for Model Form 2. Given the limited number of median openings per segment, the CURE plots are not particularly useful, as this does not represent a continuous variable. Instead, assessment tables are more useful for comparing calibration factors among discrete categories. Table 87 shows assessment table results from the Calibrator, which in essence provide a calibration factor for each level of number of median openings. Refer to Appendix C for guidance on interpreting assessment tables. Site Types Number of Sites Number of Crashes Plotted Variable Factor MAX DEV % CURE >2 S.D. 4D 133 600 Fitted Value 62.64 1 4D 133 600 Number of Full Median Openings 67.42 11 4D 133 600 Number of 1-Direction Median Openings 67.42 11 4D 133 600 Number of 2-Direction Median Openings 66.45 10 4D 133 600 Number of Full Median Openings with Left-Turn Lane 71.60 14 4D 133 600 Number of 1-Direction Median Openings with Left-Turn Lane 73.84 12 4D 133 600 Number of 2-Direction Median Openings with Left-Turn Lane 76.55 17 MAX DEV = maximum deviation, S.D. = standard deviation. Table 84. Goodness-of-fit measures for median openings by type (Minnesota). Table 83. GLM results for median openings by type—Model Form 2 (Ohio). 4D Full Median Openings −0.1200 (0.0715) 0.0254 (0.1269) 0.9663 (0.1103) 4D 1-Direction Median Openings -- -- -- 4D 2-Direction Median Openings (all have left-turn lanes) −0.0900 (0.0902) −15.2024 (4.8699) 1.0449 (0.1677) 4D Full Median Openings with Left-Turn Lane −0.1325 (0.0866) 0.4167 (0.3748) 1.0806 (0.1602) 4D 1-Direction Median Openings with Left-Turn Lane -- -- -- 4D 2-Direction Median Openings with Left-Turn Lane −0.0900 (0.0902) --15.2024 (4.8699) 1.0449 (0.1677) Number of median openings is the total number of median openings for each type within the segment. -- indicates model did not converge. se = standard error, a = model coefficient for predictor variable.

96 Application of Crash Modification Factors for Access Management Corner Clearance The analysis of corner clearance looked at all segment types individually. Table 88 presents the goodness-of-fit measures for the CURE plots. For Ohio, the CURE plots (shown in Figures 43 through 57) for total crashes indicated that there is a general under-prediction in crashes as the minimum, maximum, and average corner clearance distance increases and that the bias is significant. The results are contrary to expectations. Similar to the bias issues for the number of unsignalized access points and signalized intersections, larger corner clearance may not only occur because there are fewer driveways but also because there could be fewer intersections, leading to more crashes being assigned to segments as opposed to intersections. Tables 89 through 91 show the details for the GLM models for minimum, maximum, and average corner clearance, respectively. GLM models were estimated, and all of the statistically significant parameter estimates confirmed that more crashes are associated with segments with larger minimum, maximum, and average corner clearance measurements (i.e., crashes increase as corner clearance increases). A few site type/measurement combinations did have parameter estimates indicating fewer crashes with longer corner clearance measurements, but these were not statistically significant. Table 85. GLM results for median openings by type—Model Form 1 (Minnesota). 4D Full Median Openings 0.0666 (0.1126) 0.2945 (0.1746) 0.7672 (0.1407) 4D 1-Direction Median Openings -- -- -- 4D 2-Direction Median Openings (all have left-turn lanes) -- -- -- 4D Full Median Openings with Left-Turn Lane 0.0688 (0.1135) 0.3147 (0.1787) 0.7829 (0.1444) 4D 1-Direction Median Openings with Left-Turn Lane -- -- -- 4D 2-Direction Median Openings with Left-Turn Lane -- -- -- Number of median openings is the total number of median openings for each type within the segment. -- indicates model did not converge. se = standard error, a = model coefficient for predictor variable. Table 86. GLM results for median openings by type—Model Form 2 (Minnesota). 4D Full Median Openings 0.1188 (0.1095) 0.6232 (0.6446) 0.7833 (0.1427) 4D 1-Direction Median Openings -- -- -- 4D 2-Direction Median Openings (all have left-turn lanes) -- -- -- 4D Full Median Openings with Left-Turn Lane 0.1247 (0.1113) 0.6430 (0.6651) 0.8026 (0.1468) 4D 1-Direction Median Openings with Left-Turn Lane -- -- -- 4D 2-Direction Median Openings with Left-Turn Lane -- -- -- Number of median openings is the total number of median openings for each type within the segment. -- indicates model did not converge. se = standard error, a = model coefficient for predictor variable.

Number of Full Median Openings Number of Openings 0 1 2 Observed 306 267 27 Calibration Bias Factor 0.8256 1.3275 0.9573 Number of Sites 91 38 4 Number of 1-Direction Median Openings Number ofOpenings 0 1 2 Observed 594 6 -- Calibration Bias Factor 1.0058 0.6360 -- Number of Sites 132 1 -- Number of 2-Direction Median Openings Number of Openings 0 1 2 Observed 600 0 -- Calibration Bias Factor 1.0016 0 -- Number of Sites 132 1 -- Number of Jug Handle Median Openings Number of Openings 0 1 2 Observed 600 -- -- Calibration Bias Factor 1 -- -- Number of Sites 133 -- -- Number of Median Openings with Left-Turn Lane Number of Openings 0 1 2 Observed 317 262 21 Calibration Bias Factor 0.8195 1.3476 1.1188 Number of Sites 94 36 3 Number of 1-Direction Median Openings with Left-Turn Lane Number of Openings 0 1 2 Observed 543 57 -- Calibration Bias Factor 0.9832 1.1940 -- Number of Sites 122 11 -- Number of 2-Direction Median Openings with Left-Turn Lane Number of Openings 0 1 2 Observed 366 221 13 Calibration Bias Factor 0.8476 1.4521 0.8119 Number of Sites 104 27 2 -- indicates no data. Table 87. Assessment table results for median openings by type (Minnesota). Site Types Number of Sites Number of Crashes Plotted Variable Factor MAX DEV % CURE >2 S.D. 2U 152 1,131 Fitted Value 95.47 3 2U 152 1,131 Minimum Corner Clearance 203.70 82 2U 152 1,131 Maximum Corner Clearance 144.31 42 2U 152 1,131 Average Corner Clearance 232.83 64 3T 72 499 Fitted Value 47.46 1 3T 72 499 Minimum Corner Clearance 61.04 25 3T 72 499 Maximum Corner Clearance 61.34 36 3T 72 499 Average Corner Clearance 96.43 56 4D 180 1,532 Fitted Value 112.25 9 4D 180 1,532 Minimum Corner Clearance 148.07 26 4D 180 1,532 Maximum Corner Clearance 96.45 1 4D 180 1,532 Average Corner Clearance 90.47 1 4U 137 1,169 Fitted Value 148.66 4 4U 137 1,169 Minimum Corner Clearance 138.02 1 4U 137 1,169 Maximum Corner Clearance 158.05 22 4U 137 1,169 Average Corner Clearance 96.96 1 5T 112 2,190 Fitted Value 294.41 15 5T 112 2,190 Minimum Corner Clearance 237.77 25 5T 112 2,190 Maximum Corner Clearance 270.04 32 5T 112 2,190 Average Corner Clearance 231.66 23 MAX DEV = maximum deviation, S.D. = standard deviation. Table 88. Goodness-of-fit measures for corner clearance (Ohio).

98 Application of Crash Modification Factors for Access Management -250 -200 -150 -100 -50 0 50 100 150 0 200 400 600 800 1000 1200 1400 Cu m ul ati ve R es id ua ls Minimum Corner Clearance Series1 Series2 Series3 Figure 43. CURE plot of 2U minimum corner clearance (Ohio). -200 -150 -100 -50 0 50 100 150 0 5000 10000 15000 20000 25000 Cu m ul ati ve R es id ua ls Maximum Corner Clearance Series1 Series2 Series3 Figure 44. CURE plot of 2U maximum corner clearance (Ohio).

Analysis Results 99   -300 -250 -200 -150 -100 -50 0 50 100 150 0 500 1000 1500 2000 2500 Cu m ul ati ve R es id ua ls Average Corner Clearance Series1 Series2 Series3 Figure 45. CURE plot of 2U average corner clearance (Ohio). -80 -60 -40 -20 0 20 40 60 80 0 50 100 150 200 250 300 350 400 Cu m ul ati ve R es id ua ls Minimum Corner Clearance Series1 Series2 Series3 Figure 46. CURE plot of 3T minimum corner clearance (Ohio).

100 Application of Crash Modification Factors for Access Management -80 -60 -40 -20 0 20 40 60 80 0 100 200 300 400 500 600 700 800 Cu m ul ati ve R es id ua ls Maximum Corner Clearance Series1 Series2 Series3 Figure 47. CURE plot of 3T maximum corner clearance (Ohio). -120 -100 -80 -60 -40 -20 0 20 40 60 80 0 100 200 300 400 500 600 Cu m ul ati ve R es id ua ls Average Corner Clearance Series1 Series2 Series3 Figure 48. CURE plot of 3T average corner clearance (Ohio).

Analysis Results 101   -200 -150 -100 -50 0 50 100 150 0 200 400 600 800 1000 1200 Cu m ul ati ve R es id ua ls Minimum Corner Clearance Series1 Series2 Series3 Figure 49. CURE plot of 4D minimum corner clearance (Ohio). -150 -100 -50 0 50 100 150 0 200 400 600 800 1000 1200 1400 1600 Cu m ul ati ve R es id ua ls Maximum Corner Clearance Series1 Series2 Series3 Figure 50. CURE plot of 4D maximum corner clearance (Ohio).

102 Application of Crash Modification Factors for Access Management -150 -100 -50 0 50 100 150 0 200 400 600 800 1000 1200 1400 Cu m ul ati ve R es id ua ls Average Corner Clearance Series1 Series2 Series3 Figure 51. CURE plot of 4D average corner clearance (Ohio). -200 -150 -100 -50 0 50 100 150 200 0 200 400 600 800 1000 1200 1400 1600 Cu m ul ati ve R es id ua ls Minimum Corner Clearance Series1 Series2 Series3 Figure 52. CURE plot of 4U minimum corner clearance (Ohio).

Analysis Results 103   -200 -150 -100 -50 0 50 100 150 200 0 500 1000 1500 2000 2500 Cu m ul ati ve R es id ua ls Maximum Corner Clearance Series1 Series2 Series3 Figure 53. CURE plot of 4U maximum corner clearance (Ohio). -200 -150 -100 -50 0 50 100 150 200 0 200 400 600 800 1000 1200 1400 1600 Cu m ul ati ve R es id ua ls Average Corner Clearance Series1 Series2 Series3 Figure 54. CURE plot of 4U average corner clearance (Ohio).

104 Application of Crash Modification Factors for Access Management -300 -200 -100 0 100 200 300 0 100 200 300 400 500 600 Cu m ul ati ve R es id ua ls Minimum Corner Clearance Series1 Series2 Series3 Figure 55. CURE plot of 5T minimum corner clearance (Ohio). -300 -200 -100 0 100 200 300 0 200 400 600 800 1000 1200 1400 1600 1800 Cu m ul ati ve R es id ua ls Maximum Corner Clearance Series1 Series2 Series3 Figure 56. CURE plot of 5T maximum corner clearance (Ohio).

Analysis Results 105   -300 -200 -100 0 100 200 300 0 200 400 600 800 1000 1200 1400 Cu m ul ati ve R es id ua ls Average Corner Clearance Series1 Series2 Series3 Figure 57. CURE plot of 5T average corner clearance (Ohio). Table 89. GLM results for minimum corner clearance (Ohio). 2U −0.6766 (0.1478) 1.9205 (0.9804) 1.3984 (0.2230) 3T −1.0037 (0.2480) 4.0794 (1.9871) 1.3623 (0.3116) 4D −0.0524 (0.1146) −0.1193 (0.4503) 0.8073 (0.1248) 4U −0.8615 (0.1653) 0.8193 (1.2780) 1.7510 (0.2512) 5T −1.2807 (0.1417) 3.4903 (0.9748) 1.0437 (0.1714) Corner clearance is defined as the distance from the nearest driveway on the mainline to the corner of the intersection. Minimum corner clearance is the shortest corner clearance among all intersections within the segment. se = standard error, a = model coefficient for predictor variable. Table 90. GLM results for maximum corner clearance (Ohio). 2U −0.4512 (0.1183) −0.0160 (0.0791) 1.4744 (0.2304) 3T −1.5329 (0.4149) 2.7546 (1.1491) 1.3428 (0.3055) 4D 0.0682 (0.1670) −0.3340 (0.3424) 0.8020 (0.1239) 4U −0.6548 (0.1947) −0.3899 (0.4390) 1.7468 (0.2509) 5T −1.2629 (0.2119) 0.9682 (0.4614) 1.1845 (0.1871) Corner clearance is defined as the distance from the nearest driveway on the mainline to the corner of the intersection. Maximum corner clearance is the longest corner clearance among all intersections within the segment. se = standard error, a = model coefficient for predictor variable.

106 Application of Crash Modification Factors for Access Management For crash-type models, there was little evidence of bias, and GLM models were not very strong in general. Those models that could be estimated showed little improvement in overall goodness of fit with the addition of corner clearance variables. Validation of the results was conducted by comparing the Ohio results to the Minnesota results. Table 92 presents the goodness-of-fit measures for the CURE plots shown in Figures 58 through 72. Some bias is seen in the predictions, particularly for 2U maximum and average spacing. Tables 93 through 95 show the details for the GLM models for minimum, maximum, and average corner clearance, respectively. The GLM models, more often than not, were logical in predicting fewer crashes with increasing corner clearance, but the parameter estimates were not statistically significant at any reasonable level of significance. An additional analysis was undertaken to see if the trends for corner clearance measure- ments hold for the corner clearance for vehicles arriving versus departing the intersection. GLM models were run using the Ohio data. Tables 96 through 98 show the details of the GLM models for minimum, maximum, and average corner clearance by approaching and departing leg. Site Types Number of Sites Number of Crashes Plotted Variable Factor MAX DEV % CURE >2 S.D. 2U 64 134 Fitted Value 23.55 64 2U 64 134 Minimum Corner Clearance 20.53 3 2U 64 134 Maximum Corner Clearance 22.77 38 2U 64 134 Average Corner Clearance 21.29 14 3T 24 49 Fitted Value 8.51 21 3T 24 49 Minimum Corner Clearance 6.77 0 3T 24 49 Maximum Corner Clearance 4.59 0 3T 24 49 Average Corner Clearance 5.37 0 4D 37 207 Fitted Value 33.47 11 4D 37 207 Minimum Corner Clearance 35.80 16 4D 37 207 Maximum Corner Clearance 16.86 3 4D 37 207 Average Corner Clearance 17.98 0 4U 45 103 Fitted Value 8.51 2 4U 45 103 Minimum Corner Clearance 9.25 2 4U 45 103 Maximum Corner Clearance 12.76 16 4U 45 103 Average Corner Clearance 12.53 11 5T 21 109 Fitted Value 7.92 10 5T 21 109 Minimum Corner Clearance 8.70 5 5T 21 109 Maximum Corner Clearance 9.95 10 5T 21 109 Average Corner Clearance 7.07 5 MAX DEV = maximum deviation, S.D. = standard deviation. Table 92. Goodness-of-fit measures for corner clearance (Minnesota). Table 91. GLM results for average corner clearance (Ohio). 2U −0.7913 (0.1897) 1.3655 (0.6825) 1.4080 (0.2228) 3T −1.7116 (0.4058) 5.4220 (1.8941) 1.2635 (0.2927) 4D 0.0173 (0.1536) −0.3121 (0.4464) 0.8068 (0.1244) 4U −0.8355 (0.2081) 0.2554 (0.8965) 1.7576 (0.2518) 5T −1.5211 (0.2009) 2.8135 (0.8040) 1.0754 (0.1740) Corner clearance is defined as the distance from the nearest driveway on the mainline to the corner of the intersection. Average corner clearance is the average value of all corner clearance measurements within the segment. se = standard error, a = model coefficient for predictor variable.

Analysis Results 107   -25 -20 -15 -10 -5 0 5 10 15 20 25 0 200 400 600 800 1000 1200 1400 1600 Cu m ul ati ve R es id ua ls Minimum Corner Clearance Series1 Series2 Series3 Figure 58. CURE plot of 2U minimum corner clearance (Minnesota). -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 0 20000 40000 60000 80000 100000 120000 Cu m ul ati ve R es id ua ls Maximum Corner Clearance Series1 Series2 Series3 Figure 59. CURE plot of 2U maximum corner clearance (Minnesota).

108 Application of Crash Modification Factors for Access Management -25 -20 -15 -10 -5 0 5 10 15 20 25 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 Cu m ul ati ve R es id ua ls Average Corner Clearance Series1 Series2 Series3 Figure 60. CURE plot of 2U average corner clearance (Minnesota). -15 -10 -5 0 5 10 15 0 200 400 600 800 1000 1200 1400 Cu m ul ati ve R es id ua ls Minimum Corner Clearance Series1 Series2 Series3 Figure 61. CURE plot of 3T minimum corner clearance (Minnesota).

Analysis Results 109   -15 -10 -5 0 5 10 15 0 200 400 600 800 1000 1200 1400 Cu m ul ati ve R es id ua ls Maximum Corner Clearance Series1 Series2 Series3 Figure 62. CURE plot of 3T maximum corner clearance (Minnesota). -15 -10 -5 0 5 10 15 0 200 400 600 800 1000 1200 1400 Cu m ul ati ve R es id ua ls Average Corner Clearance Series1 Series2 Series3 Figure 63. CURE plot of 3T average corner clearance (Minnesota).

110 Application of Crash Modification Factors for Access Management -40 -30 -20 -10 0 10 20 30 40 0 100 200 300 400 500 600 700 800 900 Cu m ul ati ve R es id ua ls Minimum Corner Clearance Series1 Series2 Series3 Figure 64. CURE plot of 4D minimum corner clearance (Minnesota). -30 -20 -10 0 10 20 30 0 100 200 300 400 500 600 700 800 900 Cu m ul ati ve R es id ua ls Maximum Corner Clearance Series1 Series2 Series3 Figure 65. CURE plot of 4D maximum corner clearance (Minnesota).

Analysis Results 111   -40 -30 -20 -10 0 10 20 30 40 0 100 200 300 400 500 600 700 800 900 Cu m ul ati ve R es id ua ls Average Corner Clearance Series1 Series2 Series3 Figure 66. CURE plot of 4D average corner clearance (Minnesota). -20 -15 -10 -5 0 5 10 15 20 0 100 200 300 400 500 600 700 Cu m ul ati ve R es id ua ls Minimum Corner Clearance Series1 Series2 Series3 Figure 67. CURE plot of 4U minimum corner clearance (Minnesota).

112 Application of Crash Modification Factors for Access Management -20 -15 -10 -5 0 5 10 15 20 0 500 1000 1500 2000 2500 3000 Cu m ul ati ve R es id ua ls Maximum Corner Clearance Series1 Series2 Series3 Figure 68. CURE plot of 4U maximum corner clearance (Minnesota). -15 -10 -5 0 5 10 15 0 100 200 300 400 500 600 700 800 900 Cu m ul ati ve R es id ua ls Average Corner Clearance Series1 Series2 Series3 Figure 69. CURE plot of 4U average corner clearance (Minnesota).

Analysis Results 113   -20 -15 -10 -5 0 5 10 15 20 0 100 200 300 400 500 Cu m ul ati ve R es id ua ls Minimum Corner Clearance Series1 Series2 Series3 Figure 70. CURE plot of 5T minimum corner clearance (Minnesota). -20 -15 -10 -5 0 5 10 15 20 0 200 400 600 800 1000 1200 Cu m ul ati ve R es id ua ls Maximum Corner Clearance Series1 Series2 Series3 Figure 71. CURE plot of 5T maximum corner clearance (Minnesota).

114 Application of Crash Modification Factors for Access Management -20 -15 -10 -5 0 5 10 15 20 0 100 200 300 400 500 600 700 800 Cu m ul ati ve R es id ua ls Average Corner Clearance Series1 Series2 Series3 Figure 72. CURE plot of 5T average corner clearance (Minnesota). Table 93. GLM results for minimum corner clearance (Minnesota). 2U −0.5912 (0.1523) 0.6958 (0.3378) 0.2508 (0.1441) 3T −0.4166 (0.2547) −0.4830 (0.8572) 0.4346 (0.3083) 4D 0.5651 (0.2346) −0.4540 (0.7781) 0.5204 (0.1948) 4U −0.2990 (0.2085) −0.1058 (1.1698) 0.3430 (0.1818) 5T −0.2469 (0.2806) −2.3187 (1.8628) 0.3078 (0.1712) se = standard error, a = model coefficient for predictor variable. Corner clearance is defined as the distance from the nearest driveway on the mainline to the corner of the intersection. Minimum corner clearance is the shortest corner clearance among all intersections within the segment. Table 94. GLM results for maximum corner clearance (Minnesota). 2U −0.3974 (0.1254) −0.0028 (0.0093) 0.3495 (0.1660) 3T −0.3588 (0.3186) −0.4818 (0.8263) 0.4257 (0.3071) 4D 0.1284 (0.3859) 0.6629 (0.7244) 0.5235 (0.1931) 4U −0.1016 (0.1830) −0.6307 (0.3938) 0.2824 (0.1671) 5T −0.6041 (0.3038) 0.2190 (0.7629) 0.3549 (0.1867) Corner clearance is defined as the distance from the nearest driveway on the mainline to the corner of the intersection. Maximum corner clearance is the longest corner clearance among all intersections within the segment. se = standard error, a = model coefficient for predictor variable.

Table 95. GLM results for average corner clearance (Minnesota). 2U −0.4028 (0.1292) −0.0018 (0.0545) 0.3523 (0.1666) 3T −0.3832 (0.2862) −0.5067 (0.8578) 0.4286 (0.3072) 4D 0.4692 (0.3445) −0.0316 (0.8924) 0.5318 (0.1973) 4U −0.0876 (0.2238) −0.9831 (0.7938) 0.3034 (0.1740) 5T −0.4214 (0.3118) −0.5253 (1.2443) 0.3450 (0.1845) Corner clearance is defined as the distance from the nearest driveway on the mainline to the corner of the intersection. Average corner clearance is the average value of all corner clearance measurements within the segment. se = standard error, a = model coefficient for predictor variable. Table 96. GLM results for minimum corner clearance by upstream/downstream corner (Ohio). 2U −0.7490 (0.1630) 0.0019 (0.0010) 1.3996 (0.2233) −0.6047 (0.1437) 0.0007 (0.0007) 1.4422 (0.2320) 3T −1.1292 (0.2380) 0.0040 (0.0015) 1.2960 (0.3104) −0.9660 (0.2574) 0.0030 (0.0017) 1.3653 (0.3063) 4D −0.1444 (0.1292) 0.0002 (0.0004) 0.7886 (0.1258) 0.0004 (0.1196) −0.0003 (0.0004) 0.8191 (0.1285) 4U −1.0071 (0.1609) 0.0007 (0.0009) 1.5630 (0.2375) −0.8511 (0.1797) 0.0011 (0.0014) 1.6575 (0.2391) 5T −1.1620 (0.1470) 0.0012 (0.0008) 1.1020 (0.1749) −1.3212 (0.1423) 0.0031 (0.0008) 1.1015 (0.1733) Corner clearance is defined as the distance from the nearest driveway on the mainline to the corner of the intersection. Upstream corners are the corners on which vehicles are moving toward the intersection. Downstream corners are the corners on which vehicles just passed the intersection and are moving away from it. Minimum corner clearance is the shortest corner clearance among upstream or downstream corners within the segment. se = standard error, a = model coefficient for predictor variable. Table 97. GLM results for maximum corner clearance by upstream/downstream corner (Ohio). 2U −0.7692 (0.1760) 0.0008 (0.0004) 1.3858 (0.2206) −0.4984 (0.1177) −0.0000 (0.0001) 1.4600 (0.2333) 3T −0.9942 (0.3681) 0.0016 (0.0012) 1.5119 (0.3484) −1.0210 (0.3542) 0.0016 (0.0011) 1.3982 (0.3128) 4D −0.1192 (0.1619) 0.0001 (0.0004) 0.7918 (0.1260) 0.2292 (0.1453) −0.0008 (0.0003) 0.7923 (0.1244) 4U −0.8383 (0.1706) −0.0003 (0.0004) 1.5685 (0.2379) −0.6245 (0.1937) −0.0005 (0.0005) 1.6511 (0.2391) 5T −1.2907 (0.1820) 0.0008 (0.0005) 1.0898 (0.1734) −1.4064 (0.1915) 0.0015 (0.0005) 1.1746 (0.1812) Corner clearance is defined as the distance from the nearest driveway on the mainline to the corner of the intersection. Upstream corners are the corners on which vehicles are moving toward the intersection. Downstream corners are the corners on which vehicles just passed the intersection and are moving away from it. Maximum corner clearance is the longest corner clearance among upstream or downstream corners within the segment. se = standard error, a = model coefficient for predictor variable.

116 Application of Crash Modification Factors for Access Management Similar to the previous Ohio models that did not differentiate between arriving or departing corner clearance, the new GLM models also indicated that in most cases more crashes are asso- ciated with segments with larger minimum, maximum, or average corner clearance measure- ments. A few site type/measurement combinations did have parameter estimates indicating fewer crashes with longer corner clearance measurements; however, most parameter estimates were not statistically significant. Signalized Intersection Spacing The structure of the data for the Highway Safety Manual (1st Edition) Part C Predictive Method is such that roadways are segmented by intersection and midblock areas, and crashes are assigned to one of the two. One of the important findings of this research was that as the number of intersections in a segment increased, the expected number of segment crashes often decreased. This is contrary to expectations since the presence of more intersections should lead to more conflicts, certainly not fewer, even away from the intersections. However, the structure of the data may contribute to this counterintuitive finding. Specifically, if more intersections are present, then it is more likely that a crash will be assigned to an intersection and not a segment. This finding suggests the data are not conducive to segment-level analysis of some variables (e.g., intersection density, spacing, etc.). Instead, these variables are better assessed at the cor- ridor level. Corridor-level analyses are discussed in Chapter 5 of NCHRP Research Report 974, Volume 1: Practitioner’s Guide (Gross et al. 2021). There were limited sites in the dataset with information on minimum and maximum spacing. As such, signalized intersection spacing could not be analyzed. This is again a result of the structure of the data. Signalized intersections often define the start and end points of segments; in measuring signalized intersection spacing, the signalized intersections at either end of the segment are not counted. Number of Signalized Intersections and Density The structure of the data for the Highway Safety Manual (1st Edition) Part C Predictive Method is such that roadways are segmented by intersection and midblock areas, and crashes Table 98. GLM results for average corner clearance by upstream/downstream corner (Ohio). 2U −1.1015 (0.1943) 0.0027 (0.0008) 1.2702 (0.2090) −0.6005 (0.1631) 0.0004 (0.0005) 1.4551 (0.2326) 3T −1.2763 (0.3296) 0.0034 (0.0015) 1.3725 (0.3252) −1.3683 (0.3724) 0.0039 (0.0017) 1.3188 (0.2988) 4D −0.1684 (0.1582) 0.0003 (0.0004) 0.7885 (0.1258) 0.1290 (0.1398) −0.0007 (0.0004) 0.8109 (0.1268) 4U −0.9659 (0.1837) 0.0002 (0.0007) 1.5744 (0.2384) −0.8001 (0.2112) 0.0003 (0.0010) 1.6643 (0.2399) 5T −1.3044 (0.1859) 0.0013 (0.0007) 1.0875 (0.1729) −1.5552 (0.1834) 0.0030 (0.0008) 1.0882 (0.1716) Corner clearance is defined as the distance from the nearest driveway on the mainline to the corner of the intersection. Upstream corners are the corners on which vehicles are moving toward the intersection. Downstream corners are the corners on which vehicles just passed the intersection and are moving away from it. Average corner clearance is the average value of all corner clearance measurements among upstream and downstream corners within the segment. se = standard error, a = model coefficient for predictor variable.

Analysis Results 117   are assigned to one of the two. One of the important findings of this research was that as the number of intersections in a segment increased, the expected number of segment crashes often decreased. This is contrary to expectations since the presence of more intersections should lead to more conflicts, certainly not fewer, even away from the intersections. How- ever, the structure of the data may contribute to this counterintuitive finding. Specifically, if more intersections are present, then it is more likely that a crash will be assigned to an inter- section and not a segment. This finding suggests the data are not conducive to segment-level analysis of some variables (e.g., intersection density, spacing, etc.). Instead, these variables are better assessed at the corridor level. Corridor-level analyses are discussed in Chapter 5 of NCHRP Research Report 974, Volume 1: Practitioner’s Guide (Gross et al. 2021). The find- ings at the segment level are still presented next for completeness, but again, the results are counterintuitive. The analysis of number and density of signalized intersections looked at all segment types individually. The CURE plots of the Ohio data provide some evidence of bias, including: • 2U—number of signals and signalized intersection density; • 4D—number of signals and signalized intersection density; • 4U—number of signals and signalized intersection density; and • 5T—fitted value, number of signals, and signalized intersection density. Table 99 presents the goodness-of-fit measures for the CURE plots shown in Figure 73 through Figure 82. Table 100 and Table 101 show the details for the GLM models for signal- ized intersection density and the number of signalized intersections, respectively. The results are similar to unsignalized access (combined unsignalized intersections and driveways) in that for most site types, more signals and increased signal density are associated with fewer segment crashes; however, most parameter estimates are not statistically significant if added to a GLM model. The model fit of the GLM models also seems little improved when adding additional variables. Again, the reason for this could be that the Highway Safety Manual (1st Edition) approach measures the entire length of the segment, but intersection-related crashes are not included in the segment crash total. As the number of signalized intersections increases, the likelihood that a crash is not counted as a segment crash may increase as well. The results for crash-type models similarly showed few signs of significant bias. GLM models consistently had statistically insignificant parameter estimates and did not improve model fit. Site Types Number of Sites Number of Crashes Plotted Variable Factor MAX DEV % CURE >2 S.D. 2U 337 1,975 Fitted Value 71.68 1 2U 337 1,975 Number of Signalized Intersections 194.25 11 2U 337 1,975 Signalized Intersection Density 218.02 15 3T 113 624 Fitted Value 44.97 1 3T 113 624 Number of Signalized Intersections 41.98 1 3T 113 624 Signalized Intersection Density 57.34 1 4D 387 3,247 Fitted Value 111.04 7 4D 387 3,247 Number of Signalized Intersections 266.58 39 4D 387 3,247 Signalized Intersection Density 298.90 22 4U 216 1,408 Fitted Value 167.83 9 4U 216 1,408 Number of Signalized Intersections 187.06 18 4U 216 1,408 Signalized Intersection Density 141.87 6 5T 157 2,779 Fitted Value 399.26 27 5T 157 2,779 Number of Signalized Intersections 299.01 15 5T 157 2,779 Signalized Intersection Density 226.40 13 MAX DEV = maximum deviation; S.D. = standard deviation. Table 99. Goodness-of-fit measures for signalized intersections (Ohio).

118 Application of Crash Modification Factors for Access Management -150 -100 -50 0 50 100 150 200 250 0 1 2 3 4 5 6 7 8C um ul ati ve R es id ua ls Number of Signalized Intersections Series1 Series2 Series3 Figure 73. CURE plot of 2U number of signalized intersections (Ohio). -150 -100 -50 0 50 100 150 200 250 0 5 10 15 20 25 30C um ul ati ve R es id ua ls Signalized Intersection Density Series1 Series2 Series3 Figure 74. CURE plot of 2U signalized intersection density (Ohio).

Analysis Results 119   -80 -60 -40 -20 0 20 40 60 80 0 1 2 3 4 5 6 Cu m ul ati ve R es id ua ls Number of Signalized Intersections Series1 Series2 Series3 Figure 75. CURE plot of 3T number of signalized intersections (Ohio). -80 -60 -40 -20 0 20 40 60 80 0 5 10 15 20 Cu m ul ati ve R es id ua ls Signalized Intersection Density Series1 Series2 Series3 Figure 76. CURE plot of 3T signalized intersection density (Ohio).

120 Application of Crash Modification Factors for Access Management -300 -200 -100 0 100 200 300 0 5 10 15 20 25 30 Cu m ul ati ve R es id ua ls Number of Signalized Intersections Series1 Series2 Series3 Figure 77. CURE plot of 4D number of signalized intersections (Ohio). -400 -300 -200 -100 0 100 200 300 0 5 10 15 20 25 30 Cu m ul ati ve R es id ua ls Signalized Intersection Density Series1 Series2 Series3 Figure 78. CURE plot of 4D signalized intersection density (Ohio).

Analysis Results 121   -200 -150 -100 -50 0 50 100 150 200 250 0 2 4 6 8 10 12 14 16 18 Cu m ul ati ve R es id ua ls Number of Signalized Intersections Series1 Series2 Series3 Figure 79. CURE plot of 4U number of signalized intersections (Ohio). -200 -150 -100 -50 0 50 100 150 200 0 5 10 15 20 25 30 Cu m ul ati ve R es id ua ls Signalized Intersection Density Series1 Series2 Series3 Figure 80. CURE plot of 4U signalized intersection density (Ohio).

122 Application of Crash Modification Factors for Access Management -400 -300 -200 -100 0 100 200 300 0 2 4 6 8 10 12 Cu m ul ati ve R es id ua ls Number of Signalized Intersections Series1 Series2 Series3 Figure 81. CURE plot of 5T number of signalized intersections (Ohio). -300 -200 -100 0 100 200 300 0 5 10 15 20 25 Cu m ul ati ve R es id ua ls Signalized Intersection Density Series1 Series2 Series3 Figure 82. CURE plot of 5T signalized intersection density (Ohio).

Analysis Results 123   Validation of the results was done by comparing the Ohio results to the Minnesota results. Table 102 presents the goodness-of-fit measures for the CURE plots shown in Figures 83 through 92. In the Minnesota data, most sites did not have a signal within the segment, and those that did mostly had only one and at most two, so the data are not very useful for developing CURE plots. As such, CURE plot results are only shown for signal density. There is some evidence of bias from the CURE plot measures for • 3T—signalized intersection density, and • 5T—fitted value and signalized intersection density. Site Types Number of Sites Number of Crashes Plotted Variable Factor MAX DEV % CURE >2 S.D. 2U 140 263 Fitted Value 23.14 1 2U 140 263 Signalized Intersection Density 28.05 1 3T 47 91 Fitted Value 6.95 9 3T 47 91 Signalized Intersection Density 7.99 9 4D 133 600 Fitted Value 62.64 1 4D 133 600 Signalized Intersection Density 46.70 3 4U 95 195 Fitted Value 10.07 1 4U 95 195 Signalized Intersection Density 19.14 6 5T 28 130 Fitted Value 10.33 7 5T 28 130 Signalized Intersection Density 12.42 11 MAX DEV = maximum deviation; S.D. = standard deviation. Table 102. Goodness-of-fit measures for signalized intersections (Minnesota). Table 100. GLM results for signalized intersection density (Ohio). 2U −0.1505 (0.0792) −0.2870 (0.2540) 1.4634 (0.1653) 3T −0.4612 (0.1760) −0.2783 (0.5693) 1.4314 (0.2716) 4D −0.1941 (0.0731) 0.2724 (0.2645) 0.8916 (0.0935) 4U −0.7008 (0.0985) −0.4049 (0.2082) 1.3792 (0.1540) 5T -- -- -- Signalized intersection density is defined as the total number of signalized intersections within the segment, without counting either end of the segment, per mile. -- indicates the model did not converge. se = standard error, a = model coefficient for predictor variable. Table 101. GLM results for signalized intersection count (Ohio). 2U −0.1804 (0.0780) −0.0272 (0.0301) 1.3925 (0.1531) 3T −0.5649 (0.1605) 0.0175 (0.0366) 1.4249 (0.2707) 4D −0.1793 (0.0696) 0.0135 (0.0159) 0.8932 (0.0937) 4U −0.7287 (0.1275) −0.0246 (0.0304) 1.6783 (0.2061) 5T −0.8562 (0.1268) −0.0243 (0.0341) 1.1831 (0.1607) Number of signalized intersections is the total number of signalized intersections within the segment, without counting either end of the segment. se = standard error, a = model coefficient for predictor variable.

124 Application of Crash Modification Factors for Access Management -40 -30 -20 -10 0 10 20 30 40 0 2 4 6 8 10 12 Cu m ul ati ve R es id ua ls Highway Safety Manual (1st Edition) Calibrated Prediction Series1 Series2 Series3 Figure 83. CURE plot of 2U fitted values (Minnesota). -40 -30 -20 -10 0 10 20 30 40 0 2 4 6 8 10 Cu m ul ati ve R es id ua ls Signalized Intersection Density Series1 Series2 Series3 Figure 84. CURE plot of 2U signalized intersection density (Minnesota).

Analysis Results 125   -20 -15 -10 -5 0 5 10 15 20 0 1 2 3 4 5 6 Cu m ul ati ve R es id ua ls Highway Safety Manual (1st Edition) Calibrated Prediction Series1 Series2 Series3 Figure 85. CURE plot of 3T fitted values (Minnesota). -20 -15 -10 -5 0 5 10 15 20 0 2 4 6 8 10 12 Cu m ul ati ve R es id ua ls Signalized Intersection Density Series1 Series2 Series3 Figure 86. CURE plot of 3T signalized intersection density (Minnesota).

126 Application of Crash Modification Factors for Access Management -80 -60 -40 -20 0 20 40 60 80 0 5 10 15 20 25 Cu m ul ati ve R es id ua ls Highway Safety Manual (1st Edition) Calibrated Prediction Series1 Series2 Series3 Figure 87. CURE plot of 4D fitted values (Minnesota). -80 -60 -40 -20 0 20 40 60 80 0 2 4 6 8 10 12 14 Cu m ul ati ve R es id ua ls Signalized Intersection Density Series1 Series2 Series3 Figure 88. CURE plot of 4D signalized intersection density (Minnesota).

Analysis Results 127   -25 -20 -15 -10 -5 0 5 10 15 20 25 0 1 2 3 4 5 6 7 8 9 Cu m ul ati ve R es id ua ls Highway Safety Manual (1st Edition) Calibrated Prediction Series1 Series2 Series3 Figure 89. CURE plot of 4U fitted values (Minnesota). -25 -20 -15 -10 -5 0 5 10 15 20 25 0 2 4 6 8 10 12 14 16 18 Cu m ul ati ve R es id ua ls Signalized Intersection Density Series1 Series2 Series3 Figure 90. CURE plot of 4U signalized intersection density (Minnesota).

128 Application of Crash Modification Factors for Access Management -25 -20 -15 -10 -5 0 5 10 15 20 25 0 5 10 15 20 25 Cu m ul ati ve R es id ua ls Highway Safety Manual (1st Edition) Calibrated Prediction Series1 Series2 Series3 Figure 91. CURE plot of 5T fitted values (Minnesota). -25 -20 -15 -10 -5 0 5 10 15 20 25 0 1 2 3 4 5 6 7 8 9 Cu m ul ati ve R es id ua ls Signalized Intersection Density Series1 Series2 Series3 Figure 92. CURE plot of 5T signalized intersection density (Minnesota).

Analysis Results 129   Tables 103 and 104 show details for the GLM models for signalized intersection density and the number of signalized intersections, respectively. The GLM models show that the parameter estimates, with only one exception, indicate more crashes as the number of signals increase. The parameter estimates are not statistically significant, with one exception, and improvement in overall model fit is minimal. Unsignalized Intersection Spacing The structure of the data for the Highway Safety Manual (1st Edition) Part C Predictive Method is such that roadways are segmented by intersection and midblock areas, and crashes are assigned to one of the two. One of the important findings of this research was that as the number of intersections in a segment increased, the expected number of segment crashes often decreased. This is contrary to expectations since the presence of more intersections should lead to more conflicts, certainly not fewer, even away from the intersections. However, the structure of the data may contribute to this counterintuitive finding. Specifically, if more intersections are present, then it is more likely that a crash will be assigned to an intersection and not a segment. This finding suggests the data are not conducive to segment-level analysis of some variables (e.g., intersection density, spacing, etc.). Instead, these variables are better assessed at the cor- ridor level. Corridor-level analyses are discussed in Chapter 5 of NCHRP Research Report 974, Volume 1: Practitioner’s Guide (Gross et al. 2021). The findings at the segment level are still presented next for completeness, but again, the results are counterintuitive. The Ohio data did not include minimum and maximum spacing for unsignalized inter- sections, so the analysis was restricted to the Minnesota data. In this dataset, only 48 sites with a total of 101 crashes included a spacing measurement for unsignalized intersections. Due to this small sample, all site types were combined for analysis. Table 103. GLM results for signalized intersection density (Minnesota). 2U −0.5341 (0.1074) 0.0885 (0.0475) 0.6614 (0.1682) 3T −0.5344 (0.1542) 0.0629 (0.0722) 0.4028 (0.2199) 4D 0.1123 (0.1040) 0.0328 (0.0275) 0.7807 (0.1413) 4U −0.4882 (0.1034) 0.0602 (0.0253) 0.2688 (0.1247) 5T −0.6343 (0.1847) −0.0005 (0.0480) 0.3129 (0.1532) Signalized intersection density is defined as the total number of signalized intersections within the segment, without counting either end of the segment, per mile. se = standard error, a = model coefficient for predictor variable. Table 104. GLM results for number of signalized intersections (Minnesota). 2U −0.5187 (0.1100) 1.1228 (1.0121) 0.6864 (0.1711) 3T −0.5261 (0.1578) 0.5309 (1.0300) 0.4172 (0.2224) 4D 0.1511 (0.1011) 0.2800 (0.5519) 0.7938 (0.1426) 4U −0.4801 (0.1044) 1.0244 (0.5750) 0.2831 (0.1252) 5T −0.6646 (0.1774) 0.3359 (1.1900) 0.3130 (0.1529) Number of signalized intersections is the total number of signalized intersections within the segment, without counting either end of the segment. se = standard error, a = model coefficient for predictor variable.

130 Application of Crash Modification Factors for Access Management Table 105 presents the goodness-of-fit measures for the CURE plots. The CURE plots (shown in Figures 93 through 95) do show bias for the fitted value and both minimum and maximum spacing when considering all types combined. There is some indication that the crash prediction models over-predict for low spacing and under-predict for large spacing, the opposite of what is expected. For the GLM models, models could only be developed for 2U and 4U sites. Tables 106 and 107 show the details for the GLM models for minimum spacing and maximum spacing, respectively. For these models, the param- eter estimates were highly insignificant and did not improve the model fit. Number of Unsignalized Intersections and Density The structure of the data for the Highway Safety Manual (1st Edition) Part C Predictive Method is such that roadways are segmented by intersection and midblock areas, and crashes are assigned to one of the two. One of the important findings of this research was that as the number of intersections in a segment increased, the expected number of segment crashes often decreased. This is contrary to expectations since the presence of more intersections should lead to more conflicts, certainly not fewer, even away from the intersections. However, the Site Types Number of Sites Number of Crashes Plotted Variable Factor MAX DEV % CURE >2 S.D. All 48 101 Fitted Value 12.63 30 48 101 Minimum Unsignalized Intersection Spacing 21.66 21 48 101 Maximum Unsignalized Intersection Spacing 20.55 21 MAX DEV = maximum deviation, S.D. = standard deviation. Table 105. Goodness-of-fit measures for unsignalized intersection spacing (Minnesota). -20 -15 -10 -5 0 5 10 15 20 0 1 2 3 4 5 6 7 8 Cu m ul ati ve R es id ua ls Highway Safety Manual (1st Edition) Calibrated Prediction Series1 Series2 Series3 Figure 93. CURE plot of unsignalized intersections fitted values (Minnesota).

Analysis Results 131   -25 -20 -15 -10 -5 0 5 10 15 20 0 200 400 600 800 1000 1200 Cu m ul ati ve R es id ua ls Unsignalized Intersections Maximum Spacing Series1 Series2 Series3 Figure 94. CURE plot of unsignalized intersections maximum spacing (Minnesota). -25 -20 -15 -10 -5 0 5 10 15 20 0 200 400 600 800 1000 1200 Cu m ul ati ve R es id ua ls Unsignalized Intersections Minimum Spacing Series1 Series2 Series3 Figure 95. CURE plot of unsignalized intersections minimum spacing (Minnesota). structure of the data may contribute to this counterintuitive finding. Specifically, if more inter- sections are present, then it is more likely that a crash will be assigned to an intersection and not a segment. This finding suggests the data are not conducive to segment-level analysis of some variables (e.g., intersection density, spacing, etc.). Instead, these variables are better assessed at the corridor level. Corridor-level analyses are discussed in Chapter 5 of NCHRP Research Report 974, Volume 1: Practitioner’s Guide (Gross et al. 2021). The findings at the segment level are still presented next for completeness, but again, the results are counterintuitive.

132 Application of Crash Modification Factors for Access Management The analysis of number and density of unsignalized intersections looked at all segment types individually. The Ohio data provide some evidence of bias from the CURE plot measures, including: • 2U—number of unsignalized intersections and unsignalized intersection density, • 3T—number of unsignalized intersections and unsignalized intersection density, • 4U—number of unsignalized intersections and unsignalized intersection density, and • 5T—number of unsignalized intersections and unsignalized intersection density. Table 108 presents the goodness-of-fit measures for the CURE plots shown in Figures 96 through 105. Tables 109 and 110 show the details for the GLM models for unsignalized inter- section density and the number of unsignalized intersections, respectively. The results are similar to signalized intersections in that, for most site types, more unsignalized intersections and increased unsignalized intersection density are associated with fewer segment crashes. In contrast to the results for signalized intersections, most parameter estimates are statistically significant at the 95 percent confidence level when added to the GLM model. Still, the overall model fit of the GLM models seems little improved when adding these variables. Again, the reason for this could be that the Highway Safety Manual (1st Edition) approach measures the entire length of the segment, but intersection-related crashes are not included in the segment crash total. As the number of unsignalized intersections increases, the likelihood that a crash is not counted as a segment crash may increase as well. The results for crash-type models similarly showed consistent results. Table 106. GLM results for minimum unsignalized intersection spacing (Minnesota). 2U −0.3835 (0.2967) 0.0000 (0.0006) 0.2247 (0.2302) 3T -- -- -- 4D -- -- -- 4U −1.1363 (0.6304) 0.0036 (0.0025) 0.4347 (0.3095) 5T -- -- -- Minimum unsignalized intersection spacing is defined as the shortest distance (in ft) between two unsignalized intersections within the segment. -- indicates model did not converge. se = standard error, a = model coefficient for predictor variable. Table 107. GLM results for maximum unsignalized intersection spacing (Minnesota). 2U −0.5498 (0.3635) 0.0004 (0.0006) 0.2039 (0.2261) 3T -- -- -- 4D -- -- -- 4U 0.0874 (0.5566) −0.0008 (0.0011) 0.5371 (0.3492) 5T -- -- -- Maximum unsignalized intersection spacing is defined as the longest distance (in ft) between two unsignalized intersections within the segment. -- indicates model did not converge. se = standard error, a = model coefficient for predictor variable.

Analysis Results 133   -150 -100 -50 0 50 100 150 200 0 2 4 6 8 10 12 14 16 Cu m ul ati ve R es id ua ls Number of Unsignalized Intersections Series1 Series2 Series3 Figure 96. CURE plot of 2U number of unsignalized intersections (Ohio). Table 108. Goodness-of-fit measures for unsignalized intersections (Ohio). Site Types Number of Sites Number of Crashes Plotted Variable Factor MAX DEV % CURE >2 S.D. 2U 338 1,975 Fitted Value 71.68 1 2U 338 1,975 Number of Unsignalized Intersections 157.98 26 2U 338 1,975 Unsignalized Intersection Density 157.98 55 3T 114 624 Fitted Value 44.97 1 3T 114 624 Number of Unsignalized Intersections 51.46 12 3T 114 624 Unsignalized Intersection Density 66.04 24 4D 388 3,247 Fitted Value 111.04 7 4D 388 3,247 Number of Unsignalized Intersections 155.09 10 4D 388 3,247 Unsignalized Intersection Density 155.09 11 4U 217 1,408 Fitted Value 167.83 9 4U 217 1,408 Number of Unsignalized Intersections 147.45 15 4U 217 1,408 Unsignalized Intersection Density 142.28 16 5T 158 2,779 Fitted Value 399.26 27 5T 158 2,779 Number of Unsignalized Intersections 267.97 17 5T 158 2,779 Unsignalized Intersection Density 267.97 31 MAX DEV = maximum deviation, S.D. = standard deviation.

134 Application of Crash Modification Factors for Access Management -150 -100 -50 0 50 100 150 200 0 10 20 30 40 50 60 Cu m ul ati ve R es id ua ls Unsignalized Intersection Density Series1 Series2 Series3 Figure 97. CURE plot of 2U unsignalized intersection density (Ohio). -80 -60 -40 -20 0 20 40 60 80 0 2 4 6 8 10 12 14 16 Cu m ul ati ve R es id ua ls Number of Unsignalized Intersections Series1 Series2 Series3 Figure 98. CURE plot of 3T number of unsignalized intersections (Ohio).

Analysis Results 135   -80 -60 -40 -20 0 20 40 60 80 0 5 10 15 20 25 Cu m ul ati ve R es id ua ls Unsignalized Intersection Density Series1 Series2 Series3 Figure 99. CURE plot of 3T unsignalized intersection density (Ohio). -250 -200 -150 -100 -50 0 50 100 150 200 250 0 5 10 15 20 25 Cu m ul ati ve R es id ua ls Number of Unsignalized Intersections Series1 Series2 Series3 Figure 100. CURE plot of 4D number of unsignalized intersections (Ohio).

136 Application of Crash Modification Factors for Access Management -250 -200 -150 -100 -50 0 50 100 150 200 250 0 2 4 6 8 10 12 14 16 Cu m ul ati ve R es id ua ls Unsignalized Intersection Density Series1 Series2 Series3 Figure 101. CURE plot of 4D unsignalized intersection density (Ohio). -200 -150 -100 -50 0 50 100 150 200 0 10 20 30 40 50 60 Cu m ul ati ve R es id ua ls Number of Unsignalized Intersections Series1 Series2 Series3 Figure 102. CURE plot of 4U number of unsignalized intersections (Ohio).

Analysis Results 137   -200 -150 -100 -50 0 50 100 150 200 0 5 10 15 20 25 Cu m ul ati ve R es id ua ls Unsignalized Intersection Density Series1 Series2 Series3 Figure 103. CURE plot of 4U unsignalized intersection density (Ohio). -400 -300 -200 -100 0 100 200 300 0 5 10 15 20 25 30 Cu m ul ati ve R es id ua ls Number of Unsignalized Intersections Series1 Series2 Series3 Figure 104. CURE plot of 5T number of unsignalized intersections (Ohio).

138 Application of Crash Modification Factors for Access Management -400 -300 -200 -100 0 100 200 300 0 5 10 15 20 25 Cu m ul ati ve R es id ua ls Unsignalized Intersection Density Series1 Series2 Series3 Figure 105. CURE plot of 5T unsignalized intersection density (Ohio). Table 109. GLM results for unsignalized intersection density (Ohio). 2U −0.0863 (0.0807) −0.0732 (0.0213) 1.3025 (0.1459) 3T −0.3197 (0.1381) −0.1308 (0.0363) 1.2420 (0.2426) 4D −0.1012 (0.0594) −0.0516 (0.0248) 0.8837 (0.0928) 4U −0.6643 (0.1082) −0.0746 (0.0262) 1.5973 (0.1988) 5T −0.7440 (0.1086) −0.0739 (0.0229) 1.1049 (0.1526) Unsignalized intersection density is defined as the total number of unsignalized intersections within the segment, without counting driveways or either end of the segment, per mile. se = standard error, a = model coefficient for predictor variable. Table 110. GLM results for unsignalized intersection count (Ohio). 2U −0.1831 (0.0740) −0.0794 (0.0301) 1.3795 (0.1520) 3T -- -- -- 4D −0.1239 (0.0564) −0.2035 (0.0943) 0.8862 (0.0932) 4U −0.7890 (0.0976) −0.0379 (0.0904) 1.6768 (0.2067) 5T -- -- -- Number of unsignalized intersections is the total number of unsignalized intersections within the segment, without counting driveways or either end of the segment. -- indicates the model did not converge. se = standard error, a = model coefficient for predictor variable.

Analysis Results 139   Validation of the results was done by comparing the Ohio results to the Minnesota results. Table 111 presents the goodness-of-fit measures for the CURE plots shown in Figures 106 through 115. There is some evidence of bias from the CURE plot measures for • 3T—unsignalized intersection density and number of unsignalized intersections, • 4U—unsignalized intersection density and number of unsignalized intersections, and • 5T—unsignalized intersection density and number of unsignalized intersections. Tables 112 and 113 show the details for the GLM models for unsignalized intersection density and the number of unsignalized intersections, respectively. Most of the GLM models show that the parameter estimates indicate more crashes as the number and density of unsignal- ized intersections increase, but the parameter estimates are not statistically significant. For some site types, the models did not converge. -150 -100 -50 0 50 100 150 200 0 2 4 6 8 10 12 14 16 Cu m ul ati ve R es id ua ls Number of Unsignalized Intersections Series1 Series2 Series3 Figure 106. CURE plot of 2U number of unsignalized intersections (Minnesota). Table 111. Goodness-of-fit measures for unsignalized intersections (Minnesota). Site Types Number of Sites Number of Crashes Plotted Variable Factor MAX DEV % CURE >2 S.D. 2U 140 263 Fitted Value 23.59 0 2U 140 263 Unsignalized Intersection Density 25.47 2 2U 140 263 Number of Unsignalized Intersections 25.47 1 3T 114 624 Fitted Value 44.97 1 3T 114 624 Unsignalized Intersection Density 66.04 24 3T 114 624 Number of Unsignalized Intersections 51.46 12 4D 388 3,247 Fitted Value 111.04 7 4D 388 3,247 Unsignalized Intersection Density 155.09 11 4D 388 3,247 Number of Unsignalized Intersections 155.09 10 4U 217 1,408 Fitted Value 167.83 9 4U 217 1,408 Unsignalized Intersection Density 142.28 16 4U 217 1,408 Number of Unsignalized Intersections 147.45 15 5T 158 2,779 Fitted Value 399.26 27 5T 158 2,779 Unsignalized Intersection Density 267.97 31 5T 158 2,779 Number of Unsignalized Intersections 267.97 17 MAX DEV = maximum deviation, S.D. = standard deviation.

140 Application of Crash Modification Factors for Access Management -150 -100 -50 0 50 100 150 200 0 10 20 30 40 50 60 Cu m ul ati ve R es id ua ls Unsignalized Intersection Density Series1 Series2 Series3 Figure 107. CURE plot of 2U unsignalized intersection density (Minnesota). -80 -60 -40 -20 0 20 40 60 80 0 2 4 6 8 10 12 14 16 Cu m ul ati ve R es id ua ls Number of Unsignalized Intersections Series1 Series2 Series3 Figure 108. CURE plot of 3T number of unsignalized intersections (Minnesota).

Analysis Results 141   -80 -60 -40 -20 0 20 40 60 80 0 5 10 15 20 25 Cu m ul ati ve R es id ua ls Unsignalized Intersection Density Series1 Series2 Series3 Figure 109. CURE plot of 3T unsignalized intersection density (Minnesota). -250 -200 -150 -100 -50 0 50 100 150 200 250 0 5 10 15 20 25 Cu m ul ati ve R es id ua ls Number of Unsignalized Intersections Series1 Series2 Series3 Figure 110. CURE plot of 4D number of unsignalized intersections (Minnesota).

142 Application of Crash Modification Factors for Access Management -250 -200 -150 -100 -50 0 50 100 150 200 250 0 2 4 6 8 10 12 14 16 Cu m ul ati ve R es id ua ls Unsignalized Intersection Density Series1 Series2 Series3 Figure 111. CURE plot of 4D unsignalized intersection density (Minnesota). -200 -150 -100 -50 0 50 100 150 200 0 10 20 30 40 50 60 Cu m ul ati ve R es id ua ls Number of Unsignalized Intersections Series1 Series2 Series3 Figure 112. CURE plot of 4U number of unsignalized intersections (Minnesota).

Analysis Results 143   -200 -150 -100 -50 0 50 100 150 200 0 5 10 15 20 25 Cu m ul ati ve R es id ua ls Unsignalized Intersection Density Series1 Series2 Series3 Figure 113. CURE plot of 4U unsignalized intersection density (Minnesota). -400 -300 -200 -100 0 100 200 300 0 5 10 15 20 25 30 Cu m ul ati ve R es id ua ls Number of Unsignalized Intersections Series1 Series2 Series3 Figure 114. CURE plot of 5T number of unsignalized intersections (Minnesota).

144 Application of Crash Modification Factors for Access Management -400 -300 -200 -100 0 100 200 300 0 5 10 15 20 25 Cu m ul ati ve R es id ua ls Unsignalized Intersection Density Series1 Series2 Series3 Figure 115. CURE plot of 5T unsignalized intersection density (Minnesota). Table 112. GLM results for unsignalized intersection density (Minnesota). 2U −0.6244 (0.3398) 0.0197 (0.0215) 0.2173 (0.2208) 3T −0.5534 (0.3056) −0.0041 (0.0498) −0.1193 (0.1682) 4D 1.1460 (5.1302) −0.2261 (0.5326) −0.1667 (0.0000) 4U 0.2257 (0.6342) −0.0482 (0.0562) 0.5292 (0.3433) 5T -- -- -- Unsignalized intersection density is defined as the total number of unsignalized intersections within the segment, without counting driveways or either end of the segment, per mile. -- indicates the model did not converge. se = standard error, a = model coefficient for predictor variable. Table 113. GLM results for unsignalized intersection count (Minnesota). 2U −0.2603 (0.3668) −0.0996 (0.2912) 0.2498 (0.2488) 3T -- -- -- 4D -- -- -- 4U 0.2241 (0.4026) −0.7590 (0.5953) 0.5099 (0.3321) 5T -- -- -- Number of unsignalized intersections is the total number of unsignalized intersections within the segment, without counting driveways or either end of the segment. -- indicates the model did not converge. se = standard error, a = model coefficient for predictor variable.

Analysis Results 145   Number of Unsignalized Access Points and Density The structure of the data for the Highway Safety Manual (1st Edition) Part C Predictive Method is such that roadways are segmented by intersection and midblock areas, and crashes are assigned to one of the two. One of the important findings of this research was that as the number of intersections in a segment increased, the expected number of segment crashes often decreased. This is contrary to expectations since the presence of more intersections should lead to more conflicts, certainly not fewer, even away from the intersections. However, the structure of the data may contribute to this counterintuitive finding. Specifically, if more intersections are present, then it is more likely that a crash will be assigned to an intersection and not a segment. This finding suggests that the data are not conducive to segment-level analysis of some vari- ables (e.g., intersection density, spacing, etc.). Instead, these variables are better assessed at the corridor level. Corridor-level analyses are discussed in Chapter 5 of NCHRP Research Report 974, Volume 1: Practitioner’s Guide (Gross et al. 2021). The findings at the segment level are still pre- sented for completeness in the following, but again, the results are counterintuitive. The analysis of unsignalized access points and density looked at all segment types individually. The Ohio data suggest there is some evidence of bias from the CURE plot measures, including • 2U—number of unsignalized access points per mile (density); • 4D—number of unsignalized access points; • 4U—number of unsignalized access points; and • 5T—fitted value, number of unsignalized access points, and number of unsignalized access points per mile (density). Table 114 presents the goodness-of-fit measures for the CURE plots shown in Figures 116 through 125. Contrary to what is expected, the results mostly indicate that the crash prediction models over-predict for higher numbers of access points and access point density. The reason for this could be that the Highway Safety Manual (1st Edition) approach measures the entire length of the segment, but crashes considered to be intersection-related are not included in the segment crash total. As the number of unsignalized intersections increases, the likelihood that a crash is not counted as a segment crash may increase as well. The one exception is 5T, which shows an under-prediction in total crashes as the number of access points and density increase. Site Types Number of Sites Number of Crashes Plotted Variable Factor MAX DEV % CURE >2 S.D. 2U 337 1,975 Fitted Value 71.68 1 2U 337 1,975 Number of Unsignalized Access Points 82.56 2 2U 337 1,975 Unsignalized Access Density 231.58 66 3T 113 624 Fitted Value 44.97 1 3T 113 624 Number of Unsignalized Access Points 31.65 6 3T 113 624 Unsignalized Access Density 39.21 1 4D 387 3,247 Fitted Value 111.04 7 4D 387 3,247 Number of Unsignalized Access Points 175.49 19 4D 387 3,247 Unsignalized Access Density 141.34 8 4U 216 1,408 Fitted Value 167.83 9 4U 216 1,408 Number of Unsignalized Access Points 275.17 39 4U 216 1,408 Unsignalized Access Density 135.16 0 5T 157 2,779 Fitted Value 399.26 27 5T 157 2,779 Number of Unsignalized Access Points 346.33 29 5T 157 2,779 Unsignalized Access Density 260.46 20 MAX DEV = maximum deviation, S.D. = standard deviation. Table 114. Goodness-of-fit measures for unsignalized access (Ohio).

146 Application of Crash Modification Factors for Access Management -150 -100 -50 0 50 100 150 0 50 100 150 200 250 300 Cu m ul ati ve R es id ua ls Number of Unsignalized Access Points Series1 Series2 Series3 Figure 116. CURE plot of 2U number of unsignalized access points (Ohio). -150 -100 -50 0 50 100 150 200 250 300 0 50 100 150 200 250 300 350 Cu m ul ati ve R es id ua ls Unsignalized Access Density Series1 Series2 Series3 Figure 117. CURE plot of 2U unsignalized access density (Ohio).

Analysis Results 147   -80 -60 -40 -20 0 20 40 60 80 0 20 40 60 80 100 120 Cu m ul ati ve R es id ua ls Number of Unsignalized Access Points Series1 Series2 Series3 Figure 118. CURE plot of 3T number of unsignalized access points (Ohio). -80 -60 -40 -20 0 20 40 60 80 0 50 100 150 200 250 Cu m ul ati ve R es id ua ls Unsignalized Access Density Series1 Series2 Series3 Figure 119. CURE plot of 3T unsignalized access density (Ohio).

148 Application of Crash Modification Factors for Access Management -250 -200 -150 -100 -50 0 50 100 150 200 250 0 20 40 60 80 100 120 140 160 180 Cu m ul ati ve R es id ua ls Number of Unsignalized Access Points Series1 Series2 Series3 Figure 120. CURE plot of 4D number of unsignalized access points (Ohio). -250 -200 -150 -100 -50 0 50 100 150 200 250 0 50 100 150 200 250 300 350 Cu m ul ati ve R es id ua ls Unsignalized Access Density Series1 Series2 Series3 Figure 121. CURE plot of 4D unsignalized access density (Ohio).

Analysis Results 149   -200 -150 -100 -50 0 50 100 150 200 250 300 0 20 40 60 80 100 120 140 160 180Cu m ul ati ve R es id ua ls Number of Unsignalized Access Points Series1 Series2 Series3 Figure 122. CURE plot of 4U number of unsignalized access points (Ohio). -200 -150 -100 -50 0 50 100 150 200 0 50 100 150 200 250 300 Cu m ul ati ve R es id ua ls Unsignalized Access Density Series1 Series2 Series3 Figure 123. CURE plot of 4U unsignalized access density (Ohio).

150 Application of Crash Modification Factors for Access Management -400 -300 -200 -100 0 100 200 300 400 0 50 100 150 200 250 Cu m ul ati ve R es id ua ls Number of Unsignalized Access Points Series1 Series2 Series3 Figure 124. CURE plot of 5T number of unsignalized access points (Ohio). -300 -200 -100 0 100 200 300 0 50 100 150 200 Cu m ul ati ve R es id ua ls Unsignalized Access Density Series1 Series2 Series3 Figure 125. CURE plot of 5T unsignalized access density (Ohio).

Analysis Results 151   Tables 115 and 116 show the details for the GLM models for unsignalized access density and the number of unsignalized access points, respectively. The estimated parameters of the GLM models were inconsistent in either indicating more crashes or fewer crashes with more unsignalized access points and were not statistically significant. The one exception was for 4D segments and the number of unsignalized access points, which was significant and indicates more crashes as the number of access points increases. The results for the crash-type models indicated that for 2U segments there was little bias for rear-end crashes, with some indication of under-prediction for larger numbers of access points. The GLM models were not statistically significant and did not improve model fit. Some bias was also seen for multivehicle non-driveway crashes, but in the opposite direction to expectations. The GLM model was also not significant and did not improve the model fit. The remaining segment types followed a similar pattern: some indications of bias for some crash types but often counter to expectations, GLM models were not statistically significant, and additional variables did not improve the overall model fit. Validation of the results was done by comparing the Ohio results to the Minnesota results. Table 117 presents the goodness-of-fit measures for the CURE plots shown in Figures 126 through 140. The Minnesota data showed some evidence of bias for 2U and 4D segments for total crashes. The trends for over- and/or under-prediction appear similar to that for Ohio for 2U. For 4D, the Minnesota results look more as expected, with an over-prediction for low access points (i.e., fewer expected crashes as the number of access points decreases) and under- prediction at high numbers of access points (i.e., more expected crashes as the number of access points increases). Tables 118 and 119 show the details for the GLM models for unsignalized access density and the number of unsignalized access points, respectively. The GLM models follow the Ohio trends in that the parameter estimates are not consistent in sign, not statisti- cally significant, and do not result in an improved model fit. Table 115. GLM results for unsignalized access density (Ohio). 2U 0.0525 (0.1163) −0.0065 (0.0022) 1.3416 (0.1492) 3T −0.8411 (0.2234) 0.0057 (0.0034) 1.3688 (0.2633) 4D −0.1746 (0.0658) 0.0016 (0.0018) 0.8942 (0.0937) 4U −0.7914 (0.1523) −0.0001 (0.0029) 1.6825 (0.2067) 5T −0.8961 (0.1793) −0.0004 (0.0033) 1.1878 (0.1612) Unsignalized access density is defined as the number of unsignalized access points (i.e., both driveways and unsignalized intersections) per mile. se = standard error, a = model coefficient for predictor variable. Table 116. GLM results for unsignalized access points (Ohio). 2U −0.2710 (0.1056) 0.0112 (0.0126) 1.3924 (0.1530) 3T −0.7839 (0.2875) 0.0527 (0.0488) 1.4122 (0.2683) 4D −0.1566 (0.0673) 0.0087 (0.0247) 0.8939 (0.0938) 4U −0.7824 (0.1086) −0.0036 (0.0145) 1.6810 (0.2067) 5T −0.8453 (0.1142) −0.0344 (0.0315) 1.1791 (0.1604) Number of unsignalized access points is defined as the number of unsignalized access points (i.e., both driveways and unsignalized intersections) within the segment. se = standard error, a = model coefficient for predictor variable.

152 Application of Crash Modification Factors for Access Management -40 -30 -20 -10 0 10 20 30 40 0 2 4 6 8 10 12 Cu m ul ati ve R es id ua ls Highway Safety Manual (1st Edition) Calibrated Prediction Series1 Series2 Series3 Figure 126. CURE plot of 2U fitted values (Minnesota). Table 117. Goodness-of-fit measures for unsignalized access (Minnesota). Site Types Number of Sites Number of Crashes Plotted Variable Factor MAX DEV % CURE >2 S.D. 2U 139 263 Fitted Value 23.59 0 2U 139 263 Number of Unsignalized Access Points 35.46 13 2U 139 263 Unsignalized Access Density 25.47 2 3T 47 91 Fitted Value 6.95 9 3T 47 91 Number of Unsignalized Access Points 14.32 13 3T 47 91 Unsignalized Access Density 9.20 2 4D 133 600 Fitted Value 62.64 1 4D 133 600 Number of Unsignalized Access Points 86.95 29 4D 133 600 Unsignalized Access Density 77.46 22 4U 95 195 Fitted Value 10.07 1 4U 95 195 Number of Unsignalized Access Points 11.90 1 4U 95 195 Unsignalized Access Density 8.59 1 5T 28 130 Fitted Value 10.33 7 5T 28 130 Number of Unsignalized Access Points 9.30 0 5T 28 130 Unsignalized Access Density 9.08 0 MAX DEV = maximum deviation, S.D. = standard deviation.

Analysis Results 153   -40 -30 -20 -10 0 10 20 30 40 0 5 10 15 20 25 Cu m ul ati ve R es id ua ls Number of Unsignalized Access Points Series1 Series2 Series3 Figure 127. CURE plot of 2U unsignalized access points (Minnesota). -40 -30 -20 -10 0 10 20 30 40 0 20 40 60 80 100 120 140 160 Cu m ul ati ve R es id ua ls Unsignalized Access Density Series1 Series2 Series3 Figure 128. CURE plot of 2U unsignalized access density (Minnesota).

154 Application of Crash Modification Factors for Access Management -20 -15 -10 -5 0 5 10 15 20 0 1 2 3 4 5 6 Cu m ul ati ve R es id ua ls Highway Safety Manual (1st Edition) Calibrated Prediction Series1 Series2 Series3 Figure 129. CURE plot of 3T fitted values (Minnesota). -20 -15 -10 -5 0 5 10 15 20 0 5 10 15 20 25 Cu m ul ati ve R es id ua ls Number of Unsignalized Access Points Series1 Series2 Series3 Figure 130. CURE plot of 3T unsignalized access points (Minnesota).

Analysis Results 155   -20 -15 -10 -5 0 5 10 15 20 0 20 40 60 80 100 120 Cu m ul ati ve R es id ua ls Unsignalized Access Density Series1 Series2 Series3 Figure 131. CURE plot of 3T unsignalized access density (Minnesota). -80 -60 -40 -20 0 20 40 60 80 0 5 10 15 20 25 Cu m ul ati ve R es id ua ls Highway Safety Manual (1st Edition) Calibrated Prediction Series1 Series2 Series3 Figure 132. CURE plot of 4D fitted values (Minnesota).

156 Application of Crash Modification Factors for Access Management -100 -80 -60 -40 -20 0 20 40 60 80 0 2 4 6 8 10 12 14 Cu m ul ati ve R es id ua ls Number of Unsignalized Access Points Series1 Series2 Series3 Figure 133. CURE plot of 4D unsignalized access points (Minnesota). -100 -80 -60 -40 -20 0 20 40 60 80 0 10 20 30 40 50 60 70 Cu m ul ati ve R es id ua ls Unsignalized Access Density Series1 Series2 Series3 Figure 134. CURE plot of 4D unsignalized access density (Minnesota).

Analysis Results 157   -25 -20 -15 -10 -5 0 5 10 15 20 25 0 1 2 3 4 5 6 7 8 9 Cu m ul ati ve R es id ua ls Highway Safety Manual (1st Edition) Calibrated Prediction Series1 Series2 Series3 Figure 135. CURE plot of 4U fitted values (Minnesota). -25 -20 -15 -10 -5 0 5 10 15 20 25 0 5 10 15 20 25 30 Cu m ul ati ve R es id ua ls Number of Unsignalized Access Points Series1 Series2 Series3 Figure 136. CURE plot of 4U unsignalized access points (Minnesota).

158 Application of Crash Modification Factors for Access Management -25 -20 -15 -10 -5 0 5 10 15 20 25 0 20 40 60 80 100 120 Cu m ul ati ve R es id ua ls Unsignalized Access Density Series1 Series2 Series3 Figure 137. CURE plot of 4U unsignalized access density (Minnesota). -25 -20 -15 -10 -5 0 5 10 15 20 25 0 5 10 15 20 25 Cu m ul ati ve R es id ua ls Highway Safety Manual (1st Edition) Calibrated Prediction Series1 Series2 Series3 Figure 138. CURE plot of 5T fitted values (Minnesota).

Analysis Results 159   -25 -20 -15 -10 -5 0 5 10 15 20 25 0 20 40 60 80 100 120 140 Cu m ul ati ve R es id ua ls Unsignalized Access Density Series1 Series2 Series3 Figure 140. CURE plot of 5T unsignalized access density (Minnesota). -25 -20 -15 -10 -5 0 5 10 15 20 25 0 5 10 15 20 25 Cu m ul ati ve R es id ua ls Number of Unsignalized Access Points Series1 Series2 Series3 Figure 139. CURE plot of 5T unsignalized access points (Minnesota).

160 Application of Crash Modification Factors for Access Management Table 118. GLM results for unsignalized access density (Minnesota). 2U −0.3094 (0.1487) −0.0059 (0.0042) 0.7153 (0.1727) 3T −0.3345 (0.2995) −0.0034 (0.0055) 0.4232 (0.2208) 4D 0.0667 (0.1072) 0.0115 (0.0066) 0.7499 (0.1397) 4U −0.3195 (0.1784) −0.0014 (0.0032) 0.3356 (0.1350) 5T −0.8237 (0.2595) 0.0043 (0.0050) 0.3019 (0.1487) Unsignalized access density is defined as the number of unsignalized access points (i.e., both driveways and unsignalized intersections) per mile. se = standard error, a = model coefficient for predictor variable. Table 119. GLM results for unsignalized access points (Minnesota). 2U -- -- -- 3T −0.3745 (0.2235) −0.0308 (0.0450) 0.4250 (0.2213) 4D 0.2004 (0.0984) −0.0616 (0.0687) 0.7998 (0.1427) 4U −0.4199 (0.1508) 0.0078 (0.0276) 0.3324 (0.1348) 5T −0.7000 (0.2626) 0.0381 (0.1277) 0.3125 (0.1525) Number of unsignalized access points is defined as the number of unsignalized access points (i.e., both driveways and unsignalized intersections) within the segment. -- indicates model did not converge se = standard error, a = model coefficient for predictor variable.