Consideration of Roadside Features in the Highway Safety Manual (2022)

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63 CMFROADWAY DERIVATION Roadway characteristics that are thought to affect the probability of a vehicle leaving the roadway based on other HSM predictive models, the encroachment probability model, and the literature include: • Direction and degree of horizontal curvature (i.e., curve to the left versus curve to the right), • Direction and percent of grade (i.e., vehicle going up a grade versus down a grade), • Number of lanes, • Lane width, • Shoulder width and type, • Edge rumble strips, • Access density, and • Posted Speed Limit. These roadway characteristics modify the likelihood of a vehicle leaving the roadway but do not affect the expected severity of a ROR crash. The functional form of the ROR prediction method was presented and discussed above. This functional form includes two crash modification functions: CMFROADWAY and a CMFROADSIDE. CMFROADWAY is first presented and discussed above in equation (2) and repeated here for convenience: 𝐶𝐶𝐶𝐶𝐶𝐶𝑅𝑅𝑂𝑂𝐴𝐴𝐴𝐴𝑅𝑅𝐴𝐴𝑆𝑆 = �𝐶𝐶𝐶𝐶𝐶𝐶𝑝𝑝 𝑛𝑛 𝑝𝑝=1 (4) CMFROADWAY was developed using a cross-sectional study. RURAL DIVIDED HIGHWAY MODEL The same dataset used to develop the SPFEDGE model was used for this model, however, it was subjected to different filtering criteria. The resulting segments, therefore, are much different. Recall the data includes 124,458 rural divided highway primary direction segments. The data were filtered as shown below. The remaining segments are noted in parenthesis. • Consider only segment where the length in miles is 0.1 ≤ L ≥ 2 (58,210) • Consider only segments where AADT > 0 (58,196) • Consider only segments where lane width > 0 (58,196) • Consider only segments where the posted speed limit > 0mph (58,196). This filtering of the dataset resulted in 58,196 segments being included in the analysis. The descriptive statistics for this dataset is shown in Table 33. This table includes shorthand for the categorical variable names to allow the information to be displayed in table format. SW.PRE=1 is for the primary right edge shoulder width equal to one foot. NL=2 is for number of lanes equal to two. LW=10 is for lane width of ten feet. Each number after the equal sign represents the value of that variable associated with that indicator variable. Table 34 provides a summary of the cross-sectional model developed for divided rural roads. Cross-sectional models were also developed, using the same coefficients, for right edge crashes and left edge crashes to facilitate the development of the curvature and grade CMFs and

64 coordination with RSAPv3. These models are shown in Table 35 and Table 36 respectively. Each table includes the coefficients estimated in the left column followed by the estimated value of the standard error, p-value and 95% confidence interval. At the end of each table are the AIC, pseudo R2, and dispersion parameter (a) for the models. Table 33. Descriptive Statistics for Rural Divided Highway Dataset. Continuous Variables Min. 1st Qu. Median Mean 3rd Qu. Max. L 0.1 0.14 0.22 0.3619 0.41 2 AADT 200 10370 15741 21179 27770 120224 Lane width 8 12 12 12.16 12 24 Right Shoulder Width 0 8 10 9.071 10 22 Left Shoulder Width 0 4 4 4.099 4 29 Posted Speed Limit 25 60 65 63.3 70 70 Median Width 1 40 52 142.9 76 9999 Inverse Radius 0 0 0 3.363e-05 0 4.712e-02 DOC 0 0 0 0.1927 0 270 PG 0 0 0 0.5151 0.26 12 PT 0 0 11.72 14.81 25.62 67.12 PRE 0 0 0 0.2232 0 15 PLE 0 0 0 0.2099 0 14 UNK 0 0 0 0.1987 0 22 Categorical Variables Proportion of Feature (%) Categorical Variables Proportion of Feature (%) Categorical Variables Proportion of Feature (%) PSL=25 0.11 SW.PRE=0 1.23 SW.PLE=0 9.05 PSL=30 0.01 SW.PRE=1 0.53 SW.PLE=1 2.12 PSL=35 1.07 SW.PRE=2 0.53 SW.PLE=2 2.46 PSL=40 0.15 SW.PRE=3 1.19 SW.PLE=3 3.65 PSL=45 0.98 SW.PRE=4 3.52 SW.PLE=4 65.64 PSL=50 1.59 SW.PRE=5 0.37 SW.PLE=5 2.79 PSL=55 20.03 SW.PRE=6 1.93 SW.PLE=6 7.85 PSL=60 13.73 SW.PRE=7 0.14 SW.PLE=7 0.21 PSL=65 25.77 SW.PRE=8 18.15 SW.PLE=8 1.57 PSL=70 36.55 SW.PRE=9 0.96 SW.PLE=9 0.03 SW.PRE=10 71.45 SW.PLE=10 4.61 NL=2 3.33 LW<12 1.60 LW=13 0.52 NL=4 85.01 LW=10 0.30 LW=14 0.21 NL=6 8.90 LW=11 1.21 LW=15 0.21 NL=8 0.09 LW=12 94.28 LW>15 3.38

65 Table 34. Negative Binomial Model for All ROR Crashes on Rural Divided Roadways. Coefficients: Parameter Estimate Standard Error P-value 95% Confidence Interval (Intercept) -7.7753 0.17 < 2e-16 -8.1127 -7.4373 ln(AADT) 0.7653 0.01 < 2e-16 0.7372 0.7934 PT 0.0063 0.00 < 2e-16 0.0051 0.0076 DOC_L 0.0141 0.00 6.97e-09 0.0039 NA DOC_R 0.0391 0.00 < 2e-16 NA NA PG_U 0.0492 0.01 3.02e-11 0.0346 0.0637 PG_D 0.0596 0.01 3.57e-16 0.0452 0.0739 no_lanes 0.1145 0.01 < 2e-16 0.0933 0.1357 lanewid 0.0927 0.01 < 2e-16 0.0738 0.1113 SHLDR_PRE -0.0385 0.00 2.47e-16 -0.0478 -0.0292 spd_limt -0.0147 0.00 < 2e-16 -0.0179 -0.0114 AIC 92048 Dispersion parameter (a) 1.2045 Standard Error 0.03 LL (full) -46013.12 LL (intercept) -53096.84 Pseudo R2 0.13

66 Table 35. Negative Binomial Model for Right Edge Only ROR Crashes on Rural Divided Highways. Coefficients: Parameter Estimate Standard Error P-value 95% Confidence Interval (Intercept) -7.6769 0.23 < 2e-16 -8.1194 -7.2314 ln(AADT) 0.6848 0.02 < 2e-16 0.6484 0.7213 PT 0.0047 0.00 6.86e-09 0.0031 0.0062 DOC_L 0.0083 0.00 0.0051 -0.0010 0.0191 DOC_R 0.0112 0.00 3.06e-05 0.0031 0.0225 PG_U 0.0755 0.01 2.77e-15 0.0567 0.0941 PG_D 0.0859 0.01 < 2e-16 0.0673 0.1043 no_lanes 0.0745 0.01 < 2e-16 0.0467 0.1025 lanewid 0.0895 0.01 2.07e-07 0.0644 0.1138 SHLDR_PRE -0.0250 0.01 6.40e-05 -0.0372 -0.0126 spd_limt -0.0142 0.00 5.58e-11 -0.0184 -0.0099 AIC 58599 Dispersion parameter (a) 1.2675 Standard Error 0.05 LL (full) -29288.72 LL (intercept) -33287.95 Pseudo R2 0.12

67 Table 36. Negative Binomial Model for Left Edge Only ROR Crashes on Rural Divided Roadways. Coefficients: Parameter Estimate Standard Error P-value 95% Confidence Interval (Intercept) -9.5757 0.24 < 2e-16 -10.0547 -9.0930 ln(AADT) 0.7991 0.02 < 2e-16 0.7601 0.8383 PT 0.0075 0.00 < 2e-16 0.0059 0.0092 DOC_L 0.0092 0.00 2.72E-03 0.0012 0.0183 DOC_R 0.0108 0.00 1.70E-04 0.0013 0.0233 PG_U 0.0365 0.01 5.44E-04 0.0156 0.0571 PG_D 0.0510 0.01 8.09E-07 0.0306 0.0711 no_lanes 0.1404 0.01 < 2e-16 0.1123 0.1685 lanewid 0.1013 0.01 8.43E-14 0.0739 0.1277 SHLDR_PRE -0.0195 0.01 3.89E-03 -0.0326 -0.0062 spd_limt -0.0115 0.00 9.26E-07 -0.0162 -0.0069 AIC 54664 Dispersion parameter (a) 1.2117 Standard Error 0.05 LL (full) -27320.96 LL (intercept) -31667.34 Pseudo R2 0.14

68 RURAL UNDIVIDED HIGHWAY MODEL The same dataset used to develop the SPFEDGE undivided model was used here, however, it was subjected to different filtering criteria resulting in many different segments being included in the analysis. Initially, the dataset included: 2,058,268 undivided rural segment edges. The data were filtered as follows (remaining segments noted in parenthesis): • Consider only segment where the length in miles (L) is 0.1 ≤ L ≥ 2 (637,060) • Consider only segments where AADT > 0 (635,464) • Consider only posted speed limit > 0mph (634,814) This filtering of the dataset resulted in 634,814 segment edges being included in the analysis. The descriptive statistics for this dataset is shown in Table 37. This table includes shorthand for the categorical variable names to allow the information to be displayed in table format. SW.PRE=1 is for the primary right edge shoulder width equal to one foot. NL=2 is for number of lanes equal to two. LW=10 is for lane width of ten feet. PSL=50 is for the posted speed limit of 50 miles per hour. Each number after the equal sign represents the value of that variable associated with that indicator variable. Table 38 provides a summary of the cross-sectional model developed for undivided rural roadway edges (i.e., PR+OL+unk). Table 39 summarizes the model of primary right departures only (i.e., PL and unk are excluded) which is used to coordinate this research with the RSAPv3 model. These tables include the estimated coefficients, the standard error, p-value and 95% confidence interval for each variable. At the end of each table are the AIC, pseudo R2, and dispersion parameter (a).

69 Table 37. Descriptive Statistics for Rural Undivided Highway Dataset. Continuous Variables Min. 1st Qu. Median Mean 3rd Qu. Max. L 0.10 0.13 0.18 0.2876 0.31 2.00 AADT 10 1060 2100 3025 4040 35254 Lane width 5.00 10.00 11.00 10.92 12.00 36.00 Right Shoulder Width 0 2.00 3.00 3.962 6.00 40.00 Posted Speed Limit 20 55 55 52.6 55 65 DOC 0 0 0 0.317 0 76.0 PG 0 0 0 0.8318 0 20 PT 0 5.01 8.247 10.892 14.483 69.140 PR 0 0 0 0.07445 0 9 OL 0 0 0 0.04279 0 6 UNK 0 0 0 0.06322 0 17 Categorical Variables Proportion of Feature (%) Categorical Variables Proportion of Feature (%) SW.PRE=0 5.11 LW<10 18.67 SW.PRE=1 6.18 LW<12 63.88 SW.PRE=2 21.09 LW=10 25.77 SW.PRE=3 19.07 LW=11 19.44 SW.PRE=4 18.19 LW=12 32.38 SW.PRE=5 5.16 LW=13 0.82 SW.PRE=6 7.79 LW=14 0.44 SW.PRE=7 3.34 LW=15 0.64 SW.PRE=8 9.46 LW>15 2.48 SW.PRE=9 0.54 NL=2 98.59 SW.PRE=10 4.07 NL=4 1.13 PSL=25 1.29 PSL=30 0.16 PSL=50 4.93 PSL=35 7.56 PSL=55 65.32 PSL=40 1.89 PSL=60 9.98 PSL=45 6.55 PSL=65 2.31

70 Table 38. Negative Binomial Model for Right Edge ROR Crashes on Rural Undivided Roadways. Coefficients: Parameter Estimate Standard Error P-value 95% Confidence Interval (Intercept) -13.4200 0.05 < 2e-16 -13.5320 -13.3142 aadt -0.0001 0.00 < 2e-16 -0.0001 -0.0001 PT -0.0157 0.00 < 2e-16 -0.0168 -0.0145 DOC_L 0.0635 0.00 < 2e-16 0.0580 0.0690 DOC_R 0.0286 0.00 < 2e-16 0.0221 0.0349 PG_U 0.0104 0.00 3.88E-06 0.0060 0.0147 PG_D 0.0194 0.00 < 2e-16 0.0152 0.0237 lanewid -0.0474 0.00 < 2e-16 -0.0527 -0.0420 no_lanes 0.0892 0.01 8.51E-11 0.0619 0.1163 SHLDR_PRE -0.0745 0.00 < 2e-16 -0.0778 -0.0712 spd_limt -0.0026 0.00 8.58E-06 -0.0038 -0.0015 AIC 441467 Dispersion parameter (a) 1.0200 Standard Error 0.02 LL (full) -220722.4 LL (intercept) -251213.9 Pseudo R2 0.12

71 Table 39. Negative Binomial Model for Primary Right Departure Only ROR Crashes on Rural Undivided Roadways. Coefficients: Parameter Estimate Standard Error P-value 95% Confidence Interval (Intercept) -13.4300 0.08 < 2e-16 -13.5771 -13.2816 aadt -0.0001 0.00 < 2e-16 -0.0001 -0.0001 PT -0.0154 0.00 < 2e-16 -0.0169 -0.0140 DOC_L 0.0756 0.00 < 2e-16 0.0692 0.0818 DOC_R 0.0204 0.00 1.87E-06 0.0118 0.0287 PG_U 0.0024 0.00 4.06E-01 -0.0033 0.0081 PG_D 0.0302 0.00 < 2e-16 0.0250 0.0354 lanewid -0.1341 0.00 < 2e-16 -0.1423 -0.1260 no_lanes -0.0591 0.02 3.00E-03 -0.0986 -0.0203 SHLDR_PRE -0.0681 0.00 < 2e-16 -0.0724 -0.0639 spd_limt 0.0091 0.00 < 2e-16 0.0075 0.0107 AIC 300359 Dispersion parameter (a) 1.1733 Standard Error 0.03 LL (full) -150168.4 LL (intercept) -170047.7 Pseudo R2 0.12

72 URBAN DIVIDED HIGHWAY MODEL The same dataset used to develop the SPFEDGE model was used here, however, it was subjected to different filtering criteria. The resulting segments, therefore, are much different. Recall the data includes 244,050 divided urban primary direction segments. The data were filtered as shown below. The remaining segments are noted in parenthesis. • Consider only segment where the length in miles is 0.1 ≤ L ≥ 2 (105,802) • Consider only segments where AADT > 0 (105,318) • Consider only segments where the posted speed limit > 0mph (104,468). This filtering of the dataset resulted in 104,468 segments being included in the analysis. The descriptive statistics for this dataset is shown in Table 40. This table includes shorthand for the categorical variable names to allow the information to be displayed in table format. SW.PRE=1 is for the primary right edge shoulder width equal to one foot. NL=2 is for number of lanes equal to two. LW=10 is for lane width of ten feet. Each number after the equal sign represents the value of that variable associated with that indicator variable. Table 41 provides a summary of the cross-sectional model developed for urban divided roads. Cross-sectional models were also developed, using the same coefficients, for right edge crashes and left edge crashes to facilitate the development of the curvature and grade CMFs as well as coordination with the RSAPv3 model. These models are shown in Table 42 and Table 43 respectively. Each table includes the coefficients estimated in the left column followed by the estimated value of the standard error, p-value and 95% confidence interval. At the end of each table are the AIC, pseudo R2, and dispersion parameter (a) for the models.

73 Table 40. Descriptive Statistics for Urban Divided Highway Dataset. Continuous Variables Min. 1st Qu. Median Mean 3rd Qu. Max. L 0.1 0.14 0.20 0.3152 0.35 2 AADT 110 19790 39870 56514 80304 283640 Lane width 8 12 12 12.33 12 35 Right Shoulder Width 0 8 10 8.325 10 23 Left Shoulder Width 0 0 4 3.927 5 36 Posted Speed Limit 20 55 60 57.22 65 70 Median Width 1 12 30 108.5 53 9999 DOC 0 0 0 0.2261 0 270 PG 0 0 0 0.3796 0 11 PT 0 4.55 8.60 10.19 13.09 56.98 PRE 0 0 0 0.3511 0 18 PLE 0 0 0 0.3577 0 17 UNK 0 0 0 1.592 1 338 Categorical Variables Proportion of Feature (%) Categorical Variables Proportion of Feature (%) Categorical Variables Proportion of Feature (%) PSL=25 0.82 SW.PRE=0 9.53 SW.PLE=0 29.00 PSL=30 0.23 SW.PRE=1 0.36 SW.PLE=1 2.31 PSL=35 5.35 SW.PRE=2 0.78 SW.PLE=2 2.86 PSL=40 1.92 SW.PRE=3 2.99 SW.PLE=3 42.22 PSL=45 3.60 SW.PRE=4 2.42 SW.PLE=4 37.99 PSL=50 6.96 SW.PRE=5 0.22 SW.PLE=5 0 PSL=55 20.75 SW.PRE=6 2.07 SW.PLE=6 3.18 PSL=60 33.38 SW.PRE=7 0.09 SW.PLE=7 1.25 PSL=65 21.88 SW.PRE=8 18.92 SW.PLE=8 2.35 PSL=70 5.05 SW.PRE=9 0.77 SW.PLE=9 0.09 SW.PRE=10 63.11 SW.PLE=10 11.61 NL=2 3.41 LW<10 0.12 LW=13 3.70 NL=4 63.59 LW<12 2.28 LW=14 1.16 NL=6 19.74 LW=10 0.36 LW=15 0.75 NL=8 6.24 LW=11 1.80 LW>15 5.72 LW=12 87.13 .

74 Table 41. Negative Binomial Model for All ROR Crashes on Urban Divided Roadways. Coefficients: Parameter Estimate Standard Error P-value 95% Confidence Interval (Intercept) -5.2741 0.09 < 2e-16 -5.4527 -5.0957 ln(AADT) 0.6305 0.01 < 2e-16 0.6142 0.6468 PT 0.0251 0.00 < 2e-16 0.0238 0.0263 DOC_L -0.0124 0.00 9.87E-03 -0.0227 -0.0041 DOC_R -0.0019 0.00 4.58E-01 -0.0074 0.0028 PG_U -0.1670 0.01 < 2e-16 -0.1784 -0.1557 PG_D -0.1433 0.01 < 2e-16 -0.1544 -0.1322 no_lanes 0.0599 0.00 < 2e-16 0.0510 0.0688 lanewid 0.0414 0.00 < 2e-16 0.0328 0.0500 SHLDR_PRE -0.0105 0.00 2.58E-07 -0.0145 -0.0065 spd_limt -0.0165 0.00 < 2e-16 -0.0181 -0.0149 AIC 285248 Dispersion parameter (a) 0.8056 Standard Error 0.01 LL (full) -142612.9 LL (intercept) -161012.9 Pseudo R2 0.11

75 Table 42. Negative Binomial Model for Right Edge Only ROR Crashes on Urban Divided Roadways. Coefficients: Parameter Estimate Standard Error P-value 95% Confidence Interval (Intercept) -7.1629 0.13 < 2e-16 -7.4284 -6.8970 ln(AADT) 0.5741 0.01 < 2e-16 0.5517 0.5966 PT 0.0133 0.00 < 2e-16 0.0118 0.0149 DOC_L 0.0032 0.00 2.91E-01 -0.0044 0.0086 DOC_R 0.0064 0.00 3.78E-03 0.0010 0.0109 PG_U -0.0869 0.01 < 2e-16 -0.1034 -0.0706 PG_D -0.0410 0.01 1.91E-07 -0.0563 -0.0257 no_lanes 0.0359 0.01 6.01E-10 0.0245 0.0473 lanewid 0.0310 0.01 6.12E-06 0.0174 0.0443 SHLDR_PRE 0.0089 0.00 2.27E-03 0.0033 0.0145 spd_limt 0.0052 0.00 1.19E-05 0.0029 0.0075 AIC 137588 Dispersion parameter (a) 1.3546 Standard Error 0.03 LL (full) -68782.87 LL (intercept) -79051.33 Pseudo R2 0.11

76 Table 43. Negative Binomial Model for Left Edge Only ROR Crashes on Urban Divided Roadways. Coefficients: Parameter Estimate Standard Error P-value 95% Confidence Interval (Intercept) -8.9455 0.14 < 2e-16 -9.2252 -8.6657 ln(AADT) 0.6727 0.01 < 2e-16 0.6494 0.6961 PT 0.0169 0.00 < 2e-16 0.0153 0.0185 DOC_L 0.0066 0.00 6.80E-03 0.0004 0.0116 DOC_R 0.0101 0.00 3.37E-08 0.0055 0.0145 PG_U -0.0550 0.01 1.87E-11 -0.0711 -0.0390 PG_D -0.0274 0.01 4.97E-04 -0.0429 -0.0121 no_lanes 0.0353 0.01 1.69E-09 0.0238 0.0469 lanewid 0.0468 0.01 2.28E-11 0.0328 0.0605 SHLDR_PRE 0.0144 0.00 2.03E-06 0.0085 0.0202 spd_limt 0.0122 0.00 < 2e-16 0.0097 0.0147 AIC 137706 Dispersion parameter (a) 1.1891 Standard Error 0.03 LL (full) -68841.75 LL (intercept) -79435.92 Pseudo R2 0.11

77 URBAN UNDIVIDED HIGHWAY MODEL The same dataset used to develop the SPFEDGE undivided highway model was used here, however, it was subjected to different filtering criteria resulting in many different segments being included in the analysis. Initially, the dataset included: 485,898 undivided urban segment edges. The data were filtered as follows (remaining segments noted in parenthesis): • Consider only segment where the length in miles (L) is 0.1 ≤ L ≥ 2 (181,340) • Consider only segments where AADT > 0 (179,788) • Consider only posted speed limit > 0mph (174,376) This filtering of the dataset resulted in 174,376 segment edges being included in the analysis. The descriptive statistics for this dataset is shown in Table 44. Table 45 provides a summary of the cross-sectional model developed for urban undivided road edges. Table 46 summarizes the model of primary right departures only used to facilitate coordination with RSAPv3.

78 Table 44. Descriptive Statistics for Urban Undivided Highway Dataset. Continuous Variables Min. 1st Qu. Median Mean 3rd Qu. Max. L 0.1 0.13 0.20 0.30 0.36 1.99 AADT 60 6205 10180 12184 16101 86155 Lane width 5.00 11.00 12.00 13.07 14.50 44.00 Right Shoulder Width 0 0 2.00 2.94 5.00 30.00 Posted Speed Limit 20 35 40 40.98 50 70 DOC 0 0 0 0.1027 0 76 PG 0 0 0 0.3664 0 18 PT 0 2.71 4.37 5.56 7.01 50.11 PR 0 0 0 0.1287 0 9 OL 0 0 0 0.0825 0 7 UNK 0 0 0 1.088 1 132 Categorical Variables Proportion of Feature (%) Categorical Variables Proportion of Feature (%) SW.PRE=0 42.88 LW=10 14.60 SW.PRE=1 2.53 LW=11 11.84 SW.PRE=2 6.82 LW=12 34.61 SW.PRE=3 16.51 LW=13 7.58 SW.PRE=4 11.12 LW=14 4.40 SW.PRE=5 1.88 LW=15 7.66 SW.PRE=6 7.12 PSL=25 9.76 SW.PRE=7 1.50 PSL=30 1.57 SW.PRE=8 9.60 PSL=35 38.35 SW.PRE=9 0.47 PSL=40 8.04 SW.PRE=10 5.22 PSL=45 14.34 NL=2 66.33 PSL=50 8.49 NL=4 29.34 PSL=55 17.93 NL=6 1.26 PSL=60 1.40

79 Table 45. Negative Binomial Model for Right Edge ROR Crashes on Urban Undivided Roadways. Coefficients: Parameter Estimate Standard Error P-value 95% Confidence Interval (Intercept) -14.7700 0.04 < 2e-16 -14.8607 -14.6874 aadt -0.0001 0.00 < 2e-16 -0.0001 -0.0001 PT -0.0130 0.00 < 2e-16 -0.0154 -0.0106 DOC_L 0.0068 0.01 2.91E-01 -0.0065 0.0196 DOC_R -0.0154 0.01 3.76E-02 -0.0302 -0.0010 PG_U -0.0303 0.00 1.01E-11 -0.0387 -0.0219 PG_D -0.0245 0.00 2.54E-08 -0.0329 -0.0162 lanewid 0.0503 0.00 < 2e-16 0.0468 0.0537 no_lanes 0.2105 0.01 < 2e-16 0.1980 0.2230 SHLDR_PRE -0.0250 0.00 < 2e-16 -0.0287 -0.0214 spd_limt -0.0005 0.00 4.36E-01 -0.0018 0.0008 AIC 341277.9 Dispersion parameter (a) 0.4963 Standard Error 0.00 LL (full) -170628 LL (intercept) -185999.2 Pseudo R2 0.08

80 Table 46. Negative Binomial Model for Primary Right Departures Only on Urban Undivided Roadways. Coefficients: Parameter Estimate Standard Error P-value 95% Confidence Interval (Intercept) -15.4000 0.07 < 2e-16 -15.5278 -15.2638 aadt 0.0000 0.00 < 2e-16 0.0000 0.0000 PT -0.0107 0.00 3.60E-09 -0.0143 -0.0072 DOC_L 0.0486 0.01 < 2e-16 0.0354 0.0610 DOC_R 0.0064 0.01 5.48E-01 -0.0159 0.0259 PG_U -0.0043 0.01 5.42E-01 -0.0181 0.0093 PG_D 0.0255 0.01 6.61E-05 0.0129 0.0379 lanewid -0.0333 0.00 < 2e-16 -0.0391 -0.0276 no_lanes -0.0439 0.01 3.96E-06 -0.0626 -0.0252 SHLDR_PRE -0.0331 0.00 < 2e-16 -0.0388 -0.0274 spd_limt 0.0144 0.00 < 2e-16 0.0126 0.0163 AIC 127574 Dispersion parameter (a) 1.2099 Standard Error 0.05 LL (full) -63775.91 LL (intercept) -69455.56 Pseudo R2 0.08

81 CMFROADWAY RESULTS Non-Directional CMFs The non-directionally dependent CMFs were derived from the cross-sectional models developed using the total crash frequency (i.e., not a single encroachment direction), as shown in Table 34, Table 38, Table 41, and Table 45. CMF for Average Lane Width The representation of lane width within each of the databases has been repeated in Table 47 for convenience. One should be mindful that these values are the calculated average lane widths of all of the lanes within a segment (i.e., surface width minus shoulder width then divided by number of lanes). While twelve-foot lanes dominate all four of these datasets, some smaller than expected and some larger than expected values are observed. It is suggested that the tabulation of the average lane width CMF (CMFLW) be bound by the available data and exclude the outlining data points to ensure the CMF is a true representation of the data it was generated from. Recall that the SPF base condition for lane width is twelve feet. The base condition for this companion CMF is therefore also twelve feet. Table 47. Lane Width Database Representation. Rural Divided Rural Undivided Urban Divided Urban Undivided Min. 8 5 8 5 1st Qu. 12 10 12 11 Median 12 11 12 12 Mean 12.16 10.92 12.33 13.07 3rd Qu. 12 12 12 14.5 Max. 24 36 35 44 The CMFLW generated under this research for average lane width to adjust from the base condition of twelve-foot lanes is shown in Table 48 for rural divided and undivided roadways and in Table 49 for urban divided and undivided roadways. These values are shown graphically in Figure 26. Referring to Figure 26, there is a clear trend in each of these datasets that as lane widths increase, ROR crashes are expected to increase. It is recommended that future research evaluate the interaction of lane width and shoulder width. It is possible that as lane width increases on each of these roads that the shoulder width was decreased to accommodate the larger lane widths.

82 Table 48. Rural Average Lane Width CMF (CMFLW). Average Lane width (feet) Divided Undivided CMF 95% Confidence Pr(>|z|) CMF 95% Confidence Pr(>|z|) 10 0.80 0.83 0.76 < 2e-16 0.84 0.88 0.79 8.51E-11 11 0.89 0.91 0.87 0.91 0.94 0.89 12 1.00 1.00 1.00 1.00 1.00 1.00 13 1.12 1.10 1.15 1.09 1.06 1.12 14 1.26 1.21 1.31 1.20 1.13 1.26 15 1.41 1.32 1.50 1.31 1.20 1.42 Table 49. Urban Average Lane Width CMF (CMFLW). Average Lane width (feet) Divided Undivided CMF 95% Confidence Pr(>|z|) CMF 95% Confidence Pr(>|z|) 10 0.92 0.94 0.90 < 2e-16 0.66 0.67 0.64 < 2e-16 11 0.96 0.97 0.95 0.81 0.82 0.80 12 1.00 1.00 1.00 1.00 1.00 1.00 13 1.04 1.03 1.05 1.23 1.22 1.25 14 1.09 1.07 1.11 1.52 1.49 1.56 15 1.13 1.10 1.16 1.88 1.81 1.95 Figure 26. Lane Width CMF (CMFLW). 0.00 0.50 1.00 1.50 2.00 10 11 12 13 14 15 C M F Average Lane Width (feet) Urban Div Urban Undiv Rural Div Rural Undiv

83 CMF for Right Shoulder Width The representation of right shoulder width within each of the databases has been repeated in Table 50 for convenience. Notice that there is a good deal of variety between divided and undivided roadways, however, the same variety is not observed by area type. It is suggested that the tabulation of the right shoulder width CMF (CMFSW) be bound by the available data and exclude the outlining data points to ensure the CMF is a true representation of the data it was generated from. Recall that the SPF base condition for right shoulder width is equal to or greater than eight feet. The base condition for this companion CMF is therefore the same. Table 50. Right Shoulder Width Database Representation. Rural Divided Rural Undivided Urban Divided Urban Undivided Min. 0 0 0 0 1st Qu. 8 2 8 0 Median 10 3 10 2 Mean 9.071 3.962 8.325 2.94 3rd Qu. 10 6 10 5 Max. 22 40 23 30 The CMFSW generated under this research to adjust from the base condition of eight foot shoulders is shown in Table 51 for rural divided and undivided roadways and in Table 52 for urban divided and undivided roadways. These values are shown graphically in Figure 27. Referring to Figure 27, there is a clear trend in each of these datasets that as shoulder width increases, the expected number of ROR crashes decreases. This observation is more dominant in the rural environment than in the urban environment. Table 51. Rural Average Right Shoulder Width CMF (CMFSW). Right shoulder width (feet) Divided Undivided CMF 95% Confidence Pr(>|z|) CMF 95% Confidence Pr(>|z|) 2 1.26 1.33 1.19 2.47E-16 1.56 1.59 1.53 < 2e-16 4 1.17 1.21 1.12 1.35 1.37 1.33 6 1.08 1.10 1.06 1.16 1.17 1.15 ≥8 1.00 1.00 1.00 1.00 1.00 1.00 Table 52. Urban Right Shoulder Width CMF (CMFSW). Right shoulder width (feet) Divided Undivided CMF 95% Confidence Pr(>|z|) CMF 95% Confidence Pr(>|z|) 2 1.06 1.09 1.04 2.58E-07 1.16 1.19 1.14 < 2e-16 4 1.04 1.06 1.03 1.11 1.12 1.09 6 1.02 1.03 1.01 1.05 1.06 1.04 ≥8 1.00 1.00 1.00 1.00 1.00 1.00

84 Figure 27. Right Shoulder Width CMF (CMFSW). CMF for Posted Speed Limit Posted speed limit was investigated as a major constraint and used to characterize the SPFs along with highway and area type. It was found, however, that posted speed limit does not present a clear trend for crash frequency in either urban or rural environments. The posted speed limit limitation was therefore removed from the SPF development. It was desirable, however, to capture the influence posted speed limit has on crash frequency through a CMF. Posted Speed Limit has been found, in other roadside safety research, to have a counterintuitive effect on crash frequency (i.e., increases in posted speed lead to decreases in frequency). These CMFs have been developed to validate these previous findings and capture the influence of posted speed limit. The representation of posted speed limit within each of the databases has been repeated in Table 53 for convenience. The rural divided dataset is generally posted at a higher speed than the other dataset sets. The minimum and maximum values, however, appear to be generally the same. The posted speed limit CMF (CMFPSL) is bound by the available data and should be tabulated to convey these boundaries. The base condition for this CMF has been established as 55 miles per hour (mph). Table 53. Posted Speed Limit Database Representation. Rural Divided Rural Undivided Urban Divided Urban Undivided Min. 25 20 20 20 1st Qu. 60 55 55 35 Median 65 55 60 40 Mean 63.3 52.6 57.22 40.98 3rd Qu. 70 55 65 50 Max. 70 65 70 70 0.00 0.50 1.00 1.50 2.00 2 3 4 5 6 7 8 C M F Right Shoulder Width (feet) Urban Div Urban Undiv Rural Div Rural Undiv

85 The CMFPSL generated under this research to understand the influence of posted speed limit on ROR crash frequency is shown in Table 54 for rural divided and undivided roadways and in Table 55 for urban divided and undivided roadways. These values are shown graphically in Figure 28. Referring to Figure 28, for both urban and rural undivided roadways, the posted speed limit does not influence ROR crash frequency. Both urban and rural divided roadways, however, present a downward trend in ROR crash frequency as the posted speed limit increases. Similar findings for encroachment data were found under NCHRP 22-27. [Ray12] Table 54. Rural Posted Speed Limit CMF (CMFPSL). Posted Speed Limit (mph) Divided Undivided CMF 95% Confidence Pr(>|z|) CMF 95% Confidence Pr(>|z|) 25 1.55 1.71 1.41 < 2e-16 1.08 1.12 1.04 8.58E-06 30 1.44 1.57 1.33 1.07 1.10 1.04 35 1.34 1.43 1.26 1.05 1.08 1.03 40 1.25 1.31 1.19 1.04 1.06 1.02 45 1.16 1.20 1.12 1.03 1.04 1.01 50 1.08 1.09 1.06 1.01 1.02 1.01 55 1.00 1.00 1.00 1.00 1.00 1.00 60 0.93 0.91 0.94 0.99 0.98 0.99 65 0.86 0.84 0.89 0.97 0.96 0.99 70 0.80 0.76 0.84 0.96 0.94 0.98 Table 55. Urban Posted Speed Limit CMF (CMFPSL). Posted Speed Limit (mph) Divided Undivided CMF 95% Confidence Pr(>|z|) CMF 95% Confidence Pr(>|z|) 25 1.64 1.72 1.56 < 2e-16 1.02 1.05 0.98 4.36E-01 30 1.51 1.57 1.45 1.01 1.05 0.98 35 1.39 1.44 1.35 1.01 1.04 0.98 40 1.28 1.31 1.25 1.01 1.03 0.99 45 1.18 1.20 1.16 1.01 1.02 0.99 50 1.09 1.09 1.08 1.00 1.01 1.00 55 1.00 1.00 1.00 1.00 1.00 1.00 60 0.92 0.91 0.93 1.00 0.99 1.00 65 0.85 0.83 0.86 1.00 0.98 1.01 70 0.78 0.76 0.80 0.99 0.97 1.01

86 Figure 28. Posted Speed Limit CMF (CMFPSL). CMF for Number of Lanes The proportional representation of the number of lanes per segment within each of the databases has been repeated in Table 56 for convenience. Not surprisingly, the divided roadways are dominated by four-lane roadways and the undivided roadways are dominated by two lanes roadways. The tabulation of the number of lanes CMF (CMFNL) will be bound by the available data to ensure the CMFs accurately represent the data from which they were derived. Recall that the SPF base condition for divided roadways is four lanes (i.e., two lanes per barrel, NL=4) and the base condition for undivided roadways is two lanes. The base condition for these companion CMFs is therefore the same. Table 56. Number of Lanes by Proportion within Databases. Rural Divided Rural Undivided Urban Divided Urban Undivided NL=2 3.33 98.59 3.41 66.33 NL=4 85.01 1.13 63.59 29.34 NL=6 8.90 --- 19.74 1.26 NL=8 0.09 --- 6.24 --- The CMFNL generated under this research for number of lanes to adjust from the base condition of two for undivided and four for divided, as shown in Table 57 for rural divided and undivided roadways and in Table 58 for urban divided and undivided roadways. These values are shown graphically in Figure 29. Referring to Figure 29, for all datasets except the rural undivided, as the number of lanes increases the expected ROR crash frequency also increases. 0.00 0.50 1.00 1.50 2.00 25 35 45 55 65 C M F Posted Speed Limit (mph) Urban Div Urban Undiv Rural Div Rural Undiv

87 Table 57. Rural Number of Lanes CMF (CMFNL). Number of Lanes Divided Undivided CMF 95% Confidence Pr(>|z|) CMF 95% Confidence Pr(>|z|) 2 0.83 0.86 0.80 < 2e-16 1.00 1.00 1.00 < 2e-16 4 1.00 1.00 1.00 0.91 0.90 0.92 6 1.20 1.16 1.25 --- --- --- 8 1.45 1.34 1.56 --- --- --- Table 58. Urban Number of Lanes CMF (CMFNL). Number of Lanes Divided Undivided CMF 95% Confidence Pr(>|z|) CMF 95% Confidence Pr(>|z|) 2 0.89 0.90 0.87 < 2e-16 1.00 1.00 1.00 < 2e-16 4 1.00 1.00 1.00 1.11 1.10 1.11 6 1.13 1.11 1.15 --- --- --- 8 1.27 1.23 1.32 --- --- --- Figure 29. Number of Lanes CMF (CMFNL). Directional Divided and Undivided CMFs The direction of travel in relation to the highway alignment and grade was believed to be a crucial element of predicting ROR crash frequency. The representation of both degree of curve (DOC) and percent grade (PG) within each of the datasets has been repeated in Table 59 and Table 60 for convenience. -0.10 0.10 0.30 0.50 0.70 0.90 1.10 1.30 1.50 2 4 6 8 C M F Number of Lanes Urban Div Urban Undiv Rural Div Rural Undiv

88 Table 59. DOC Database Representation. Rural Divided Rural Undivided Urban Divided Urban Undivided Min. 0 0 0 0 1st Qu. 0 0 0 0 Median 0 0 0 0 Mean 0.1927 0.3170 0.2261 0.1027 3rd Qu. 0 0 0 0 Max. 270 76 270 76 Table 60. PG Database Representation. Rural Divided Rural Undivided Urban Divided Urban Undivided Min. 0 0 0 0 1st Qu. 0 0 0 0 Median 0 0 0 0 Mean 0.5151 0.8318 0.3796 0.3664 3rd Qu. 0.26 0 0 0 Max. 12 20 11 18 Recall that the SPF base conditions for highway alignment is straight and flat. The base condition for these companion CMFs are therefore straight and flat. The Ohio segment data were collected in such a way that grades of ±3 percent were not recorded (i.e., flat). The Washington data were therefore considered flat at ±3 percent for consistency. The percent of grade CMF (CMFPG) has been derived and set to unity at ±3 percent. There is no definition of which degree of curvature or radius is considered straight enough to be straight, however there are practical limitations to only considering those roadways with a DOC of zero as straight. It is recommended that a DOC of ten or less be considered the base condition (i.e., straight) for the purposes of developing CMFDOC. Undivided Highway CMF for Horizontal Curvature The Horizontal Curve CMF for undivided roadways considered vehicles which exited the right roadway edge, in the direction of travel under consideration. This assessment included, therefore, vehicles traveling in the primary direction and exiting right and vehicles traveling in the opposing direction and existing left (relative to the primary direction). For analysis purposes, the analyst will predict the number of right edge crashes in the primary direction then right edge crashes in the opposing direction. The coefficients from the models for right edge crash frequency to be used as companion CMFs for undivided roadways are shown in Table 61. Note the CMF xi variable input is DOC. The results are shown graphically in Figure 30 for DOC. Negative numbers in Figure 30 represent left curving curves. As can be seen in Figure 30, right edge crashes increase more when the road curves to the left with respect to the direction of travel for both rural and urban roadways than when the road curves to the right with respect to the direction of travel. The urban CMF, however, does not have a large size effect and the confidence intervals include unity. While the urban CMFDOC can be referenced to observe a trend, it is not suggested for inclusion in the HSM.

89 Table 61. Horizontal Curve CMF for Undivided Right Edge in Direction Under Evaluation (CMFDOC). 𝐶𝐶𝐶𝐶𝐶𝐶𝑝𝑝 = 𝑒𝑒𝛽𝛽𝑖𝑖∙(𝑋𝑋𝑖𝑖−10) CMFi Alignment change Rural Undivided Right edge in direction under evaluation Urban Undivided Right edge in direction under evaluation ßi 95% Confidence ßi 95% Confidence CMFDOC Curve L 0.0635 0.0580 0.0068 0.0068 -0.0065 0.0196 Curve R 0.0286 0.0221 -0.0154 -0.0154 -0.0302 -0.0010 Where xi is the degree of curvature. Figure 30. Undivided Highway Horizontal Curve CMF. Divided Highway CMF for Horizontal Curvature The divided highway analysis for horizontal curves considered two different cross- sectional models for both the urban and the rural highway types. The models considered only right edges or only left edges. The coefficients proposed for the rural divided highway curvature CMFs are shown in Table 62 and for the urban divided curvature CMFs are shown in Table 63. 0.00 0.50 1.00 1.50 2.00 2.50 3.00 -25 -15 -5 5 15 25 C M F Degree of Curvature Urban Undiv Rural Undiv

90 Table 62. Rural Divided Highway Horizontal Curve CMF (CMFDOC). 𝐶𝐶𝐶𝐶𝐶𝐶𝑝𝑝 = 𝑒𝑒𝛽𝛽𝑖𝑖∙(𝑋𝑋𝑖𝑖−10) CMFi Alignment change in direction under evaluation Divided Left edge in direction under evaluation Divided Right edge in direction under evaluation ßi 95% Confidence ßi 95% Confidence CMFDOC Curve L 0.0092 0.0012 0.0183 0.0083 -0.0010 0.0191 Curve R 0.0108 0.0013 0.0233 0.0111 0.0031 0.0225 Where xi is the degree of curvature Table 63. Urban Divided Highway Horizontal Curve CMF (CMFDOC). 𝐶𝐶𝐶𝐶𝐶𝐶𝑝𝑝 = 𝑒𝑒𝛽𝛽𝑖𝑖∙(𝑋𝑋𝑖𝑖−10) CMFi Alignment change in direction under evaluation Divided Left edge in direction under evaluation Divided Right edge in direction under evaluation ßi 95% Confidence ßi 95% Confidence CMFDOC Curve L 0.0066 0.0004 0.0116 0.0032 -0.0044 0.0086 Curve R 0.0101 0.0055 0.0145 0.0064 0.0010 0.0109 Where xi is the degree of curvature A visual assessment of the divided right and left edge models can be made with the assistance of Figure 31 for horizontal curvature. Negative numbers on the x-axis represent left curving curves. The analysis of the effect of DOC on ROR crashes for divided highways in both urban and rural areas shows a trend toward increasing crashes with increasing DOC, however, the size effect is small and the confidence interval is wide. It is suggested, therefore, that a DOC CMF for divided roadway ROR crash frequency be excluded from the HSM.

91 a) Divided Left edge in direction under evaluation b) Divided Right edge in direction under evaluation Figure 31. Visual Assessment of Rural and Urban Divided Highway Horizontal Curve CMF (CMFDOC). 0.00 0.50 1.00 1.50 2.00 2.50 3.00 -25 -15 -5 5 15 25 C M F Degree of Curvature Urban Div Rural Div 0.00 0.50 1.00 1.50 2.00 2.50 3.00 -25 -15 -5 5 15 25 C M F Degree of Curvature Urban Div Rural Div

92 Undivided Highway CMF for Vertical Grade The Vertical Grade CMF for undivided roadways considered vehicles which exited the right roadway edge, in the direction of travel under consideration. This assessment included, therefore, vehicles traveling in the primary direction and exiting right and vehicles traveling in the opposing direction and existing left (relative to the primary direction). For analysis purposes, the analyst will predict the number of right edge crashes in the primary direction then right edge crashes in the opposing direction. The coefficients from the models for right edge crash frequency to be used as companion CMFs for undivided roadways, are shown in Table 64 for rural and urban undivided roadways. Note the CMF xi variable input is PG as a percentage. The results are shown graphically in Figure 32 for PG. Negative numbers represent down-grades. The PG for urban and rural roads have opposite effects. While the effects are small, the effects are significant. Observations for DOC and PG in urban areas would suggest that introduction of either curvature or grade in an urban area may reduce ROR crashes on undivided roadways while it has the opposite effect in rural areas. Table 64. Rural and Urban Undivided Highway Vertical Grade CMF (CMFPG). 𝐶𝐶𝐶𝐶𝐶𝐶𝑝𝑝 = 𝑒𝑒𝛽𝛽𝑖𝑖∙(𝑋𝑋𝑖𝑖−3) CMFi Alignment change Rural Undivided Right edge in direction under evaluation Urban Undivided Right edge in direction under evaluation ßi 95% Confidence ßi 95% Confidence CMFPG Uphill 0.0104 0.0060 0.0147 -0.0303 -0.0387 -0.0219 Downhill 0.0194 0.0152 0.0237 -0.0245 -0.0329 -0.0162 Where xi is the percent of grade. Figure 32. Undivided Highway Vertical Grade CMF. 0.00 0.50 1.00 1.50 2.00 2.50 3.00 -15 -10 -5 0 5 10 15 C M F Percent Grade Urban Undiv Rural Undiv

93 Divided Highway CMF for Vertical Grade The divided highway analysis for vertical grade considered cross-sectional models which included both right and left edge crashes for the urban and the rural highway types. The coefficients proposed for the rural and urban divided highway grade CMFs are shown in in Table 65. Table 65. Rural and Urban Divided Highway Vertical Grade CMF (CMFPG). 𝐶𝐶𝐶𝐶𝐶𝐶𝑝𝑝 = 𝑒𝑒𝛽𝛽𝑖𝑖∙(𝑋𝑋𝑖𝑖−3) CMFi Alignment change in direction under evaluation Rural Divided edges in direction under evaluation Urban Divided edges in direction under evaluation ßi 95% Confidence ßi 95% Confidence CMFPG Uphill 0.0492 0.0346 0.0637 -0.1670 -0.1784 -0.1557 Downhill 0.0596 0.0452 0.0739 -0.1433 -0.1544 -0.1322 Where xi is the percent of grade The PG CMFs are summarized in Figure 33. The size effect is large and the confidence interval is small, therefore, these findings are evidence of the influence PG has on ROR crash frequency. These findings should be considered for implementation in the HSM. Figure 33. Visual Assessment of Rural and Urban Divided Highway Vertical Grade CMF (CMFPG). 0.00 0.50 1.00 1.50 2.00 -15 -10 -5 0 5 10 15 C M F Percent Grade (%) RURAL URBAN

94 Discussion of CMFROADWAY Results Documented above are the cross-sectional models used to model the influence of on- road features on ROR crash frequency. Numerous CMFs have been developed from these models, including: • Lane width, • Right shoulder width, • Posted Speed Limit, • Number of lanes, • Percentage of heavy vehicles, • Horizontal Curvature, and • Vertical Grade. The 95% confidence intervals are shown with the CMFs derived above and represent very little variation in the CMF value, indicating that the CMFs shown here are suitable for inclusion in the HSM. Several of the CMFs proposed here are either new concepts or applied in a conceptually new way (i.e., directionally dependent). It is essential to remember that many of these concepts are only new to the HSM and have been well established in roadside safety literature for several decades. It is recommended that the CMFs presented above for lane width, shoulder width, posted speed limit, number of lanes, horizontal curvature, and vertical grade be considered for inclusion in the HSM except where noted.