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

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36 SPFEDGE DERIVATION Many model constructs were explored. This research considered speed as a major design constraint, however, it was revealed that speed does not present a clear trend toward predicting ROR crash frequency. It was found, however, that the highway characteristics of urban and rural areas have differing influence over predicting ROR crash frequency, therefore it was recommended that the distinction between the urban and rural areas which is present in other chapters of the HSM be maintained for predicting ROR crashes. The vehicle mix, as represented by PT, was found to significantly and differently influence crash frequency in rural and urban areas. Traditionally, the HSM does not model PT, however, PT is generally explicitly considered in roadside design (e.g., test level of barrier). PT is typically available along with AADT information in roadway data. After consultation with the AASHTO HSM Steering Committee, it was decided to deviate from traditional HSM model formation to include PT for the reasons noted. Regression models which include more traditional HSM exposure terms such as AADT and segment length variables, but did not include vehicle-miles-traveled (VMT) or PT were compared to forms which did include VMT and PT, variables more traditionally used to explain roadside encroachments. Models were explored where AADT was considered as the sole independent variable and segment length was offset, therefore, had no coefficient. Models were explored with both AADT and VMT and a segment length offset. Models with only VMT and a segment length offset were reviewed. Finally, models with AADT as the independent variable and VMT offset were also reviewed. The rural and urban divided roadways are best represented by a model having a log transformed AADT as an explanatory variable, PT as an explanatory variable, and segment length as the offset. The rural and urban undivided roadways are best represented by a model which included AADT and PT as the explanatory variables while including VMT as the offset. The undivided models, therefore, include AADT twice where the divided models include AADT only once. This additional AADT term is believed to be needed to represent the cross-centerline vehicles which may perpetuate a ROR crash or prevent an ROR crash (i.e., avoiding a side swipe may lead to running off the road or a head-on crash on the road may preclude the lane departure from becoming a run-off-road crash). The second AADT term in the undivided model is likely necessary to distinguish between lower and higher volume roadways and the probability of crashing to the left verses a head-on crash; the probability of an opposite-direction side swipe resulting in a vehicle leaving the roadway; and/or the probability of evasive maneuvers to avoid opposite-direction crashes resulting in ROR crashes. The divided and undivided highway SPFs take the form here: 𝑆𝑆𝑆𝑆𝐶𝐶𝑈𝑈𝑈𝑈𝐴𝐴𝐹𝐹𝑆𝑆 = 𝑒𝑒𝐴𝐴1∙𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 ∙ 𝑒𝑒𝐴𝐴2∙𝑃𝑃𝐴𝐴 ∙ 𝑒𝑒𝐴𝐴3 ∙ 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 ∙ 365 ∙ 𝐿𝐿 𝑆𝑆𝑆𝑆𝐶𝐶𝐴𝐴𝐹𝐹𝑆𝑆 = 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴4 ∙ 𝑒𝑒𝐴𝐴5∙𝑃𝑃𝐴𝐴 ∙ 𝑒𝑒𝐴𝐴6 ∙ 𝐿𝐿 Where: SPFi = Frequency of ROR crashes by segment edge per year. AADT = Annual Average Daily Traffic (vpd). PT = Percent Trucks (%). L = Segment Length (miles). Ai = Regression coefficients.

37 Models were developed by crash edge and are documented below. For some crashes, the edge could not be determined, however, it was important to maintain “unknown edge” crashes in the counts of total frequency. A model was developed for the right and left encroachment directions, the right plus left direction, and right plus left plus half the unknown encroachment directions for both divided and undivided roadways. Half of the unknown crashes were used in the development of the fourth model because it was assumed that there was an equal probability that a vehicle could drive off the road in the primary or opposing direction and the edge could then be proportioned based on the known departure proportions. The results of the modeling efforts were used to develop a relationship for the number of vehicles which crashed on each edge for divided roadways. It is important to develop this relationship and subsequently account for the unknown departure crashes to ensure under- predicting the frequency is not an issue. The unknown crashes were explicitly modeled for undivided roadways. Crashes by encroachment (i.e., not crash) direction, however, were modeled for each direction for both divided and undivided roadways. While all of these models are not used in the final SPFEDGE, each are documented herein for comparison and completeness. Exponential relationships were used for divided highways to improve the understanding of edge departures. This series of equations shows the steps taken to reduce the model to find these relationships: 𝑆𝑆𝑆𝑆𝐶𝐶𝐴𝐴𝐹𝐹𝑆𝑆𝑎𝑎 = 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴4𝑎𝑎 ∙ 𝑒𝑒𝐴𝐴5𝑎𝑎∙𝑃𝑃𝐴𝐴 ∙ 𝑒𝑒𝐴𝐴6𝑎𝑎 ∙ 𝐿𝐿 𝑆𝑆𝑆𝑆𝐶𝐶𝐴𝐴𝐹𝐹𝑆𝑆𝑏𝑏 = 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴4𝑏𝑏 ∙ 𝑒𝑒𝐴𝐴5𝑏𝑏∙𝑃𝑃𝐴𝐴 ∙ 𝑒𝑒𝐴𝐴6𝑏𝑏 ∙ 𝐿𝐿 𝑆𝑆𝑆𝑆𝐶𝐶𝐴𝐴𝐹𝐹𝑆𝑆𝑎𝑎 𝑆𝑆𝑆𝑆𝐶𝐶𝐴𝐴𝐹𝐹𝑆𝑆𝑏𝑏 = 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴(𝐴𝐴4𝑎𝑎−𝐴𝐴4𝑏𝑏) ∙ 𝑒𝑒(𝐴𝐴5𝑎𝑎−𝐴𝐴5𝑏𝑏)∙𝑃𝑃𝐴𝐴 ∙ 𝑒𝑒(𝐴𝐴6𝑎𝑎−𝐴𝐴6𝑏𝑏) After knowing this relationship, it can be applied to the model which includes the unknown crash frequency to develop coefficients for the SPF which model the crashes by edge and include the crashes where the edge could not be determined. 𝑆𝑆𝑆𝑆𝐶𝐶𝐴𝐴𝐹𝐹𝑆𝑆𝑎𝑎 𝑆𝑆𝑆𝑆𝐶𝐶𝐴𝐴𝐹𝐹𝑆𝑆𝑏𝑏 ∙ 𝑆𝑆𝑆𝑆𝐶𝐶𝐴𝐴𝐹𝐹𝑆𝑆𝐶𝐶 = 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 (𝐴𝐴4𝑎𝑎−𝐴𝐴4𝑏𝑏+𝐴𝐴4𝑝𝑝) ∙ 𝑒𝑒(𝐴𝐴5𝑎𝑎−𝐴𝐴5𝑏𝑏+𝐴𝐴5𝑝𝑝)∙𝑃𝑃𝐴𝐴 ∙ 𝑒𝑒(𝐴𝐴6𝑎𝑎−𝐴𝐴6𝑏𝑏+𝐴𝐴6𝑝𝑝) RURAL DIVIDED ROADWAYS The dataset used included data from Ohio for 2002 through 2010 and Washington from 2002 through 2007. These data were obtained from HSIS. The resulting PRE-PLE dataset included 124,458 rural, divided segment edges. The data were filtered as follows where the number following the colon is the number of segment edges remaining after that filter: • Consider only segments ≤ 2miles and ≥ 0.1miles: 58,210 segments. • Consider only segments AADT > 0: 58,196 segments. • Consider only twelve-foot lanes: 54,200 segments. • Consider only flat segments (i.e., |Grade| ≤ 3%): 47,810 segments. • Consider only straight segments: 39,386 segments. • Consider only 8 foot or greater right shoulders: 36,916 segments. • Consider only segments with two lanes per barrel (i.e., 4 lanes): 32,306 segments.

38 • Consider only segments with four foot left shoulders: 25,414 segments. A summary of the filtered dataset is provided in Table 14. Each data element was reviewed to determine how closely increases in one element correlate with increases in another data element. For example, if the AADT increases do vehicle crashes increase? This correlation analysis was conducted using the Pearson and Spearman’s correlation coefficients. The results for the divided highway dataset are shown in Table 15. Note that each element is perfectly correlated with itself (i.e., a value of one indicates that one is a linear function of the other). A value of zero indicates the data elements are not correlated. Negative values indicate inverse correlation. Data elements with higher values should be considered for use in the development of the SPF. Pearson’s correlation coefficient assumes: (1) the data elements are normally distributed and (2) if a relationship exists between the elements, it is linear. The Spearman test does not make either of these assumptions but is interpreted in the same manner (i.e., values approaching unity are more closely correlated, zero are not correlated and negative values are inversely correlated). Both correlation measures have been shown in Table 15. By inspection, the VMT appears to have the highest correlation and posted speed limit (PSL) appears to be inversely correlated. Table 14. Descriptive Statistics of Filtered Rural Divided Highway Dataset. Min. 1st Qu. Median Mean 3rd Qu. Max. L 0.1 0.16 0.27 0.4324 0.54 2.00 AADT 710 11,260 15,732 19,053 24,262 67,390 Median width 2 40 60 78.34 76 9999 PT 0 0 13.64 16.45 27.65 63.66 PSL 35 60 65 64.51 70 70 PRE 0 0 0 0.2421 0 10 PLE 0 0 0 0.2211 0 13 UNK 0 0 0 0.1984 0 22 All* 0 0 0 0.5196 1 20 VMT † 44,676 890,469 1,614,461 3,096,834 3,485,969 42,202,760 * All=PRE+PLE+UNK/2 † VMT= 365* AADT * L

39 Table 15. Correlation Matrix for Divided Highway ROR Events and Data Elements. Pearson Correlation Index All PRE PLE L AADT PT PSL VMT All 1.0000 PRE 0.7909 1.0000 PLE 0.7917 0.3557 1.0000 L 0.4404 0.3616 0.3489 1.0000 AADT 0.2782 0.1974 0.2336 0.0539 1.0000 PT 0.1823 0.1490 0.1559 0.2543 0.1704 1.0000 PSL -0.0434 -0.0472 -0.0227 -0.1569 0.1732 -0.2301 1.0000 VMT 0.5646 0.4348 0.4534 0.7619 0.5109 0.2944 -0.0107 1.0000 Spearman Correlation Index All PRE PLE L AADT PT PSL VMT All 1.0000 PRE 0.7561 1.0000 PLE 0.7173 0.2597 1.0000 L 0.3820 0.3104 0.2955 1.0000 AADT 0.2542 0.1845 0.2134 -0.0098 1.0000 PT 0.1932 0.1600 0.1618 0.2619 0.0792 1.0000 PSL -0.0982 -0.0919 -0.0624 -0.1885 0.1298 -0.3731 1.0000 VMT 0.4442 0.3445 0.3479 0.7869 0.5694 0.2611 -0.0748 1.0000 The four rural divided highway models, coefficients for the SPF, and the fit statistics are shown in Table 16. Table 17 shows the derivation of the coefficients for the rural divided SPFEDGE model.

40 Table 16. Resulting Rural Divided Highway SPFEDGE Coefficients and Fit Statistics. glm.nb(formula = PRE ~ log(aadt) + PT + offset(log(SegL)), data = alldata_f, init.theta = 1.5936, link = log) Estimate Std. Error z value Pr(>|z|) A6 (Intercept) -8.0913 0.25 -32.01 <2e-16 A4 log(AADT) 0.7546 0.02 29.14 <2e-16 A5 PT 0.0042 0.00 4.06 4.99e-05 AIC: 26827 BIC 26851 Theta: 1.594 LL -13410.36 Std. Err.: 0.11 Pseudo R2 0.4444 glm.nb(formula = PLE ~ log(aadt) + PT + offset(log(SegL)), data = alldata_f, init.theta = 1.3257, link = log) Estimate Std. Error z value Pr(>|z|) A6 (Intercept) -10.1517 0.28 -36.66 <2e-16 A4 log(AADT) 0.9478 0.03 33.54 <2e-16 A5 PT 0.0057 0.00 5.09 3.55e-07 AIC: 24680 BIC 24704 Theta: 1.3257 LL -12336.82 Std. Err.: 0.09 Pseudo R2 0.4889 glm.nb(formula = (PRE + PLE) ~ log(aadt) + PT + offset(log(SegL)), data = alldata_f, init.theta = 1.6326, link = log) Estimate Std. Error z value Pr(>|z|) A6 (Intercept) -8.3668 0.20 -41.95 <2e-16 A4 log(AADT) 0.8446 0.02 41.37 <2e-16 A5 PT 0.0054 0.00 6.67 2.49e-11 AIC: 38975 BIC 39000 Theta: 1.6326 LL -19484.74 Std. Err.: 0.07 Pseudo R2 0.1927 glm.nb(formula = (All)~ log(aadt) + PT + offset(log(SegL)), data = alldata_f, init.theta = 1.5258, link = log) Estimate Std. Error z value Pr(>|z|) A6 (Intercept) -8.7840 0.20 -44.92 <2e-16 A4 log(AADT) 0.8987 0.02 44.92 <2e-16 A5 PT 0.0048 0.00 6.05 1.46e-09 AIC: 41222 BIC 41247 Theta: 1.5258 LL -20608.11 Std. Err.: 0.06 Pseudo R2 0.1462 *All=PRE+PLE+UNK/2

41 Table 17. Derivation of Rural Divided Highway SPFEDGE Coefficients. SPF Coefficients Proportion of Right edge crashes Proportion of Left edge crashes Right edge crashes per segment per year Left edge crashes per segment per year PRE/(PRE+PLE) PLE/(PRE+PLE) (PRE/(PRE+PLE)) *All (PLE/(PRE+PLE)) *All A4: AADT -0.0900 0.1032 0.8087 1.0019 A5: PT -0.0012 0.0003 0.0036 0.0051 A6: Intercept 0.2755 -1.7849 -8.5085 -10.5689 RURAL UNDIVIDED ROADWAYS The dataset included data from Ohio for 2002 through 2010 and Washington from 2002 through 2007. These data were obtained from HSIS. The resulting PRE and ORE dataset included 2,058,268 rural segment edges. The data were filtered as follows: • Consider only segments ≤ 2miles and ≥ 0.1miles: 637,060 segments. • Consider only segments AADT > 0: 635,464 segments. • Consider only twelve-foot lanes: 204,162 segments. • Consider only flat segments (i.e., |Grade| ≤ 3%): 163,948 segments. • Consider only straight segments: 137,310 segments. • Consider only 8 foot or greater right shoulders: 39,556 segments. • Consider only segments with a posted speed value > 0: 39,520 segments. • Consider only segments with two lanes: 38,974 segments. A summary of the filtered dataset is provided in Table 18. The Pearson and Spearman’s correlation analysis is shown in Table 19. As was found for divided highways, segment length and vehicle-miles-traveled are most closely correlated with crash frequency. Table 18. Descriptive Statistics of Filtered Undivided Highway Dataset. Min. 1st Qu. Median Mean 3rd Qu. Max. L 0.1 0.14 0.23 0.3618 0.42 2.00 AADT 40 2,795 4,514 5,142 6,430 27,540 PT 0.00 6.92 12.02 13.94 18.59 67.15 PSL 25 55 55 54.22 60 65 PR 0 0 0 0.0835 0 5 OL 0 0 0 0.0549 0 4 UNK 0 0 0 0.0759 0 8 All* 0 0 0 0.1523 0 9 VMT 6,643 207,959 386,316 672,453 787,296 8,886,108 *All=PR+OL+UNK/2

42 Table 19. Correlation Matrix for Undivided Highway ROR Events and Data Elements. Pearson Correlation Index All PR OL L AADT PT PSL VMT All 1.0000 PR 0.7846 1.0000 OL 0.6568 0.1515 1.0000 L 0.3307 0.2625 0.2341 1.0000 AADT 0.0925 0.0807 0.0377 -0.0162 1.0000 PT -0.0195 -0.0156 -0.0078 0.0440 -0.1043 1.0000 PSL -0.0045 0.0019 0.0058 0.0467 -0.0966 0.2281 1.0000 VMT 0.3589 0.2920 0.2301 0.8001 0.4156 0.0087 0.0034 1.0000 Spearman Correlation Index All PR OL L AADT PT PSL VMT All 1.0000 PR 0.7659 1.0000 OL 0.6285 0.1311 1.0000 L 0.2559 0.1992 0.1804 1.0000 AADT 0.1116 0.0928 0.0598 -0.0097 1.0000 PT -0.0424 -0.0353 -0.0218 -0.0017 -0.0740 1.0000 PSL -0.0550 -0.0473 -0.0285 -0.0185 -0.1040 0.4053 1.0000 VMT 0.2704 0.2129 0.1793 0.7335 0.6299 -0.0570 -0.1008 1.0000 The four undivided highway models, SPF coefficients and model fit statistics are shown in Table 20. Table 21 shows the derivation of the coefficients for the rural undivided SPFEDGE model.

43 Table 20. Resulting Rural Undivided Highway SPFEDGE Coefficients and Fit Statistics. Glm.nb(formula = PR ~ aadt + PT + offset(lVMT), data = d, init.theta = 1.2804, link = log) Estimate Std. Error z value Pr(>|z|) A3 (Intercept) -1.541e+01 0.04 -315.65 < 2e-16 A1 AADT -5.706e-05 0.00 -10.11 < 2e-16 A2 PT -8.974e-03 0.00 -4.63 3.75e-06 AIC: 20431 BIC 20457 Theta: 1.296 LL -10212.54 Std. Err.: 0.15 Pseudo R2 0.3717 glm.nb(formula = OL ~ aadt + PT + offset(lVMT), data = d init.theta = 1.1893, link = log) Estimate Std. Error z value Pr(>|z|) A3 (Intercept) -1.558e+01 0.05 -260.58 < 2e-16 A1 AADT -1.018e-04 0.00 -13.46 < 2e-16 A2 PT -7.730e-03 0.00 -3.32 0.00091 AIC: 15000 BIC 15026 Theta: 1.189 LL -7497.20 Std. Err.: 0.19 Pseudo R2 0.5388 glm.nb(formula = (PRE)~ aadt + PT + offset(lVMT), data = d, init.theta = 1.3302, link = log) Estimate Std. Error z value Pr(>|z|) A3 (Intercept) -1.481e+01 0.03 -378.32 < 2e-16 A1 AADT -7.419e-05 0.00 -15.83 < 2e-16 A2 PT -8.590e-03 0.00 -5.53 3.28e-08 AIC: 28856 BIC 28882 Theta: 1.330 LL -14425.15 Std. Err.: 0.11 Pseudo R2 0.1125 glm.nb(formula = All ~ aadt + PT + offset(lVMT), data = d, init.theta = 1.1863, link =log) Estimate Std. Error z value Pr(>|z|) A3 (Intercept) -1.475e+01 0.03 -389.43 < 2e-16 A1 AADT -6.535e-05 0.00 -14.67 < 2e-16 A2 PT -9.441e-03 0.00 -6.21 5.17e-10 AIC: 30742 BIC 30768 Theta: 1.1863 LL -15368 Std. Err.: 0.0811 Pseudo R2 0.1113 *All=PRE+UNK/2

44 Table 21. Rural Undivided Highway SPFEDGE Coefficients. SPF Coefficients Right edge crashes per segment per year A1: AADT -6.535e-05 A2: PT -9.441e-03 A3: Intercept -1.475e+01 URBAN DIVIDED ROADWAYS The dataset included data from Ohio for 2002 through 2010 and Washington from 2002 through 2011. These data were obtained from HSIS. The resulting multi-state (i.e., Washington and Ohio) PRE-PLE dataset included 244,050 urban, divided highway segment edges. The data were filtered as follows where the number following the colon is the number of segment edges remaining after that filter: • Consider only segments ≤ 2miles and ≥ 0.1miles: 105,802 segments. • Consider only segments AADT > 0: 105,318 segments. • Consider only twelve-foot lanes: 89,380 segments. • Consider only flat segments (i.e., |Grade| ≤ ±3%): 82,070 segments. • Consider only straight segments: 70,222 segments. • Consider only 8 foot or greater right shoulders: 64,292 segments. • Consider only greater then 0mph: 63,963 segments. • Consider only segments with two lanes per barrel (i.e., 4 lanes): 39,920 segments. • Consider only segments with four foot left shoulders: 24,025 segments. A summary of the filtered dataset is provided in Table 22. The correlation analysis was conducted using the Pearson and Spearman’s correlation coefficients, as shown in Table 23.

45 Table 22. Descriptive Statistics of Filtered Multi-State Urban Divided Highway Dataset. Min. 1st Qu. Median Mean 3rd Qu. Max. L 0.1 0.16 0.27 0.4152 0.52 2.00 AADT 780 18,181 29,883 34,464 45,611 155,340 Median width 2 40 44 83.92 64 9999 PT 0.00 6.59 11.04 13.86 19.22 55.44 PSL 20 55 60 60.31 65 70 PRE 0 0 0 0.3669 0 14 PLE 0 0 0 0.3691 0 11 UNK 0 0 0 1.555 1 141 All* 0 0 0 1.456 2 74 VMT † 34,164 1,554,352 2,974,969 5,072,729 6,342,094 50,969,272 * All=PRE+PLE+UNK/2 † VMT= (365* AADT * L) Table 23. Correlation Matrix for Multi-State Urban Divided Highway Dataset. Pearson Correlation Index All PRE PLE L AADT PT PSL VMT All 1.0000 PRE 0.6187 1.0000 PLE 0.6064 0.4063 1.0000 L 0.4560 0.3850 0.3816 1.0000 AADT 0.1423 0.1389 0.1504 -0.0504 1.0000 PT 0.0963 0.0796 0.0974 0.1072 -0.0941 1.0000 PSL 0.0359 0.0885 0.1040 0.0646 0.1946 0.2318 1.0000 VMT 0.5073 0.4509 0.4544 0.7490 0.4516 0.0658 0.1623 1.0000 Spearman Correlation Index All PRE PLE L AADT PT PSL VMT All 1.0000 PRE 0.6565 1.0000 PLE 0.6554 0.3163 1.0000 L 0.4523 0.3348 0.3228 1.0000 AADT 0.1902 0.1505 0.1769 -0.0289 1.0000 PT 0.1524 0.0984 0.1061 0.1574 -0.0630 1.0000 PSL 0.0970 0.0983 0.1195 0.0840 0.2513 0.3004 1.0000 VMT 0.4791 0.3588 0.3671 0.7329 0.6283 0.0553 0.2250 1.0000

46 Table 24. Resulting Urban Divided Highway SPFEDGE Coefficients and Fit Statistics. glm.nb(formula = PRE ~ log(aadt) + PT+offset(log(SegL)), data = alldata_f, init.theta = 1.2643, link=log) Estimate Std. Error z value Pr(>|z|) A6 (Intercept) -7.1613 0.23 -31.57 <2e-16 A4 AADT 0.6623 0.02 30.76 <2e-16 A5 PT 0.0114 0.00 9.40 <2e-16 AIC: 33344 BIC 33368 Theta: 1.2643 LL -16668.99 Std. Err.: 0.06 Pseudo R2 0.11 glm.nb(formula = PLE ~ log(aadt) + PT + offset(log(SegL)), data = alldata_f, init.theta = 1.1968, link = log) Estimate Std. Error z value Pr(>|z|) A6 (Intercept) -8.1723 0.23 -35.26 <2e-16 A4 AADT 0.7535 0.02 34.33 <2e-16 A5 PT 0.0155 0.00 12.76 <2e-16 AIC: 33375 BIC 33400 Theta: 1.1968 LL -16684.67 Std. Err.: 0.06 Pseudo R2 0.11 glm.nb(formula = (PRE + PLE) ~ log(aadt) + PT + offset(log(SegL)), data = alldata_f, init.theta = 1.3446, link = log) Estimate Std. Error z value Pr(>|z|) A6 (Intercept) -6.9417 0.18 -39.17 <2e-16 A4 AADT 0.7042 0.02 41.85 <2e-16 A5 PT 0.0140 0.00 14.64 <2e-16 AIC: 49187 BIC 49221 Theta: 1.3446 LL -24590.53 Std. Err.: 0.04 Pseudo R2 0.18 glm.nb(formula = (All)~ log(aadt) + PT + offset(log(SegL)), data = alldata_f, init.theta = 0.7822, link = log) Estimate Std. Error z value Pr(>|z|) A6 (Intercept) -5.2816 0.16 -32.08 <2e-16 A4 AADT 0.6092 0.02 38.77 <2e-16 A5 PT 0.0143 0.00 15.42 <2e-16 AIC: 68772 BIC 68796 Theta: 0.7822 LL -34382.95 Std. Err.: 0.02 Pseudo R2 0.09 *All=PRE+PLE+UNK/2

47 Table 25. Derivation of Urban Divided Highway SPFEDGE Coefficients. SPF Coefficients Proportion of Right edge crashes Proportion of Left edge crashes Right edge crashes per segment per year Left edge crashes per segment per year (PRE/(PRE+PLE)) *All (PLE/(PRE+PLE)) *All A4: AADT -0.0419 0.0493 0.5673 0.6585 A5: PT -0.0026 0.0015 0.0117 0.0158 A6: Intercept -0.2196 -1.2306 -5.5012 -6.5122 URBAN UNDIVIDED ROADWAYS The dataset included data from Ohio for 2002 through 2010 and Washington from 2002 through 2011. These data were obtained from HSIS. The resulting PRE and ORE dataset included 485,898 urban segment edges. The data were filtered as follows: • Consider only segments ≤ 2miles and ≥ 0.1miles: 181,340 segments. • Consider only segments AADT > 0: 179,788 segments. • Consider only twelve-foot lanes: 57,468 segments. • Consider only flat segments (i.e., |Grade| ≤ 3%): 49,970 segments. • Consider only straight segments: 46,148 segments. • Consider only greater than 0mph: 44,652 segments. • Consider only segments with two lanes: 37,140 segments. • Consider only 8 foot wide or greater right shoulders: 10,727 segments. A summary of the filtered dataset is provided in Table 26. The Pearson and Spearman’s correlation analysis is shown in Table 27. Table 26. Descriptive Statistics of Filtered Multi-State Urban Undivided Highway Dataset. Min. 1st Qu. Median Mean 3rd Qu. Max. L 0.1 0.14 0.22 0.3304 0.38 1.94 AADT 357 5,696 8,640 9,480 11,790 42,836 PT 0.00 3.68 6.13 8.18 11.04 50.11 PSL 25 40 50 48.22 55 60 PR 0 0 0 0.1077 0 5 OL 0 0 0 0.0761 0 4 UNK 0 0 0 0.5520 0 47 All* 0 0 0 0.4145 0 26 VMT 14,334 406318 691,,420 1,122,688 1,312,350 11,504,070 *All=PR+OL+UNK/2

48 Table 27. Correlation Matrix for Multi-State Urban Undivided Highway Dataset. Pearson Correlation Index All PR OL L AADT PT PSL VMT All 1.0000 PR 0.4901 1.0000 OL 0.4420 0.2085 1.0000 L 0.3747 0.2884 0.2896 1.0000 AADT 0.0373 0.0330 0.0187 -0.0347 1.0000 PT -0.0272 0.0142 0.0058 0.0017 -0.1363 1.0000 PSL 0.0274 0.0321 0.0468 0.0763 -0.0246 0.1841 1.0000 VMT 0.3475 0.2674 0.2502 0.7899 0.4279 -0.0589 0.0278 1.0000 Spearman Correlation Index All PR OL L AADT PT PSL VMT All 1.0000 PR 0.6160 1.0000 OL 0.5280 0.1878 1.0000 L 0.3373 0.2100 0.2167 1.0000 AADT 0.0538 0.0408 0.0286 -0.0511 1.0000 PT -0.0417 -0.0091 -0.0112 -0.0316 -0.0729 1.0000 PSL 0.0123 0.0197 0.0415 0.0462 -0.0658 0.2365 1.0000 VMT 0.3138 0.2064 0.2026 0.7366 0.5937 -0.0698 0.0123 1.0000

49 Table 28. Resulting Urban Undivided Highway SPFEDGE Coefficients and Fit Statistics. glm.nb(formula = PR ~ AADT + PT + offset(lVMT), data = d, init.theta = 1.205, link = log) Estimate Std. Error z value Pr(>|z|) A3 (Intercept) -1.550E+01 0.09 -181.38 < 2e-16 A1 AADT -6.464E-05 0.00 -9.85 < 2e-16 A2 PT 6.034e-03 0.04 1.42 0.156 AIC: 6849 BIC 6871 Theta: 1.205 LL -3421.34 Std. Err.: 0.21 Pseudo R2 0.09 glm.nb(formula = OL ~ AADT + PT + offset(lVMT), data = d init.theta = 1.252, link = log) Estimate Std. Error z value Pr(>|z|) A3 (Intercept) -1.574E+01 0.10 -157.209 < 2e-16 A1 AADT -7.403E-05 0.00 -9.417 < 2e-16 A2 PT 2.873e-03 0.00 0.27 0.569 AIC: 5225 BIC 5247 Theta: 1.252 LL -2609.63 Std. Err.: 0.29 Pseudo R2 0.11 glm.nb(formula = (PRE)~ AADT + PT + offset(lVMT), data = d, init.theta = 1.103, link = log) Estimate Std. Error z value Pr(>|z|) A3 (Intercept) -1.493E+01 0.07 -217.25 < 2e-16 A1 AADT -6.809E-05 0.00 -12.83 < 2e-16 A2 PT 4.546e-03 0.00 1.31 0.193 AIC: 9695 BIC 9716 Theta: 1.108 LL -4844.29 Std. Err.: 0.12 Pseudo R2 0.10 glm.nb(formula = All ~ AADT + PT + offset(lVMT), data = d, init.theta = 0.4694, link =log) Estimate Std. Error z value Pr(>|z|) A3 (Intercept) -1.400E+01 0.06 -235.018 < 2e-16 A1 AADT -7.178E-05 0.00 -15.799 < 2e-16 A2 PT -1.156e-02 0.00 -3.408 0.00 AIC: 15469 BIC 15490 Theta: 0.4694 LL -7731.45 Std. Err.: 0.02 Pseudo R2 0.09 *All=PRE+UNK/2

50 Table 29. Derivation of Urban Undivided Highway SPFEDGE Coefficients. SPF Coefficients Right edge crashes per segment per year A1: AADT -7.178E-05 A2: PT -1.156e-02 A3: Intercept -1.400E+01 SPFEDGE RESULTS The base conditions of the rural and urban divided and undivided models are essentially the same, as shown in Table 30. Table 30. Rural and Urban Base Conditions for SPFEDGE. Condition Divided Undivided Lane width 12’ Grade ±3%: Degree of Curvature Zero Right shoulder width ≥8’ Number of lanes 2 lanes per barrel 2 lanes Left shoulder width 4’ NA The divided and undivided highway SPFs discussed above take this form before simplification: 𝑆𝑆𝑆𝑆𝐶𝐶𝑈𝑈𝑈𝑈𝐴𝐴𝐹𝐹𝑆𝑆 = 𝑒𝑒𝐴𝐴1∙𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 ∙ 𝑒𝑒𝐴𝐴2∙𝑃𝑃𝐴𝐴 ∙ 𝑒𝑒𝐴𝐴3 ∙ 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 ∙ 365 ∙ 𝐿𝐿 𝑆𝑆𝑆𝑆𝐶𝐶𝐴𝐴𝐹𝐹𝑆𝑆 = 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴4 ∙ 𝑒𝑒𝐴𝐴5∙𝑃𝑃𝐴𝐴 ∙ 𝑒𝑒𝐴𝐴6 ∙ 𝐿𝐿 Where: SPFi = Frequency of ROR crashes by segment edge per year. AADT = Annual Average Daily Traffic (vpd). PT = Percent trucks (%). L = Segment Length (miles). Ai = Regression coefficient. Table 31 summarizes the results and represents the recommendations for Undivided SPFEDGE for consideration for inclusion in the HSM. Table 32 summarizes the results and represents the recommendations for Divided SPFEDGE for consideration for inclusion in the HSM.

51 Table 31. Undivided Highway SPFEDGE Coefficients. SPF Coefficients Rural Urban PRE or ORE PRE or ORE A1: AADT -6.535e-05 -7.178E-05 A2: PT -9.441e-03 -1.156e-02 A3: Intercept -1.475e+01 -1.400E+01 Table 32. Divided Highway SPFEDGE Coefficients. SPF Coefficients Rural Urban PRE PLE PRE PLE A4: AADT 0.8087 1.0019 0.5673 0.6585 A5: PT 0.0036 0.0051 0.0117 0.0158 A6: Intercept -8.5085 -10.5689 -5.5012 -6.5122 The coefficients developed for the divided and undivided highway ROR crash models were used to visually evaluate the results. The mean value of the PT from each dataset was used for each graph. Figure 10 shows the proportion of ROR crashes by edge mile of rural divided highway for both the right and left edge. Figure 11 provides these same proportions for the urban divided model. The x-axis of these figures are AADT, however, the urban dataset includes a broader range of AADT values, therefore, the range on the figure is broader. Notice for both divided highway models (i.e., rural and urban), the proportion of vehicles which crash to the right (i.e., blue line) is larger than the proportion of vehicles which crash left (i.e., red line) at low AADT values, however, these lines cross for both models at approximately 40,000 vpd. This indicates that a higher proportion of vehicles crash to the left, that is the median side, in both rural and urban environments at volumes greater than 40,000 vpd. Figure 10. Proportion of Rural Divided Highway Vehicle ROR Crashes by Edge and AADT. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 20,000 40,000 60,000 80,000 Pr op or tio n of R O R C ra sh es AADT (vpd) PRE PLE

52 Figure 11. Proportion of Urban Divided Highway Vehicle ROR Crashes by Edge and AADT. Figure 12 provides the proportion of edge crashes for the rural undivided model. Figure 13 provides these same proportions for the urban undivided model. Notice these figures are also similar. It is theorized that approximately 55 percent of the vehicle crash right for undivided roadways and this is a constant relationship, however, the proportion of vehicles having an ROR crash from existing left across the centerline is dependent on the amount of traffic in the opposing direction. These left exiting vehicles fail to reach the roadside edge at higher traffic volumes because they become involved in head-on or opposite-direction crashes when more vehicles are present in the opposite lane. In essence, opposing traffic is blocking the encroaching vehicle from reaching the opposite edge. Figure 12. Proportion of Rural Undivided Highway Vehicle ROR Crashes by Edge Mile and AADT. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 50,000 100,000 150,000 200,000 Pr op or tio n of R O R C ra sh es AADT (vpd) PRE PLE 0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000 0 5,000 10,000 15,000 20,000 25,000 30,000 Pr op or tio n of R O R C ra sh es AADT (vpd) PR OL

53 Figure 13. Proportion of Urban Undivided Highway Vehicle ROR Crashes by Edge Mile and AADT. These figures show the effect of AADT and edges on divided and undivided roads are not the same nor is the effect constant. Figure 14 and Figure 15 show the predicted frequency of ROR crashes per edge mile for both the right and left edges of the rural divided highway and the urban divided highway. Each of these figures are bound by the data, which is to say the x-axis is limited to the AADT values used in the analysis and the y-axis is limited by the predicted crashes. A single figure, with the results on the same scale, is provided for comparison of the rural and urban divided highway edge predictions (see Figure 16). The frequency predictions for urban ROR edge crashes of all severities are higher than for rural ROR crash predictions of all severities. Figure 14. Frequency of Rural Divided Highway ROR Crashes by Edge. 0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000 0 10,000 20,000 30,000 40,000 50,000 Pr op or tio n of R O R C ra sh es AADT (vpd) PR OL 0 0.5 1 1.5 2 2.5 0 20,000 40,000 60,000 80,000 R O R C ra sh es P er E dg e M ile P er Ye ar AADT (vpd) PRE PLE

54 Figure 15. Frequency of Urban Divided Highway ROR Crashes by Edge. Figure 16. Comparison of Urban and Rural Divided SPFEDGE. Figure 17 and Figure 18 show the rural undivided and urban undivided predicted frequency of primary right edge crashes (i.e., PR plus OL departures). While it is interesting to discuss the differences in departure direction for undivided roadways, it is not relevant to the final HSM model. It is only relevant to roadside safety practitioners and will be used to coordinate the RSAPv3 findings with the HSM predictive methods. Again, these figures are bound by the AADT values found in the data. These findings are superimposed on the same scale and shown in Figure 19. Again, the urban model predicts a higher frequency of all severity ROR crashes than the rural model. 0 1 2 3 4 5 6 0 50,000 100,000 150,000 200,000 R O R C ra sh es P er E dg e M ile P er Ye ar AADT (vpd) PRE PLE 0 1 2 3 4 5 6 0 50,000 100,000 150,000 200,000 R O R C ra sh es P er E dg e M ile P er Ye ar AADT (vpd) Urban PRE Urban PLE Rural PRE Rural PLE

55 Figure 17. Frequency of Rural Undivided Highway ROR Crashes by Edge. Figure 18. Frequency of Urban Undivided Highway ROR Crashes by Edge. 0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0 5,000 10,000 15,000 20,000 25,000 30,000 R O R C ra sh es P er E dg e M ile P er Ye ar AADT (vpd) PRE 0.0000 0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000 1.6000 0 10,000 20,000 30,000 40,000 50,000 R O R C ra sh es P er E dg e M ile P er Ye ar AADT (vpd) PRE

56 Figure 19. Comparison of Urban and Rural Undivided SPFEDGE. Notice that the undivided crashes by edge, as shown in Figure 19, display what roadside safety researchers refer to as the “Cooper hump.” Cooper collected encroachment data on rural undivided Canadian roads in the 1970s. The Cooper data shows that roadside encroachments increase with volume at lower AADTs then decrease after a peak at around 10,000 veh/day as found here. [Cooper80] Comparison to Other Studies In the late 50’s and early 60’s Hutchinson and Kennedy conducted a direct observation study of encroachments (i.e., not crashes) on medians in Illinois to “determine the significance and nature of vehicle encroachments on certain types of medians under selected field conditions…” to better understand the function of medians. [Hutchinson62] Encroachment locations and extent of encroachment where identified through observation of the snow covered medians and supplemental data was gathered from available police accident reports and construction plans. In total, detailed data was collected for approximately 207 miles of road, primarily US 66 and FAI 74. Hutchinson concluded that the frequency of encroachments can be related to traffic volume below practical capacity. Furthermore, as traffic reaches capacity, the rate of encroachment becomes constant. [Hutchinson62] Hutchinson and Kennedy provided Figure 20 to demonstrate the relationship between AADT and encroachments. 0.0000 0.2000 0.4000 0.6000 0.8000 1.0000 1.2000 1.4000 1.6000 0 10,000 20,000 30,000 40,000 50,000 R O R C ra sh es P er E dg e M ile P er Ye ar AADT (vpd) Urban PRE Rural PRE

57 Figure 20. Hutchinson and Kennedy Encroachment Frequency. Another attempt at collection of encroachment data was undertaken in 1978 in five Canadian providences. This dataset has been dubbed the Cooper data. [Cooper80] Data collection took place from July to October in 1978 on 59 road sections. Approximately 20 percent of the segments were divided highways and the remainder were two-lane undivided highways with speed limits of about 80 km/hr (i.e., 50 mph). The traffic volumes ranged from 6,000 to 45,000 vpd for the divided highways and from about 1,000 to 13,000 vpd for the undivided highways. Encroachments that occurred in the median area were not collected. Cooper analyzed the data and developed the relationship presented in Figure 21. Miaou investigated the possibility of combining both approaches in, “Estimating Roadside Encroachment Rates with the Combined Strengths of Accident and Encroachment- Based Approaches.” [Miaou01] Miaou used crash prediction models without collecting additional data. He modeled the relationship of run-off-road crashes for rural two-lane roads using Negative Binomial regression models. Miaou’s model related the expected crashes to highway characteristics, using crash data. [Miaou01] The model takes this form for flat, straight, undivided, twelve-foot lanes: 𝑆𝑆 = � 365 ∗ 𝐴𝐴𝐴𝐴𝐴𝐴 1,000,000 � 𝑒𝑒𝑒𝑒𝑝𝑝�−0.42−�0.04∗ 𝐴𝐴𝐴𝐴𝐴𝐴 1,000�+0.45� Where: E = expected number of roadside crashes per mile per year ADT = average annual daily traffic between 1,000 to 12,000 vpd

58 Figure 21. Cooper Base Encroachment Rate.[Cooper80] Miaou does not explicitly state if this model is for both edges of the road or only a single edge, therefore, it is assumed all encroachment directions are included and the model included both undivided edges and should be divided by two for only one edge. The results are shown graphically for a flat, straight, undivided PRE with twelve-foot lanes in Figure 22. Figure 22. Findings of FHWA-RD-01-124. [Miaou01] 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 2,000 4,000 6,000 8,000 10,000 12,000 R ig ht E dg e C ra sh es /m i/y ea r AADT (vpd)

59 Ray et al. reanalyzed the so-called Cooper data and documented the findings in the NCHRP 22-27 final report. [Cooper80; Ray12]. Ray et al. note, with respect to encroachments on undivided roadways in the Cooper data, “…21.6 % of the right edge encroachments started as left-side departures that crossed the opposing lane before encroaching.” About 6.7% of the encroachments on four-lane divided highways were described as left-side departures which encroached toward the median and then crossed both the median and the opposite travel lanes to exit the right edge. RSAPv3 tabulates the base encroachment frequency in units of total encroachments/mi/yr while assuming there is an equal probability to encroach left and right. The undivided model is reduced by 78.4% (i.e., 100-21.6) to represent right-side encroachments on either edge, then divided by two to obtain one encroachment direction (i.e., in this case, primary right), then multiplied by four to include all possible encroachment directions. The undivided model is as follows: For AADT ≤ 15,000 veh/day ENCR/MI/YR = 0.784∙2∙1.6∙(365∙AADT/1,000,000) ∙ e(0.4997-0.2092∙AADT/1000) For AADT > 15,000 veh/day ENCR/MI/YR = 0.784∙2∙1.6∙(365*AADT/1,000,000)∙0.0715 The divided model is reduced by 0.933 to remove the vehicles which encroached across the median to the right edge. The divided model is then reduced by 0.5 to consider only the primary right edge. Finally, the model is multiplied by 4 to consider all edges of the divided highway. Therefore, the RSAPv3 divided model considers all encroachment directions under the assumption that each direction is equally probable. The divided model is as follows: For AADT ≤ 40,000 veh/day ENCR/MI/YR = 0.933∙2∙1.6∙(365∙AADT/1,000,000) ∙ e(-0.2104-0.04128∙AADT/1000) For AADT > 40,000 veh/day ENCR/MI/YR = 0.933∙2∙1.6∙(365∙AADT/1,000,000)∙0.1554

60 Figure 23. RSAPv3 Tabulated Encroachment Model. Divided Model Comparison The Hutchinson and Kennedy data is limited to medians of divided highways, therefore, is comparable to the divided PLE models developed under this effort if divided by two. The RSAPv3 tabulation of the reanalyzed Cooper data can be compared to the divided PLE model by considering ¼ of the tabulated RSAPv3 divided highway model. This comparison for divided PLE models is shown in Figure 24. Notice the Hutchinson and Kennedy encroachment curve exceeds the crash predictions and the RSAPv3 tabulation of the reanalyzed Copper data generally predicts more encroachments than the modeled crash predictions found under this research. This outcome is expected, as an encroachment does not always result in a crash. Also notice that the urban crash prediction model (i.e., red dashed line) briefly crosses the RSAPv3 encroachment prediction model at the base of the “hump” between 35,000 and 55,000 vpd. Recall the RSAPv3 encroachment prediction is assumed after 30,000 vpd for divided roadways because there is no encroachment data collected for volumes greater than 30,000 vpd. This could provide some evidence that the “hump” should be less severe, particularly for urban areas. 0.00 5.00 10.00 15.00 20.00 0 20,000 40,000 60,000 80,000 100,000 En cr oa ch m en ts /m ile /y ea r AADT (vpd) 2LN UNDIV 4LN DIV

61 Figure 24. Comparison of Divided Models for Encroachments and Crashes per Mile per Year. Undivided Model Comparison The RSAPv3 tabulation of the reanalyzed undivided Cooper data can be compared to the undivided PRE models by considering ½ of the tabulated RSAPv3 undivided highway model. This comparison for undivided PRE models is shown in Figure 25. The Miaou crash prediction model has also been divided by two, as discussed above, and is shown in Figure 25. The Miaou model is for rural roads, however, it generally tracks with the urban model. This discrepancy was not considered further due to the numerous assumptions made about the Miaou model to allow for comparison. Both the urban and rural crash prediction models (i.e., green dashed and green solid lines) predict more crashes then encroachments at the end of the available Cooper traffic volume data collection. Recall Cooper collected encroachments on undivided roadways with traffic volumes less than 12,000. This would again provide evidence that the “hump” should be less severe at the onset of the Cooper data extrapolation. Otherwise, the crash predictions are less than the encroachment predictions, as is expected. 0 1 2 3 4 5 6 7 0 50,000 100,000 150,000 200,000 R O R C ra sh es P er E dg e M ile P er Y ea r* AADT (vpd) H&K PLE Encroachments RSAPv3 Divided PLE Urban PLE Rural PLE *H&K and RSAPv3 in enc/mi/yr

62 Figure 25. Comparison of Undivided Models for Encroachments and Crashes per Mile per Year. In summary, these crash prediction models appear to represent the subtle nuances of ROR crashes and help to better extrapolate the often over-extended Cooper data. The SPFs developed under this effort generally provide predictions of crashes which are in harmony with values considered reasonable by roadside safety professionals. It is recommended that these models and accompanying coefficients be considered for inclusion in the HSM to model ROR crashes for both divided and undivided highway edges. 0.0000 0.5000 1.0000 1.5000 2.0000 2.5000 3.0000 3.5000 4.0000 4.5000 5.0000 0 10000 20000 30000 40000 50000 R ig ht E dg e C ra sh es /m i/y ea r* AADT (vpd) Urban PRE Rural PRE RSAPv3 PRE Miaou PRE *RSAPv3 in enc/mi/yr