Crash Modification Factors in the Highway Safety Manual: Resources for Evaluation (2023) / Chapter Skim
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Appendix F Development of Crash Modification Functions for Shoulder and Median Width
Appendix F Development of Crash Modification Functions for Shoulder and Median Width
Pages 126-147
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From page 126... ...
Appendix F Development of Crash Modification Functions for Shoulder and Median Width F-1
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From page 127... ...
Parameter Estimates for SV Crashes on Undivided Roadways (Model 1)
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From page 128... ...
However, it may also be that the results are not transferable to sites with different lane widths or number of lanes. In the original analysis, separate models were developed for divided and undivided roadways and for total, single-vehicle, and multi-vehicle crashes.
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From page 129... ...
4. Does the shoulder width CMF change with median width?
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Parameter Estimates for SV Crashes on Divided Roadways (Model 1) Parameter Estimate Standard Error CA -5.1871 0.3202 KY -5.8013 0.3067 MN -5.0227 0.3066 a 0.3519 0.0593 b -0.0353 0.0119 c 0.8775 0.0679 d 0.5734 0.0308 k 0.6466 0.0238 AIC 15,964 BIC 16,013 Based on Model 1, the CMF associated with changing from SHLDWID1 to SHLDWID2 will be the following: πΆπΆπΆπΆπΆπΆ = ππ β0.0353Γ(πππππππππππππ·π·2 βπππππππππππππ·π·1 )
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Parameter Estimates for SV Crashes on Divided Roadways (Model 2) Parameter Estimate Standard Error CA -5.1388 0.3200 KY -5.7166 0.3069 MN -4.9683 0.3064 a 0.3508 0.0591 b1 -0.1234 0.0255 b2 0.0832 0.0214 c 0.8791 0.0676 d 0.5715 0.0370 k 0.6427 0.0237 AIC 15,952 BIC 16,007 Based on Model 2, the CMF associated with changing from SHLDWID1 to SHLDWID2 will be the following: πΆπΆπΆπΆπΆπΆ = ππ (β0.1234+0.0832Γπ
π
π
π
π
π
)
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From page 132... ...
Parameter Estimates for SV Crashes on Divided Roadways (Model 3) Parameter Estimate Standard Error CA -9.7749 1.0183 KY -10.3552 1.0078 MN -9.5918 1.0108 a 0.3327 0.0592 b1 0.7202 0.1593 b2 -0.0781 0.0164 c 0.7906 0.0692 d 1.0462 0.1044 k 0.6365 0.0237 AIC 15,943 BIC 15,998 Based on Model 3, the CMF associated with changing from SHLDWID1 to SHLDWID2 can be estimated as follows (the CMF depends on AADT)
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From page 133... ...
Parameter Estimate Standard Error CA -9.4728 1.0177 KY -10.0217 1.0080 MN -9.2855 1.0103 a 0.3336 0.0590 b1 0.5969 0.1623 b2 -0.0737 0.0164 b3 0.0761 0.0216 c 0.7972 0.0691 d 1.0180 0.1043 k 0.6334 0.0236 AIC 15,933 BIC 15,994 Based on Model 4, the CMF associated with changing from SHLDWID1 to SHLDWID2 will be the following: πΆπΆπΆπΆπΆπΆ = ππ (0.5969β0.0737Γln(π΄π΄π΄π΄π΄π΄π΄π΄)
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From page 134... ...
Three alternate models were estimated. Variable definitions are: CA = intercept term if site is from California KY = intercept term if site is from Kentucky MN = intercept term if site is from Minnesota SHLDWID = average shoulder width in feet MEDWID = median width in feet LEFTTURN = 1 if a left-turn lane is present; 0 otherwise MBAR = 1 if a median barrier is present; 0 otherwise No evidence was seen that the CMF for shoulder width changes with AADT or that the CMF increases beyond a certain value of shoulder width.
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From page 135... ...
With this model formulation the relationship with median width still implies fewer multi-vehicle crashes as the median width increases but the amount of decrease is smaller with a median barrier. However, the overdispersion parameter, AIC, and BIC, are higher for Model 2 compared to Model 1, indicating that the simpler Model 1 could be preferred.
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From page 136... ...
Parameter Estimates for MV Crashes on Divided Roadways (Model 3) Parameter Estimate Standard Error CA -10.1114 0.4205 KY -9.9258 0.3966 MN -10.2702 0.4036 a1 -0.0079 0.0012 a2 0.0068 0.0047 b1 -0.2502 0.0322 b2 0.1123 0.0266 c 0.4654 0.1153 d 0.4545 0.0705 e 1.1775 0.0401 k 1.1549 0.0423 AIC 13,905 BIC 13,973 The results are consistent with models 1 and 2.
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From page 137... ...
Similarly, the CMF for changing median width from MEDWID1 to MEDWID2 can be estimated as follows: πΆπΆπΆπΆπΆπΆ = ππ β0.0076Γ(πππππππππππ·π·2 βπππππππππππ·π·1 ) Total Crashes For total crashes on divided roadways the following questions were identified for CMFunction development: 1.
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Parameter Estimate Standard Error CA -8.6363 0.8889 KY -8.8450 0.8827 MN -8.6124 0.8820 a -0.0017 0.0008 b1 0.1887 0.1454 b2 0.1045 0.0197 b3 -0.0393 0.0148 c 0.7221 0.0678 d 0.2542 0.0494 e 1.0649 0.0914 k 0.6893 0.0211 AIC 19,422 BIC 19,489 Recommended CMF for Total Crashes on Divided Roads The recommended CMFs are based on Model 1. The CMF associated with changing from SHLDWID1 to SHLDWID2 will be the following: πΆπΆπΆπΆπΆπΆ = ππ (0.1887β0.0393Γln(π΄π΄π΄π΄π΄π΄π΄π΄)
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From page 139... ...
Parameter Estimates for SV Crashes on Undivided Roadways (Model 1) Parameter Estimate Standard Error CA -3.5063 1.1145 KY -3.8189 1.1369 MN -4.1449 1.0959 a1 -0.5291 0.2006 a2 0.0559 0.0222 b -1.2544 0.6665 c 0.4326 0.1236 k 0.6440 0.0653 AIC 2,173 BIC 2,206 For comparison, a model was estimated with a single parameter for shoulder width, whereby the CMF is on a simple per foot basis.
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Parameter Estimate Standard Error CA -5.8996 0.6119 KY -6.2051 0.6566 MN -6.5028 0.6044 a -0.0251 0.0166 b -1.3187 0.6721 c 0.6692 0.0678 k 0.6566 0.0660 AIC 2,178 BIC 2,207 Recommended CMF for Single-Vehicle Crashes on Undivided Roads Based on Model 2, the recommended CMF for shoulder width is the following: πΆπΆπΆπΆπΆπΆ = ππ β0.0251Γ(πππππππππππππ·π·2 βπππππππππππππ·π·1 ) Multi-Vehicle Crashes For multi-vehicle crashes on undivided roadways the following questions were identified for CMFunction development: 1.
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Parameter Estimates for MV Crashes on Undivided Roadways (Model 2) Parameter Estimate Standard Error CA -7.9617 1.1933 KY -7.1789 1.2278 MN -6.9707 1.1527 a1 -0.8829 0.2310 a2 0.0895 0.0255 b 0.9055 0.1315 k 0.9393 0.0928 AIC 2,103 BIC 2,132 Recommended CMF for Multi-Vehicle Crashes on Undivided Roads Based on Model 2, the recommended CMF for changing shoulder width is the following: πΆπΆπΆπΆπΆπΆ = ππ (β0.8829+0.0895Γln (π΄π΄π΄π΄π΄π΄π΄π΄)
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From page 142... ...
Parameter Estimates for Total Crashes on Undivided Roadways (Model 1) Parameter Estimate Standard Error CA -4.9902 0.8975 KY -4.7625 0.9229 MN -4.7228 0.8759 a1 -0.5928 0.1665 a2 0.0594 0.0184 b 0.6766 0.0996 k 0.5571 0.0464 AIC 2,727 BIC 2,756 Model 2 estimated a single parameter for the right shoulder width CMF.
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From page 143... ...
For multi-vehicle crashes on divided roadways, the CMF for shoulder width was seen to be higher if the right shoulder is paved and the CMF for median width is higher if a median barrier is present. For single-vehicle and total crashes on undivided roadways, there was some indication that the CMF for shoulder width decreases as AADT increases but this more complicated model formulation may be overfit to the data.
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From page 144... ...
The base condition for this CMF is a median width of 30 ft. The CMF applies to total crashes but represents the effect of median width in reducing cross-median collisions; the CMF assumes that non intersection collision types other than cross-median collisions are not affected by median width.
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Rural Multi-Lane Undivided Roadways CMF2ru -- Shoulder Width The CMF for shoulder width on undivided segments is based on the work of Harkey et al.
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0.87 Figure 11-9. CMFWRA for Shoulder Width on Undivided Segments CMFTRA is determined from Table 11-13 based on the applicable shoulder type and shoulder width.
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From page 147... ...
Lord (2009) , Impact of Shoulder Width and Median Width on Safety, NCHRP Report 633, National Cooperative Highway Research Program.
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