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Federal Highway Administration Research and Technology
Coordinating, Developing, and Delivering Highway Transportation Innovations

 
REPORT
This report is an archived publication and may contain dated technical, contact, and link information
Publication Number:  FHWA-HRT-16-054    Date:  October 2016
Publication Number: FHWA-HRT-16-054
Date: October 2016

 

Investigating the Impact of Lack of Motorcycle Annual Average Daily Traffic Data in Crash Modeling and the Estimation of Crash Modification Factors

 

Chapter 5. Data Analysis and Results

As outlined in chapter 4, the project team investigated two groups, or avenues. The methods for avenue A focus on investigating (1) the difference in predictive performance for motorcycle SPFs calibrated with motorcycle AADT versus total AADT, (2) the relation of total crash SPFs to motorcycle crash SPFs so jurisdictions without motorcycle volumes could predict motorcycle crashes using total crash SPFs, and (3) methods to predict segment-level motorcycle AADT. The methods for avenue B focus on the differences in CMF estimates found when using motorcycle AADT versus total AADT when applying before-after or cross-sectional regression CMF estimation methods.

The avenue A models were developed with data collected from Florida and Pennsylvania, both of which had a large number of locations with an estimated motorcycle AADT and that could provide linkable roadway inventory, traffic, and crash data, Data acquired from Virginia were used for validation of the models developed.

Avenue A Model Type A1

The purpose of model type A1 was to explore how much predictive power is lost when motorcycle volumes are unknown and how this lack of information would affect an evaluation of motorcycle countermeasures. The project team attempted models for all motorcycle crashes (MOTO), single-vehicle motorcycle crashes (MOTOSINGLE), and multi-vehicle motorcycle crashes (MOTOMULTI).

For each dependent variable, the project team attempted three separate models, with motorcycle AADT, total AADT, and motorcycle and non-motorcycle AADT as separate terms. In some cases, mainly due to limited samples, it was not possible to develop robust models for each of the three dependent variables and for each of the three independent AADT variable specifications.

Additional variables were included where possible, but it should be noted that the models developed were done to derive the most accurate models for predicting crash frequency, as opposed to the objectives of causal models. With this goal, it is possible to include variables that indicate an opposite relationship to crashes than what is expected or to treat a logically categorical variable, such as speed, as continuous. If a variable correlates with other variables that affect crash risk, then the counterintuitive relationship frequently occurs.

To assess a variable for inclusion in the model, it was added to the basic SPF including the AADT terms and the model estimated. Then, an assessment was made of the improvement in fit with the additional variable as measured by the overdispersion parameter and the statistical significance of the parameter estimate.

The project team developed the A1 models using both Florida and Pennsylvania data and using data from Virginia for validation. The first three sections of this chapter detail the analysis and results based on the data from these three States. The final section presents the results of the assessment of how well the four sets of models predict motorcycle crashes for high-crash locations.

Florida

Models were successfully calibrated for site types 1–4. The data for site types 5 and 6 (rural collector/local and urban collector/local) did not allow for models to be developed. As table 4 shows, these site types had very few motorcycle crashes.

Note that the posted speed limit variable, SPDLIMT, which appears in the types 2–4 models, has been modeled as a continuous variable. Often, posted speed is considered as a categorical variable since limits are typically set in multiples of 5, (i.e. 45 mi/h (72 km/h), 55 mi/h (89km/h), etc.). During model development, however, treating posted speed as a categorical variable showed inconsistent results and no logical groupings of posted speed into similar categories.

The following sections detail the calibrated models and goodness-of-fit assessments for each site type.

Florida Type 1—Rural Freeways

For rural freeways, models were successfully calibrated for MOTO and MOTOSINGLE crashes but not for multi-vehicle motorcycle crashes. The models are of two forms, dependent on the exposure measure used, as seen in figure 13 and figure 14.

Figure 13. Equation. Florida rural freeway crashes per year using motorcycle traffic counts. Crashes per year equals the product of exponential value of intercept times length to the power of b times AVGMOTO to the power of c.

Figure 13. Equation. Florida rural freeway crashes per year using motorcycle traffic counts.

Figure 14. Equation. Florida rural freeway crashes per year using total traffic counts. Crashes per year equals the product of exponential value of intercept times length to the power of b times AVGAADT to the power of c.

Figure 14. Equation. Florida rural freeway crashes per year using total traffic counts.

Attempts to estimate models with separate terms for motorcycle and non-motorcycle volumes were not successful because illogical parameter estimates resulted in decreasing crash frequencies with motorcycle volumes. Such illogical results can occur when highly correlated variables are included in the same model. Table 19 provides the parameter estimates for these models with the SE provided in parenthesis after the parameter estimates. Table 20 provides overall goodness-of-fit statistics. Table 21 provides goodness-of-fit statistics from CURE plots for variables included in the models.

Table 19. A1 models for Florida type 1 sites.
Model Type Parameter MOTO (SE) MOTOSINGLE (SE)
Motorcycle AADT Intercept -5.5368 (0.6033) -5.1341 (0.7741)
Motorcycle AADT b 0.8239 (0.0801) 0.8939 (0.1102)
Motorcycle AADT c 0.6622 (0.1274) 0.4755 (0.1663)
Motorcycle AADT Dispersion 0.4353 (0.2160) 1.1346 (0.4327)
Total AADT Intercept -15.2081 (1.7870) -14.3297 (2.4202)
Total AADT b 0.8289 (0.0780) 0.9101 (0.1099)
Total AADT c 1.2118 (0.1684) 1.0847 (0.2292)
Total AADT Dispersion 0.2886 (0.1920) 0.9233 (0.3863)
Table 20. Goodness-of-fit statistics for A1 models for Florida type 1 sites.
Crash Type Exposure Measure Total Observed MAD Modified R2 Dispersion
MOTO Motorcycle AADT 174 0.43 0.65 0.44
MOTO Total AADT 174 0.41 0.77 0.29
MOTOSINGLE Motorcycle AADT 111 0.32 0.34 1.14
MOTOSINGLE Total AADT 111 0.31 0.44 0.92
Table 21. CURE plot statistics for A1 models for Florida type 1 sites.
Crash Type Exposure Measure Max CURE Deviation for AVGMOTO CURE Deviation for AVGMOTO (Percent) Max CURE Deviation for LENGTH CURE Deviation for LENGTH (Percent)
MOTO Motorcycle AADT 15.83 11 7.42 3
MOTO Total AADT 12.55 5 8.35 3
MOTOSINGLE Motorcycle AADT 10.42 5 7.80 3
MOTOSINGLE Total AADT 10.83 5 6.83 3

The goodness-of-fit statistics indicate that the models using motorcycle AADT performed very similarly to those using total AADT for both MOTO and MOTOSINGLE crashes. In fact, there are some indications that the models using total AADT may be slightly better when considering the modified R2 and dispersion parameter.

Florida Type 2—Urban Freeways

For urban freeways, the project team successfully calibrated models for MOTO, MOTOSINGLE, and MOTOMULTI crashes. The models are of two forms, depending on the exposure measure used, as shown in figure 15 and figure 16.

Figure 15. Equation. Florida urban freeway crashes per year using motorcycle traffic counts. Crashes per year equals the product of exponential value of intercept times length to the power of b times AVGMOTO to the power of c times exponential value of open parenthesis d times curve plus e times SPDLIMT plus f times SURFWIDTH closed parenthesis.

Figure 15. Equation. Florida urban freeway crashes per year using motorcycle traffic counts.

Figure 16. Equation. Florida urban freeway crashes per year using total traffic counts. Crashes per year equals the product of exponential value of intercept times length to the power of b times AVGAADT to the power of c times exponential value of open parenthesis d times curve plus e times SPDLIMT plus f times SURFWIDTH closed parenthesis.

Figure 16. Equation. Florida urban freeway crashes per year using total traffic counts.

Where:
CURVE = 1 if a horizontal curve is present in the segment and 0 if not.

Table 3 provides definitions for the other variables. As with the results for type 1, illogical parameter estimates resulted when terms for motorcycle and non-motorcycle volumes were included in the same model. Table 22 provides the parameter estimates for these models, and table 23 provides overall goodness-of-fit statistics. Table 24 provides goodness-of-fit statistics from CURE plots for variables included in the models. Table 25 provides calibration factors for each level of the non-continuous variables that were included in at least one of the models for that crash type.

Table 22. A1 models for Florida type 2 sites.
Model Type Parameter MOTO
(SE)
MOTOSINGLE
(SE)
MOTOMULTI
(SE)
Motorcycle AADT Intercept -0.0067
(0.4894)
-1.1643
(0.6538)
-0.2295
(0.5733)
Motorcycle AADT b 0.8107
(0.0480)
0.7942
(0.1191)
0.8121
(0.0579)
Motorcycle AADT c 0.1628
(0.0447)
0.1191
(0.0564)
0.1693
(0.0513)
Motorcycle AADT d 0.2459
(0.0987)
N/A 0.3874
(0.1236)
Motorcycle AADT e -0.0532
(0.0067)
-0.0354
(0.0091)
-0.0654
(0.0080)
Motorcycle AADT f 0.0173
(0.0023)
0.0116
(0.0031)
0.0212
(0.0027)
Motorcycle AADT Dispersion 0.4300
(0.0757)
0.2592
(0.1224)
0.3766
(0.0993)
Total AADT Intercept -10.3484
(0.8758)
-8.4768
(1.2158)
-13.1836
(1.1053)
Total AADT b 0.8080
(0.0442)
0.7853
(0.0580)
0.8194
(0.0547)
Total AADT c 1.0563
(0.0662)
0.7429
(0.0885)
1.2948
(0.0842)
Total AADT d 0.2294
(0.0913)
N/A 0.3752
(0.1153)
Total AADT e -0.0447
(0.0064)
-0.0290
(0.0091)
-0.0537
(0.0078)
Total AADT f N/A N/A N/A
Total AADT dispersion 0.2285
(0.0570)
0.1309
(0.1061)
0.1670
(0.0707)

N/A = Not applicable.

Table 23. Goodness-of-fit statistics for A1 models for Florida type 2 sites.
Crash Type Exposure Measure Total Observed MAD Modified R2 Dispersion
MOTO Motorcycle AADT 921 0.86 0.56 0.43
MOTO Total AADT 921 0.77 0.73 0.23
MOTOSINGLE Motorcycle AADT 385 0.47 0.66 0.26
MOTOSINGLE Total AADT 385 0.46 0.82 0.13
MOTOMULTI Motorcycle AADT 536 0.58 0.59 0.38
MOTOMULTI Total AADT 536 0.50 0.77 0.17
Table 24. CURE plot statistics for A1 models for Florida type 2 sites.
Crash Type Exposure Measure Max Curve Deviation for AVGMOTO CURE Deviation for AVGMOTO (Percent) Max CURE Deviation for LENGTH CURE Deviation for LENGTH (Percent) Max CURE Deviation for SPDLIMT CURE Deviation for SPDLIMT (Percent) Max CURE Deviation for SURFWIDTH CURE Deviation for SURFWIDTH (Percent)
MOTO Motorcycle AADT 54.69 35 22.11 0 65.75 46 67.7 28
MOTO Total AADT 27.39 1 21.31 0 25.59 0 41.21 9
MOTOSINGLE Motorcycle AADT 26.21 16 11.53 0 19.10 4 17.08 10
MOTOSINGLE Total AADT 15.81 0 11.83 0 18.40 3 16.58 0
MOTOMULTI Motorcycle AADT 37.34 41 18.12 16 37.07 19 42.43 30
MOTOMULTI Total AADT 14.23 2 15.88 11 15.99 1 36.81 31
Table 25. Calibration factors for A1 models for Florida type 2 sites.
Crash SPF Conditions Observed Observed/Predicted
MOTO crash SPF using motorcycle AADT with no curvature 706 1.02
MOTO crash SPF using motorcycle AADT with curvature 215 0.95
MOTO crash SPF with total AADT with no curvature 706 1.01
MOTO crash SPF with total AADT with curvature 215 0.97
MOTOMULTI crash SPF using motorcycle AADT with no curvature 423 1.01
MOTOMULTI crash SPF using motorcycle AADT with curvature 113 0.95
MOTOMULTI crash SPF with total AADT with no curvature 423 1.01
MOTOMULTI crash SPF with total AADT with curvature 113 0.98

As was the case for type 1 sites (rural freeways), the goodness-of-fit statistics indicate that the models using total AADT not only performed similarly to those with motorcycle AADT but may be slightly better, especially when considering the modified R2 and dispersion parameter. The calibration factors indicate that both sets of AADT predictor models were just as successful when applied to segments with or without horizontal curves.

Florida Type 3—Rural Arterials

For rural arterials, the project team successfully calibrated models for MOTO, MOTOSINGLE, and MOTOMULTI crashes.

The models are of three forms, one of which uses estimates of motorcycle AADT and other AADT (AVGOTHER = AVGAADT – AVGMOTO), depending on the exposure measure used, as shown in figure 17 through figure 19.

Figure 17. Equation. Florida rural arterial crashes per year using motorcycle traffic counts. Crashes per year equals the product of exponential value of intercept times length to the power of b times AVGMOTO to the power of c times exponential value of open parenthesis e times SPDLIMT plus f times DIVUND plus g times OUTSHLDWID plus h times SURFWIDTH plus i times MEDWIDTH closed parenthesis.

Figure 17. Equation. Florida rural arterial crashes per year using motorcycle traffic counts.

Figure 18. Equation. Florida rural arterial crashes per year using total traffic counts. Crashes per year equals the product of exponential value of intercept times length to the power of b times AVGAADT to the power of c times exponential value of open parenthesis e times SPDLIMT plus f times DIVUND plus g times OUTSHLDWID plus h times SURFWIDTH plus i times MEDWIDTH closed parenthesis.

Figure 18. Equation. Florida rural arterial crashes per year using total traffic counts.

Figure 19. Equation. Florida rural arterial crashes per year using separate traffic counts. Crashes per year equals the product of exponential value of intercept times length to the power of b times AVGMOTO to the power of c times AVGOTHER to the power of d times exponential value of open parenthesis e times SPDLIMT plus f times DIVUND plus g times OUTSHLDWID plus h times SURFWIDTH plus i times MEDWIDTH closed parenthesis.

Figure 19. Equation. Florida rural arterial crashes per year using separate traffic counts.

Where:
DIVUND = 1 if road is undivided; 0 if road is divided. (Note: medwidth is 0 for an undivided road.)
AVGOTHER = Non-motorcycle AADT = AVGAADT – AVGMOTO.

Table 26 provides the parameter estimates for these models, and table 27 provides overall goodness-of-fit statistics. Table 28 provides goodness-of-fit statistics from CURE plots for variables included in the models. Table 29 through table 31 provide calibration factors for each level of the non-continuous variables that were included in at least one of the models for that crash type.

Table 26. A1 models for Florida type 3 sites.
Model Type Parameter MOTO (SE) MOTOSINGLE (SE) MOTOMULTI (SE)
Motorcycle AADT Intercept -1.8929
(0.4016)
-3.5059
(0.5816)
-2.0657
(0.5044)
Motorcycle AADT b 0.8158
(0.0380)
0.8112
(0.0517)
0.8105
(0.0485)
Motorcycle AADT c 0.4904
(0.0442)
0.3901
(0.0611)
0.5806
(0.0568)
Motorcycle AADT d N/A N/A N/A
Motorcycle AADT e -0.0323
(0.0062)
-0.0206
(0.0090)
-0.0418
(0.0078)
Motorcycle AADT f -0.6195
(0.0875)
N/A -0.6275
(0.1100)
Motorcycle AADT g -0.0595
(0.0211)
N/A -0.1043
(0.0295)
Motorcycle AADT h N/A N/A N/A
Motorcycle AADT i N/A 0.0053
(0.0024)
N/A
Motorcycle AADT Dispersion 0.7653
(0.1091)
0.9094
(0.2160)
0.8522
(0.1708)
Total AADT Intercept -5.8092
(0.6436)
-5.6814
(0.8963)
-7.4544
(0.8249)
Total AADT b 0.8299
(0.0392)
0.8260
(0.0518)
0.8080
(0.0482)
Total AADT c 0.7014
(0.0649)
0.4310
(0.0836)
0.8506
(0.0786)
Total AADT d N/A N/A N/A
Total AADT e -0.0332
(0.0062)
-0.0215
(0.0088)
-0.0421
(0.0077)
Total AADT f -0.5221
(0.1262)
N/A N/A
Total AADT g -0.0881
(0.0217)
N/A -0.1364
(0.0296)
Total AADT h N/A N/A N/A
Total AADT Dispersion 0.7699
(0.1093)
1.0111
(0.2286)
0.8010
(0.1671)
Motorcycle AADT and other AADT Intercept -4.5690
(0.6860)
-4.4664
(0.9559)
-6.1709
(0.8906)
Motorcycle AADT and other AADT b 0.8158
(0.0377)
0.8254
(0.0516)
0.8103
(0.0480)
Motorcycle AADT and other AADT c 0.3042
(0.0581)
0.3203
(0.0800)
0.2960
(0.0747)
Motorcycle AADT and other AADT d 0.3820
(0.0798)
0.1493
(0.1090)
0.5771
(0.1040)
Motorcycle AADT and other AADT e -0.0333
(0.0062)
-0.0196
(0.0089)
-0.0422
(0.0077)
Motorcycle AADT and other AADT f -0.4142
(0.0967)
-0.5140
(0.1375)
-0.3190
(0.1218)
Motorcycle AADT and other AADT g -0.0714
(0.0214)
N/A -0.1214
(0.0295)
Motorcycle AADT and other AADT h N/A N/A N/A
Motorcycle AADT and other AADT Dispersion 0.7116
(0.1055)
0.9179
(0.2178)
0.7421
(0.1611)

N/A =Not applicable.

Table 27. Goodness-of-fit statistics for A1 models for Florida type 3 sites.
Crash Type Exposure Measure Total Observed MAD Modified R2 Dispersion
MOTO Motorcycle AADT 1,031 0.40 0.44 0.77
MOTO Total AADT 1,031 0.40 0.44 0.77
MOTO Motorcycle and other AADT 1,031 0.39 0.48 0.71
MOTOSINGLE Motorcycle AADT 449 0.21 0.43 0.91
MOTOSINGLE Total AADT 449 0.21 0.39 1.01
MOTOSINGLE Motorcycle and other AADT 449 0.21 0.43 0.92
MOTOMULTI Motorcycle AADT 582 0.26 0.37 0.85
MOTOMULTI Total AADT 582 0.26 0.43 0.80
MOTOMULTI Motorcycle and other AADT 582 0.26 0.46 0.74
Table 28. CURE plot statistics for A1 models for Florida type 3 sites.
Crash Type Exposure Measure Max CURE Deviation for AVGMOTO CURE Deviation for AVGMOTO (Percent) Max CURE Deviation for LENGTH CURE Deviation for LENGTH (Percent) Max CURE Deviation for SPDLIMT CURE Deviation for SPDLIMT (Percent) Max CURE Deviation for OUTSHLDWID CURE Deviation for OUTSHLDWID (Percent)
MOTO Motorcycle AADT 37.40 0 21.32 0 50.60 7 32.36 1
MOTO Total AADT 88.41 70 18.85 0 60.83 29 26.11 1
MOTO Motorcycle and other AADT 38.67 1 17.85 0 37.79 3 29.70 3
MOTOSINGLE Motorcycle AADT 24.33 1 8.21 0 16.28 3 15.25 0
MOTOSINGLE Total AADT 47.99 56 9.61 0 24.74 8 10.86 0
MOTOSINGLE Motorcycle and other AADT 25.94 2 9.01 0 15.20 3 13.29 0
MOTOMULTI Motorcycle AADT 19.71 1 20.19 6 26.67 3 18.19 2
MOTOMULTI Total AADT 44.70 47 14.53 6 35.54 23 27.60 4
MOTOMULTI Motorcycle and other AADT 20.14 1 15.73 6 24.40 3 23.13 3
Table 29. Calibration factors for A1 MOTO models for Florida type 3 sites.
Crash SPF Conditions Observed Observed/Predicted
MOTO crash SPF using motorcycle AADT for divided roads 529 1.00
MOTO crash SPF using motorcycle AADT for undivided roads 502 1.00
MOTO crash SPF with total AADT for divided roads 529 1.00
MOTO crash SPF with total AADT for undivided roads 502 1.00
MOTO crash SPF using motorcycle AADT and non-motorcycle AADT for divided roads 529 1.00
MOTO crash SPF using motorcycle AADT and non-motorcycle AADT for undivided roads 502 1.00
MOTO crash SPF using motorcycle AADT with no curvature 706 1.02
MOTO crash SPF using motorcycle AADT with curvature 215 0.95
MOTO crash SPF with total AADT with no curvature 706 1.02
MOTO crash SPF with total AADT with curvature 215 0.95
Table 30. Calibration factors for A1 MOTOSINGLE models for Florida type 3 sites.
Crash SPF Conditions Observed Observed/Predicted
MOTOSINGLE crash SPF using motorcycle AADT for divided roads 224 1.00
MOTOSINGLE crash SPF using motorcycle AADT for undivided roads 225 1.00
MOTOSINGLE crash SPF with total AADT for divided roads 224 1.01
MOTOSINGLE crash SPF with total AADT for undivided roads 225 0.99
MOTOSINGLE crash SPF using motorcycle AADT and non-motorcycle AADT for divided roads 224 1.01
MOTOSINGLE crash SPF using motorcycle AADT and non-motorcycle AADT for undivided roads 225 0.99
Table 31. Calibration factors for A1 MOTOMULIT models for Florida type 3 sites.
Crash SPF Conditions Observed Observed/Predicted
MOTOMULTI crash SPF using motorcycle AADT for divided roads 305 0.99
MOTOMULTI crash SPF using motorcycle AADT for undivided roads 277 1.01
MOTOMULTI crash SPF with total AADT for divided roads 305 0.99
MOTOMULTI crash SPF with total AADT for undivided roads 277 1.01
MOTOMULTI crash SPF using motorcycle AADT and non-motorcycle AADT for divided roads 305 0.99
MOTOMULTI crash SPF using motorcycle AADT and non-motorcycle AADT for undivided roads 277 1.01
MOTOMULTI crash SPF using motorcycle AADT with no curvature 423 1.01
MOTOMULTI crash SPF using motorcycle AADT with curvature 113 0.95
MOTOMULTI crash SPF with total AADT with no curvature 423 1.01
MOTOMULTI crash SPF with total AADT with curvature 113 0.95

The goodness-of-fit results in table 27 indicate overall that models with total AADT performed as well as those with motorcycle AADT in terms of MAD, modified R2, and dispersion parameter. However, the CURE plot statistics indicate that the models with motorcycle AADT outperformed those with total AADT for these measures. As expected, some measures (MAD, modified R2, and dispersion parameter) indicate that some models (single- and multi-vehicle crashes) that include both motorcycle AADT and non-motorcycle AADT can outperform models with only motorcycle AADT. Finally, the calibration factors in table 29 indicate that all three sets of AADT predictor models were just as successful when applied to segments with the two level s of the two indicator variables.

Florida Type 4—Urban Arterials

For urban arterials, the project team successfully calibrated models for MOTO, MOTOSINGLE, and MOTOMULTI crashes. The models are of three forms, depending on the exposure measure used, as shown in figure 20 through figure 22.

Figure 20. Equation. Florida urban arterial crashes per year using motorcycle traffic counts. Crashes per year equals the product of exponential value of intercept times length to the power of b times AVGMOTO to the power of c times exponential value of open parenthesis e times SPDLIMT plus f times DIVUND plus g times OUTSHLDWID plus h times SURFWIDTH closed parenthesis.

Figure 20. Equation. Florida urban arterial crashes per year using motorcycle traffic counts.

Figure 21. Equation. Florida urban arterial crashes per year using total traffic counts. Crashes per year equals the product of exponential value of intercept times length to the power of b times AVGAADT to the power of c times exponential value of open parenthesis e times SPDLIMT plus f times DIVUND plus g times OUTSHLDWID plus h times SURFWIDTH closed parenthesis.

Figure 21. Equation. Florida urban arterial crashes per year using total traffic counts.

Figure 22. Equation. Florida urban arterial crashes per year using separate traffic counts. Crashes per year equals the product of exponential value of intercept times length to the power of b times AVGMOTO to the power of c times AVGOTHER to the power of d times exponential value of open parenthesis e times SPDLIMT plus f times DIVUND plus g times OUTSHLDWID plus h times SURFWIDTH closed parenthesis.

Figure 22. Equation. Florida urban arterial crashes per year using separate traffic counts.

Where:
DIVUND = 1 if road is undivided and 0 if road is divided.
AVGOTHER = The non-motorcycle AADT = AVGAADT – AVGMOTO.

Table 32 provides the parameter estimates for these models, and table 33 provides overall goodness-of-fit statistics. Table 34 provides goodness-of-fit statistics from CURE plots for variables included in the models. Table 35 through table 37 provide calibration factors for each level of the non-continuous variables that were included in at least one of the models for that crash type.

Table 32. A1 models for Florida type 4 sites.
Model Type Parameter MOTO (SE) MOTOSINGLE (SE) MOTOMULTI (SE)
Motorcycle AADT Intercept -2.4685
(0.1821)
-4.5196
(0.2039)
-3.2128
(0.1911)
Motorcycle AADT b 0.7885
(0.0219)
0.7349
(0.0297)
0.7895
(0.0240)
Motorcycle AADT c 0.6274
(0.0253)
0.4006
(0.0414)
0.7543
(0.0274)
Motorcycle AADT d N/A N/A N/A
Motorcycle AADT e -0.0238
(0.0026)
N/A -0.0278
(0.0029)
Motorcycle AADT f -0.6686
(0.0595)
-0.4541
(0.1035)
N/A
Motorcycle AADT g -0.0695
(0.0070)
-0.0361
(0.0106)
-0.0905
(0.0078)
Motorcycle AADT h N/A 0.0105
(0.0018)
N/A
Motorcycle AADT Dispersion 1.1890
(0.0433)
1.1191
(0.0940)
1.3242
(0.0536)
Total AADT Intercept -9.0362
(0.3447)
-9.0785
(0.4910)
-10.4836
(0.3447)
Total AADT b 0.7936
(0.0213)
0.7408
(0.0296)
0.8154
(0.0233)
Total AADT c 0.9657
(0.0317)
0.7026
(0.0472)
1.1176
(0.0325)
Total AADT d N/A N/A N/A
Total AADT e -0.0277
(0.0025)
N/A -0.0361
(0.0028)
Total AADT f -0.2442
(0.0625)
-0.3694
(0.1022)
N/A
Total AADT g -0.0563
(0.0069)
-0.0375
(0.0105)
-0.0653
(0.0076)
Total AADT h N/A N/A N/A
Total AADT Dispersion 1.0505
(0.0403)
1.0857
(0.0931)
1.1042
(0.0478)
Motorcycle AADT and other AADT Intercept -8.3451
(0.3585)
-8.2796
(0.5137)
-9.8429
(0.3615)
Motorcycle AADT and other AADT b 0.7923
(0.0212)
0.7423
(0.0296)
0.8138
(0.0232)
Motorcycle AADT and other AADT c 0.2018
(0.0327)
0.2307
(0.0495)
0.1862
(0.0360)
Motorcycle AADT and other AADT d 0.7935
(0.0416)
0.5094
(0.0619)
0.9587
(0.0440)
Motorcycle AADT and other AADT e -0.0267
(0.0025)
N/A -0.0352
(0.0028)
Motorcycle AADT and other AADT f -0.2536
(0.0624)
-0.3815
(0.1021)
N/A
Motorcycle AADT and other AADT g -0.0570
(0.0069)
-0.0368
(0.0105)
-0.0663
(0.0076)
Motorcycle AADT and other AADT h N/A N/A N/A
Motorcycle AADT and other AADT Dispersion 1.0370
(0.0400)
1.0688
(0.0922)
1.0924
(0.0475)

N/A = Not applicable.

Table 33. Goodness-of-fit statistics for A1 models for Florida type 4 sites.
Crash Type Exposure Measure Total Observed MAD Modified R2 Dispersion
MOTO Motorcycle AADT 9,539 1.11 0.28 1.19
MOTO Total AADT 9,539 1.06 0.33 1.05
MOTO Motorcycle and other AADT 9,539 1.06 0.34 1.04
MOTOSINGLE Motorcycle AADT 2,341 0.38 0.31 1.12
MOTOSINGLE Total AADT 2,341 0.38 0.33 1.09
MOTOSINGLE Motorcycle and other AADT 2,341 0.38 0.34 1.07
MOTOMULTI Motorcycle AADT 7,198 0.91 0.25 1.32
MOTOMULTI Total AADT 7,198 0.86 0.32 1.10
MOTOMULTI Motorcycle and other AADT 7,198 0.86 0.33 1.09
Table 34. CURE plot statistics for A1 models for Florida type 4 sites.
Crash Type Exposure Measure Max CURE Deviation for AVGMOTO CURE Deviation for AVGMOTO (Percent) Max CURE Deviation for LENGTH CURE Deviation for LENGTH (Percent) Max CURE Deviation for SPDLIMT CURE Deviation for SPDLIMT (Percent) Max CURE Deviation for OUTSHLDWID CURE Deviation for OUTSHLDWID (Percent)
MOTO Motorcycle AADT 242.23 14 120.12 0 392.26 24 210.64 6
MOTO Total AADT 468.42 84 143.90 1 315.80 30 158.88 6
MOTO Motorcycle and other AADT 219.81 10 145.09 1 203.80 6 143.64 6
MOTOSINGLE Motorcycle AADT 52.04 2 51.84 0 65.67 15 72.11 13
MOTOSINGLE Total AADT 121.49 69 58.40 1 77.36 36 81.69 34
MOTOSINGLE Motorcycle and other AADT 51.58 1 58.64 1 77.66 42 84.46 39
MOTOMULTI Motorcycle AADT 178.29 8 120.03 1 223.54 3 157.08 1
MOTOMULTI Total AADT 324.78 80 119.832 1 167.83 8 98.79 1
MOTOMULTI Motorcycle and other AADT 154.31 3 125.87 1 135.86 3 101.34 5
Table 35. Calibration factors for A1 MOTO models for Florida type 4 sites.
Crash SPF Conditions Observed Observed/Predicted
MOTO crash SPF using motorcycle AADT for divided roads 623 1.09
MOTO crash SPF using motorcycle AADT for undivided roads 8,916 0.99
MOTO crash SPF with total AADT for divided roads 623 1.10
MOTO crash SPF with total AADT for undivided roads 8,916 0.99
MOTO crash SPF using motorcycle AADT and non-motorcycle AADT for divided roads 623 1.10
MOTO crash SPF using motorcycle AADT and non-motorcycle AADT for undivided Roads 8,916 0.99
Table 36. Calibration factors for A1 MOTOSINGLE models for Florida type 4 sites.
Crash SPF Conditions Observed Observed/Predicted
MOTOSINGLE crash SPF using motorcycle AADT for divided roads 151 1.00
MOTOSINGLE crash SPF using motorcycle AADT for undivided roads 2,190 1.00
MOTOSINGLE crash SPF with total AADT for divided roads 151 1.00
MOTOSINGLE crash SPF with total AADT for undivided roads 2,190 1.00
MOTOSINGLE crash SPF using motorcycle AADT and non-motorcycle AADT for divided roads 151 1.00
MOTOSINGLE crash SPF using motorcycle AADT and non-motorcycle AADT for undivided roads 2,190 1.00
Table 37. Calibration factors for A1 MOTOMULIT models for Florida type 4 sites.
Crash SPF Conditions Observed Observed/Predicted
MOTOMULTI crash SPF using motorcycle AADT for divided roads 472 0.66
MOTOMULTI crash SPF using motorcycle AADT for undivided roads 6,726 1.04
MOTOMULTI crash SPF with total AADT for divided roads 472 1.00
MOTOMULTI crash SPF with total AADT for undivided roads 6,726 1.00
MOTOMULTI crash SPF using motorcycle AADT and non-motorcycle AADT for divided roads 472 0.99
MOTOMULTI crash SPF using motorcycle AADT and non-motorcycle AADT for undivided roads 6,726 1.00

The goodness-of-fit results in table 33 indicate overall that models with total AADT performed at least as well as those with motorcycle AADT in terms of MAD, modified R2, and dispersion parameter. In fact, models with total AADT were somewhat better by these measures for MOTO and MOTOMULTI. However, the CURE plot statistics for the key AADT variable in table 34 indicate the opposite—the models with motorcycle AADT outperformed those with total AADT for the CURE measures. Not surprisingly, some measures (modified R2, dispersion parameter, and CURE plot measures) indicate that the three sets of models that include both motorcycle AADT and non-motorcycle AADT can outperform models with only motorcycle AADT. Finally, the calibration factors in table 35 through table 37 indicate that all three sets of AADT predictor models were just as successful when applied to segments with the two levels of the two indicator variables, with the exception of multi-vehicle motorcycle crashes on divided roads that are overpredicted.

Pennsylvania

Using Pennsylvania data, the project team could not calibrate separate models by area type (urban versus rural), so data were combined by area type to develop the SPFs with the use of an area type indicator variable.

Pennsylvania Type 1 and 2—Rural and Urban Freeways

For Pennsylvania freeways, the data and models pertain to one direction of travel only. For freeways, the project team successfully calibrated models for MOTO and MOTOMULTI crashes but not for single-vehicle motorcycle crashes, likely because of the small sample. The models are of three forms, depending on the exposure measure used, as shown in figure 23 through figure 25.

Figure 23. Equation. Pennsylvania rural and urban freeway crashes per year using motorcycle traffic counts. Crashes per year equals the product of exponential value of intercept times length to the power of b times AVGMOTO to the power of c times exponential value of open parenthesis e times URBRUR plus f times WIDTH plus g times LSHILDWID closed parenthesis.

Figure 23. Equation. Pennsylvania rural and urban freeway crashes per year using motorcycle traffic counts.

Figure 24. Equation. Pennsylvania rural and urban freeway crashes per year using total traffic counts. Crashes per year equals the product of exponential value of intercept times length to the power of b times AVGAADT to the power of c times exponential value of open parenthesis e times URBRUR plus f times WIDTH plus g times LSHILDWID closed parenthesis.

Figure 24. Equation. Pennsylvania rural and urban freeway crashes per year using total traffic counts.

Figure 25. Equation. Pennsylvania rural and urban freeway crashes per year using separate traffic counts. Crashes per year equals the product of exponential value of intercept times length to the power of b times AVGMOTO to the power of c times AVGOTHER to the power of d times exponential value of open parenthesis e times URBRUR plus f times WIDTH plus g times LSHILDWID closed parenthesis.

Figure 25. Equation. Pennsylvania rural and urban freeway crashes per year using separate traffic counts.

Where:
URBRUR = 1 if rural and 0 otherwise.
AVGOTHER = The non-motorcycle AADT = AVGAADT – AVGMOTO.

Other variables as defined in table 9.

Table 38 provides the parameter estimates for these models, and table 39 provides overall goodness-of-fit statistics. Table 40 provides goodness-of-fit statistics from CURE plots for variables included in the models. Table 41 provides calibration factors for the categorical variables included in the models.

Table 38. A1 models for Pennsylvania type 1 and 2 sites.
Model Type Parameter MOTO (SE) MOTOMULTI (SE)
Motorcycle AADT Intercept -5.0846
(0.2753)
-5.7901
(0.3879)
Motorcycle AADT b 0.7159
(0.1689)
0.6652
(0.2717)
Motorcycle AADT c 0.2309
(0.0399)
0.4313
(0.0686)
Motorcycle AADT d N/A N/A
Motorcycle AADT e -0.8489
(0.0873)
-1.5526
(0.1657)
Motorcycle AADT f 0.0505
(0.0048)
N/A
Motorcycle AADT g -0.0333
(0.0111)
N/A
Motorcycle AADT Dispersion 1.2724
(0.2056)
3.2825
(0.7948)
Total AADT Intercept -7.4047
(0.4663)
-10.9414
(0.7837)
Total AADT b 0.6908
(0.1621)
0.6018
(0.2491)
Total AADT c 0.3776
(0.0468)
0.7716
(0.0803)
Total AADT d N/A N/A
Total AADT e -0.6855
(0.0921)
-1.1491
(0.1752)
Total AADT f 0.0467
(0.0047)
N/A
Total AADT g -0.0293
(0.0110)
N/A
Total AADT Dispersion 1.1204
(0.1918)
2.5169
(0.6548)
Motorcycle and Other AADT Intercept -7.3820
(0.4615)
 
Motorcycle and Other AADT b 0.6891
(0.1628)
 
Motorcycle and Other AADT c 0.1256
(0.0420)
 
Motorcycle and Other AADT d 0.3151
(0.0501)
 
Motorcycle and Other AADT e -0.6651
(0.0924)
 
Motorcycle and Other AADT f 0.0460
(0.0047)
 
Motorcycle and Other AADT g -0.0291
(0.0110)
 
Motorcycle and Other AADT Dispersion 1.1196
(0.1912)
 

N/A = Parameter was not included in the model.
Blank cell = SPF was not calibrated for that crash type.

Table 39. Goodness-of-fit statistics for A1 models for Pennsylvania type 1 and 2 sites.
Crash Type Exposure Measure Total Observed MAD Modified R2 Dispersion
MOTO Motorcycle AADT 849 0.18 0.26 1.27
MOTO Total AADT 849 0.18 0.31 1.12
MOTO Motorcycle and other AADT 849 0.18 0.31 1.12
MOTOMULTI Motorcycle AADT 283 0.07 0.21 3.28
MOTOMULTI Total AADT 283 0.07 0.21 2.52
Table 40. CURE plot statistics for A1 models for Pennsylvania type 1 and 2 sites.
Crash Type Exposure Measure Max CURE Deviation for AVGMOTO CURE Deviation for AVGMOTO (Percent) Max CURE Deviation for LENGTH CURE Deviation for LENGTH (Percent) Max CURE Deviation for WIDTH CURE Deviation for WIDTH Max CURE Deviation for LSHLDWID CURE Deviation for LSHLDWID (Percent)
MOTO Motorcycle AADT 33.56 3 41.11 27 31.95 3 38.33 25
MOTO Total AADT 38.67 31 31.14 5 26.73 1 35.78 22
MOTO Motorcycle and other AADT 38.30 9 32.32 7 26.11 1 37.42 23
MOTOMULTI Motorcycle AADT 24.52 16 30.00 45 70.57 73 29.44 39
MOTOMULTI Total AADT 34.42 51 23.89 10 66.04 77 22.62 15
Table 41. Calibration factors for A1 models for Pennsylvania type 1 and 2 sites.
Crash Type Observed Observed/Predicted
MOTO with AVGMOTO urban 420 1.07
MOTO with AVGMOTO rural 359 0.93
MOTO with AVGAADT urban 420 1.07
MOTO with AVGAADT rural 359 0.92
MOTO with AVGAADT and OTHER urban 420 1.06
MOTO with AVGAADT and OTHER rural 359 0.94

The goodness-of-fit results in table 39 indicate the opposite result from the previous models—the models with motorcycle AADT outperformed those with total AADT for the CURE measures. Not surprisingly, some measures (modified R2 and dispersion parameter) indicate that the MOTO model that includes both motorcycle AADT and non-motorcycle AADT can outperform the model with only motorcycle AADT. However, its performance by these measures is similar to that of the MOTO model with only total AADT. Finally, the calibration factors in table 41 indicate that all AADT predictor models were just as successful when applied to segments with the two levels of the indicator variables.

Pennsylvania Type 3 and 4—Rural and Urban Non-Freeways

For non-freeways, the project team successfully calibrated models only for MOTO crashes and not for single- or multi-vehicle motorcycle crashes. The models are of three forms, depending on the exposure measure used, as shown in figure 26 through figure 28.

Figure 26. Equation. Pennsylvania rural and urban non-freeway crashes per year using motorcycle traffic counts. Crashes per year equals the product of exponential value of intercept times length to the power of b times AVGMOTO to the power of c times exponential value of open parenthesis e times URBRUR plus f times WIDTH plus g times AVGSHLDWID closed parenthesis.

Figure 26. Equation. Pennsylvania rural and urban non-freeway crashes per year using motorcycle traffic counts.

Figure 27. Equation. Pennsylvania rural and urban non-freeway crashes per year using total traffic counts. Crashes per year equals the product of exponential value of intercept times length to the power of b timesAVGAADT to the power of c times exponential value of open parenthesis e times URBRUR plus f times WIDTH plus g times AVGSHLDWID closed parenthesis.

Figure 27. Equation. Pennsylvania rural and urban non-freeway crashes per year using total traffic counts.

Figure 28. Equation. Pennsylvania rural and urban non-freeway crashes using separate traffic counts. Crashes per year equals the product of exponential value of intercept times length to the power of b times AVGMOTO to the power of c timesAVGOTHER to the power of d times exponential value of open parenthesis e times URBRUR plus f times WIDTH plus g times AVGSHLDWID closed parenthesis.

Figure 28. Equation. Pennsylvania rural and urban non-freeway crashes per year using separated traffic counts.

Where:
URBRUR = 1 if rural and 0 otherwise.
AVGSHLDWID = The average shoulder width on both sides of roadway.
AVGOTHER = The non-motorcycle AADT = AVGAADT – AVGMOTO.

Table 42 provides the parameter estimates for these models, and table 43 provides overall goodness-of-fit statistics. The project team calibrated the models using the full dataset, but the goodness-of-fit statistics pertain to a random sample of 6,000 road segments. The project team used a subset to make the calculations and CURE plots more manageable. Table 44 provides goodness-of-fit statistics from CURE plots for variables included in the models, and table 45 provides calibration factors for the categorical variables included in the models.

Table 42. A1 models for Pennsylvania type 3 and 4 sites.

Model Type Parameter MOTO
Motorcycle AADT Intercept -4.7635
(0.0667)
Motorcycle AADT b 0.7377
(0.0352)
Motorcycle AADT c 0.4585
(0.0123)
Motorcycle AADT d  
Motorcycle AADT e -0.4861
(0.0295)
Motorcycle AADT f 0.0263
(0.0020)
Motorcycle AADT g -0.0153
(0.0054)
Motorcycle AADT Dispersion 0.8197
(0.0528)
Total AADT Intercept -8.0110
(0.1180)
Total AADT b 0.7225
(0.0353)
Total AADT c 0.6232
(0.0146)
Total AADT d  
Total AADT e -0.1730
(0.0315)
Total AADT f 0.0150
(0.0021)
Total AADT g -0.0433
(0.0055)
Total AADT Dispersion 0.7239
(0.0497)
Motorcycle and other AADT Intercept -7.4806
(0.1329)
Motorcycle and other AADT b 0.7221
(0.0353)
Motorcycle and other AADT c 0.1414
(0.0172)
Motorcycle and other AADT d 0.5026
(0.0205)
Motorcycle and other AADT e -0.1874
(0.0315)
Motorcycle and other AADT f 0.0139
(0.0021)
Motorcycle and other AADT g -0.0438
(0.0055)
Motorcycle and other AADT Dispersion 0.7120
(0.0493)

Note: Blank cell indicates parameter was not included in the model.

Table 43. Goodness-of-fit statistics for A1 models for Pennsylvania type 3 and 4 sites.
Crash Type Exposure Measure Total Observed MAD Modified R2 Dispersion
MOTO Motorcycle AADT 779 0.21 0.42 0.84
MOTO Total AADT 779 0.20 0.46 0.74
MOTO Motorcycle and other AADT 779 0.20 0.46 0.73
Table 44. CURE plot statistics for A1 models for Pennsylvania type 3 and 4 sites.
Crash Type Exposure Measure Max CURE Deviation for AVGMOTO CURE Deviation for AVGMOTO (Percent) Max CURE Deviation for LENGTH CURE Deviation for LENGTH (Percent) Max CURE Deviation for WIDTH CURE Deviation. for WIDTH (Percent) Max CURE Deviation for AVGSHLDWID CURE Deviation for AVGSHLDWID (Percent)
MOTO Motor AADT 20.78 4 28.39 3 34.92 42 35.76 18
MOTO Total AADT 33.93 7 28.63 3 34.81 11 41.93 41
MOTO Motor and other AADT 20.04 0 29.42 4 31.87 4 41.24 32
Table 45. Calibration factors for A1 models for Pennsylvania type 3 and 4 sites.
Crash Type Observed Observed/Predicted
MOTO with AVGMOTO urban 420 1.07
MOTO with AVGMOTO rural 359 0.93
MOTO with AVGAADT urban 420 1.07
MOTO with AVGAADT rural 359 0.92
MOTO with AVGAADT and other urban 420 1.06
MOTO with AVGAADT and other rural 359 0.94

The goodness-of-fit results in table 43 indicate overall that MOTO model with total AADT performs slightly better than that with motorcycle AADT in terms of the modified R2 and dispersion parameter. However, the CURE plot statistics for the key motorcycle AADT variable in table 45 indicate that all AADT predictor models were just as successful when applied to segments with the two levels of the indicator variables.

Virginia

The project team used Virginia data to validate the A1 models developed. The goal was to assess whether the motorcycle crash SPFs transferred well to a new jurisdiction and to assess whether the models using motorcycle AADT or total AADT transferred better (or worse). Table 46 through table 51 provide a comparison of goodness-of-fit statistics for the Florida and Pennsylvania A1 models applied to Virginia data.

Because the Florida and Pennsylvania A1 models require input variables that are unavailable in Virginia, mean values of these variables in the calibration data were used to reduce the models to segment length, AADT of interest, and, when necessary, a rural/urban indicator. Mean values were determined from the descriptive statistics by individual roadway type.

Table 46. Validation of A1 models for MOTO crashes.
State Site Type AADT Type in Model Observed Crashes MAD Modified R2 Dispersion
Florida 1 Total 18 0.25 0 29.52
Florida 1 Motorcycle 18 0.26 0 17.12
Florida 2 Total 90 0.15 0 3.09
Florida 2 Motorcycle 90 0.15 0.15 2.16
Florida 3 Total 799 0.11 0.04 4.16
Florida 3 Motorcycle 799 0.11 0.11 3.07
Florida 3 Other 799 0.11 0.06 3.65
Florida 4 Total 2,705 0.18 0.14 1.12
Florida 4 Motorcycle 2,705 0.18 0.23 1.03
Florida 4 Other 2,705 0.18 0.13 1.11
Pennsylvania 1 and 2 Total 108 0.16 0.02 5.00
Pennsylvania 1 and 2 Motorcycle 108 0.16 0.04 4.59
Pennsylvania 1 and 2 Other 108 0.16 0.03 5.17
Pennsylvania 3 and 4 Total 3,504 0.16 0.16 1.53
Pennsylvania 3 and 4 Motorcycle 3,504 0.16 0.20 1.40
Pennsylvania 3 and4 Other 3,504 0.16 0.17 1.47
Table 47. CURE statistics for the validation of A1 models for MOTO crashes.
State Type AADT Type Max CURE Deviation for AVGMOTO CURE Deviation for AVGMOTO (Percent) Max CURE Deviation for LENGTH CURE Deviation for LENGTH (Percent)
Florida 1 Total 10.87 64 7.87 41
Florida 1 Motorcycle 13.57 76 5.08 31
Florida 2 Total 25.12 91 18.96 41
Florida 2 Motorcycle 8.84 0 20.20 46
Florida 3 Total 159.31 97 77.86 68
Florida 3 Motorcycle 72.69 73 68.06 74
Florida 3 Other 91.73 84 76.42 69
Florida 4 Total 362.81 99 186.12 96
Florida 4 Motorcycle 225.83 99 188.34 98
Florida 4 Other 277.37 100 207.65 98
Pennsylvania 1 and 2 Total 23.23 68 16.77 16
Pennsylvania 1 and 2 Motorcycle 19.13 33 18.67 22
Pennsylvania 1 and 2 Other 21.79 60 17.79 17
Pennsylvania 3 and 4 Total 96.99 28 190.65 94
Pennsylvania 3 and 4 Motorcycle 112.28 46 253.52 96
Pennsylvania 3 and 4 Other 77.42 27 206.63 95

The results for MOTO crashes were not clear on whether the Florida or Pennsylvania models calibrated better to the Virginia data. Whichever one was better depends on the specific measure and site type considered. What was consistent, however, is that the motorcycle AADT-based models showed a better goodness-of-fit as measured by the modified R2 and dispersion. While it is not true that the models using motorcycle AADT always are preferred in terms of maximum CURE deviation and percent CURE deviation, this is mostly true. However, all of the models showed a significant amount of bias as measured by the percent CURE deviation.

Table 48. Validation of A1 models for MOTOSINGLE crashes in Florida.
Site Type AADT Type in Model Observed Crashes MAD Modified R2 Dispersion
1 Total 16 0.23 0 30.27
1 Motorcycle 16 0.23 0 16.77
2 Total 50 0.09 0.11 2.84
2 Motorcycle 50 0.09 0.26 1.71
3 Total 410 0.06 0.05 6.12
3 Motorcycle 410 0.06 0.08 4.93
3 Other 410 0.06 0.07 5.38
4 Total 836 0.06 0.43 0.70
4 Motorcycle 836 0.06 0.44 0.68
4 Other 836 0.06 0.43 0.70
Table 49. CURE statistics for the validation of A1 models for MOTOSINGLE crashes in Florida.
Type AADT Type Max CURE Deviation for AVGMOTO CURE Deviation for AVGMOTO (Percent) Max CURE Deviation for LENGTH CURE Deviation for LENGTH (Percent)
1 Total 12.51 77 4.60 28
1 Motorcycle 9.29 56 6.66 39
2 Total 14.53 88 11.60 30
2 Motorcycle 7.78 8 12.17 32
3 Total 93.62 95 65.26 27
3 Motorcycle 42.98 73 62.86 25
3 Other 47.21 82 63.58 25
4 Total 56.50 78 39.07 16
4 Motorcycle 26.23 11 34.83 10
4 Other 65.58 87 34.21 12

For MOTOSINGLE crashes, the project team did not calibrate models from Pennsylvania. The Florida models using motorcycle AADT showed better goodness-of-fit statistics in general. These models, however, showed significant bias as measured by the percent CURE deviation.

Table 50. Validation of A1 models for MOTOMULTI crashes.
State Site Type AADT Type in Model Observed Crashes MAD Modified R2 Dispersion
Florida 2 Total 40 0.07 0 3.83
Florida 2 Motorcycle 40 0.07 0.01 3.27
Florida 3 Total 388 0.06 0.03 3.30
Florida 3 Motorcycle 388 0.06 0.12 2.48
Florida 3 Other 388 0.06 0.05 3.01
Florida 4 Total 1,865 0.13 0 1.61
Florida 4 Motorcycle 1,865 0.13 0.10 1.43
Florida 4 Other 1,865 0.13 0 1.60
Pennsylvania 1 and 2 Total 42 0.07 0.12 2.69
Pennsylvania 1 and 2 Motorcycle 42 0.07 0.18 2.20
Table 51. CURE statistics for the validation of A1 models for MOTOMULTI crashes in Pennsylvania.
Site Type AADT Type Maximum CURE Deviation for AVGMOTO CURE Deviation for AVGMOTO (Percent) Maximum CURE Deviation for LENGTH CURE Deviation for LENGTH (Percent)
2 Total 11.29 48 7.91 18
2 Motorcycle 6.40 29 8.55 26
3 Total 58.27 82 54.77 78
3 Motorcycle 28.23 26 62.30 86
3 Other 42.09 70 56.82 83
4 Total 332.44 98 191.56 97
4 Motorcycle 222.02 99 187.75 97
4 Other 236.70 97 210.38 98
1/2 Total 7.98 29 4.43 5
1/2 Motorcycle 4.67 7 7.14 9

The results for MOTOMULTI crashes indicate that the Pennsylvania models may transfer better than the Florida models to the Virginia data. The motorcycle AADT-based models in general showed better goodness-of-fit measures. However, almost all of the models showed a significant amount of bias as measured by the percent CURE deviation.

Assessment of A1 Models for Predictions at High Crash Locations

The project team conducted an assessment of how well the A1 models predict motorcycle crashes for high-crash locations. Such locations are typically of interest in treatment applications that form the basis for future CMF development. To do this, sites of a specific type were first ranked in descending order of the crash counts per mile in one period (denoted as a before period). EB estimates were then obtained for the top-ranked sites based on the calibrated SPFs using motorcycle AADT and total AADT and crash counts in that period. The sum of these EB estimates for the top-ranked sites were then compared to the sum of the crash counts for these locations in a subsequent period (denoted as an after period) after adjusting the EB estimates for the difference in years between the two periods. For Florida, the top 10 percent of sites were ranked based on a 3-year before period from 2008–2010; the after period was a 2-year period from 2011 to 2012.

For Pennsylvania, sites with at least one motorcycle crash, which constituted less than 10 percent of all sites, were top ranked based on a 3-year before period from 2009–2011; the after period was a 2-year period from 2012 to 2013. Table 52 shows the results of this assessment.

Table 52. Assessment of type 1 models for predictions at high crash locations.
State Site Type Number of Top- Ranked Sites Motorcycle Crash Count (2-Year Before Period) Motorcycle Crash Count (2-Year After Period) EB Expected Crashes in 2-Year After Period Using Model with Motorcycle AADT EB Expected Crashes in 2-Year After Period Using Model with Total AADT MAD for Comparison to after Period Crashes with EB Estimate from Model with Motorcycle AADT MAD for Comparison to after Period Crashes with EB Estimate from Model with Total AADT
Florida 1 48 45.3 13 10.28 11.13 0.363 0.364
Florida 2 96 136.7 56 43.45 47.44 0.568 0.575
Florida 3 325 311.3 109 79.43 107.99 0.408 0.433
Florida 4 872 1,584.7 926 650.37 675.17 0.849 0.852
Pennsylvania 1 and 2 434 327.3 70 26.3 29.7 0.025 0.028
Pennsylvania 3 and 4 4,348 3,126.0 632 423.5 456.6 0.212 0.215

The results in table 52 show that, although MAD tended to be slightly higher for the total AADT models, the EB estimates from the total AADT models of crashes at the top-ranked sites were marginally closer to the actual counts than those based on the motorcycle AADT models.

It should be noted in passing that before period counts (adjusted for a 2-year period) were much higher than the 2-year after period counts because of a substantial regression to the mean effect. The EB estimates were much closer, but precise matching should not be expected because trends in crash occurrence and traffic volume differences between the before and after periods were not considered as they would be in a rigorous EB before-after study. In the case of type 4 Florida sites and the Pennsylvania sites, an additional factor is that the top-ranked sites are likely heavily biased towards the ranges of variables such as traffic volume and segment length where the SPF may be underpredicting. This result would indicate that there is room for model improvement but should not be interpreted as saying these models and methods should not be applied for site-based analyses.

Avenue A Model Type A2

The purpose of model type A2 is to develop a relationship between motorcycle crash frequency and total crash frequency. The project team developed models for both motorcycle crashes and total crashes using traffic volumes for motorcycles and all vehicles, respectively. Other geometric variables from table 3 and table 9 were not included in these models because the goal is for these models to be transferable to any jurisdiction.

The goal was to infer a relationship between the models for the two crash types. This relationship can then be applied to the model for total crashes for another State to infer a model for motorcycle crashes for that State. In turn, that model can be used in the evaluation of retrospective and prospective before-after evaluations of the effects of infrastructure countermeasures on motorcycle crashes.

Because the goal is to develop models that may be transferable between jurisdictions, only length and traffic volume variables were included since other jurisdictions may not have the same data available.

The modeling is a three-step process. The first is to develop a model for total crashes, as shown in figure 29.

Figure 29. Equation. Type A2 total crashes model. Total crashes per year equals the product of exponential value of intercept times length to the power of b timesAVGAADT to the power of c.

Figure 29. Equation. Type A2 total crashes model.

The predicted values from this model are given the name PREDTOT. The second step is to develop a model for the motorcycle crashes of interest. For example, for MOTO crashes, this would be the model shown in figure 30.

Figure 30. Equation. Type A2 motorcycle crashes model. Motorcycle crashes per year equals the product of exponential value of intercept times length to the power of b times AVGMOTO to the power of c.

Figure 30. Equation. Type A2 motorcycle crashes model.

The predicted values from this model are given the name PREDMOTO. The final step is to develop a model that predicts the value of PREDMOTO/year. In developing this model, for each site, the value of PREDMOTO is the dependent variable, and the value of PREDTOT is considered as one of the possible explanatory variables in the model.

The project team pursued the A2 models using both data from Florida and Pennsylvania and using data from Virginia for validation. The remainder of this section reports on the results of model development and validation.

Florida

An exponential model and a linear model were attempted. The project team found that although the two models performed similarly over most sites, the exponential model overpredicts crashes significantly when the total crash frequency is high. For this reason, the project team adopted the linear model form as shown in figure 31 through figure 33. The error distribution for these models was assumed as a gamma distribution.

Figure 31. Equation. Florida type A2 motorcycle crash model. Predicted motorcycle crashes per year equals the sum of intercept plus b times PREDTOT plus c times AADT divided by 10,000.

Figure 31. Equation. Florida type A2 motorcycle crash model.

Figure 32. Equation. Florida type A2 motorcycle single-vehicle crash model. Predicted single-vehicle motorcycle crashes per year equals the sum of intercept plus b times PREDTOT plus c times AADT divided by 10,000.

Figure 32. Equation. Florida type A2 motorcycle single-vehicle crash model.

Figure 33. Equation. Florida type A2 motorcycle multi-vehicle crash model. Predicted multi-vehicle motorcycle crashes per year equals the sum of intercept plus b times PREDTOT plus c times AADT divided by 10,000.

Figure 33. Equation. Florida type A2 motorcycle multi-vehicle crash model.

Florida Type 1—Rural Freeways

Table 53 presents the parameter estimates for the type 1 sites. Attempts to estimate a full set of corresponding models for MOTOMULTI were unsuccessful. There are three models for each category of motorcycle crashes: the model for total crashes, the model for the motorcycle crashes of interest, and the model that predicts the value of the motorcycle crash model based on the predicted value of total crashes and total AADT. Table 54 and table 55 provide goodness-of-fit statistics for the A2 model predictions and compare them to the predictions from the A1 models using motorcycle AADT as an explanatory variable. The A2 model predictions use the third model (i.e., the model that predicts the estimate from a motorcycle crash SPF based on the prediction from a total crash SPF).

Table 53. A2 models for Florida type 1 sites.
Model Parameter MOTO MOTOSINGLE
Total crashes Intercept -10.6602
(0.7239)
-10.6602
(0.7239)
Total crashes b 0.7995
(0.0300)
0.7995
(0.0300)
Total crashes c 1.1700
(0.0697)
1.1700
(0.0697)
Total crashes Dispersion 0.4541
(0.0403)
0.4541
(0.0403)
Motorcycle crashes Intercept -5.5368
(0.6033)
-5.1341
(0.7741)
Motorcycle crashes b 0.8239
(0.0801)
0.8939
(0.1102)
Motorcycle crashes c 0.6622
(0.1274)
0.4755
(0.1663)
Motorcycle crashes Dispersion 0.4353
(0.2160)
1.1346
(0.4327)
Predicted motorcycle crashes Intercept 0.0555
(0.0037)
0.0436
(0.0020)
Predicted motorcycle crashes b 0.0187
(0.0004)
0.0125
(0.0003)
Predicted motorcycle crashes c -0.0217
(0.0016)
-0.0191
(0.0007)
Table 54. Goodness-of-fit statistics for A2 models for Florida type 1 sites.
Crash Type Exposure Measure Total Observed MAD Modified R2 Dispersion
MOTO Motorcycle AADT 174 0.43 0.65 0.44
MOTO A2 model 174 0.41 0.78 0.29
MOTOSINGLE Motorcycle AADT 111 0.32 0.34 1.14
MOTOSINGLE A2 model 111 0.31 0.46 0.93
Table 55. CURE plot statistics for A2 models for Florida type 1 sites.
Crash Type Exposure Measure Max CURE Deviation for AVGMOTO CURE Deviation for AVGMOTO (Percent) Max CURE Deviation for LENGTH CURE Deviation for LENGTH (Percent)
MOTO Motorcycle AADT 15.83 11 7.42 3
MOTO A2 model 13.08 3 7.31 3
MOTOSINGLE Motorcycle AADT 10.42 5 7.80 3
MOTOSINGLE A2 model 10.96 6 9.17 5

The results indicate (especially for the modified R2 and dispersion parameter measures) that both A2 models, which predict motorcycle crashes from predictions from a total crash versus total AADT model, outperformed the corresponding models that predict motorcycle crashes from motorcycle AADT.

Florida Type 2—Urban Freeways

Table 56 presents the parameter estimates for the type 2 sites. There are three models for each category of motorcycle crashes: the model for total crashes, the model for the motorcycle crashes of interest, and the model that predicts the value of the motorcycle crash model based on the predicted value of total crashes and total AADT. Table 57 and table 58 provide goodness-of-fit statistics for the A2 model predictions and compare them to the predictions from the A1 models using motorcycle AADT as an explanatory variable. The A2 model predictions use the third model (i.e., the model that predicts the estimate from a motorcycle crash SPF based on the prediction from a total crash SPF).

Table 56. A2 models for Florida type 2 sites.
Model Parameter MOTO MOTOSINGLE MOTOMULTI
Total crashes Intercept -12.2924
(0.4305)
-12.2924
(0.4305)
-12.2924
(0.4305)
Total crashes b 0.7559
(0.0268)
0.7559
(0.0268)
0.7559
(0.0268)
Total crashes c 1.3304
(0.0384)
1.3304
(0.0384)
1.3304
(0.0384)
Total crashes Dispersion 0.5179
(0.0264)
0.5179
(0.0264)
0.5179
(0.0264)
Motorcycle crashes Intercept -3.1295
(0.2465)
-3.3297
(0.2688)
-3.8930
(0.2930)
Motorcycle crashes B 0.7184
(0.0488)
0.7283
(0.0575)
0.6943
(0.0591)
Motorcycle crashes C 0.3553
(0.0433)
0.2371
(0.0469)
0.3910
(0.0509)
Motorcycle crashes Dispersion 0.6978
(0.0951)
0.3559
(0.1347)
0.8087
(0.1392)
Predicted motorcycle crashes Intercept 0.4952
(0.0158)
0.2362
(0.0053)
0.2762
(0.0101)
Predicted motorcycle crashes b 0.0196
(0.0007)
0.0079
(0.0002)
0.0111
(0.0004)
Predicted motorcycle crashes c -0.0520
(0.0026)
-0.0250
(0.0008)
-0.0269
(0.0017)
Table 57. Goodness-of-fit statistics for A2 models for Florida type 2 sites.
Crash Type Exposure Measure Total Observed MAD Modified R2 Dispersion
MOTO Motorcycle AADT 921 0.86 0.56 0.43
MOTO A2 model 921 0.84 0.65 0.35
MOTOSINGLE Motorcycle AADT 385 0.47 0.66 0.26
MOTOSINGLE A2 model 385 0.47 0.75 0.18
MOTOMULTI Motorcycle AADT 536 0.58 0.59 0.38
MOTOMULTI A2 model 536 0.58 0.63 0.34
Table 58. CURE plot statistics for A2 models for Florida type 2 sites.
Crash Type Exposure Measure Max CURE Deviation for AVGMOTO CURE Deviation for AVGMOTO (Percent) Max CURE Deviation for LENGTH CURE Deviation for LENGTH (Percent)
MOTO Motorcycle AADT 54.69 35 22.11 0
MOTO A2 model 90.73 80 24.3 5
MOTOSINGLE Motorcycle AADT 26.21 16 11.53 0
MOTOSINGLE A2 model 24.26 11 17.94 0
MOTOMULTI Motorcycle AADT 37.34 41 18.12 16
MOTOMULTI A2 model 71.80 83 20.62 31

The results indicate, especially for the modified R2 and dispersion parameter measures, that the three A2 models, which predict motorcycle crashes from predictions from a total-crash versus total AADT model, outperformed corresponding models that predict motorcycle crashes from motorcycle AADT. However, the CURE plot statistics for the key AADT variable, AVGMOTO, indicate the opposite for the MOTO and MOTOMULTI models.

Florida Type 3—Rural Arterials

Table 59 presents the parameter estimates for the type 3 sites. There are three models for each category of motorcycle crashes: the model for total crashes, the model for the motorcycle crashes of interest, and the model that predicts the value of the motorcycle crash model based on the predicted value of total crashes and total AADT.

Table 60 and table 61 provide goodness-of-fit statistics for the A2 model predictions and compare them to the predictions from the A1 models using motorcycle AADT as an explanatory variable. The A2 model predictions use the third model (i.e., the model that predicts the estimate from a motorcycle crash SPF based on the prediction from a total crash SPF).

Table 59. A2 models for Florida type 3 sites.
Model Parameter MOTO (SE) MOTOSINGLE (SE) MOTOMULTI (SE)
Total crashes Intercept -6.9586
(0.2236)
-6.9586
(0.2236)
-6.9586
(0.2236)
Total crashes b 0.7145
(0.0163)
0.7145
(0.0163)
0.7145
(0.0163)
Total crashes c 0.8411
(0.0256)
0.8411
(0.0256)
0.8411
(0.0256)
Total crashes Dispersion 0.8672
(0.0312)
0.8672
(0.0312)
0.8672
(0.0312)
Motorcycle crashes Intercept -4.6303
(0.1684)
-5.1015
(0.2302)
-5.5552
(0.2199)
Motorcycle crashes B 0.6780
(0.0315)
0.7210
(0.0436)
0.6494
(0.0397)
Motorcycle crashes C 0.5671
(0.0431)
0.4712
(0.0591)
0.6592
(0.0553)
Motorcycle crashes Dispersion 0.8912
(0.1194)
1.0532
(0.2348)
1.0096
(0.1892)
Predicted motorcycle crashes Intercept 0.0499
(0.0018)
0.0235
(0.0007)
0.0232
(0.0011)
Predicted motorcycle crashes b 0.0534
(0.0007)
0.0239
(0.0003)
0.0294
(0.0005)
Predicted motorcycle crashes c -0.0720
(0.0028)
-0.0404
(0.0009)
-0.0267
(0.0020)
Table 60. Goodness-of-fit statistics for A2 models for Florida type 3 sites.
Crash Type Exposure Measure Total Observed MAD Modified R2 Dispersion
MOTO Motorcycle AADT 1,031 0.40 0.44 0.77
MOTO A2 model 1,031 0.41 0.39 0.89
MOTOSINGLE Motorcycle AADT 449 0.21 0.43 0.91
MOTOSINGLE A2 model 449 0.21 0.35 1.10
MOTOMULTI Motorcycle AADT 582 0.26 0.37 0.85
MOTOMULTI A2 model 582 0.27 0.37 0.99
Table 61. CURE plot statistics for A2 models for Florida type 3 sites.
Crash Type Exposure Measure Max CURE Deviation for AVGMOTO CURE Deviation for AVGMOTO (Percent) Max CURE Deviation for LENGTH CURE Deviation for LENGTH (Percent)
MOTO Motorcycle AADT 37.40 0 21.32 0
MOTO A2 model 106.65 76 27.08 0
MOTOSINGLE Motorcycle AADT 24.33 1 8.21 0
MOTOSINGLE A2 model 41.21 25 19.82 0
MOTOMULTI Motorcycle AADT 19.71 1 20.19 6
MOTOMULTI A2 model 69.92 89 25.57 7

All of the results consistently indicate that the three models that predict motorcycle crashes from motorcycle AADT outperformed the corresponding A2 models, which predict motorcycle crashes from predictions from a total-crash vs total AADT model. This is somewhat contrary to the findings for type 1 and type 2 sites.

Florida Type 4Urban Arterials

Table 62 presents the parameter estimates for the type 4 sites. There are three models for each category of motorcycle crashes: the model for total crashes, the model for the motorcycle crashes of interest, and the model that predicts the value of the motorcycle crash model based on the predicted value of total crashes and total AADT. Table 63 and table 64 provide goodness-of-fit statistics for the A2 model predictions and compare them to the predictions from the A1 models using motorcycle AADT as an explanatory variable. The A2 model predictions use the third model (i.e., the model that predicts the estimate from a motorcycle crash SPF based on the prediction from a total crash SPF).

Table 62. A2 models for Florida type 4 sites.
Model Parameter MOTO (SE) MOTOSINGLE (SE) MOTOMULTI (SE)
Total crashes Intercept -11.6281
(0.2286)
-11.6281
(0.2286)
-11.6281
(0.2286)
Total crashes b 0.5894
(0.0204)
0.5894
(0.0204)
0.5894
(0.0204)
Total crashes c 1.3751
(0.0227)
1.3751
(0.0227)
1.3751
(0.0227)
Total crashes Dispersion 2.0547
(0.0336)
2.0547
(0.0336)
2.0547
(0.0336)
Motorcycle crashes Intercept -4.5339
(0.1272)
-5.2472
(0.1857)
-5.0429
(0.1427)
Motorcycle crashes b 0.7419
(0.0218)
0.7375
(0.0301)
0.7488
(0.0241)
Motorcycle crashes c 0.7469
(0.0248)
0.6129
(0.0360)
0.7918
(0.0278)
Motorcycle crashes Dispersion 1.3244
(0.0465)
1.2330
(0.0093)
1.4792
(0.0574)
Predicted motorcycle crashes Intercept 0.5031
(0.0067)
0.1470
(0.0015)
0.3572
(0.0051)
Predicted motorcycle crashes b 0.0479
(0.0006)
0.0114
(0.0001)
0.0367
(0.0005)
Predicted motorcycle crashes c -0.2972
(0.0054)
-0.0791
(0.0012)
-0.2204
(0.0043)
Table 63. Goodness-of-fit statistics for A2 models for Florida type 4 sites.
Crash Type Exposure Measure Total Observed MAD Modified R2 Dispersion
MOTO Motorcycle AADT 9,539 1.11 0.28 1.19
MOTO A2 model 9,539 1.10 0.30 1.20
MOTOSINGLE Motorcycle AADT 2,341 0.38 0.31 1.12
MOTOSINGLE A2 model 2,341 0.38 0.32 1.16
MOTOMULTI Motorcycle AADT 7,198 0.91 0.25 1.32
MOTOMULTI A2 model 7,198 0.90 0.27 1.32
Table 64. CURE plot statistics for A2 models for Florida type 4 sites.
Crash Type Exposure Measure Max CURE Deviation for AVGMOTO CURE Deviation for AVGMOTO (Percent) Max CURE Deviation for LENGTH CURE Deviation for LENGTH (Percent)
MOTO Motorcycle AADT 242.23 14 120.12 0
MOTO A2 model 288.17 45 644.54 95
MOTOSINGLE Motorcycle AADT 52.04 2 51.84 0
MOTOSINGLE A2 model 123.19 76 105.03 21
MOTOMULTI Motorcycle AADT 178.29 8 120.03 1
MOTOMULTI A2 model 528.91 96 223.50 34

The results indicate that the performance of the three A2 models, which predict motorcycle crashes from predictions from a total-crash versus total AADT model, was similar to that of the corresponding models that predict motorcycle crashes from motorcycle AADT. However, the CURE plot statistics for the key AADT variable, AVGMOTO, indicate that models that predict motorcycle crashes from motorcycle AADT were better in terms of the CURE measures than the corresponding A2 models. These results for urban arterials, overall, were consistent with findings for rural arterials.

Pennsylvania

The linear model form that worked for the Florida dataset failed to converge for the Pennsylvania dataset. While the exponential model form did converge for the Pennsylvania dataset, the sum of the predictions was significantly higher than the observed number of crashes. Similar to the Florida exponential model, this overprediction occurred for sites where the total crash frequency was high. For this reason, the project team concluded that the A2 models using the Pennsylvania data were not successful.

Virginia

To validate the A2 models developed, the project team split the data for Virginia into calibration and validation datasets for rural and urban arterials. The data for freeways did not include enough crashes for validation of the A2 models. The project team used the calibration datasets to develop the total crash SPF required for application of the A2 models. The project team also used the calibration data to develop motorcycle crash SPFs using total AADT to compare to the A2 models.

The project team used the validation datasets to evaluate the performance of the A2 models and compare that to the performance of a total AADT SPF for motorcycle crashes. To perform this validation, the project team calibrated the predictions from both the A2 model process and the Virginia motorcycle SPFs to the calibration data and goodness-of-fit statistics determined. Table 65 provides the summary data for split validation and calibration datasets for rural and urban arterials.

Table 65. Length and crash frequency for Virginia model type A2 validation analysis.
Type LENGTH (mi) TOT MOTO MOTOSINGLE MOTOMULTI
3A calibration 2,195.4 1,6653 373 183 189
3B validation 2,246.1 1,6672 426 227 199
4A calibration 1,665.0 6,4651 1,414 432 981
4B validation 1,658.4 6,0662 1,291 404 884

1 mi = 1.6 km.

Table 66 provides summary data for motorcycle AADT, total AADT, and number of lanes. Comparisons between calibration and validation datasets shows consistency in minimum, maximum, and average values.

Table 66. Summary statistics for Virginia model type A2 validation analysis.
Type Statistic AVGMOTO AVGAADT NOLANES
3A No. Segments 6,287 6,287 6,287
3A MIN 1.0 305.0 1.0
3A MAX 245.0 58,715.0 7.0
3A MEAN 34.8 8,187.0 2.8
3A STD 31.1 6,782.6 1.0
3B No. Segments 6,287 6,287 6,287
3B MIN 1.0 305.0 1.0
3B MAX 245.0 58,715.0 6.0
3B MEAN 34.6 8,106.6 2.8
3B STD 30.3 6,849.6 1.0
4A No. Segments 12,695 12,695 12,695
4A MIN 1.0 131.0 1.0
4A MAX 509.0 130,077.0 9.0
4A MEAN 54.8 17,705.1 3.3
4A STD 54.7 14,380.2 1.3
4B No. Segments 12,695 12,695 12,695
4B MIN 1.0 270.0 1.0
4B MAX 509.0 130,077.0 9.0
4B MEAN 53.8 17,425.2 3.3
4B STD 55.7 14,280.9 1.3

For rural arterials, the project team developed SPFs for total, motorcycle, and multi-vehicle motorcycle crashes. Total AADT and segment length were used as explanatory variables for all SPFs. Table 67 shows the parameter estimates for the total crash SPF, the motorcycle crash SPF, and the A2 model applied. Using the Virginia data, an SPF for predicting single-vehicle motorcycle crashes did not converge.

Table 67. SPFs for validating model types A2 for Virginia type 3 (rural arterial) sites.
Model Parameter MOTO (SE) MOTOMULTI (SE)
Total crash SPF Intercept -5.3321
(0.1575)
-5.3321
(0.1575)
Total crash SPF b 0.6160
(0.0122)
0.6160
(0.0122)
Total crash SPF c 0.6224
(0.0181)
0.6224
(0.0181)
Total crash SPF Dispersion 0.7529
(0.0253)
0.7529
(0.0253)
Motorcycle crash SPF using total AADT Intercept -5.3223
(0.5848)
-8.1803
(0.8208)
Motorcycle crash SPF using total AADT b 0.6302
(0.0519)
0.5152
(0.0658)
Motorcycle crash SPF using total AADT c 0.1957
(0.0679)
0.4306
(0.0927)
Motorcycle crash SPF using total AADT Dispersion 3.0688
(0.5901)
1.4954
(0.7830)
Florida A2 models Intercept 0.0499
(0.0018)
0.0232
(0.0011)
Florida A2 models b 0.0534
(0.0007)
0.0294
(0.0005)
Florida A2 models c -0.0720
(0.0028)
-0.0267
(0.0020)

For urban arterials, the project team developed SPFs for total, motorcycle, single-vehicle motorcycle, and multi-vehicle motorcycle crashes in Virginia. Total AADT and segment length were used as explanatory variables for all SPFs. Table 68 shows the parameter estimates for the total crash SPF, the motorcycle crash SPF, and the A2 model applied

Table 68. SPFs for validating A2 models for Virginia type 4 (urban arterial) sites.
Model Parameter MOTO (SE) MOTOSINGLE (SE) MOTOMULTI (SE)
Total crash SPF Intercept -6.3949
(0.1343)
-6.3949
(0.1343)
-6.3949
(0.1343)
Total crash SPF b 0.6202
(0.0109)
0.6202
(0.0109)
0.6202
(0.0109)
Total crash SPF c 0.7988
(0.0137)
0.7988
(0.0137)
0.7988
(0.0137)
Total crash SPF Dispersion 1.0363
(0.0183)
1.0363
(0.0183)
1.0363
(0.0183)
Motorcycle crash SPF using total AADT Intercept -7.9779
(0.3824)
-8.0193
(0.6428)
-8.8642
(0.4583)
Motorcycle crash SPF using total AADT b 0.6594
(0.0309)
0.8446
(0.0534)
0.5772
(0.0364)
Motorcycle crash SPF using total AADT c 0.5808
(0.0384)
0.4985
(0.0650)
0.6176
(0.0459)
Motorcycle crash SPF using total AADT Dispersion 0.9252
(0.1389)
0.9436
(0.3897)
1.1309
(0.2078)
Florida A2 models Intercept 0.5031
(0.0067)
0.1470
(0.0015)
0.3572
(0.0051)
Florida A2 models b 0.0479
(0.0006)
0.0114
(0.0001)
0.0367
(0.0005)
Florida A2 models c -0.2972
(0.0054)
-0.0791
(0.0012)
-0.2204
(0.0043)

When applying the A2 models to the validation data, the project team observed that the predictions produced some negative values for expected crashes when the total crash SPF prediction was low. This illogical result of negative crash prediction shows that the A2 models do not transfer well to another jurisdiction if the expected total crash frequency is markedly different. The project team measured the success of the A2 in how well they can predict crashes for a new jurisdiction that does not have motorcycle AADT estimates but can develop an SPF for total crashes using total AADT. For this reason, the results concluded that the A2 modeling was not successful.

The possibility of negative crash predictions was made possible by the linear model form of the A2 models, shown in figure 34, where the parameter c was estimated to be negative.

Figure 34. Equation. A2 linear model form. Predicted motorcycle crashes per year equals the sum of intercept plus b times PREDTOT plus c times AADT divided by 10,000.

Figure 34. Equation. A2 linear model form.

When developing the A2 models, other model forms that would not allow such negative predictions were not successful in that they significantly overpredicted crashes at high AADTs.

Avenue A Model Type A3

The purpose of investigating model type 3 was to attempt the development of models to estimate motorcycle traffic volumes based on roadway characteristics and other variables that may influence motorcycle trip generation. If successful, such models could be used to estimate motorcycle volumes in similar jurisdictions, and these volumes could be used for any study design where motorcycle volumes are desired.

The A3 models were estimated using simple linear regression, which assumes a normal distribution for the error term. The form was adopted from and is consistent with the forms used for trip generation models in the transportation planning field. Figure 35 shows an example of an estimated model form.

Figure 35. Equation. Type A3 model form example. Motorcycle AADT equals the sum of intercept plus b times LANES plus c times SPDLIMT plus d times POP060210 plus e times INC110213 plus f times LFE305213 plus f times SEX255213.

Figure 35. Equation. Type A3 model form example.

Where:
MOTOAADT = The motorcycle AADT on a roadway segment.
LANES = 0 if the roadway has two lanes and 1 if the roadway has more than two lanes.
SPDLIMT = The posted speed limit in mi/h.
POP060210 = The population per mi2.
INC110213 = The median household income.
LFE305213 = The mean travel time to work in min for workers age 16+.
SEX255213 = The percentage of the population that is female.

The project team attempted models for site types 1 through 4 in both Florida and Pennsylvania. For both datasets, the project team could not consider the models developed successful. Although the models did include parameter estimates that were statistically significant at the 95-percent confidence limit, the explanatory power of the models was very low and only marginally better than simply assuming the average level of motorcycle AADT for all sites. This is likely because variables that are most related to motorcycle AADT may not have been available for inclusion.

The lack of explanatory power provided by the models was evident from examining the R2 coefficient. The R2 coefficient is a statistical measure of how much variation in the data is being explained by the model. In equation form, this is expressed as shown in figure 36 and is always between 0 and 100 percent.

Figure 36. Equation. R2 coefficient. R-squared equals explained variation divided by total variation.

Figure 36. Equation. R2 coefficient.

The models developed for Florida and Pennsylvania showed R2 values typically between 5 and 15 percent, indicating that they are not explaining much of the variation in motorcycle AADT between road segments and are thus not very useful. For this reason, the project team did not consider the A3 modeling a success.

Avenue B Model Type B1

The model type B1 analyses were conducted using the data for types 1 (rural freeway) and 3 (rural arterial) in Florida. The approach used for simulating data is described in chapter 4 in the subsection titled Avenue B Databases. The open-source software R was used for simulating the data and model estimation. Several parameters were changed in running several simulations to examine their effects on the results. These included the number of treatment sites, the assumed CMF, and how the project team selected the treatment sites.

Florida Type 1

Table 69 shows the results for simulation 1 using the Florida type 1 data. In simulation 1, the treated sites were selected as those with the highest crash frequency per mi in the before period. For simulation 1, there were 100 treatment sites and 382 reference sites. The assumed CMF was 0.70, and there were 3 years of before and after data. There were 10 separate trials indicated by trial ID in the table. For each trial, the project team simulated the observed number of crashes for all sites so that the data were different for each trial. For each trial, the table provides the estimated CMF and its SE using the SPF with motorcycle AADT as an explanatory variable, the estimated CMF and its SE using the SPF with total AADT as an explanatory variable, and the absolute value of the difference between the two estimated CMFs and the SE of this difference. The average values are provided in the last row.

Table 69. Model type B2 results for simulation 1 using type 1 Florida data.
Trial CMF MOTO SE MOTO CMF AADT SE AADT Difference SE Difference
1 1.13 0.22 1.13 0.22 0.00 0.31
2 1.28 0.24 1.28 0.24 0.00 0.34
3 1.03 0.20 1.09 0.21 0.06 0.29
4 0.78 0.15 0.85 0.17 0.07 0.23
5 0.82 0.17 0.88 0.18 0.06 0.25
6 0.93 0.19 0.82 0.17 0.11 0.25
7 1.76 0.30 1.74 0.30 0.02 0.42
8 0.57 0.13 0.59 0.14 0.02 0.19
9 1.19 0.21 1.27 0.23 0.08 0.31
10 0.57 0.14 0.54 0.13 0.03 0.19
Average 1.01 0.20 1.02 0.20 0.05 0.28

The results from simulation 1 showed that the estimated CMF could vary a lot between trials, and the SEs of the CMF estimates were high. Very few of the CMF estimates were statistically different from a value of 1.0.

A value of 1.0 for a CMF indicated that there was no effect on crashes. This illustrates the difficulty in estimating accurate CMFs using motorcycle crashes, which are rare. While this is illustrative of this fact, the prime interest is to investigate whether the CMF estimates differ greatly depending on whether the SPFs using motorcycle AADT or total AADT are applied in the EB before-after study approach. For this comparison, the results showed little difference. The average CMFs using the motorcycle and total AADT respectively were 1.01 and 1.02, and the average difference across all trials was 0.05.

The estimated CMFs that tended to be higher than 0.70 indicated that regression-to-the-mean was being overcorrected. Because the treatment sites were selected based on high crash rate, this left low crash rate sites for the reference sites, and the SPFs required predicted very few crashes since they are based on these remaining low crash sites.

In simulation 2, the project team used 200 sites as treatment sites and only 282 as reference sites. The CMF and number of years before and after stayed the same. The results, shown in table 70, were very similar to those in simulation 1, although the SEs of estimates were slightly smaller due to the larger sample size of treated sites.

Table 70. B2 results for simulation 2 using type 1 Florida data.
Trial CMF MOTO SE MOTO CMF AADT SE AADT Difference SE Difference
11 1.54 0.24 1.62 0.25 0.08 0.35
12 1.07 0.19 1.07 0.19 0.00 0.27
13 0.87 0.15 0.90 0.16 0.03 0.22
14 0.84 0.15 0.79 0.14 0.05 0.21
15 1.21 0.20 1.29 0.22 0.08 0.30
16 0.70 0.15 0.67 0.14 0.03 0.21
17 1.04 0.19 0.96 0.17 0.08 0.25
18 1.01 0.19 1.00 0.19 0.01 0.27
19 0.76 0.14 0.79 0.15 0.03 0.21
20 0.86 0.16 0.82 0.16 0.04 0.23
Average 0.99 0.18 0.99 0.18 0.04 0.25

In simulation 3, the number of sites and assumed CMF was identical to simulation 2, but now the treatment sites were selected by a random variable and not by taking the highest crash rate sites in the before period. This random selection would minimize any regression to the mean in the data. For these results, shown in table 71, there were near-identical estimates for the CMF between using the motorcycle or total AADT model. The average value of estimated CMFs was 0.69 for both the motorcycle and total AADT SPF approaches. However, significant variation in the CMF estimates for between trials remained.

Table 71. B2 results for simulation 3 using type 1 Florida.
Trial CMF MOTO SE MOTO CMF AADT SE AADT Difference SE Difference
21 0.93 0.16 0.93 0.16 0.00 0.23
22 0.55 0.11 0.55 0.11 0.00 0.16
23 0.58 0.12 0.59 0.12 0.01 0.17
24 0.58 0.11 0.58 0.11 0.00 0.16
25 0.61 0.11 0.59 0.11 0.02 0.16
26 0.53 0.11 0.53 0.11 0.00 0.16
27 0.62 0.12 0.64 0.12 0.02 0.17
28 0.80 0.14 0.78 0.14 0.02 0.20
29 0.81 0.13 0.80 0.14 0.01 0.19
30 0.93 0.16 0.93 0.16 0.00 0.23
Average 0.69 0.13 0.69 0.13 0.01 0.18

In simulation 4, the treatment sites were selected using a random variable only for sites that had one or more motorcycle crashes in the before period. The project team also reduced the number of treatment sites to 50. The results are shown in table 72. Again, the results showed that the estimates using the two SPFs were close, with the average difference being 0.05. The average values of the estimated CMFs were also close to 0.70.

Table 72. Results for simulation 4 using type 1 Florida data.
Trial CMF MOTO SE MOTO CMF AADT SE AADT Difference SE Difference
31 0.56 0.16 0.61 0.18 0.05 0.24
32 0.88 0.20 0.94 0.21 0.06 0.29
33 0.86 0.19 0.88 0.20 0.02 0.28
34 0.78 0.18 0.82 0.19 0.04 0.26
35 0.75 0.18 0.79 0.19 0.04 0.26
36 0.49 0.15 0.49 0.16 0.00 0.22
37 0.68 0.17 0.72 0.18 0.04 0.25
38 0.52 0.16 0.54 0.17 0.02 0.23
39 0.89 0.22 0.97 0.24 0.08 0.33
40 0.98 0.25 0.88 0.23 0.10 0.34
Average 0.74 0.19 0.76 0.20 0.05 0.27

Florida Type 3

Table 73 shows the results for simulation 1 using the Florida type 3 data. In simulation 1, the project team selected the treated sites using a random number for sites that had one or more before period crashes. There were 200 treatment sites and 2,997 reference sites. The CMF was 0.90 with 3 years before and 3 years after.

Similar to the results for the type 1 sites, the results from simulation 1 showed that the estimated CMF could vary a lot between trials. However, the differences for each trial between the estimates of the CMF using the SPF with motorcycle AADT versus total AADT were small. The average CMFs using the motorcycle and total AADT were 0.78 and 0.73, respectively, and the average difference across all trials was 0.05. The CMF estimates tended to be low, indicating that the correction for regression to the mean was not large enough.

Table 73. Results for simulation 1 using type 3 Florida data.
Trial CMF MOTO SE MOTO CMF AADT SE AADT Difference SE Difference
1 0.67 0.09 0.64 0.08 0.03 0.12
2 0.78 0.11 0.72 0.10 0.06 0.15
3 0.55 0.08 0.52 0.08 0.03 0.11
4 0.86 0.11 0.82 0.10 0.04 0.15
5 0.77 0.10 0.72 0.09 0.05 0.13
6 0.79 0.10 0.75 0.10 0.04 0.14
7 0.74 0.10 0.67 0.09 0.07 0.13
8 0.88 0.10 0.82 0.10 0.06 0.14
9 0.77 0.10 0.72 0.09 0.05 0.13
10 0.97 0.12 0.90 0.11 0.07 0.16
Average 0.78 0.10 0.73 0.09 0.05 0.14

In simulation 2, the number of treatment sites decreased from 200 to 100, the number of reference sites increased slightly from 2,997 to 3,097, and the true CMF reduced from 0.90 to 0.70.

The results from simulation 2 were consistent, as shown in table 74. However, the estimated CMF can vary greatly between trials, and the differences for each trial between the estimates of the CMF using the SPF with motorcycle AADT versus total AADT were small. The average CMFs using the motorcycle and total AADT respectively were 0.60 and 0.64, and the average difference across all trials was 0.04. As with simulation 1, the correction for regression to the mean appears not to be enough on average.

Table 74. Results for simulation 2 using type 3 Florida data.
Trial CMF MOTO SE MOTO CMF AADT SE AADT Difference SE Difference
11 0.73 0.13 0.78 0.14 0.05 0.19
12 0.30 0.08 0.31 0.08 0.01 0.11
13 0.50 0.11 0.50 0.11 0.00 0.16
14 0.65 0.12 0.63 0.12 0.02 0.17
15 0.72 0.14 0.76 0.15 0.04 0.21
16 0.57 0.12 0.64 0.14 0.07 0.18
17 0.54 0.11 0.58 0.13 0.04 0.17
18 0.64 0.13 0.69 0.15 0.05 0.20
19 0.81 0.15 0.89 0.16 0.08 0.22
20 0.55 0.12 0.59 0.13 0.04 0.18
Average 0.60 0.12 0.64 0.13 0.04 0.18

In simulation 3, the number of treatment sites increased to 1,000, the number of reference sites decreased to 2,197, and the true CMF remained 0.70.

As shown in table 75, the results from simulation 3 were also consistent in that the estimated CMF can vary between trials, and the differences for each trial between the estimates of the CMF using the SPF with motorcycle AADT versus total AADT were small. The average CMFs using the motorcycle and total AADT were 1.06 and 1.07, respectively, and the average difference across all trials was 0.03.

For simulation 3, the correction for regression to the mean appeared too large. With so many of the sites in the treatment group, the mean motorcycle crash rate of the reference group would be very low.

Table 75. Results for simulation 3 using type 3 Florida data.
Trial CMF MOTO SE MOTO CMF AADT SE AADT Difference SE Difference
21 0.99 0.08 0.99 0.08 0.00 0.11
22 1.21 0.09 1.23 0.09 0.02 0.13
23 0.96 0.07 0.99 0.08 0.03 0.11
24 0.93 0.07 0.94 0.07 0.01 0.10
25 1.38 0.10 1.45 0.10 0.07 0.14
26 1.00 0.08 0.98 0.08 0.02 0.11
27 0.98 0.08 1.03 0.09 0.05 0.12
28 1.15 0.09 1.12 0.09 0.03 0.13
29 0.99 0.08 1.00 0.08 0.01 0.11
30 0.97 0.08 0.96 0.08 0.01 0.11
Average 1.06 0.08 1.07 0.08 0.03 0.12

Avenue B Model Type B2

The model type B2 analyses were conducted using the data for types 1 (rural freeway) and 3 (rural arterial) in Florida and for type 3 (rural non-freeway) in Pennsylvania.

Florida Type 1

Simulation 1

Figure 37 shows the model used to simulate the data for simulation 1 where dispersion equals 0.4975 and the CMF for AVGSHLDWID equals 0.89.

Figure 37. Equation. Florida type 1 simulation model 1. Motorcycle crashes equals the product of exponential value raised to the power of -5.3785 times AVGMOTO raised to the power of 0.8438 times LENGTH raised to the power of 0.8227 times exponential value raised to the power of -0.118 times AVGSHLDWID.

Figure 37. Equation. Florida type 1 simulation model 1.

The goal of the analysis was to re-estimate the model, including the parameter in the model for the average shoulder width variable, AVGSHLDWID. The project did this once with AVGMOTO and once with AVGAADT as the exposure measure.

Column 1 in table 76 indicates the trial number. Columns 2 and 3 show the parameter estimate and SE for the AVGSHLDWID variable using AVGMOTO in the model. Columns 4 and 5 show the same information for the model using AVGAADT in the model. Columns 6 and 7 provide the absolute value of the difference in parameter estimates and the SE of this difference. Columns 8 and 9 provide the inferred CMFs for the parameter values estimated. The last row shows the average value for all estimates across all trials. The estimated CMFs using the two exposure measures were very close for each trial and the average over all trials was very close to the true value of 0.89.

Table 76. B2 results simulation 1 for Florida type 1 data.
Trial Estimate Using Motorcycle AADT SE Using Motorcycle AADT Estimate Using Total AADT SE Using Total AADT Difference in Estimates Standard Deviation Of Difference CMF Using Motorcycle AADT CMF Using Total AADT
1 -0.0153 0.0567 -0.0146 0.0655 0.0007 0.0866 0.98 0.99
2 -0.1098 0.0571 -0.0775 0.0669 0.0323 0.0880 0.90 0.93
3 -0.1182 0.0570 -0.1342 0.0670 0.0160 0.0880 0.89 0.87
4 -0.1999 0.0624 -0.2226 0.0718 0.0227 0.0951 0.82 0.80
5 -0.1039 0.0585 -0.0976 0.0684 0.0063 0.0900 0.90 0.91
6 -0.0946 0.0544 -0.1419 0.0622 0.0473 0.0826 0.91 0.87
7 -0.0682 0.0586 -0.0511 0.0671 0.0171 0.0891 0.93 0.95
8 -0.1488 0.0572 -0.1584 0.0663 0.0096 0.0876 0.86 0.85
9 -0.1155 0.0553 -0.0678 0.0642 0.0477 0.0847 0.89 0.93
10 -0.1397 0.0511 -0.1606 0.0601 0.0209 0.0789 0.87 0.85
11 -0.1443 0.0635 -0.2093 0.0722 0.0650 0.0962 0.87 0.81
12 -0.2069 0.0645 -0.2454 0.0737 0.0385 0.0979 0.81 0.78
13 -0.2297 0.0589 -0.2360 0.0702 0.0063 0.0916 0.79 0.79
14 -0.1308 0.0541 -0.1274 0.0639 0.0034 0.0837 0.88 0.88
15 -0.1457 0.0561 -0.1459 0.0655 0.0002 0.0862 0.86 0.86
16 -0.1323 0.0574 -0.1216 0.0665 0.0107 0.0878 0.88 0.89
17 -0.0811 0.0554 -0.0614 0.0634 0.0197 0.0842 0.92 0.94
18 -0.1994 0.0577 -0.1742 0.0680 0.0252 0.0892 0.82 0.84
19 -0.1478 0.0548 -0.1817 0.0625 0.0339 0.0831 0.86 0.83
20 -0.0923 0.0589 -0.0910 0.0678 0.0013 0.0898 0.91 0.91
Average -0.1312 0.0575 -0.1360 0.0667 0.0212 0.0880 0.88 0.87
STD N/A N/A N/A N/A N/A N/A 0.05 0.06
Minimum N/A N/A N/A N/A N/A N/A 0.79 0.78
Maximum N/A N/A N/A N/A N/A N/A 0.98 0.99

N/A = The statistic is not of interest and was not calculated.

Simulation 2

For simulation 2, the project team applied the same model used for simulation 1 (see figure 38) but with a much higher dispersion parameter equal to 5. The CMF for AVGSHLDWID equaled 0.89 per 1-ft increase in average shoulder width. The impact of the larger dispersion parameter was to create much more variability in crash counts between sites with similar road characteristics and traffic volumes.

Figure 38. Equation. Florida type 1 simulation model 2. Motorcycle crashes equals the product of exponential value raised to the power of -5.3785 times AVGMOTO raised to the power of 0.8438 times LENGTH raised to the power of 0.8227 times exponential value raised to the power of -0.118 times AVGSHLDWID.

Figure 38. Equation. Florida type 1 simulation model 2.

The results in table 77 again show that the estimated CMFs are close when using either the motorcycle or total AADT as an exposure measure. The average over all trials was close to the true value of 0.89: 0.92 for the motorcycle AADT model and 0.91 for the total AADT model. However, the standard deviation of the CMF estimates between trials is about double that for simulation 1.

Table 77. Model type B2 results simulation 2 for Florida type 1 data.
Trial Estimate Using Motorcycle AADT SE Using Motorcycle AADT Estimate Using Total AADT SE Using Total AADT Difference in Estimates Standard Deviation Of Difference CMF Using Motorcycle AADT CMF Using Total AADT
21 0.0017 0.0899 0.0692 0.1021 0.0675 0.1360 1.00 1.07
22 -0.0753 0.0871 -0.0740 0.0995 0.0013 0.1322 0.93 0.93
23 -0.1427 0.0894 -0.1690 0.1023 0.0263 0.1359 0.87 0.84
24 -0.0513 0.0919 -0.0833 0.1042 0.0320 0.1389 0.95 0.92
25 -0.1485 0.0850 -0.2201 0.0977 0.0716 0.1295 0.86 0.80
26 -0.2881 0.0975 -0.3399 0.1120 0.0518 0.1485 0.75 0.71
27 -0.0678 0.0852 -0.1569 0.0985 0.0891 0.1302 0.93 0.85
28 -0.1741 0.0901 -0.2295 0.1053 0.0554 0.1386 0.84 0.79
29 -0.0775 0.0901 -0.0503 0.1023 0.0272 0.1363 0.93 0.95
30 -0.0762 0.0821 -0.0764 0.0923 0.0002 0.1235 0.93 0.93
31 0.0582 0.0777 0.0634 0.0892 0.0052 0.1183 1.06 1.07
32 0.0217 0.0801 0.0276 0.0908 0.0059 0.1211 1.02 1.03
33 0.0406 0.0867 -0.0363 0.0976 0.0769 0.1305 1.04 0.96
34 -0.0211 0.0856 0.0024 0.0967 0.0235 0.1291 0.98 1.00
35 -0.1611 0.0912 -0.1655 0.1043 0.0044 0.1385 0.85 0.85
36 -0.2299 0.0951 -0.3021 0.1119 0.0722 0.1469 0.79 0.74
37 -0.2107 0.0916 -0.1018 0.1021 0.1089 0.1372 0.81 0.90
38 -0.2393 0.0834 -0.2532 0.0965 0.0139 0.1275 0.79 0.78
39 0.1332 0.0902 0.1433 0.1008 0.0101 0.1353 1.14 1.15
40 -0.1198 0.0808 -0.1585 0.0932 0.0387 0.1233 0.89 0.85
Average -0.09 0.09 -0.11 0.10 0.04 0.13 0.92 0.91
STD N/A N/A N/A N/A N/A N/A 0.10 0.12
Minimum N/A N/A N/A N/A N/A N/A 0.75 0.71
Maximum N/A N/A N/A N/A N/A N/A 1.14 1.15

N/A = The statistic is not of interest and was not calculated.

Florida Type 3

Simulation 1

For the type 3 data in Florida, the project team pursued the simultaneous estimation of two CMFs. Figure 39 shows the model used to simulate the data for simulation 1. In this figure, dispersion equals 0.3390. The CMF for AVGSHLDWID equals 0.89 per 1-ft increase in average shoulder width. The CMF for MEDWIDTH equals 0.99 per 1-ft increase in median width.

Figure 39. Equation. Florida type 3 simulation model 1. Motorcycle crashes equals the product of exponential value raised to the power of -4.1264 times AVGMOTO raised to the power of 0.6155 times LENGTH raised to the power of 0.6683 times exponential value raised to the power of -0.118 times AVGSHLDWID minus 0.01 times MEDWIDTH.

Figure 39. Equation. Florida type 3 simulation model 1.

The results in table 78 and table 79 show that the estimated CMFs were close when using either the motorcycle or total AADT as an exposure measure. The average over all trials was also very close to the true value CMF values.

Table 78. Model type B2 results simulation 1 for Florida type 3 data for AVGSHLDWID.
Trial Estimate Using Motorcycle AADT SE Using Motorcycle AADT Estimate Using Total AADT SE Using Total AADT Difference in Estimates Standard Deviation of Difference CMF Using Motorcycle AADT CMF Using Total AADT
1 -0.1039 0.0237 -0.1226 0.0245 0.0187 0.0341 0.90 0.88
2 -0.1580 0.0247 -0.1801 0.0256 0.0221 0.0356 0.85 0.84
3 -0.1532 0.0254 -0.1736 0.0267 0.0204 0.0369 0.86 0.84
4 -0.1054 0.0229 -0.1259 0.0237 0.0205 0.0330 0.90 0.88
5 -0.1086 0.0226 -0.1281 0.0233 0.0195 0.0325 0.90 0.88
6 -0.1122 0.0232 -0.1330 0.0240 0.0208 0.0334 0.89 0.88
7 -0.0117 0.0021 -0.1604 0.0255 0.1487 0.0256 0.99 0.85
8 -0.1490 0.0238 -0.1661 0.0245 0.0171 0.0342 0.86 0.85
9 -0.0937 0.0226 -0.1091 0.0231 0.0154 0.0323 0.91 0.90
10 -0.1248 0.0234 -0.1474 0.0242 0.0226 0.0269 0.88 0.86
11 -0.1088 0.0230 -0.1321 0.0240 0.0233 0.0332 0.90 0.88
12 -0.1175 0.0243 -0.1365 0.0250 0.0190 0.0349 0.89 0.87
13 -0.1180 0.0231 -0.1381 0.0238 0.0201 0.0332 0.89 0.87
14 -0.1680 0.0254 -0.1860 0.0260 0.0180 0.0363 0.85 0.83
15 -0.1233 0.0242 -0.1423 0.0246 0.0190 0.0345 0.88 0.87
16 -0.1047 0.0233 -0.1283 0.0242 0.0236 0.0336 0.90 0.88
17 -0.1164 0.0236 -0.1333 0.0245 0.0169 0.0340 0.89 0.88
18 -0.1392 0.0234 -0.0159 0.0243 0.1233 0.0337 0.87 0.98
19 -0.1568 0.0246 -0.1780 0.0252 0.0212 0.0352 0.85 0.84
20 -0.1251 0.0237 -0.1472 0.0246 0.0221 0.0342 0.88 0.86
Average -0.1199 0.0227 -0.1392 0.0246 0.0316 0.0334 0.89 0.87
STD N/A N/A N/A N/A N/A N/A 0.03 0.03
Minimum N/A N/A N/A N/A N/A N/A 0.85 0.83
Maximum N/A N/A N/A N/A N/A N/A 0.99 0.98

N/A = The statistic is not of interest and was not calculated.

Table 79. Model type B2 results simulation 1 for Florida type 3 data for MEDWIDTH.
Trial Estimate Using Motorcycle AADT SE Using Motorcycle AADT Estimate Using Total AADT SE Using Total AADT Difference in Estimates Standard Deviation of Difference CMF Using Motorcycle AADT CMF Using Total AADT
. -0.0062 0.0020 -0.0095 0.0024 0.0033 0.0031 0.99 0.99
2 -0.0107 0.0020 -0.0131 0.0024 0.0024 0.0031 0.99 0.99
3 -0.0114 0.0021 -0.0127 0.0025 0.0013 0.0033 0.99 0.99
4 -0.0122 0.0021 -0.0169 0.0025 0.0047 0.0033 0.99 0.98
5 -0.0125 0.0020 -0.0169 0.0024 0.0044 0.0031 0.99 0.98
6 -0.0113 0.0021 -0.0146 0.0024 0.0033 0.0032 0.99 0.99
7 -0.0117 0.0021 -0.0156 0.0025 0.0039 0.0033 0.99 0.98
8 -0.0101 0.0020 -0.0132 0.0023 0.0031 0.0030 0.99 0.99
9 -0.0111 0.0021 -0.0155 0.0024 0.0044 0.0032 0.99 0.98
10 -0.0087 0.0020 -0.0132 0.0024 0.0045 0.0031 0.99 0.99
11 -0.0075 0.0019 -0.0104 0.0023 0.0029 0.0030 0.99 0.99
12 -0.0071 0.0020 -0.0109 0.0024 0.0038 0.0031 0.99 0.99
13 -0.0105 0.0020 -0.0140 0.0023 0.0035 0.0030 0.99 0.99
14 -0.0117 0.0021 -0.0146 0.0024 0.0029 0.0032 0.99 0.99
15 -0.0090 0.0020 -0.0137 0.0024 0.0047 0.0031 0.99 0.99
16 -0.0103 0.0021 -0.0143 0.0025 0.0040 0.0033 0.99 0.99
17 -0.0101 0.0021 -0.0125 0.0024 0.0024 0.0032 0.99 0.99
18 -0.0147 0.0020 -0.0180 0.0024 0.0033 0.0031 0.99 0.98
19 -0.0121 0.0020 -0.0166 0.0024 0.0045 0.0031 0.99 0.98
20 -0.0110 0.0020 -0.0155 0.0024 0.0045 0.0031 0.99 0.98
Average -0.0105 0.0020 -0.0141 0.0024 0.0036 0.0032 0.99 0.99
STD N/A N/A N/A N/A N/A STD 0.00 0.00
Minimum N/A N/A N/A N/A N/A Minimum 0.99 0.98
Maximum N/A N/A N/A N/A N/A Maximum 0.99 0.99

N/A = The statistic is not of interest and was not calculated.

Simulation 2

In simulation 2, the project team chose a random sample of 200 segments to investigate the results when the sample size is small. All other assumptions used in simulation 1 remained the same. The results in table 80 and table 81 show that as before, the CMF estimates for both geometric variables were very close between using motorcycle AADT or total AADT as the exposure measure. The average value over all trials was also close to the true value estimates. However, with the smaller sample size, the standard deviation of the CMF estimates was much higher.

Table 80. Model type B2 results simulation 2 for Florida type 3 data for AVGSHLDWID.
Trial Estimate Using Motorcycle AADT SE Using Motorcycle AADT Estimate Using Total AADT SE Using Total AADT Difference in Estimates Standard Deviation of Difference CMF Using Motorcycle AADT CMF Using Total AADT
1 -0.0864 0.2578 -0.0934 0.2509 0.0070 0.3597 0.92 0.91
2 -0.0921 0.2073 -0.1389 0.1859 0.0468 0.2784 0.91 0.87
3 -0.1128 0.3773 -0.1289 0.3831 0.0161 0.5377 0.89 0.88
4 -0.0865 0.1781 -0.1167 0.1825 0.0302 0.2550 0.92 0.89
5 -0.0328 0.1932 -0.0309 0.1874 0.0019 0.2692 0.97 0.97
6 -0.1992 0.2649 -0.2326 0.2808 0.0334 0.3860 0.82 0.79
7 -0.5430 0.3211 -0.5201 0.3140 0.0229 0.4491 0.58 0.59
8 -0.2165 0.2271 -0.2120 0.2226 0.0045 0.3180 0.81 0.81
9 0.0156 0.1320 0.0043 0.1488 0.0113 0.1989 1.02 1.00
10 0.0322 0.1865 0.0432 0.1783 0.0110 0.2580 1.03 1.04
Average -0.1322 0.2345 -0.1426 0.2334 0.0185 0.3310 0.89 0.88
STD N/A N/A N/A N/A N/A N/A 0.13 0.13
Minimum N/A N/A N/A N/A N/A N/A 0.58 0.59
Maximum N/A N/A N/A N/A N/A N/A 1.03 1.04

N/A = The statistic is not of interest and was not calculated.

Table 81. Model type B2 results simulation 2 for Florida type 3 data for MEDWIDTH.
Trial Estimate Using Motorcycle AADT SE Using Motorcycle AADT Estimate Using Total AADT SE Using Total AADT Difference in Estimates Standard Deviation of Difference CMF Using Motorcycle AADT CMF Using Total AADT
1 -0.0065 0.0195 -0.0219 0.0248 0.0154 0.0315 0.99 0.98
2 -0.0066 0.0127 -0.0171 0.0153 0.0105 0.0199 0.99 0.98
3 0.0174 0.0167 0.0183 0.0184 0.0009 0.0248 1.02 1.02
4 0.0133 0.0112 0.0123 0.0153 0.0010 0.0190 1.01 1.01
5 0.0051 0.0193 0.0021 0.0205 0.0030 0.0282 1.01 1.00
6 -0.0121 0.0223 0.0028 0.0250 0.0149 0.0335 0.99 1.00
7 -0.0120 0.0201 -0.0114 0.0221 0.0006 0.0299 0.99 0.99
8 -0.0065 0.0161 -0.0082 0.0175 0.0017 0.0238 0.99 0.99
9 -0.0438 0.0308 -0.0482 0.0312 0.0044 0.0438 0.96 0.95
10 0.0002 0.0158 0.0024 0.0191 0.0022 0.0248 1.00 1.00
Average -0.0052 0.0185 -0.0069 0.0209 0.0055 0.0279 0.99 0.99
STD N/A N/A N/A N/A N/A STD 0.02 0.02
Minimum N/A N/A N/A N/A N/A Minimum 0.96 0.95
Maximum N/A N/A N/A N/A N/A Maximum 1.02 1.02

N/A = The statistic is not of interest and was not calculated.

Pennsylvania Type 3

The project team ran one simulation using the type 3 sites in Pennsylvania. For this simulation, two geometric variables were included in the model: average shoulder width (AVGSHLDWID) and total surface width (SURFWIDTH). In this model, dispersion equals 0.8647. The CMF for AVGSHLDWID equals 0.97 per 1-ft increase in average shoulder width. The CMF for SURFWIDTH equals 1.03 per 1-ft increase in total surface width. Figure 40 shows the model used to simulate the data for simulation 1.

Figure 40. Equation. Pennsylvania type 3 simulation model 1. Motorcycle crashes equals the product of exponential value raised to the power of -5.0123 times AVGMOTO raised to the power of 0.4623 times LENGTH raised to the power of 0.7370 times exponential value raised to the power of -0.0278 times AVGSHLDWID plus 0.0256 times SURFWIDTH.

Figure 40. Equation. Pennsylvania type 3 simulation model 1.

For estimating the new models, the project team selected a random subset of 200 sites for each trial. This random selection allowed the project team to evaluate the impact of small sample sizes on the results.

The results in table 82 and table 83 show that, as before, the CMF estimates for both geometric variables are very close between using motorcycle AADT or total AADT as the exposure measure. The average value over all trials is also very close to the true value estimates.

Table 82. Model type B2 results simulation 1 for Pennsylvania type 3 data for AVGSHLDWID.
Trial Estimate Using Motorcycle AADT SE Using Motorcycle AADT Estimate Using Total AADT SE Using Total AADT Difference in Estimates Standard Deviation of Difference CMF Using Motorcycle AADT CMF Using Total AADT
1 0.0050 0.0572 0.0071 0.0597 0.0021 0.0827 1.01 1.01
2 0.0123 0.0536 0.0300 0.0555 0.0177 0.0772 1.01 1.03
3 -0.0634 0.0631 -0.0652 0.0655 0.0018 0.0909 0.94 0.94
4 -0.0944 0.0628 -0.0814 0.0651 0.0130 0.0905 0.91 0.92
5 -0.0294 0.0555 -0.0273 0.0577 0.0021 0.0801 0.97 0.97
6 -0.0954 0.0595 -0.0593 0.0620 0.0361 0.0859 0.91 0.94
7 -0.0981 0.0676 -0.1270 0.0708 0.0289 0.0979 0.91 0.88
8 -0.0457 0.0589 -0.0543 0.0618 0.0086 0.0854 0.96 0.95
9 -0.1707 0.0658 -0.1966 0.0690 0.0259 0.0953 0.84 0.82
10 -0.0223 0.0561 -0.0359 0.0584 0.0136 0.0810 0.98 0.96
11 -0.0400 0.0555 -0.0303 0.0578 0.0097 0.0801 0.96 0.97
12 -0.0504 0.0616 -0.0423 0.0642 0.0081 0.0890 0.95 0.96
13 0.0799 0.0545 0.0858 0.0564 0.0059 0.0784 1.08 1.09
14 -0.1335 0.0555 -0.1436 0.0585 0.0101 0.0806 0.88 0.87
15 -0.0061 0.0555 0.0012 0.0579 0.0073 0.0802 0.99 1.00
16 -0.0273 0.0560 -0.0276 0.0586 0.0003 0.0811 0.97 0.97
17 -0.0726 0.0645 -0.0939 0.0674 0.0213 0.0933 0.93 0.91
18 0.0023 0.0606 -0.0089 0.0629 0.0112 0.0873 1.00 0.99
19 -0.0777 0.0632 -0.0726 0.0657 0.0051 0.0912 0.93 0.93
20 -0.0379 0.0556 -0.0234 0.0578 0.0145 0.0802 0.96 0.98
Average -0.0483 0.0591 -0.0483 0.0616 0.0122 0.0854 0.95 0.95
STD N/A N/A N/A N/A N/A N/A 0.05 0.06
Minimum N/A N/A N/A N/A N/A N/A 0.84 0.82
Maximum N/A N/A N/A N/A N/A N/A 1.08 1.09

N/A = The statistic is not of interest and was not calculated.

Table 83. Model type B2 results simulation 1 for Pennsylvania type 3 data for SURFWIDTH.
Trial Estimate Using Motorcycle AADT SE Using Motorcycle AADT Estimate Using Total AADT SE Using Total AADT Difference in Estimates Standard Deviation of Difference CMF Using Motorcycle AADT CMF Using Total AADT
1 0.0132 0.0275 0.0203 0.0275 0.0071 0.0389 1.01 1.02
2 0.0415 0.0221 0.0532 0.0216 0.0117 0.0309 1.04 1.05
3 0.0303 0.0289 0.0361 0.0290 0.0058 0.0409 1.03 1.03
4 0.0536 0.0246 0.0658 0.0241 0.0122 0.0344 1.06 1.07
5 0.0265 0.0243 0.0327 0.0241 0.0062 0.0342 1.03 1.03
6 0.0331 0.0244 0.0544 0.0228 0.0213 0.0334 1.03 1.06
7 0.0110 0.0323 0.0030 0.0339 0.0080 0.0468 1.01 1.00
8 -.0303 0.0336 -0.0229 0.0342 0.0074 0.0479 0.97 0.98
9 0.0258 0.0291 0.0185 0.0306 0.0073 0.0422 1.03 1.02
10 0.0201 0.0261 0.0207 0.0267 0.0006 0.0373 1.02 1.02
11 0.0233 0.0249 0.0333 0.0243 0.0100 0.0348 1.02 1.03
12 0.0209 0.0284 0.0315 0.0279 0.0106 0.0398 1.02 1.03
13 0.0485 0.0226 0.0568 0.0225 0.0083 0.0319 1.05 1.06
14 0.0587 0.0200 0.0608 0.0201 0.0021 0.0284 1.06 1.06
15 0.0296 0.0244 0.0392 0.0241 0.0096 0.0343 1.03 1.04
16 -.0245 0.0318 -0.0147 0.0320 0.0098 0.0451 0.98 0.99
17 0.0238 0.0298 0.0184 0.0309 0.0054 0.0429 1.02 1.02
18 0.0389 0.0264 0.0401 0.0267 0.0012 0.0375 1.04 1.04
19 0.0328 0.0293 0.0391 0.0294 0.0063 0.0415 1.03 1.04
20 0.0211 0.0257 0.0351 0.0250 0.0140 0.0359 1.02 1.04
Average 0.0249 0.0268 0.0311 0.0269 0.0082 0.0380 1.03 1.03
STD N/A N/A N/A N/A N/A N/A 0.02 0.02
Minimum N/A N/A N/A N/A N/A N/A 0.97 0.98
Maximum N/A N/A N/A N/A N/A N/A 1.06 1.07

N/A = The statistic is not of interest and was not calculated.

 

 

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