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From page 51... ... 35 4 MODELS FOR MULTILANE RURAL HIGHWAYS 4.1 ROADWAY SEGMENTS Estimation and Validation Data The data we used for estimation of segment SPFs were collected from Texas (2009–11) and California (2010–11) Read the entire page →
From page 52... ... 36 Table 4‐2: Sample Size by Conditions, Four‐Lane Undivided (4U) Segments Condition Lane width Shoulder width Shoulder type Auto‐speed enforcement Texas Base condition 12.ft. 6.ft. paved not present 48 Modified condition 12.ft. 6.ft. or wider paved not present 401 Table 4‐3: Descriptive Statistics for Base Condition SPFs, Four‐Lane Undivided (4U) Read the entire page →
From page 53... ... 37 Table 4‐4: Descriptive Statistics for Base Condition Validation Data, Four‐Lane Undivided (4U) Segments Texas (N = 402, 170.531 mi) Read the entire page →
From page 54... ... 38 in Table 4 6. Table 4‐7 shows descriptive statistics for base condition SPFs for divided segments. Also, descriptive statistics produced from the validation data for the divided segments are presented in Table 4‐8 and Table 4‐9. We chose California's data for SPF estimation because California has the largest range of AADTs, as shown in Table 4‐7; Illinois and Washington data were chosen for validation. Table 4‐6: Sample Size by Condition, Four‐Lane Divided (4D) Segments Condition Lane Width Shoulder Width Median Width Auto‐Speed Enforcement California Base condition 12 feet 8 feet 30 feet Not present 0 Modified condition 12 feet 8 feet 30 feet or wider Not present 138 Table 4‐7: Descriptive Statistics for Base Condition SPFs, Four‐Lane Divided (4D) Read the entire page →
From page 55... ... 39 Table 4‐8: Descriptive Statistics for Base Condition Validation Data, Four‐Lane Divided (4D) Segments ‐ Illinois Illinois (N = 592, 145.500 mi) Read the entire page →
From page 56... ... 40 Table 4‐9: Descriptive Statistics for Base Condition Validation Data, Four‐Lane Divided (4D) Segments ‐ Washington Washington (N = 214, 91.727 mi) Read the entire page →
From page 57... ... 41 Table 4‐10: Base Condition SPFs, Four‐Lane Undivided (4U) Segments Crash Type Texas (N = 401, 176.925 mi) Read the entire page →
From page 58... ... 42 Table 4‐11: Base Condition SPFs, Four‐Lane Divided (4D) Segments Crash Type California (N = 138, 73.366 mi) Read the entire page →
From page 59... ... 43 Validation of Models Calibration and validation of the SPFs of rural multilane undivided and divided segments are presented in Table 4‐12 through Table 4‐14. The Texas 2012 data are used for calibration and validation of undivided segment SPFs and the Illinois and Washington data for divided segment SPFs. The calibration factors obtained using the HSM method are less than 1, except for SV SPFs. Use of the calibration function (Srinivasan et al. 2016) improves model fit better than the HSM calibration technique in some cases, as indicated by the MADs and MSPEs. Due to the lack of samples, the same‐direction KA, intersecting‐ direction KAB, intersecting‐direction KA, and opposite‐direction KA crash SPFs cannot be calibrated using the calibration function. Read the entire page →
From page 60... ... 44 Table 4‐12: Calibration of the Texas (2009–11) Safety Performance Functions Using the Texas (2012) Read the entire page →
From page 61... ... 45 Table 4‐13: Calibration of the California (2009–10) Safety Performance Functions Using the Illinois (2009–11) Read the entire page →
From page 62... ... 46 Table 4‐14: Calibration of the California (2009–10) Safety Performance Functions Using the Washington (2009–11) Read the entire page →
From page 63... ... 47 4.2 INTERSECTIONS Estimation and Validation Data The data used for estimation of intersection SPFs were collected from Minnesota (2009–11) Read the entire page →
From page 64... ... 48 Table 4‐16: Descriptive Statistics for Base Condition SPFs, Multilane Three‐Leg Stop‐ Controlled (3ST) Intersections Variable Minnesota (N = 149) Read the entire page →
From page 65... ... 49 Table 4‐17: Descriptive Statistics for Base Condition Validation Data, Multilane Three‐Leg Stop‐Controlled (3ST) Intersections Variable Ohio (N = 117) Read the entire page →
From page 66... ... 50 Table 4‐18: Descriptive Statistics for Base Condition SPFs, Multilane Four‐Leg Stop‐Controlled (4ST) Intersections Variable Minnesota (N = 139) Read the entire page →
From page 67... ... 51 Table 4‐19: Descriptive Statistics for Base Condition Validation Data, Multilane Four‐Leg Stop‐ Controlled (4ST) Intersections Variable Ohio (N = 83) Read the entire page →
From page 68... ... 52 Table 4‐20: Base Condition Criteria and Data Availability, Multilane Four‐Leg Signal‐Controlled (4SG) Intersections Base Condition Criteria Ohio Intersection skew angle 0°–5° X Intersection left‐turn lanes None X Intersection right‐turn lanes None X Red light violation cameras None Lighting Present X Table 4‐21: Descriptive Statistics for Base Condition SPFs, Multilane Four‐Leg Signal‐ Controlled (4SG) Read the entire page →
From page 69... ... 53 Table 4‐22: Descriptive Statistics for Base Condition Validation Data, Multilane Four‐Leg Signal‐Controlled (4SG) Intersections Variable Minnesota (N = 24) Read the entire page →
From page 70... ... 54 Estimated Models Base condition SPFs for 3ST intersections are exhibited in Table 4‐23. We tried to estimate regression coefficients for both the major‐ and minor‐road traffic volumes. In cases where the minor‐road traffic volume was statistically insignificant, we estimated a coefficient for the total entering volume instead. In either case, the coefficients do not indicate the relationship between crashes at 3ST intersections, and entering volumes are linear. In addition, only 10 reported KA crashes are sampled for analysis, rendering all KA crash model results unreliable. Such SPFs should be used with caution. This also applies for the single‐vehicle KAB crash SPF, all opposite‐direction crash SPFs, and the same‐direction KAB crash SPF. The MADs indicate the average deviations between crash counts, predicted by SPFs, and the observed ones are relatively low. Base condition SPFs for 4ST intersections are presented in Table 4‐24. Apart from KABCO, KABC, KAB, same‐direction KABCO, and intersecting‐direction KABCO crash SPFs, the total entering volume is used as the exposure variable in the SPF development process. This is because statistically insignificant minor‐ road traffic volumes result when estimating SPFs using both major‐ and minor‐road volumes. Similar to the 3SG intersection KA crash patterns, only 14 reported KA crashes are available in the data, and any KA crash SPF should be used with caution. We also suggest the same‐direction KAB crash SPF, the single‐ vehicle KAB crash SPF, and all opposite‐direction SPFs be used only with extra care due to the small samples modeled. The MAD measures indicate low average residuals. Base condition SPFs for various crash types for 4SG intersections are shown in Table 4‐25. In all SPFs, we used the total entering volume, since minor‐road volumes are insignificant when using both the major‐ and minor‐road volumes as independent variables. The total entering‐volume estimated coefficients range from –0.682 to 1.921. They indicate nonlinear relationships between crashes and entering volume. Yet, the volume is almost linearly correlated with intersecting‐direction KABCO crashes, as indicated by the volume coefficient. In addition, we used Moore‐Penrose inverse matrices for all KA SPFs, the opposite‐ direction KABC SPF, the opposite‐direction KAB SPF, the single‐vehicle KABC SPF, and the single‐vehicle KAB SPF, due to inadequate samples. We suggest those SPFs be used with caution. Finally, the average residuals are reasonably low, as indicated by the MADs. Validation of Models We conducted calibration and validation of rural multilane intersection SPFs using the Ohio data for 3ST and 4ST intersections and the Minnesota data for the 4SG intersections. The results are presented in tables 4‐26 through 4‐27. The calibration factors, obtained using the HSM calibration method, are not near 1. The calibration function performs slightly better than the HSM calibration method in a few cases. It should be noted that we used the Moore‐Penrose inverse matrix for several SPFs for the severe crash categories due to limited samples. Read the entire page →
From page 71... ... 55 Table 4‐23: Base Condition SPFs, Multilane Three‐Leg Stop‐Controlled (3ST) Intersections Crash Type Minnesota (N = 149) Read the entire page →
From page 72... ... 56 Table 4‐24: Base Condition SPFs, Multilane Four‐Leg Stop‐Controlled (4ST) Intersections Crash Type Minnesota (N = 139) Read the entire page →
From page 73... ... 57 Table 4‐25: Base Condition SPFs, Multilane Four‐Leg Signal‐Controlled (4SG) Intersections Crash Type Ohio (N = 53) Read the entire page →
From page 74... ... 58 Table 4‐26: Validation of the Minnesota (2009–11) Safety Performance Functions Using the Ohio (2009–11) Read the entire page →
From page 75... ... 59 Table 4‐27: Calibration of the Minnesota (2009–11) Safety Performance Functions Using the Ohio (2009–11) Read the entire page →
From page 76... ... 60 Table 4‐28: Calibration of the Ohio (2009–11) Safety Performance Functions Using the Minnesota (2009–11) Read the entire page →

From page 51...

... 35 4 MODELS FOR MULTILANE RURAL HIGHWAYS 4.1 ROADWAY SEGMENTS Estimation and Validation Data The data we used for estimation of segment SPFs were collected from Texas (2009–11) and California (2010–11)