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Intersection Crash Prediction Methods for the Highway Safety Manual (2021)

Chapter: Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control

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Suggested Citation:"Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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Suggested Citation:"Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
×
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Suggested Citation:"Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control." National Academies of Sciences, Engineering, and Medicine. 2021. Intersection Crash Prediction Methods for the Highway Safety Manual. Washington, DC: The National Academies Press. doi: 10.17226/26153.
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57 Chapter 3. Development of Models for Use in HSM Crash Prediction Methods: Intersections with All-Way Stop Control This section of the report describes the development of crash prediction models for all-way stop- controlled intersections and presents the final models recommended for incorporation in the second edition of the HSM. None of the HSM Part C chapters in the first edition of the HSM include crash prediction models for all-way stop-controlled intersections. Crash prediction models are recommended for the following intersection types for the second edition of the HSM: • Four-leg intersections with all-way stop control (4aST) on rural two-lane roads • Three-leg intersections with all-way stop control (3aST) in urban and suburban areas • Four-leg intersections with all-way stop control (4aST) in urban and suburban areas Section 3.1 describes the site selection and data collection process for developing the crash prediction models for all-way stop-controlled intersections. Section 3.2 presents descriptive statistics of the databases used for model development. Section 3.3 presents the statistical analysis and SPFs developed for all-way stop-controlled intersections. Section 3.4 presents the CMFs recommended for use with the SPFs. Section 3.5 presents the results of an analysis to develop SDFs for use with the total SPF for all-way stop-controlled intersections, and Section 3.6 summarizes the recommendations for incorporating new crash prediction models for intersections with all-way stop in the second edition of the HSM. 3.1 Site Selection and Data Collection A list of potential intersections for model development was initially created using Highway Safety Information System (HSIS) or Safety Analyst databases from five states: • California (CA) • Illinois (IL) • Minnesota (MN) • Nevada (NV) • Ohio (OH) Each intersection in the list was initially screened using Google Earth® to determine if the site was suitable for inclusion in model development. Several reasons a site could be deemed inappropriate for use in model development were: • The traffic control at the intersection was something other than all-way stop control. • A private driveway was located in close proximity to the intersection. • One or more of the approaches to the intersection was a private/commercial access. • Google Street View® was not available to identify leg specific attributes. • One or more of the intersection legs was a one-way street.

58 Each intersection that was initially deemed appropriate for inclusion in model development was given a unique identification code and included in a refined database for detailed data collection. Three types of data were collected for each intersection during detailed data collection: site characteristic, crash, and traffic volume data. Google Earth® was used to collect detailed site characteristics of the intersections. To reduce potential errors during data collection and to streamline data entry, a data collection tool was created using Visual Basic for Applications. Figure 4 shows a screenshot of the data collection tool used to collect detailed site characteristic data for all-way stop-controlled intersections. Figure 4. Data collection tool The items in the data collection tool dynamically changed based on intersection type and presence of features. For example, if the data collector input that the intersection was a three-leg intersection, then the form dynamically changed to only include attributes for three legs. As an additional example, if the data collector selected “no median present” for an approach, then median related attributes would dynamically disappear from the form. Table 3 lists the

59 intersection attributes collected, their definitions, and permitted values for all-way stop- controlled intersections. Once all necessary data were entered into the data collection tool and saved for a given intersection, the data collection tool was used to validate the inputs for that particular intersection consistent with the range and/or permitted values for the respective variables/parameters. Table 3. Site characteristic variables collected for all-way stop-controlled intersections Variable/Parameter Definition Range or Permitted Values General Intersection Attributes Intersection configuration (i.e., number of legs and type of traffic control) Indicates the number of legs and type of traffic control 3aST, 4aST Area type (urban/rural) Indicates whether the intersection is in a rural or urban area Rural, urban Presence of flashing beacons Indicates if overhead flashing beacons are present at the intersection proper Yes, no Presence of intersection lighting Indicates if overhead lighting is present at the intersection proper Yes, no Approach Specific Attributes Route name or number Specify the route name or number of the approach Location at intersection Side/quadrant of the intersection the approach is located N, S, E, W, NE, NW, SE, SW Number of through lanes This includes dedicated through lanes and any lanes with shared movements. On the minor approach of a 3-leg intersection, if there is only one lane, then it should be classified as a through lane 0, 1, 2, 3 Presence/number of left-turn lanes The number of lanes in which only a left-turn movement can be made 0, 1, 2, 3 Left-turn channelization Type of left-turn channelization used on the intersection approach Raised or depressed island, painted, none Presence/number of right-turn lanes The number of lanes in which only a right-turn movement can be made 0, 1, 2, 3 Right-turn channelization Type of right-turn channelization used on the intersection approach Raised or depressed island, painted, none Median width Measured from outside of outer most through lane of approaching lanes to outside of lane in opposing direction Values in feet Median type Type of median separating opposing directions of travel Raised, depressed, flush, barrier, two-way left-turn lane (TWLTL) Presence of transverse rumble strips Indicates the presence of transverse rumble strips on the intersection approach Yes, no, unknown Presence/type of supplementary pavement markings Indicates the presence of supplementary pavement markings on the intersection approach Yes, no, unknown Presence of stop ahead warning signs Indicates the presence of Stop Ahead warning signs on the intersection approach Yes, no, unknown Presence of advance warning flashers Indicates the presence of advance warning flashers on the intersection approach Yes, no, unknown Horizontal alignment of intersection approach Indicates whether the approaching roadway, within 250 ft of the intersection, is a tangent or curved section of roadway Tangent, curve Horizontal curve radius Indicates the radius of the curve on the intersection approach if a curve is present within 250 ft of the intersection 2,000-ft Maximum Range: 45-1960 ft Posted speed limit Posted speed limit on the intersection approach 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, unknown Presence of crosswalk Indicates the presence of a crosswalk perpendicular to the intersection approach Yes, no, unknown Presence of bike lane Indicates the presence of a marked bike lane parallel to the intersection approach Yes, no, unknown Presence of railroad crossing Indicates the presence of a railroad crossing on the intersection approach within 250 ft of the intersection Yes, no, unknown

60 During detailed data collection, to the extent possible, the research team reviewed historical aerial images to determine if a site had recently been reconstructed or improved to determine which years of data should be used in model development. Crash and traffic volume data were obtained for California and Minnesota using HSIS databases. For Illinois, Ohio, and Nevada, crash and traffic volume data were obtained from Safety Analyst databases. The goal was to obtain the most recent four to six years of crash and traffic volume data for each site for model development. All of the data (i.e., site characteristics, crash, and traffic volume) were assembled into one database for the purposes of model development. 3.2 Descriptive Statistics of Database Data for 405 sites—12 rural three-leg, 199 rural four-leg, 33 urban three-leg, and 161 urban four-leg intersections—were available for development of crash prediction models for all-way stop-controlled intersections. The data collection sites were located in five states—California, Illinois, Minnesota, Nevada, and Ohio. To remain consistent with the standards for development of the intersection predictive models in the first edition of the HSM, the goal of this research was to develop crash prediction models with a minimum of 200 site-years of data, and preferably 450 site-years of data or more. Traffic Volumes and Site Characteristics Traffic volume and crash data were available for varying periods but were typically collected over a five- or six-year period. Table 4 shows the breakdown of all sites by area type and intersection type. Study period (date range), number of sites and site-years, and basic traffic volume statistics are shown by state in each category and across all states within a category. Of the intersection characteristics collected in Google Earth® (see Table 3), many showed no or very little variability across sites within a category (i.e., most intersections were predominantly of one type for a specific variable) and were thus excluded from modeling. The remaining variables (percent of “Yes” by area type indicated in parentheses) of potential interest in modeling were: • presence of intersection lighting (rural: 78%; urban: 93%) • presence of a flashing beacon (rural: 44%; urban: 28%) • presence of left-turn lanes on major road (rural: 12%; urban: 21%) • presence of right-turn lanes on major road (rural: 32%; urban: 19%) • presence of supplementary pavement marking on major road (rural: 20%; urban: 16%) • presence of supplementary pavement marking on minor road (rural: 19%; urban: 14%) The use of some of these site characteristics is discussed later in the SPF model development section (Section 3.3).

61 Crashes Of the 405 intersections included in the database, 70 (17%) experienced no crashes over the entire study period; their breakdown by area type and intersection type is as follows: • Rural three-leg intersections: 5 out of 12 • Rural four-leg intersections: 39 out of 199 • Urban three-leg intersections: 3 out of 33 • Urban four-leg intersections: 23 out of 161 Intersection crashes were defined as those crashes that occurred within 250 ft of the intersection and were classified as “at intersection” or “intersection-related”, consistent with recommended practice in the HSM for assigning crashes to an intersection. Table 5 (rural intersections) and Table 6 (urban intersections) show all crashes combined, SV, and MV crash counts over the study period for each state within an intersection type. Crash counts by total, FI, and PDO severity levels are shown for all times of day and separately for nighttime. SV crashes at rural intersections include crashes with a bicycle or a pedestrian, while these two collision types are shown separately for urban intersections. This approach is consistent with Chapters 10, 11, and 12 in the first edition of the HSM. Crash counts are also tallied by collision type and manner of collision across all states, separately for each intersection type, in Table 7 (rural intersections) and Table 8 (urban intersections).

62 Table 4. Major- and minor road AADTs and total AADT statistics by area type at all-way stop-controlled intersections Major Road AADT (veh/day) Minor Road AADT (veh/day) AADTtotal (veh/day) State Date Range Number of Sites Number of Site-Years Min Max Mean Median Min Max Mean Median Min Max Mean Median RURAL THREE-LEG INTERSECTIONS IL 2008-2012 8 40 400 5,200 2,049 1,725 50 6,500 1,956 750 450 11,700 4,005 2,550 OH 2009-2013 4 20 560 6,250 2,921 2,438 650 4,384 2,061 1,605 1,402 10,634 4,982 3,947 All states 2008-2013 12 60 400 6,250 2,340 1,725 50 6,500 1,991 796 425 11,700 4,331 2,550 RURAL FOUR-LEG INTERSECTIONS CA 2006-2011 29 174 1,696 12,983 5,946 5,300 684 9,985 2,686 2,100 2,628 21,427 8,632 7,667 IL 2008-2012 87 435 421 9,100 2,518 2,300 275 3,750 1,517 1,450 696 11,850 4,034 4,100 MN 2007-2011 17 85 716 8,233 4,378 4,980 614 7,059 3,259 2,980 1,330 15,292 7,637 8,270 OH 2009-2013 66 327 798 8,214 3,062 2,690 130 5,680 1,628 1,475 1,262 13,538 4,690 4,283 All states 2006-2013 199 1,021 421 12,983 3,357 2,799 130 9,985 1,873 1,638 696 21,427 5,230 4,506 URBAN THREE-LEG INTERSECTIONS CA 2006-2011 4 24 3,725 12,000 7,433 7,004 501 4,872 2,469 2,251 3,801 15,300 8,682 7,534 IL 2008-2012 17 85 175 15,000 4,535 3,360 300 11,000 2,895 2,000 475 16,000 7,429 5,841 OH 2009-2013 7 35 2,450 6,821 4,534 4,470 914 6,456 4,534 5,124 3,384 24,705 11,277 9,487 All states 2006-2013 28 144 175 15,000 4,948 4,185 300 11,000 3,244 2,433 475 24,705 8,901 8,400 URBAN FOUR-LEG INTERSECTIONS CA 2006-2011 13 78 2,730 11,792 7,300 7,660 400 8,250 4,959 5,200 3,818 18,207 12,260 12,515 IL 2008-2012 60 300 1,150 10,900 4,820 4,100 438 8,500 2,822 2,650 1,950 17,400 7,643 7,000 MN 2007-2011 28 138 1,283 10,896 5,823 5,966 417 6,700 3,129 3,008 2,124 17,127 8,953 8,428 NV 2007-2011 26 130 2,156 12,955 9,731 10,230 770 11,982 6,493 6,872 2,926 24,770 16,224 16,991 OH 2009-2013 34 170 1,789 10,232 4,913 4,659 504 4,871 2,171 2,032 2,701 13,684 7,084 6,969 All states 2006-2013 161 816 1,150 12,955 6,008 5,400 400 11,982 3,503 3,000 1,950 24,770 9,511 8,108

63 Table 5. All crashes combined and single- and MV crash counts by intersection type and crash severity— rural all-way stop-controlled intersections State Date Range Number of Sites Number of Site-Years Time of Day All Crashes Combined SV Crashes a MV Crashes Total FI PDO Total FI PDO Total FI PDO RURAL THREE-LEG INTERSECTIONS IL 2008-2012 8 40 All 34 9 25 8 4 4 26 5 21 Night 11 4 7 6 3 3 5 1 4 OH 2009-2013 4 20 All 9 5 4 3 2 1 6 3 3 Night 5 3 2 3 2 1 2 1 1 All states 2008-2013 12 60 All 43 14 29 11 6 5 32 8 24 Night 16 7 9 9 5 4 7 2 5 RURAL FOUR-LEG INTERSECTIONS CA 2006-2011 29 174 All 252 77 175 26 4 22 226 73 153 Night 49 12 37 7 0 7 42 12 30 IL 2008-2012 87 435 All 405 99 306 42 14 28 363 85 278 Night 86 22 64 12 5 7 74 17 57 MN 2007-2011 17 85 All 55 22 33 12 6 6 43 16 27 Night 13 7 6 5 1 4 8 6 2 OH 2009-2013 66 327 All 279 75 204 48 13 35 231 62 169 Night 83 19 64 26 7 19 57 12 45 All states 2006-2013 199 1,021 All 991 273 718 128 37 91 863 236 627 Night 231 60 171 50 13 37 181 47 134 a Total and FI SV crashes include pedestrian and bicycle crashes.

64 Table 6. All crashes combined, single- and MV, and pedestrian and bicycle crash counts by intersection type and crash severity—urban all-way stop- controlled intersections State Date Range Number of Sites Number of Site Years Time of Day All Crashes Combined SV Crashes Multiple-Vehicle Crashes Pedestrian Crashes Bicycle Crashes Total FI PDO Total FI PDO Total FI PDO FI FI URBAN THREE-LEG INTERSECTIONS CA 2006-2011 5 30 All 18 9 9 10 6 4 8 3 5 0 0 Night 7 4 3 4 2 2 3 2 1 0 0 IL 2008-2012 17 85 All 83 21 62 8 2 6 71 15 56 3 1 Night 26 3 23 5 0 5 20 2 18 1 0 OH 2009-2013 11 55 All 78 16 62 22 5 17 55 10 45 0 1 Night 24 4 20 12 3 9 12 1 11 0 0 All States 2006-2013 33 170 All 179 46 133 40 13 27 134 28 106 3 2 Night 57 11 46 21 5 16 35 5 30 1 0 URBAN FOUR-LEG INTERSECTIONS CA 2006-2011 13 78 All 89 34 55 14 3 11 73 29 44 2 0 Night 16 5 11 7 1 6 9 4 5 0 0 IL 2008-2012 60 300 All 608 132 476 20 2 18 566 108 458 14 8 Night 127 33 94 5 0 5 118 29 89 4 0 MN 2007-2011 28 138 All 115 36 79 14 4 10 97 28 69 1 3 Night 22 5 17 7 2 5 15 3 12 0 0 NV 2007-2011 26 130 All 180 67 113 28 9 19 152 58 94 0 0 Night 67 30 37 16 6 10 51 24 27 0 0 OH 2009-2013 34 170 All 140 24 116 14 3 11 124 19 105 0 2 Night 36 7 29 4 1 3 32 6 26 0 0 All States 2006-2013 161 816 All 1132 293 839 90 21 69 1012 242 770 17 13 Night 268 80 188 39 10 29 225 66 159 4 0

65 Table 7. Crash counts by collision type and manner of collision and crash severity at rural all-way stop- controlled intersections Rural Three-Leg Intersections Rural Four-Leg Intersections Total FI PDO Total FI PDO SINGLE-VEHICLE CRASHES Collision with animal 0 0 0 5 2 3 Collision with bicycle 0 0 0 4 4 0 Collision with pedestrian 0 0 0 1 1 0 Overturned 0 0 0 6 5 1 Other SV collision 11 6 5 112 25 87 Total SV crashes 11 6 5 128 37 91 MULTIPLE-VEHICLE CRASHES Angle collision 11 3 8 453 136 317 Head-on collision 0 0 0 14 4 10 Rear-end collision 18 5 13 289 81 208 Sideswipe collision 2 0 2 61 7 54 Other MV collision 1 0 1 46 8 38 Total MV crashes 32 8 24 863 236 627 Total Crashes 43 14 29 991 273 718 Table 8. Crash counts by collision type and manner of collision and crash severity at urban all-way stop- controlled intersections Collision Type Urban Three-Leg Intersections Urban Four-Leg Intersections Total FI PDO Total FI PDO SINGLE-VEHICLE CRASHES Collision with animal 0 0 0 0 0 0 Collision with bicycle 2 2 0 13 13 0 Collision with pedestrian 3 3 0 17 17 0 Overturned 2 2 0 2 1 1 Other SV collision 38 11 27 88 20 68 Total SV crashes 45 18 27 120 51 69 MULTIPLE-VEHICLE CRASHES Angle collision 39 7 32 547 143 404 Head-on collision 1 1 0 6 3 3 Rear-end collision 69 18 51 316 62 254 Sideswipe collision 9 1 8 43 4 39 Other MV collision 16 1 15 104 30 70 Total MV crashes 134 28 106 1012 242 770 Total Crashes 179 46 133 1132 293 839 3.3 Safety Performance Functions—Model Development Intersection SPFs were developed using either Equation 2 or Equation 3: 𝑵𝒔𝒑𝒇 𝒊𝒏𝒕 = 𝒆𝒙𝒑 𝒂 + 𝒃 × 𝒍𝒏 𝑨𝑨𝑫𝑻𝒎𝒂𝒋 + 𝒄 × 𝒍𝒏(𝑨𝑨𝑫𝑻𝒎𝒊𝒏) (Eq. 2) 𝑵𝒔𝒑𝒇 𝒊𝒏𝒕 = 𝒆𝒙𝒑 𝒂 + 𝒅 × 𝒍𝒏(𝑨𝑨𝑫𝑻𝒕𝒐𝒕𝒂𝒍) (Eq. 3)

66 Where: Nspf int = predicted average crash frequency for an intersection with base conditions (crashes/year) AADTmaj = AADT on the major road (veh/day) AADTmin = AADT on the minor road (veh/day) AADTtotal = AADT on the major and minor roads combined (veh/day) a, b, c, and d = estimated regression coefficients Based on a review of the number of states, sites, site-years, and crashes for the database assembled, data for all sites were used for model development to maximize the sample size rather than using a portion of the data for model development and a portion for model validation. All SPFs were developed using a NB regression model based on all sites combined within a given area type and intersection type. In all models, state was included as a random blocking effect, with sites nested within their respective state. A significance level of 0.20 for inclusion in a model was selected for an individual parameter. This was based on previous models included in the first edition of the HSM (Harwood et al., 2007); however, as presented below, all parameters in the final models for all-way stop-controlled intersections were significant at the 0.10 level. PROC GLIMMIX of SAS 9.3 was used for all modeling (SAS, 2013). Intersection characteristics varied widely among the sites in the database as mentioned earlier. For example, only a very small number of intersections satisfied the conditions of no lighting, and no left- and right-turn lanes on the major road. Initially, an attempt was made to perform a cross-sectional analysis including characteristics such as the presence of left- and right-turn lanes and others (e.g., presence of flashing beacon, supplementary pavement marking on major or minor road) in the model as binary variables in the hope of estimating a corresponding CMF. However, except for lighting for some intersection types, none of the site characteristics was statistically significant. Therefore, model development progressed using only the absence of lighting at an intersection as the base condition, consistent with the base condition for intersection lighting in Chapters 10 and 12 in the HSM. None of the other roadway characteristics were considered in the modeling. In the database, the distributions of intersections with and without lighting were as follows: • Rural three-leg intersections: 8 lighted; 4 unlighted (33% unlighted) • Rural four-leg intersections: 157 lighted; 42 unlighted (21% unlighted) • Rural three- and four-leg intersections: 165 lighted; 46 unlighted (22% unlighted) • Urban three-leg intersections: 28 lighted; 5 unlighted (15% unlighted) • Urban four-leg intersections: 152 lighted; 9 unlighted (5.6% unlighted) • Urban three- and four-leg intersections: 180 lighted; 14 unlighted (7.2% unlighted)

67 Based on these distributions, the following final modeling approach was chosen: • Rural three-leg intersections: Because of the small number of intersections, SPFs were developed using both lighted and unlighted intersections combined; total crashes at lighted intersections were adjusted in reverse using the CMF for lighting based on the work by Elvik and Vaa (2004) and shown in Equation 10-24 in Chapter 10 in the HSM (i.e., divide rather than multiply the crashes by the CMF), and the proportion of total crashes for unlighted intersections that occurred at night in the current database; and • All other intersections: SPFs were developed using lighted intersections only and adjusting in reverse for total crashes at lighted intersections using the CMF for lighting based on the work by Elvik and Vaa (2004) and shown in Equation 10-24 in Chapter 10 and Equation 12-36 in Chapter 12 in the HSM (i.e., divide rather than multiply the crashes by the CMF). For consistency with Chapters 10 and 12 in the HSM, an attempt was made to develop SPFs for the following crash severity levels and collision types: • Rural three- and four-leg intersections: total crashes, including pedestrian and bicycle crashes (similar to Equations 10-8 and 10-9 in the HSM) • Urban three- and four-leg intersections: total, FI, and PDO crashes (excluding pedestrian and bicycle crashes), separately for single- and MV crashes (similar to Equations 12-21 and 12-24 in the HSM) SPFs for vehicle-pedestrian and vehicle-bicycle crashes at urban intersections could not be developed as pedestrian and bicycle volumes were not available. All potential models outlined above were estimated. Several models of the form shown in Equation 2 (using major- and minor road AADTs) did not converge. In those cases, SPFs of the form shown in Equation 3 (using AADTtotal which is the sum of AADTmaj and AADTmin) were estimated. Developing SPFs at urban intersections separately for single- and MV crashes produced no usable models (i.e., either the model did not converge or the coefficient of AADT was counterintuitive); therefore, single- and MV crashes were modeled together. The final SPFs for total crashes (i.e., all severity levels combined) at rural all-way stop- controlled intersections are shown in Table 9; only models with AADTtotal were found to be significant. The table shows the model coefficients and overdispersion parameter (estimate), their standard error, and associated p-values (or significance level) for each intersection type. Figure 5 (three-leg) and Figure 6 (four-leg) graphically present the SPFs shown in Table 9 for various major- and minor approach AADT levels. Similar to Tables 10-5 and 10-6 in the HSM, Tables 10 and 11 provide percentages for crash severity levels and collision types and manner of collision, respectively, for rural all-way stop- controlled intersections. These percentages were calculated based on all crash counts at all intersections—lighted and unlighted—in all states combined.

68 Table 9. SPF coefficients for intersections with all-way stop control on rural two-lane highways Intersection Type Parameter Estimate Standard Error Pr > F Significance Level TOTAL CRASHESa Three-Leg Intercept -9.05 3.28 -- -- ln(AADTtotal) 1.06 0.40 0.03 Significant at 95% level Overdispersion 0.94 0.58 -- -- Four-Leg Intercept -9.67 1.09 -- -- ln(AADTtotal) 1.12 0.12 <.01 Significant at 99% level Overdispersion 0.39 0.07 -- -- a Includes SV, MV, pedestrian, and bicycle crashes. Base condition: absence of lighting. Figure 5. Graphical representation of the SPF for total crashes at rural three-leg, all-way stop-controlled intersections

69 Figure 6. Graphical representation of the SPF for total crashes at rural four-leg, all-way stop-controlled intersections Table 10. Distributions for crash severity level at rural all-way stop-controlled intersections Crash Severity Level Percentage of Total Crashes Rural Three-Leg All-Way Stop-Controlled Intersections Rural Four-Leg All-Way Stop-Controlled Intersections Fatal 0.0 0.3 Incapacitating injury 4.7 3.6 Non-incapacitating injury 14.0 11.2 Possible injury 14.0 12.4 Total fatal plus injury 32.6 27.5 Property-damage-only 67.4 72.5 Total 100.0 100.0

70 Table 11. Distributions for collision type and manner of collision and crash severity at rural all-way stop- controlled intersections Collision Type Percentage of Total Crashes by Collision Type Rural Three-Leg All-Way Stop-Controlled Intersections Rural Four-Leg All-Way Stop-Controlled Intersections Total FI PDO Total FI PDO Single-Vehicle Crashes Collision with animal 0.0 0.0 0.0 0.5 0.7 0.4 Collision with bicycle 0.0 0.0 0.0 0.4 1.5 0.0 Collision with pedestrian 0.0 0.0 0.0 0.1 0.4 0.0 Overturned 0.0 0.0 0.0 0.6 1.8 0.1 Other SV collision 25.6 42.9 17.2 11.3 9.2 12.1 Total SV crashes 25.6 42.9 17.2 12.9 13.6 12.7 Multiple-Vehicle Crashes Angle collision 25.6 21.4 27.6 45.7 49.8 44.2 Head-on collision 0.0 0.0 0.0 1.4 1.5 1.4 Rear-end collision 41.9 35.7 44.8 29.2 29.7 29.0 Sideswipe collision 4.7 0.0 6.9 6.2 2.6 7.5 Other MV collision 2.3 0.0 3.4 4.6 2.9 5.3 Total MV crashes 74.4 57.1 82.8 87.1 86.4 87.3 Total Crashes 100.0 100.0 100.0 100.0 100.0 100.0 Table 12 shows the coefficients and associated statistics of the final SPFs for urban all-way stop- controlled intersections. Usable models were developed for FI and PDO severity levels, but none for total severity (i.e., all severity levels combined). For these intersection types, crashes for total severity can be estimated by summing predicted FI and PDO severity crashes. Figures 7-10 graphically present the SPFs shown in Table 12 for various major- and minor approach AADTs. Table 12. SPF coefficients for intersections with all-way stop control on urban and suburban arterials Intersection Typea Parameter Estimate Standard Error Pr > F Significance Level FI Crashesa Three-Leg Intersections Intercept -8.19 2.78 -- -- ln(AADTtotal) 0.77 0.31 0.02 Significant at 95% level Overdispersion 0.07 0.20 -- -- Four-Leg Intersections Intercept -11.62 1.88 -- -- ln(AADTmaj) 0.92 0.24 <.01 Significant at 99% level ln(AADTmin) 0.32 0.17 0.06 Significant at 90% level Overdispersion 0.66 0.14 -- -- PDO Crashes Three-Leg Intersections Intercept -7.94 2.40 -- -- ln(AADTtotal) 0.85 0.26 <.01 Significant at 99% level Overdispersion 0.37 0.19 -- -- Four-Leg Intersections Intercept -8.58 1.58 -- -- ln(AADTmaj) 0.64 0.20 <.01 Significant at 99% level ln(AADTmin) 0.36 0.15 0.01 Significant at 99% level Overdispersion 0.78 0.12 -- -- a Includes single-and MV crashes only (i.e., pedestrian and bicycle crashes are excluded). Base Condition: Absence of lighting.

71 Figure 7. Graphical representation of the SPF for FI crashes at urban and suburban three-leg, all-way stop- controlled intersections Figure 8. Graphical representation of the SPF for PDO crashes at urban and suburban three-leg, all-way stop-controlled intersections

72 Figure 9. Graphical representation of the SPF for FI crashes at urban and suburban four-leg, all-way stop- controlled intersections Figure 10. Graphical representation of the SPF for PDO crashes at urban and suburban four-leg, all-way stop- controlled intersections

73 Table 13 (similar to Table 11 for rural intersections) provides percentages of total crashes by collision type and severity level for urban all-way stop-controlled intersections. These percentages were calculated based on all crash counts at all intersections—lighted and unlighted—in all states combined. Table 13. Distributions for collision type and manner of collision and crash severity at urban and suburban all-way stop-controlled intersections Collision Type Percentage of Total Crashes by Collision Type Urban Three-Leg All-Way Stop-Controlled Intersections Urban Four-Leg All-Way Stop-Controlled Intersections Total FI PDO Total FI PDO SINGLE-VEHICLE CRASHES Collision with animal 0.0 0.0 0.0 0.0 0.0 0.0 Overturned 1.1 4.8 0.0 0.2 0.4 0.1 Other SV collision 21.76 26.2 20.3 8.0 7.8 8.1 Total SV crashes 22.9 31.0 20.3 8.2 8.2 8.2 MULTIPLE-VEHICLE CRASHES Angle collision 22.3 16.7 24.1 49.4 53.6 48.1 Head-on collision 0.6 2.4 0.0 0.5 1.1 0.4 Rear-end collision 39.4 42.9 38.3 28.5 23.3 30.2 Sideswipe collision 5.1 2.4 6.0 3.9 1.5 4.6 Other MV collision 9.7 4.8 11.3 9.4 12.4 8.5 Total MV crashes 77.1 69.0 79.7 91.8 91.8 91.8 Total Crashes 100.0 100.0 100.0 100.0 100.0 100.0 For urban intersections, the predicted average crash frequency excludes vehicle-pedestrian and vehicle-bicycle crashes. To calculate a predicted average crash frequency of an intersection that includes vehicle-pedestrian and vehicle-bicycle crashes, the predictive model is given by 𝑵𝒑𝒓𝒆𝒅𝒊𝒄𝒕𝒆𝒅 𝒊𝒏𝒕 = 𝑵𝒃𝒊 + 𝑵𝒑𝒆𝒅𝒊 + 𝑵𝒃𝒊𝒌𝒆𝒊 × 𝑪𝒊 (Eq. 4) Where: Npredicted int = predicted average crash frequency for an individual intersection for the selected year (crashes/year) Nbi = predicted average crash frequency of an intersection (excluding vehicle- pedestrian and vehicle-bicycle crashes) (crashes/year) Npedi = redicted average crash frequency of vehicle-pedestrian crashes of an intersection (crashes/year) Nbikei = predicted average crash frequency of vehicle-bicycle crashes of an intersection (crashes/year) Ci = calibration factor to adjust the SPF for intersection type i to local conditions Similar to Table 12-16 in the HSM, Table 14 provides pedestrian crash adjustment factors for urban all-way stop-controlled intersections. The number of vehicle-pedestrian crashes per year for an all-way stop-controlled intersection is estimated as:

74 𝑁 = 𝑁 × 𝑓 (Eq. 9) Where: fpedi = pedestrian crash adjustment factor for intersection type i Table 14. Pedestrian crash adjustment factors for urban and suburban all-way stop-controlled intersections Intersection Type Pedestrian Crash Adjustment Factor (fpedi) Three-Leg 0.017 Four-Leg 0.015 Similar to Table 12-17 in the HSM, Table 15 provides bicycle crash adjustment factors for urban all-way stop-controlled intersections. The number of vehicle-bicycle crashes per year for an all- way stop-controlled intersection is estimated as: 𝑁 = 𝑁 × 𝑓 (Eq. 12) Where: fbikei = bicycle crash adjustment factor for intersection type i Table 15. Bicycle crash adjustment factors for urban and suburban all-way stop-controlled intersections Intersection Type Bicycle Crash Adjustment Factor (fbikei) Three-Leg 0.011 Four-Leg 0.011 Following the development of the crash prediction models for rural and urban and suburban all- way stop-controlled intersections, the research team conducted compatibility testing of the new models to confirm that the new models provide reasonable results over a broad range of input conditions and that the new models integrate seamlessly with existing intersection crash prediction models in the first edition of the HSM. The graphical representations of the crash prediction models in Figures 5-10 provide some sense of the reasonableness of the new models for all-way stop-controlled intersections. Nothing from these figures suggests that the models provide unreasonable results. In addition, the new models for all-way stop-controlled intersections were compared to the associated minor road stop-controlled intersection SPFs in the HSM. Figure 11 illustrates a comparison of the predicted average crash frequency for total crashes based on the 4aST model for rural two-lane roads (Table 9) to the predicted average crash frequency based on the 4ST model in Chapter 10 of the HSM. In the figure, the dashed lines represent the predicted average crash frequency for the 4aST model, and the solid lines represent the predicted average crash frequency for the 4ST model in the HSM. Similarly, Figure 12 illustrates a comparison of the predicted average crash frequency for FI crashes based on the 4aST model for urban and suburban arterials (Table 12) to the predicted average crash frequency based on the 4ST model in Chapter 12 of the HSM. In both instances, as major approach AADT increases, the 4aST SPFs predict fewer crashes than the 4ST SPFs in the HSM

75 which seems reasonable as the traffic control at all-way stop-controlled intersections provides more direction in terms of defining the right of way through the intersection for drivers so it is reasonable to expect fewer crashes at all-way stop-controlled intersections than intersections with minor road stop control, given the same traffic volumes. Although not presented herein, a similar trend was found in terms of the 3aST SPFs predicting fewer crashes than the 3ST SPFs in the HSM as the major road AADT increases for intersections on urban and suburban arterials. In summary, the models for all-way stop-controlled intersections appear to provide reasonable results over a broad range of input conditions and can be integrated seamlessly with existing intersection crash prediction models in the first edition of the HSM. Figure 11. Comparison of new crash prediction model to existing model in HSM: 4aST vs 4ST on rural two-lane roads (total crashes)

76 Figure 12. Comparison of new crash prediction model to existing model in HSM: 4aST vs 4ST on urban and suburban arterials (FI crashes) 3.4 Crash Modification Factor During the development of the crash prediction models for all-way stop-controlled intersections, three potential sources of CMFs for use with the SPFs were considered: • CMFs developed as part of this research based on a cross-sectional study design and regression modeling • CMFs already incorporated into the first edition of the HSM and applicable to all-way stop-controlled intersections • High quality CMFs applicable to all-way stop-controlled intersections developed using defensible study designs (e.g., observational before-after evaluation studies using SPFs— the EB method), as referenced in FHWA’s CMF Clearinghouse with four or five-star quality ratings or based on a review of relevant intersection safety literature Based on the regression modeling as part of this research, no geometric features or traffic control devices were identified for CMF development. Based on a review of the CMFs already incorporated in the first edition of the HSM and other potential high-quality CMFs developed using defensible study designs, the only CMF that was identified for potential use with the crash prediction models for all-way stop-controlled intersections was the CMF for intersection lighting based on the work by Elvik and Vaa (2004), which is identified for use with the intersection crash prediction models in Chapters 10, 11, and 12 of the first edition of the HSM.

77 Thus, the only CMF recommended for use with the final SPFs for all-way stop-controlled intersections is the CMF for intersection lighting based on the work by Elvik and Vaa (2004). With this CMF, the base condition is the absence of intersection lighting. The CMF for lighted intersections is similar to the CMF in Equation 10-24 (rural intersections) and Equation 12-36 (urban intersections) in the HSM and has the form: 𝐶𝑀𝐹 = 1 − 0.38 × 𝑝 (Eq. 39) Where: CMFi = crash modification factor for the effect of lighting on total crashes; and pni = proportion of total crashes for unlighted intersections that occur at night. This CMF applies to total intersection crashes. Table 16 (similar to Tables 10-15 and 12-27 in the HSM) presents values for the nighttime crash proportion, pni, by area type and intersection type. Table 16. Nighttime proportions for unlighted all-way stop-controlled intersections by area and intersection type Intersection Type Proportion of Nighttime Crashes (pni) RURAL INTERSECTIONS Three-Leg 0.363 Four-Leg 0.284 URBAN AND SUBURBAN INTERSECTIONS Three-Leg 0.187 Four-Leg 0.277 Recent research by Washington State DOT has raised concerns about whether use of the lighting CMF in the HSM is appropriate. Based on their research, van Schalkwyk et al. (2016) concluded that the contribution of continuous illumination to nighttime crash reduction is negligible. However, we have recommended this CMF for application to all-way stop-controlled intersections because this CMF has been used in the HSM first edition. If any decision to remove or change the lighting CMFs is made, this should be done consistently for all facility types as part of the development of the HSM second edition. 3.5 Severity Distribution Functions Development of SDFs was explored for all-way stop-controlled intersections using methods outlined in Section 2.2.3 of this report. SDFs were not used in the development of crash prediction methods in the first edition of the HSM but were subsequently used in the Supplement to the HSM for freeways and ramps (AASHTO, 2014). The database used to explore SDFs for all-way stop-controlled intersections consisted of the same crashes and intersections as the database used to estimate the SPFs for rural three-leg, rural four-leg, urban three-leg, and urban four-leg intersections, but restructured so that the basic observation unit (i.e., database row) is a crash instead of an intersection.

78 No traffic or geometric variables showed consistent and statistically significant effects in the SDFs for rural three-leg, rural four-leg, urban three-leg, or urban four-leg all-way stop-controlled intersections. Therefore, distributions for rural all-way stop-controlled intersections in Table 10 and SPFs by severity for urban all-way stop-controlled intersections in Table 12 are recommended for addressing severity at all-way stop-controlled intersections. 3.6 Summary of Recommended Models for Incorporation in the HSM In summary, several crash prediction models were developed for intersections with all-way stop control for consideration in the second edition of the HSM, including models for: • Rural three-leg intersections with all-way stop control • Rural four-leg intersections with all-way stop control • Urban and suburban three-leg intersections with all-way stop control • Urban and suburban four-leg intersections with all-way stop control The final models for rural four-leg intersections with all-way stop control (total crashes), urban and suburban three-leg intersections with all-way stop control (FI and PDO crashes), and urban and suburban four-leg intersections with all-way stop control (FI and PDO crashes) are recommended for inclusion in the second edition of the HSM (see Tables 9 and 12). The model for rural three-leg intersections with all-way stop control is not recommended for inclusion in the second edition of the HSM because the number of sites used to develop the model is not considered sufficient for including the model in the HSM. In addition, no traffic or geometric variables showed consistent and statistically significant effects in the SDFs for all-way stop-controlled intersections. Therefore, it is recommended for the second edition of the HSM that crash severity for all-way stop-controlled intersections on rural two-lane highways and urban and suburban arterials be addressed in a manner consistent with existing methods in Chapter 10 and Chapter 12 of the HSM, respectively, without use of SDFs. Appendix A presents recommended text for incorporating the final recommended models for all- way stop-controlled intersections into Chapters 10 and 12 of the HSM.

Next: Chapter 4. Development of Models for Use in HSM Crash Prediction Methods: Three-Leg Intersections with Signal Control on Rural Highways »
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 Intersection Crash Prediction Methods for the Highway Safety Manual
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The first edition of the Highway Safety Manual (HSM), in 2010, included Safety Performance Functions (SPFs) for roadway segments and intersections. However, not all intersection types are covered in the first edition of the HSM.

The TRB National Cooperative Highway Research Program's NCHRP Web-Only Document 297: Intersection Crash Prediction Methods for the Highway Safety Manual develops SPFs for new intersection configurations and traffic control types not covered in the first edition of the HSM, for consideration in the second edition of the HSM.

Supplemental to the Document is recommended draft text for the second edition if the HSM, a worksheet for Chapter 10, a worksheet for Chapter 11, a worksheet for Chapter 12, a worksheet for Chapter 19, and a presentation.

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