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Publication Number: FHWA-RD-98-096
Date: September 1997

Modeling Intersection Crash Counts and Traffic Volume - Final Report

FOREWORD

This research explored the feasibility of modeling crash counts at intersections with use of available exposure measures. The basic purpose of "exposure" is to serve as a size factor to allow comparison of crash counts among populations of different sizes. In the context of highway crash studies, at first glance, vehicle miles of travel (VMT) appears to be a natural exposure measure. However, VMT is closely related to traffic density and this raises doubts if it can serve the intended purpose of an exposure measure. Data from four–leg signalized intersections in Washtenaw County, Michigan, and the states of California and Minnesota were used in this study. Traffic volumes on the approaches are the routinely available exposure measure. It was noted that in these data sets the same values of traffic volume were often "carried over" several intersections. Using such values of traffic volume as measures of exposure results in correlations between errors of the independent variables, which violates the requirements of standard statistical procedures.

It was found that the relationships between crash counts and traffic volumes could not be adequately represented by the standard loglinear model that is also the basis for more sophisticated models. Therefore, nonparametric regression in the form of kernel smoothing was used. This allowed a realistic representation of complex relationships. The relationships found differed among the three data sets, with California showing dramatic deviations from the loglinear model. The relationship between crash counts and traffic volumes on the approaches to the intersection and those within the intersection were found to be very different. This makes it unlikely that realistic models for all intersection–related crashes can be developed. Turning counts are plausible candidates for exposure measures for turn–related intersection crashes. However, since turning counts are not routinely available, the possibility of using proportions of crashes involving turns was explored. The results were negative, but because of the small case number, no definite conclusions could be drawn.

A. George Ostensen
Director, Office of Safety and
Traffic Operations Research
and Development

 

NOTICE

This document is disseminated under the sponsorship of the Department of Transportation in the interest of information exchange. The United States Government assumes no liability for its contents or use thereof. This report does not constitute a standard, specification, or regulation.

The United States Government does not endorse products or manufacturers. Trade and manufacturers' names appear in this report only because they are considered essential to the object of the document.

 


TECHNICAL REPORT DOCUMENTATION PAGE

1. Report No.

FHWA–RD–98–096

2. Government Accession No. 3. Recipient's Catalog No.
4. Title and Subtitle

MODELING INTERSECTION CRASH COUNTS AND TRAFFIC VOLUME

5. Report Date
7. Author(s)

Hans C. Joksch and Lidia P. Kostyniuk

8. Performing Organization Report No.

UMTRI-97-39

9. Performing Organization Name and Address

The University of Michigan
Transportation Research Institute
2901 Baxter Road
Ann Arbor, MI 48109

10. Work Unit No. (TRAIS)

NCP:3A3B

11. Contract or Grant No.

DTFH61–93–C–00123

12. Sponsoring Agency Name and Address

Office of Safety and Traffic Operations R&D
Federal Highway Administration
6300 Georgetown Pike
McLean, VA 22101–2296

13. Type of Report and Period Covered

November 1995 – March 1997

14. Sponsoring Agency Code
15. Supplementary Notes

Contracting Officer's Technical Representative (COTR): Joe Bared, HSR–20

16. Abstract

This research explored the feasibility of modeling crash counts at intersections with use of available exposure measures. The basic purpose of "exposure" is to serve as a size factor to allow comparison of crash counts among populations of different sizes. In the context of highway crash studies, at first glance, vehicle miles of travel (VMT) appears to be a natural exposure measure. However, VMT is closely related to traffic density and this raises doubts if it can serve the intended purpose of an exposure measure. Data from four–leg signalized intersections in Washtenaw County, Michigan, and the states of California and Minnesota were used in this study. Traffic volumes on the approaches are the routinely available exposure measure. It was noted that in these data sets the same values of traffic volume were often "carried over" several intersections. Using such values of traffic volume as measures of exposure results in correlations between errors of the independent variables, which violates the requirements of standard statistical procedures.

It was found that the relationships between crash counts and traffic volumes could not be adequately represented by the standard loglinear model that is also the basis for more sophisticated models. Therefore, nonparametric regression in the form of kernel smoothing was used. This allowed a realistic representation of complex relationships. The relationships found differed among the three data sets, with California showing dramatic deviations from the loglinear model. The relationship between crash counts and traffic volumes on the approaches to the intersection and those within the intersection were found to be very different. This makes it unlikely that realistic models for all intersection–related crashes can be developed. Turning counts are plausible candidates for exposure measures for turn–related intersection crashes. However, since turning counts are not routinely available, the possibility of using proportions of crashes involving turns was explored. The results were negative, but because of the small case number, no definite conclusions could be drawn.

17. Key Words

Intersection crashes, exposure, intersection characteristics, smoothing

18. Distribution Statement

No restrictions. This document is available to the public through the National Technical Information Service, Springfield, Virginia, 22161.

19. Security Classif. (of this report)

Unclassified

20. Security Classif. (of this page)

Unclassified

21. No. of Pages

174

22. Price
Form DOT F 1700.7 (8-72) Reproduction of completed page authorized

 


TABLE OF CONTENTS

1.1 The concept of exposure

1.2 The purposes of modeling intersection crash counts

1.3 Some critical assumptions

1.4 The conventional statistical approach

1.5 Smoothing techniques

2. The smoothing technique used

3. The data

3.1 Washtenaw County

3.2 California data

3.3 Minnesota data

3.4 Identifying unrealizable intersection approach volumes

4. Selected intersections in Washtenaw County, Michigan

4.1 Smoothing for signalized four-leg intersections

4.2 Analytical models

4.3 Visual comparison of actual data and models

4.4 Stop-controlled intersections

5. Signalized four-leg urban intersections, California

5.1 Distribution of interextions by traffic volumes

5.2 Total crash counts

5.3 Crashes withing and near the intersection

5.4 Crash types withing the intersection

5.5 Intersection characteristics

5.6 The length of the influence zone

5.7 Analytical modeling

5.8 Conclusion regarding the four-leg signalized intersections in California

6. Minnesota intersections

6.1 Distribution of intersections by traffic volumes

6.2 Smoothed crash counts

6.3 An analytical model

6.4 Crash types

6.5 Relating proportions of crash types to number of intersection crashes

6.6 Conclusion

7. Conclusions on modeling intersection crashes in relation to traffic volumes as exposure measures

7.1 Relations between crash counts and traffic volumes at four–leg signalized intersections

7.2 What can currently be done?

7.3 Substantive research needed

7.4 Methodological research needs

 


TABLES

Table 3.4-1. Four-Leg Urban Stop-Controlled Intersections Violating Condition (3-26)

Table 3.4-2. Four-Leg Rural Stop-Controlled Intersections Violating Condition (3-26)

 


FIGURES

Figure 1. Representation of a Gaussian kernel, as represented by (2-1).

Figure 2. Representation of a Gaussian kernel with an exponent of 10.

Figure 3A. Example of two-way volumes and possible explanations

Figure 3. Flows distinguished at an intersection.

Figure 4. Different representation of the traffic flows shown in Figure 3.

Figure 5. Deriving other realizable solutions from a given realizable solution, d is the value by which the original flows are changed.

Figure 6. A new flow pattern, resulting from a modification shown in Figure 5, and possible further modifications of the flow pattern.

Figure 7. The simplest flow patterns obtainable if x is a minimal volume on the legs.

Figure 8. Reduced flow pattern to derive conditions for reliability of leg volumes.

Figure 9. Distribution of traffic volumes at signalized four-leg intersections in Washtenaw County, Michigan. X=volume on major, Y=volume on minor road. 62

Figure 10. Signalized four-leg intersections in Washtenaw County, Michigan. Accident counts smoothed with a 4,000 x 4,000 window.

Figure 11. Signalized four-leg intersections in Washtenaw County, Michigan. Accident counts smoothed with a 6,000 x 6,000 window.

Figure 12. Signalized four-leg intersections in Washtenaw County, Michigan. Surface represents the analytical model 4-1.

Figure 13. Signalized four-leg intersections in Washtenaw County, Michigan. Surface represents the analytical model 4-4.

Figure 14. Signalized four-leg intersections in Washtenaw County, Michigan. Surface represents the analytical model 4.5.

Figure 15. Signalized four-leg intersections in Washtenaw County, Michigan. Surface represents the analytical model 4-6.

Figure 16. Signalized four-leg intersection in Washtenaw County, Michigan. Cross- sections through the surfaces in Figures 11,12, 13, and 14 at minor volumes of 4,000 and 14,000

Figure 17. Cross-sections at major volume of 16,000

Figure 18. Stop-controlled four-leg intersections in Washtenaw County, Michigan. Accident count smoothed with a 3,000 x 3,000 window.

Figure 19. Stop-controlled four-leg intersections in Washtenaw County, Michigan. Accident count smoothed with a 6,000 x 6,000 window.

Figure 20. Distribution of volumes at signalized urban intersection from California data file.

Figure 21. Distribution of four-leg signalized intersections in California by volume of the major and minor approaches. The width of the lines is proportional to the number of cases in each cell.

Figure 22. California four-leg signalized urban intersections. Total accident count smoothed with a 5,000 x 5,000 window.

Figure 23. California four-leg signalized urban intersections. Total accident count smoothed with a 10,000 x 5,000 window.

Figure 24. California four-leg signalized urban intersections. Major volume # 60,000, minor volume #20,000. Total accidents, smoothed with a 10,000 x 5,000 window.

Figure 25. California four-leg signalized urban intersections. Total accidents for intersections with major volume # 60,000, minor volume >20,000, smoothed with a 10,000 x 5,000 window 78

Figure 26. California four-leg signalized urban intersections. Total accidents for intersections with major volume > 60,000. 79

Figure 27. California four-leg signalized urban intersections with the same data and surface as in Figure 23, but with surface for major volume # 60,000 and minor volume # 20,000 not shown.

Figure 28. California four-leg signalized urban intersections. Total accidents within the intersection, smoothed with a 10,000 x 5,000 window.

Figure 29. California four-leg signalized urban intersections. Total accidents on major approaches, smoothed with a 10,000 x 5,000 window.

Figure 30. California four-leg signalized urban intersections. The same data and smoothing as in Figure 29, but with the surface not shown below minor volume of 20,000.

Figure 31. California four-leg signalized urban intersections. The same data and surface as in Figure 29, but with the surface below minor volumes of 40,000 not shown.

Figure 32. California four-leg signalized urban intersections. The same data and surface as in Figure 29, but with the surface below minor volume of 60,000 not shown. . 85

Figure 33. California four-leg signalized urban intersections. Total accidents on minor approaches, smoothed with a 10,000 x 5,000 window.

Figure 34. The same surface as in Figure 33, but not shown for major volume below 20,000.

Figure 35. The same surface as in Figure 33, but not shown for major volumes below 40,000

Figure 36. The same surface as in Figure 33, but with major volumes not shown below 60,000.

Figure 37. California four-leg signalized urban intersections. Left-turn accidents within the intersection, smoothed with a 10,000 x 5,000 window.

Figure 38. California four-leg signalized urban intersections. Right-turn accidents within the intersection, smoothed with a 10,000 x 5,000 window.

Figure 39. California four-leg signalized urban intersections. Rear-end collisions within the intersection, smoothed with a 10,000 x 5,000 window.

Figure 40. California four-leg signalized urban intersections. Angle collisions within the intersection, smoothed with a 10,000 x 5,000 window.

Figure 41. California four-leg signalized urban intersections. "Other" collisions within the intersection, smoothed with a 10,000 x 5,000 window.

Figure 42. California four-leg signalized urban intersections. Left-turn collisions within intersection, smoothed with a 15,000 x 10,000 window. Based on the same data as Figure 37 but more smoothed.

Figure 43. California four-leg signalized urban intersections. Right-turn collision within intersection, smoothed with a 15,000 x 10,000 window. Based on the same data as Figure 38 but more smoothed.

Figure 44. California four-leg signalized urban intersections. Rear-end collisions within intersection, smoothed with a 15,000 x 10,000 window. Based on the same data as Figure 39 but more smoothed.

Figure 45. California four-leg signalized urban intersections. Angle - collision within intersection, smoothed with a 15,000 x 10,000 window. Based on the same data as Figure 40 but more smoothed.

Figure 46. California four-leg signalized urban intersections. "Other"' collisions within intersection, smoothed with a 15,000 x 10,000 windown. Based on the same data as Figure 41 but more smoothed.

Figure 47. California four-leg signalized urban intersections. Proportion of left- and U-turn accidents within intersection, smoothed with a 15,000 x 10,000 window

Figure 48. California four-leg signalized urban intersections. Proportion of right-turn accidents within intersections, smoothed with a 15,000 x 10,000 window.

Figure 49. California four-leg signalized urban intersections. Proportion of rear-end accidents within intersections, smoothed with a 15,000 x 10,000 window.

Figure 50. California four-leg signalized urban intersections. Proportion of angle accidents within intersection, smoothed with a 15,000 x 10,000 window.

Figure 51. California four-leg signalized urban intersections. Proportion of "other" accidents within intersection, smoothed with a 15,000 x 10,000 window. 104

Figure 52. California four-leg signalized urban intersections. Design speed, smoothed with a 10,000 x 5,000 window. 105

Figure 53. California four-leg signalized urban intersections. Proportion of intersections with multi-phase signals, smoothed with a 10,000 x 5,000 window.

Figure 54. California four-leg signalized urban intersections. Proportion of intersections with left-turn channelization on the main road, smoothed with a 10,000 x 5,000 window.

Figure 55. California four-leg signalized urban intersections. Proportion of intersections with left-turn channelization on the minor road, smoothed with a 10,000 x 5,000 window.

Figure 56. California four-leg signalized urban intersections. Proportion of intersections with free right turns on major road, smoothed with a 10,000 x 5,000 window.

Figure 57. California four-leg signalized urban intersections. Proportion of intersections with free right turns on minor road, smoothed with a 10,000 x 5,000 window

Figure 58. California four-leg signalized urban intersections. Number of lanes on major road, smoothed with a 10,000 x 5,000 window.

Figure 59. California four-leg signalized urban intersections. Number of lanes on minor road, smoothed with a 10,000 x 5,000 window.

Figure 60. California four-leg signalized urban intersections with median on main road, smoothed with a 10,000 x 5,000 window.

Figure 61. The same surface as in Figure 60, shown only for major volume above 40,000.

Figure 62. The same surface as Figure 60, shown only for major volume above 50,000.

Figure 63. The same surface as Figure 60, shown only for major volume above 60,000.

Figure 64. California four-leg signalized intersections with median on main road. Accidents on major approaches, smoothed with a 10,000 x 5,000 window.

Figure 65. California four-leg signalized intersections with no median on main road. Accidents on major approaches, smoothed with a 10,000 x 5,000 window.

Figure 66. California four-leg intersection accidents. Length of influence zone on main (not major) road, smoothed with a 10,000 x 5,000 window.

Figure 67. California four-leg signalized intersection. Number of collision accidents on main (not major) road, smoothed with a 10,000 x 5,000 window.

Figure 68. California four-leg signalized urban intersections. Model (5-2) fitted to total accidents.

Figure 69. The same surface as in Figure 68, but cut out at major volume 62,500, minor volume = 20,000.

Figure 70. Cross-sections at y = 20,000 through the surfaces shown in Figures 23, 24, 25, 26, and 68.

Figure 71. Cuts through the same surface as in Figure 70 but at (a) x = 20,000, (b) x = 40,000, (c) x = 60,000.

Figure 72. Distribution of traffic volumes for 71 signalized urban four-leg intersections from Minnesota data files.

Figure 73. Distribution of approach volumes of four-leg signalized urban intersections in Minnesota. The width of the gridlines is proportional to the number of intersections in each cell.

Figure 74. Signalized four-leg urban intersections in Minnesota. Counts of accidents within intersections smoothed with a 4,000 x 4,000 window.

Figure 75. The same surface as in Figure 74 but cut-off at a minor volume of 6,000.

Figure 76. The same surface as in Figure 74, but cut-off at a minor volume of 10,000

Figure 77. Signalized four-leg urban intersections in Minnesota. Accident counts within intersections smoothed with a 8,000 x 4,000 window

Figure 78. Signalized four-leg urban intersections in Minnesota. Surface represents model (6-1) for within intersection accident counts.

Figure 79. The same surface as in Figure 78, but cut-off at y = 6,000.

Figure 80. The same surface as in Figure 78, but cut-off at y = 10,000.

Figure 81. Signalized four-leg urban intersections in Minnesota. All accidents in the intersection and on the approaches within 200=, smoothed with a 5,000 x 5,000 window.

Figure 82. Signalized four-leg urban intersections in Minnesota. All accidents in the intersection and on the approaches within 60 meters, smoothed with a 15,000 x 10,000 window.

Figure 83. Signalized four-leg urban intersections in Minnesota. All accidents on the approaches outside the intersection within 60 meters, smoothed with a 5,000 x 5,000 window.

Figure 84. Signalized four-leg urban intersections in Minnesota. All accidents on the approaches outside the intersection within 60 meters, smoothed with a 10,000 x 10,000 window.

Figure 85. Signalized four-leg urban intersections in Minnesota. Distribution of intersections with typical intersection accidents by volumes of the two roads.

Figure 86. Signalized four-leg urban intersections in Minnesota. Typical intersection accident, smoothed with a 10,000 x 5,000 window.

Figure 87. Signalized four-leg urban intersections in Minnesota. Typical intersection accident within the intersection, smoothed with a 20,000 x 10,000 window.

Figure 88. Signalized four-leg urban intersection in Minnesota. Left-turn accidents within the intersection as proportion of typical intersection accidents, smoothed with a 10,000 x 15,000 window.

Figure 89. Signalized four-leg urban intersections in Minnesota. Angle collisions within the intersection as proportion of typical intersection accidents, smoothed with a 10,000 x 5,000 window.

Figure 90. Signalized four-leg urban intersections in Minnesota. Rear-end collisions within the intersection as proportion of typical intersection accidents, smoothed with a 10,000 x 5,000 window.

Figure 91. Signalized four-leg urban intersections in Minnesota. Other collisions within the intersection as proportion of typical intersection accidents, smoothed with a 10,000 x 6,000 window.

Figure 92. Signalized four-leg intersections in Minnesota. Accidents in intersections versus proportion of angle collisions.

Figure 93. Signalized four-leg intersections in Minnesota. Accidents in intersections versus proportion of left-turn accidents.

Figure 94. Signalized four-leg intersections in Minnesota. Accidents in intersections versus proportion of rear-end accidents.

Figure 95. Signalized four-leg intersections in Minnesota. Accidents in intersections versus proportion of "other" accidents.

Figure 96. Signalized four-leg intersections in Minnesota. Proportion of angle collisions versus number of accidents in intersections.

Figure 97. Signalized four-leg intersections in Minnesota. Proportion of left-turn collisions versus number of accidents in intersections.

Figure 98. Signalized four-leg intersections in Minnesota. Proportion of rear-end collisions versus number of accidents in intersections.

Figure 99. Signalized four-leg intersections in Minnesota. Proportion of "other"' collisions versus number of accidents in intersections.

Figure 100. Signalized four-leg intersections in Minnesota. Proportion of rear-end collisions versus difference of accident counts against smoothed values.

Figure 101. Results of 10 smoothing fits using wide window.

Figure 102. The same curves as in Figure 101, but shown only in the range 0 to 1 for the ordinate.

Figure 103. Signalized four-leg intersections in Minnesota. Ten bootstrap replications of a quadratic model fit for the proportion of rear-end collisions.

Figure 104. The same curves as in Figure 103, but shown only in the range 0 to 1 for the ordinate.

Figure 105. Signalized four-leg intersections in Minnesota. Ten bootstrap replications of a linear model fit for the proportion of rear-end collisions.

 

FHWA-RD-98-096

 

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