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Publication Number: FHWARD98096
Date: September 1997 
Modeling Intersection Crash Counts and Traffic Volume  Final ReportFOREWORDThis 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
NOTICEThis 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
TABLE OF CONTENTS1.2 The purposes of modeling intersection crash counts 1.4 The conventional statistical approach 2. The smoothing technique used3. The data3.1 Washtenaw County3.2 California data3.3 Minnesota data3.4 Identifying unrealizable intersection approach volumes4. Selected intersections in Washtenaw County, Michigan4.1 Smoothing for signalized fourleg intersections4.2 Analytical models4.3 Visual comparison of actual data and models4.4 Stopcontrolled intersections5. Signalized fourleg urban intersections, California5.1 Distribution of interextions by traffic volumes5.2 Total crash counts5.3 Crashes withing and near the intersection5.4 Crash types withing the intersection5.5 Intersection characteristics5.6 The length of the influence zone5.7 Analytical modeling5.8 Conclusion regarding the fourleg signalized intersections in California6. Minnesota intersections6.1 Distribution of intersections by traffic volumes6.2 Smoothed crash counts6.3 An analytical model6.4 Crash types6.5 Relating proportions of crash types to number of intersection crashes6.6 Conclusion7. Conclusions on modeling intersection crashes in relation to traffic volumes as exposure measures7.1 Relations between crash counts and traffic volumes at four–leg signalized intersections7.2 What can currently be done?7.3 Substantive research needed7.4 Methodological research needs
TABLESTable 3.41. FourLeg Urban StopControlled Intersections Violating Condition (326)Table 3.42. FourLeg Rural StopControlled Intersections Violating Condition (326)
FIGURESFigure 1. Representation of a Gaussian kernel, as represented by (21). Figure 2. Representation of a Gaussian kernel with an exponent of 10. Figure 3A. Example of twoway 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 fourleg intersections in Washtenaw County, Michigan. X=volume on major, Y=volume on minor road. 62 Figure 10. Signalized fourleg intersections in Washtenaw County, Michigan. Accident counts smoothed with a 4,000 x 4,000 window. Figure 11. Signalized fourleg intersections in Washtenaw County, Michigan. Accident counts smoothed with a 6,000 x 6,000 window. Figure 12. Signalized fourleg intersections in Washtenaw County, Michigan. Surface represents the analytical model 41. Figure 13. Signalized fourleg intersections in Washtenaw County, Michigan. Surface represents the analytical model 44. Figure 14. Signalized fourleg intersections in Washtenaw County, Michigan. Surface represents the analytical model 4.5. Figure 15. Signalized fourleg intersections in Washtenaw County, Michigan. Surface represents the analytical model 46. Figure 16. Signalized fourleg 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. Crosssections at major volume of 16,000 Figure 18. Stopcontrolled fourleg intersections in Washtenaw County, Michigan. Accident count smoothed with a 3,000 x 3,000 window. Figure 19. Stopcontrolled fourleg 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 fourleg 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 fourleg signalized urban intersections. Total accident count smoothed with a 5,000 x 5,000 window. Figure 23. California fourleg signalized urban intersections. Total accident count smoothed with a 10,000 x 5,000 window. Figure 24. California fourleg 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 fourleg 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 fourleg signalized urban intersections. Total accidents for intersections with major volume > 60,000. 79 Figure 27. California fourleg 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 fourleg signalized urban intersections. Total accidents within the intersection, smoothed with a 10,000 x 5,000 window. Figure 29. California fourleg signalized urban intersections. Total accidents on major approaches, smoothed with a 10,000 x 5,000 window. Figure 30. California fourleg 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 fourleg 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 fourleg 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 fourleg 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 fourleg signalized urban intersections. Leftturn accidents within the intersection, smoothed with a 10,000 x 5,000 window. Figure 38. California fourleg signalized urban intersections. Rightturn accidents within the intersection, smoothed with a 10,000 x 5,000 window. Figure 39. California fourleg signalized urban intersections. Rearend collisions within the intersection, smoothed with a 10,000 x 5,000 window. Figure 40. California fourleg signalized urban intersections. Angle collisions within the intersection, smoothed with a 10,000 x 5,000 window. Figure 41. California fourleg signalized urban intersections. "Other" collisions within the intersection, smoothed with a 10,000 x 5,000 window. Figure 42. California fourleg signalized urban intersections. Leftturn 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 fourleg signalized urban intersections. Rightturn 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 fourleg signalized urban intersections. Rearend 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 fourleg 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 fourleg 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 fourleg signalized urban intersections. Proportion of left and Uturn accidents within intersection, smoothed with a 15,000 x 10,000 window Figure 48. California fourleg signalized urban intersections. Proportion of rightturn accidents within intersections, smoothed with a 15,000 x 10,000 window. Figure 49. California fourleg signalized urban intersections. Proportion of rearend accidents within intersections, smoothed with a 15,000 x 10,000 window. Figure 50. California fourleg signalized urban intersections. Proportion of angle accidents within intersection, smoothed with a 15,000 x 10,000 window. Figure 51. California fourleg signalized urban intersections. Proportion of "other" accidents within intersection, smoothed with a 15,000 x 10,000 window. 104 Figure 52. California fourleg signalized urban intersections. Design speed, smoothed with a 10,000 x 5,000 window. 105 Figure 53. California fourleg signalized urban intersections. Proportion of intersections with multiphase signals, smoothed with a 10,000 x 5,000 window. Figure 54. California fourleg signalized urban intersections. Proportion of intersections with leftturn channelization on the main road, smoothed with a 10,000 x 5,000 window. Figure 55. California fourleg signalized urban intersections. Proportion of intersections with leftturn channelization on the minor road, smoothed with a 10,000 x 5,000 window. Figure 56. California fourleg 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 fourleg 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 fourleg signalized urban intersections. Number of lanes on major road, smoothed with a 10,000 x 5,000 window. Figure 59. California fourleg signalized urban intersections. Number of lanes on minor road, smoothed with a 10,000 x 5,000 window. Figure 60. California fourleg 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 fourleg signalized intersections with median on main road. Accidents on major approaches, smoothed with a 10,000 x 5,000 window. Figure 65. California fourleg signalized intersections with no median on main road. Accidents on major approaches, smoothed with a 10,000 x 5,000 window. Figure 66. California fourleg intersection accidents. Length of influence zone on main (not major) road, smoothed with a 10,000 x 5,000 window. Figure 67. California fourleg signalized intersection. Number of collision accidents on main (not major) road, smoothed with a 10,000 x 5,000 window. Figure 68. California fourleg signalized urban intersections. Model (52) 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. Crosssections 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 fourleg intersections from Minnesota data files. Figure 73. Distribution of approach volumes of fourleg signalized urban intersections in Minnesota. The width of the gridlines is proportional to the number of intersections in each cell. Figure 74. Signalized fourleg 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 cutoff at a minor volume of 6,000. Figure 76. The same surface as in Figure 74, but cutoff at a minor volume of 10,000 Figure 77. Signalized fourleg urban intersections in Minnesota. Accident counts within intersections smoothed with a 8,000 x 4,000 window Figure 78. Signalized fourleg urban intersections in Minnesota. Surface represents model (61) for within intersection accident counts. Figure 79. The same surface as in Figure 78, but cutoff at y = 6,000. Figure 80. The same surface as in Figure 78, but cutoff at y = 10,000. Figure 81. Signalized fourleg 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 fourleg 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 fourleg 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 fourleg 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 fourleg urban intersections in Minnesota. Distribution of intersections with typical intersection accidents by volumes of the two roads. Figure 86. Signalized fourleg urban intersections in Minnesota. Typical intersection accident, smoothed with a 10,000 x 5,000 window. Figure 87. Signalized fourleg urban intersections in Minnesota. Typical intersection accident within the intersection, smoothed with a 20,000 x 10,000 window. Figure 88. Signalized fourleg urban intersection in Minnesota. Leftturn accidents within the intersection as proportion of typical intersection accidents, smoothed with a 10,000 x 15,000 window. Figure 89. Signalized fourleg 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 fourleg urban intersections in Minnesota. Rearend collisions within the intersection as proportion of typical intersection accidents, smoothed with a 10,000 x 5,000 window. Figure 91. Signalized fourleg 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 fourleg intersections in Minnesota. Accidents in intersections versus proportion of angle collisions. Figure 93. Signalized fourleg intersections in Minnesota. Accidents in intersections versus proportion of leftturn accidents. Figure 94. Signalized fourleg intersections in Minnesota. Accidents in intersections versus proportion of rearend accidents. Figure 95. Signalized fourleg intersections in Minnesota. Accidents in intersections versus proportion of "other" accidents. Figure 96. Signalized fourleg intersections in Minnesota. Proportion of angle collisions versus number of accidents in intersections. Figure 97. Signalized fourleg intersections in Minnesota. Proportion of leftturn collisions versus number of accidents in intersections. Figure 98. Signalized fourleg intersections in Minnesota. Proportion of rearend collisions versus number of accidents in intersections. Figure 99. Signalized fourleg intersections in Minnesota. Proportion of "other"' collisions versus number of accidents in intersections. Figure 100. Signalized fourleg intersections in Minnesota. Proportion of rearend 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 fourleg intersections in Minnesota. Ten bootstrap replications of a quadratic model fit for the proportion of rearend 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 fourleg intersections in Minnesota. Ten bootstrap replications of a linear model fit for the proportion of rearend collisions.
FHWARD98096
