FHWA-HRT-23-122.pdf

Research, Development, and Technology Turner-Fairbank Highway Research Center 6300 Georgetown Pike McLean, VA 22101-2296

PUBLICATION NO. FHWA-HRT-23-122 MARCH 2024

DREDGE (Disaggregate Realistic Artificial Data Generator)—Design, Development, and Application for Crash Safety Analysis, Volume Ⅱ

FOREWORD

Data-driven safety analysis models help State and local agencies quantify safety data, identify high-risk roadway features, and predict the effects of proposed safety measures. However, even a model that performs well overall may not accurately represent interactions between variables for a specific location or crash because underlying relationships in the real world are unknown. One proposed solution is to generate realistic artificial data (RAD) with predetermined safety relationships built into them. Since these datasets are known, the RAD can serve as a test bed, indicating how well a model reflects underlying cause-and-effect relationships.

This report details a study performed by researchers working under the Federal Highway

Administration’s Exploratory Advanced Research Program. In the study, the researchers created a RAD generation framework on macroscopic and microscopic levels for a diverse selection of roadway facility types and developed a web-based tool. The tool’s framework provides users with the ability to generate RAD for multiple years at macroscopic segment and microscopic trip levels. This report should be of interest to academics and researchers developing crash modification factors or functions and statistical models to determine how the models best represent real-world relationships. This volume is the second in a series. Volume Ⅰ in the series is

FHWA-HRT-23-121.

Brian P. Cronin, P.E.

Director, Office of Safety and Operations

Research and Development

Notice

This document is disseminated under the sponsorship of the U.S. Department of Transportation

(USDOT) in the interest of information exchange. The U.S. Government assumes no liability for the use of the information contained in this document.

Non-Binding Contents

Except for the statutes and regulations cited, the contents of this document do not have the force and effect of law and are not meant to bind the States or the public in any way. This document is intended only to provide information regarding existing requirements under the law or agency policies.

Quality Assurance Statement

The Federal Highway Administration (FHWA) provides high-quality information to serve

Government, industry, and the public in a manner that promotes public understanding. Standards and policies are used to ensure and maximize the quality, objectivity, utility, and integrity of its information. FHWA periodically reviews quality issues and adjusts its programs and processes to ensure continuous quality improvement.

Disclaimer for Product Names and Manufacturers

The U.S. Government does not endorse products or manufacturers. Trademarks or manufacturers’ names appear in this document only because they are considered essential to the objective of the document. They are included for informational purposes only and are not intended to reflect a preference, approval, or endorsement of any one product or entity.

TECHNICAL REPORT DOCUMENTATION PAGE

1. Report No.

FHWA-HRT-23-122

2. Government Accession No.

3. Recipient’s Catalog No.

4. Title and Subtitle

DREDGE (Disaggregate Realistic Artificial Data Generator)—

Design, Development, and Application for Crash Safety

Analysis, Volume Ⅱ

5. Report Date

March 2024

6. Performing Organization Code:

7. Author(s):

John Ivan (ORCID: 0000-0002-8517-4354), Shanshan Zhao

(ORCID: 0000-0001-5476-6894), Kai Wang

(ORCID:0000-0003-1452-4000), Oluwaseun Olufowobi

(ORCID: 0009-0001-1339-9095), Naveen Eluru (ORCID: 0000-

0003-1221-4113), Tanmoy Bhowmik (ORCID:0000-0002-0258-

1692), Lauren Hoover (ORCID: 0009-0004-2431-0860), Md I.

Jahan (ORCID: 0000-0002-4056-7816), Sudipta Tirtha (ORCID:

0000-0002-6228-0904), and Mohamad Abdel-Aty (ORCID:

0000-0002-4838-1573)

8. Performing Organization Report No.

9. Performing Organization Name and Address

University of Connecticut

Connecticut Transportation Institute

270 Middle Turnpike, Unit 5202

Storrs, CT 06269-5202

10. Work Unit No.

11. Contract or Grant No.

693JJ31950017

12. Sponsoring Agency Name and Address

Office of Research and Development

Federal Highway Administration

6300 Georgetown Pike

McLean, VA 22101–2296

13. Type of Report and Period Covered

Final report; August 2019– March 2024

14. Sponsoring Agency Code

HRSO-2

15. Supplementary Notes

The contracting officer’s representative was Yusuf Mohamedshah (HRSO-2; ORCID: 0000-0003-0105-5559).

16. Abstract

Safety analysis primarily focuses on identifying and quantifying the influences of contributing factors to traffic collisions and the consequences of these factors. A practice of relying on observed data only allows relative comparisons between analysis methods and may not lead to determining how well the methods mimic the true underlying crash-generation process, which is often unobserved or known only partially, with varying degrees of certainty. This report describes a study, performed by researchers working under the Federal Highway Administration, to help address this data limitation.

Researchers used two approaches to generate realistic artificial data (RAD): In the macroscopic approach, researchers generated RAD at site level by segment or intersection after generating traffic and roadway characteristics by segment or intersection for various facility types. Crashes were then generated using known model structures, based on these characteristics. The microscopic approach built a high-resolution, disaggregate data-generation process that mimics crash occurrences on road facilities at the trip level and accommodates the influence of a full range of crash-contributing factors to generate crashes. The crash generation employs data describing the generated trips and involves identifying the vehicles involved in the crash, crash location, severity of occupant injuries, and crash type. These generated crashes can be aggregated at any spatial or temporal resolution to estimate and evaluate safety models. The researchers thus developed a RAD generator as a standalone, customizable software application tool that can prepare multiple realizations of RAD. The tool was evaluated using two case studies involving segment crashes and intersection crashes. This volume is the second in a series. Volume Ⅰ is FHWA-HRT-23-121.

17. Key Words

Realistic artificial data, crash analysis, RAD generator

18. Distribution Statement

No restrictions. This document is available to the public through the National

Technical Information Service, Springfield, VA 22161.

https://www.ntis.gov

19. Security Classif. (of this report)

Unclassified

20. Security Classif. (of this page)

Unclassified

21. No. of Pages

22. Price

N/A

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

https://orcid.org/0000-0002-0258-1692 https://orcid.org/0000-0002-0258-1692 https://orcid.org/0000-0002-4056-7816 https://orcid.org/0000-0002-6228-0904 https://www.ntis.gov/ ii

SI* (MODERN METRIC) CONVERSION FACTORS

APPROXIMATE CONVERSIONS TO SI UNITS

Symbol When You Know Multiply By To Find Symbol

LENGTH

in inches 25.4 millimeters mm ft feet 0.305 meters m yd yards 0.914 meters m mi miles 1.61 kilometers km

AREA

in2 square inches 645.2 square millimeters mm2 ft2 square feet 0.093 square meters m2 yd2 square yard 0.836 square meters m2 ac acres 0.405 hectares ha mi2 square miles 2.59 square kilometers km2

VOLUME

fl oz fluid ounces 29.57 milliliters mL gal gallons 3.785 liters L ft3 cubic feet 0.028 cubic meters m3 yd3 cubic yards 0.765 cubic meters m3

NOTE: volumes greater than 1,000 L shall be shown in m3

MASS

oz ounces 28.35 grams g lb pounds 0.454 kilograms kg

T short tons (2,000 lb) 0.907 megagrams (or “metric ton”) Mg (or “t”)

TEMPERATURE (exact degrees)

°F Fahrenheit 5 (F-32)/9

Celsius °C or (F-32)/1.8

ILLUMINATION

fc foot-candles 10.76 lux lx fl foot-Lamberts 3.426 candela/m2 cd/m2

FORCE and PRESSURE or STRESS lbf poundforce 4.45 newtons N lbf/in2 poundforce per square inch 6.89 kilopascals kPa

APPROXIMATE CONVERSIONS FROM SI UNITS

Symbol When You Know Multiply By To Find Symbol

LENGTH

mm millimeters 0.039 inches in m meters 3.28 feet ft m meters 1.09 yards yd km kilometers 0.621 miles mi

AREA

mm2 square millimeters 0.0016 square inches in2 m2 square meters 10.764 square feet ft2 m2 square meters 1.195 square yards yd2 ha hectares 2.47 acres ac km2 square kilometers 0.386 square miles mi2

VOLUME

mL milliliters 0.034 fluid ounces fl oz

L liters 0.264 gallons gal m3 cubic meters 35.314 cubic feet ft3 m3 cubic meters 1.307 cubic yards yd3

MASS

g grams 0.035 ounces oz kg kilograms 2.202 pounds lb

Mg (or “t”) megagrams (or “metric ton”) 1.103 short tons (2,000 lb) T

TEMPERATURE (exact degrees) °C Celsius 1.8C+32 Fahrenheit °F

ILLUMINATION

lx lux 0.0929 foot-candles fc cd/m2 candela/m2 0.2919 foot-Lamberts fl

FORCE and PRESSURE or STRESS N newtons 2.225 poundforce lbf kPa kilopascals 0.145 poundforce per square inch lbf/in2

*SI is the symbol for International System of Units. Appropriate rounding should be made to comply with Section 4 of ASTM E380.

(Revised March 2003) iii

TABLE OF CONTENTS

APPENDIX A. MICROSCOPIC GENERATION COMPARISONS

APPENDIX B. TWO-LANE, TWO-WAY UNDIVIDED SEGMENT POISSON

REGRESSION

APPENDIX C. NEGATIVE BINOMIAL REGRESSION

APPENDIX D. POISSON REGRESSION—RANDOM PARAMETERS

APPENDIX E. NEGATIVE BINOMIAL—RANDOM PARAMETERS

APPENDIX F. UNIVARIATE POISSON LOGNORMAL

APPENDIX G. MULTIVARIATE POISSON LOGNORMAL

APPENDIX H. FOUR-LEG URBAN SIGNALIZED INTERSECTION POISSON

REGRESSION

APPENDIX I. NEGATIVE BINOMIAL REGRESSION

APPENDIX J. POISSON REGRESSION—RANDOM PARAMETERS

APPENDIX K. NEGATIVE BINOMIAL—RANDOM PARAMETERS

APPENDIX L. UNIVARIATE POISSON LOGNORMAL

APPENDIX M. MULTIVARIATE POISSON LOGNORMAL

REFERENCES

iv

LIST OF FIGURES

Figure 1. Graph. Comparison of crash type results

Figure 2. Graph. Comparison of driver demographic results

Figure 3. Graph. Comparison of vehicle characteristic results

Figure 4. Graph. Comparison of crash severity results v

LIST OF TABLES

Table 1. Poisson regression of 150 mi (dataset 1)

Table 2. Poisson regression of 300 mi (dataset 2)

Table 3. Poisson regression of 500 mi (dataset 3)

Table 4. Poisson regression of 750 mi (dataset 4)

Table 5. Poisson regression of 1,000 mi (dataset 5)

Table 6. Poisson regression of 150 mi (dataset 6)

Table 7. Poisson regression of 300 mi (dataset 7)

Table 8. Poisson regression of 500 mi (dataset 8)

Table 9. Poisson regression of 750 mi (dataset 9)

Table 10. Negative binomial regression of 150 mi (dataset 1)

Table 11. Negative binomial regression of 300 mi (dataset 2)

Table 12. Negative binomial regression of 500 mi (dataset 3)

Table 13. Negative binomial regression of 750 mi (dataset 4)

Table 14. Negative binomial regression of 1,000 mi (dataset 5)

Table 15. Negative binomial regression of 150 mi (dataset 6)

Table 16. Negative binomial regression of 300 mi (dataset 7)

Table 17. Negative binomial regression of 500 mi (dataset 8)

Table 18. Negative binomial regression of 750 mi (dataset 9)

Table 19. Poisson regression—random parameters of 150 mi (dataset 1)

Table 20. Poisson regression—random parameters of 300 mi (dataset 2)

Table 21. Poisson regression—random parameters of 500 mi (dataset 3)

Table 22. Poisson regression—random parameters of 750 mi (dataset 4)

Table 23. Poisson regression—random parameters of 1,000 mi (dataset 5)

Table 24. Poisson regression—random parameters of 150 mi (dataset 6)

Table 25. Poisson regression—random parameters of 300 mi (dataset 7)

Table 26. Poisson regression—random parameters of 500 mi (dataset 8)

Table 27. Poisson regression—random parameters of 750 mi (dataset 9)

Table 28. Negative binomial—random parameters of 150 mi (dataset 1)

Table 29. Negative binomial—random parameters of 300 mi (dataset 2)

Table 30. Negative binomial—random parameters of 500 mi (dataset 3)

Table 31. Negative binomial—random parameters of 750 mi (dataset 4)

Table 32. Negative binomial—random parameters of 1,000 mi (dataset 5)

Table 33. Negative binomial—random parameters of 150 mi (dataset 6)

Table 34. Negative binomial—random parameters of 300 mi (dataset 7)

Table 35. Negative binomial—random parameters of 500 mi (dataset 8)

Table 36. Negative binomial—random parameters of 750 mi (dataset 9)

Table 37. Negative binomial—random parameters of 1,000 mi (dataset 10)

Table 38. Univariate Poisson lognormal of 150 mi (dataset 1)

Table 39. Univariate Poisson lognormal of 300 mi (dataset 2)

Table 40. Univariate Poisson lognormal of 500 mi (dataset 3)

Table 41. Univariate Poisson lognormal of 750 mi (dataset 4)

Table 42. Univariate Poisson lognormal of 1,000 mi (dataset 5)

Table 43. Univariate Poisson lognormal of 150 mi (dataset 6)

Table 44. Univariate Poisson lognormal of 300 mi (dataset 7) vi

Table 45. Univariate Poisson lognormal of 500 mi (dataset 8)

Table 46. Univariate Poisson lognormal of 750 mi (dataset 9)

Table 47. Univariate Poisson lognormal of 1,000 mi (dataset 10)

Table 48. Multivariate Poisson lognormal of 150 mi (dataset 1)

Table 49. Multivariate Poisson lognormal of 300 mi (dataset 2)

Table 50. Multivariate Poisson lognormal of 500 mi (dataset 3)

Table 51. Multivariate Poisson lognormal of 750 mi (dataset 4)

Table 52. Multivariate Poisson lognormal of 1,000 mi (dataset 5)

Table 53. Multivariate Poisson lognormal of 150 mi (dataset 6)

Table 54. Multivariate Poisson lognormal of 300 mi (dataset 7)

Table 55. Multivariate Poisson lognormal of 500 mi (dataset 8)

Table 56. Multivariate Poisson lognormal of 750 mi (dataset 9)

Table 57. Poisson regression of 1,000 intersections (dataset 1)

Table 58. Poisson regression of 2,000 intersections (dataset 2)

Table 59. Poisson regression of 3,000 intersections (dataset 3)

Table 60. Poisson regression of 4,000 intersections (dataset 4)

Table 61. Poisson regression of 5,000 intersections (dataset 5)

Table 62. Poisson regression of 1,000 intersections (dataset 6)

Table 63. Poisson regression of 2,000 intersections (dataset 7)

Table 64. Poisson regression of 3,000 intersections (dataset 8)

Table 65. Poisson regression of 4,000 intersections (dataset 9)

Table 66. Poisson regression of 5,000 intersections (dataset 10)

Table 67. Negative binomial regression of 1,000 intersections (dataset 1)

Table 68. Negative binomial regression of 2,000 intersections (dataset 2)

Table 69. Negative binomial regression of 3,000 intersections (dataset 3)

Table 70. Negative binomial regression of 4,000 intersections (dataset 4)

Table 71. Negative binomial regression of 5,000 intersections (dataset 5)

Table 72. Negative binomial regression of 1,000 intersections (dataset 6)

Table 73. Negative binomial regression of 2,000 intersections (dataset 7)

Table 74. Negative binomial regression of 3,000 intersections (dataset 8)

Table 75. Negative binomial regression of 4,000 intersections (dataset 9)

Table 76. Negative binomial regression of 5,000 intersections (dataset 10)

Table 77. Poisson regression—random parameters of 1,000 intersections (dataset 1)

Table 78. Poisson regression—random parameters of 2,000 intersections (dataset 2)

Table 79. Poisson regression—random parameters of 3,000 intersections (dataset 3)

Table 80. Poisson regression—random parameters of 4,000 intersections (dataset 4)

Table 81. Poisson regression—random parameters of 5,000 intersections (dataset 5)

Table 82. Poisson regression—random parameters of 1,000 intersections (dataset 6)

Table 83. Poisson regression—random parameters of 2,000 intersections (dataset 7)

Table 84. Poisson regression—random parameters of 3,000 intersections (dataset 8)

Table 85. Poisson regression—random parameters of 4,000 intersections (dataset 9)

Table 86. Poisson regression—random parameters of 5,000 intersections (dataset 10)

Table 87. Negative binomial—random parameters of 1,000 intersections (dataset 1)

Table 88. Negative binomial—random parameters of 2,000 intersections (dataset 2)

Table 89. Negative binomial—random parameters of 3,000 intersections (dataset 3)

Table 90. Negative binomial—random parameters of 4,000 intersections (dataset 4) vii

Table 91. Negative binomial regression—random parameters of 5,000 intersections

(dataset 5)

Table 92. Negative binomial—random parameters of 1,000 intersections (dataset 6)

Table 93. Negative binomial—random parameters of 2,000 intersections (dataset 7)

Table 94. Negative binomial—random parameters of 3,000 intersections (dataset 8)

Table 95. Negative binomial—random parameters of 4,000 intersections (dataset 9)

Table 96. Negative binomial—random parameters of 5,000 intersections (dataset 10)

Table 97. Univariate Poisson lognormal of 1,000 intersections (dataset 1)

Table 98. Univariate Poisson lognormal of 2,000 intersections (dataset 2)

Table 99. Univariate Poisson lognormal of 3,000 intersections (dataset 3)

Table 100. Univariate Poisson lognormal of 4,000 intersections (dataset 4)

Table 101. Univariate Poisson lognormal of 5,000 intersections (dataset 5)

Table 102. Univariate Poisson lognormal of 1,000 intersections (dataset 6)

Table 103. Univariate Poisson lognormal of 2,000 intersections (dataset 7)

Table 104. Univariate Poisson lognormal of 3,000 intersections (dataset 8)

Table 105. Univariate Poisson lognormal of 4,000 intersections (dataset 9)

Table 106. Univariate Poisson lognormal of 5,000 intersections (dataset 10)

Table 107. Multivariate Poisson lognormal of 1,000 intersections (dataset 1)

Table 108. Multivariate Poisson lognormal of 2,000 intersections (dataset 2)

Table 109. Multivariate Poisson lognormal of 3,000 intersections (dataset 3)

Table 110. Multivariate Poisson lognormal of 4,000 intersections (dataset 4)

Table 111. Multivariate Poisson lognormal of 5,000 intersections (dataset 5)

Table 112. Multivariate Poisson lognormal of 1,000 intersections (dataset 6)

Table 113. Multivariate Poisson lognormal of 2,000 intersections (dataset 7)

Table 114. Multivariate Poisson lognormal of 3,000 intersections (dataset 8)

Table 115. Multivariate Poisson lognormal of 4,000 intersections (dataset 9)

Table 116. Multivariate Poisson lognormal of 5,000 intersections (dataset 10)

APPENDIX A. MICROSCOPIC GENERATION COMPARISONS

This appendix documents a comparison of the generated microscopic realistic artificial data

(RAD) that researchers generated for this report with the source data employed for generation

(NHTSA n.d.). The comparison results are presented for crash type, driver demographics, vehicle characteristics, and crash severity variables. Overall, the results illustrate that the RAD represent the source data reasonably well. Figure 1 through figure 4 illustrate these comparison results.

Source: FHWA.

Figure 1. Graph. Comparison of crash type results.

Figure 2. Graph. Comparison of driver demographic results.

Figure 3. Graph. Comparison of vehicle characteristic results.

Figure 4. Graph. Comparison of crash severity results.

APPENDIX B. TWO-LANE, TWO-WAY UNDIVIDED SEGMENT POISSON REGRESSION

Table 1 through table 9 contain the model estimation results for Poisson regression on two-lane, two-way undivided segments for datasets 1 through 9, which were generated by the project (as described in volume 1).

Table 1. Poisson regression of 150 mi (dataset 1).

Variables

K† A† B† C† PDO

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Intercept −66.698* 13221 −3.560 1.783 −6.848 3.897 −4.042 1.974 −0.697 0.835

Ln (Length) 2.844 0.961 0.984 0.078 1.200 0.168 0.906 0.082 0.952 0.036

Ln (AADT) 2.751 1.385 0.490 0.144 0.898 0.326 0.354 0.151 0.342 0.065

Shoulder Width

8 ft Base Level

<2 ft −13.512* 3804.5 0.790 0.560 −19.015* 10109.5 0.864 0.642 −0.028 0.353

≥2 ft < 4 ft −0.774 1.325 0.498 0.187 −0.581 0.441 0.441 0.197 0.412 0.088

≥4 ft < 6 ft 2.916 1.490 0.318 0.172 −0.189 0.304 −0.028 0.188 0.220 0.081

≥6 ft < 8 ft −23.189* 7067.421 0.097 0.215 −0.733 0.442 −0.155 0.220 0.305 0.092

Lane Width

>12 ft Base Level

9 ft or less — — — — — — — — — —

9.5 ft–10.5 ft −15.982* 2163 −0.012 0.440 0.076 0.926 0.028 0.578 0.219 0.200

11 ft–11.5 ft 0.821 1.912 0.165 0.200 0.033 0.400 0.014 0.231 0.035 0.097

Speed Limit

45 mph Base Level

25 mph 0.623* 18777.62 0.922 0.381 −0.051 0.657 0.996 0.357 0.376 0.147

30 mph 2.756* 29538.03 1.202 0.465 −0.317 0.916 0.780 0.487 −0.143 0.238

35 mph 28.253* 13227.19 0.453 0.668 −18.355* 6226.64 1.050 0.457 −0.784 0.336

40 mph 2.341* 23545.65 −0.288 0.567 −1.628 1.141 −1.452 0.781 −0.844 0.254

50 mph 4.566* 25063.45 −0.216 0.677 1.365 0.790 0.508 0.532 0.097 0.219

55 mph 19.033* 13227.19 0.354 0.335 −0.131 0.488 −0.182 0.327 −0.173 0.121

Roadside Hazard Rating (Zegeer et al. 1988)

3 Base Level

4 0.632* 1.634 0.303 0.188 −0.387 0.358 0.035 0.204 0.152 0.084

5 −0.833 1.766 0.398 0.245 0.346 0.462 0.378 0.264 0.137 0.117

6 −18.741* 9773.750 0.048 0.339 −0.404 0.680 0.065 0.338 0.080 0.150

Variables

K† A† B† C† PDO

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

7 4.464* 3.107 −0.527 0.566 −17.781* 4508.09 0.064 0.501 0.137 0.230

Pavement Condition 0.512 0.492 −0.013 0.029 0.012 0.058 0.029 0.034 −0.002 0.014

Pavement Roughness 0.019 0.025 −0.001 0.004 −0.007 0.009 0.001 0.004 0.000 0.002

Presence of Lighting −21.728* 13587.73 0.543 0.352 −17.602* 3789.50 0.543 0.345 −0.709 0.218

Presence of Horizontal

Curve −17.430* 14901.54 −15.615 666.718 −18.327* 4904.58 −1.152 0.722 −0.218 0.231

Vertical Curve

Approaching Slope 0.469 10318.99 −0.113 0.442 1.068 2911.52 −0.085 0.410 −0.062 0.125

Vertical Curve Leaving

Slope −2.825* 10166.13 −0.286 0.412 −0.512* 2972.77 −0.045 0.419 0.120 0.140

Grade −8.067* 12357.37 0.091 0.511 −13.360* 3555.84 −0.124 0.501 −0.043 0.166

Curvature Degree 0.022 0.025 0.002 0.009 0.011 0.019 0.008 0.007 −0.009 0.006

Fit Statistics

AIC 102.29 N/A 1204.9 N/A 464.34 N/A 1148.4 N/A 3027.5 N/A

BIC 242.83 N/A 1345.44 N/A 604.89 N/A 1288.96 N/A 3168.00 N/A

—No data.

*Variables are insignificant at a 90-percent confidence level.

†Ratings are based on the KABCO Injury Classification Scale: K = Fatal Injury; A = Incapacitating/Serious Injury; B = Nonincapacitating/Visible Injury;

C = Possible Injury/Complaint; PDO = Property Damage Only (NHTSA 2017).

AADT = average annual daily traffic; AIC= Akaike information criterion; BIC = Bayesian information criterion; N/A = not applicable; PDO = property damage only; std. error = standard error.

Table 2. Poisson regression of 300 mi (dataset 2).

Variables

K A B C PDO

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Intercept −62.409* 10429.82 −5.449 1.211 −9.001 2.389 −1.836 1.011 −2.982 0.476

Ln (Length) 0.957 0.406 1.146 0.068 1.200 0.127 1.011 0.060 1.006 0.026

Ln (AADT) 0.490 0.546 0.636 0.085 0.414 0.150 0.519 0.076 0.612 0.034

Shoulder Width

8 ft Base Level

<2 ft 18.736* 7023.832 −0.260 0.264 −0.399 0.431 −0.333 0.237 0.027 0.117

≥2 ft < 4 ft 18.126* 7023.832 −0.368 0.274 −0.542 0.460 −0.525 0.249 −0.060 0.121

≥4 ft < 6 ft 17.973* 7023.832 −0.313 0.273 −0.827 0.475 −0.407 0.247 −0.005 0.120

≥6 ft < 8 ft 16.850* 7023.832 −0.658 0.266 −0.794 0.445 −0.782 0.242 −0.465 0.119

Lane Width

>>12 ft Base Level

9 ft or less 17.530* 4100.589 −0.245 0.237 0.063 0.514 −0.330 0.200 −0.134 0.095

9.5 ft–10.5 ft 16.620* 4100.589 −0.560 0.269 −0.518 0.554 −0.336 0.224 −0.305 0.107

11 ft–11.5 ft 19.461* 35559.45 −10.003 427.783 −12.462 3114.82 −11.436 404.751 0.527 1.020

Speed Limit

45 mph Base Level

25 mph 18.651* 6529.2 0.331 0.431 0.241 1.170 −0.075 0.396 0.103 0.196

30 mph −1.464 12762 −1.407 0.761 1.888 0.756 −0.750 0.476 −0.870 0.259

35 mph −0.337 8413.9 −0.794 0.383 0.038 0.784 −1.140 0.372 −1.039 0.180

40 mph −1.311 84015 −0.874 0.342 −0.347 0.747 −0.463 0.281 −0.194 0.133

50 mph −0.279 8926.8 −0.055 0.347 0.058 0.863 −0.460 0.326 −0.141 0.151

55 mph 17.338* 65292 −0.687 0.272 −0.055 0.634 −0.775 0.239 −0.530 0.117

Roadside Hazard Rating (Zegeer et al. 1988)

3 Base Level

4 −1.383 0.585 0.093 0.070 0.089 0.129 −0.012 0.066 0.017 0.028

5 0.171 0.164 0.052 0.026 0.142 0.052 −0.009 0.021 0.020 0.010

6 0.021 0.020 0.000 0.003 0.002 0.005 0.002 0.002 0.003 0.001

7 −16.084* 4045.797 −0.658 0.323 −0.405 0.519 −0.451 0.285 −0.480 0.121

Pavement Condition −15.759* 6302.943 −0.265 0.586 −13.484 549.429 −1.692 1.004 0.286 0.171

Pavement Roughness −0.730 3787.960 −0.360 0.236 0.062 0.251 −0.114 0.188 −0.013 0.077

Presence of Lighting −13.977 2704.390 −0.418 0.207 0.448 0.322 −0.030 0.185 0.045 0.072

Presence of Horizontal

Curve

0.798 3787.961 0.601 0.267 −0.192 0.386 0.132 0.238 0.040 0.098

K A B C PDO

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Vertical Curve

Approaching Slope −0.094 0.129 0.004 0.006 −0.034 0.025 0.001 0.006 0.002 0.003

Vertical Curve Leaving

Slope −1.383 0.585 0.093 0.070 0.089 0.129 −0.012 0.066 0.017 0.028

Grade 0.171 0.164 0.052 0.026 0.142 0.052 −0.009 0.021 0.020 0.010

Curvature Degree 0.021 0.020 0.000 0.003 0.002 0.005 0.002 0.002 0.003 0.001

Fit Statistics

AIC 151.36 N/A 1958.8 N/A 2249.4 N/A 2249.4 N/A 5847.4 N/A

BIC 299.17 N/A 2106.65 N/A 2397.18 N/A 2397.18 N/A 5995.256 N/A

—No data.

*Variables are insignificant at a 90-percent confidence level.

Table 3. Poisson regression of 500 mi (dataset 3).

Variables

K A B C PDO

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Intercept −10.582* 4.997 −7.817 0.905 −2.538 1.308 −3.431 0.790 −2.020 0.334

Ln (Length) 1.157 0.264 0.963 0.046 1.162 0.085 0.999 0.044 1.012 0.019

Ln (AADT) 0.766 0.389 0.869 0.068 0.268 0.102 0.447 0.058 0.544 0.026

Shoulder Width

8 ft Base Level

<2 ft −17.782* 3672.071 0.342 0.152 0.288 0.320 0.794 0.137 0.244 0.069

≥2 ft < 4 ft 0.585 0.550 0.449 0.110 0.456 0.189 0.466 0.107 0.274 0.046

≥4 ft < 6 ft 0.253 0.547 0.103 0.111 0.438 0.185 0.328 0.104 0.292 0.043

≥6 ft < 8 ft −0.741 0.781 −0.004 0.130 −0.015 0.232 0.187 0.122 0.151 0.051

Lane Width

>>12 ft Base Level

9 ft or less 1.380 0.953 0.395 0.204 −0.217 0.352 0.338 0.180 0.075 0.080

9.5 ft–10.5 ft 0.336 0.600 0.253 0.113 0.335 0.183 0.128 0.110 0.201 0.045

11 ft–11.5 ft −17.171* 10097.34 1.172 0.383 −0.784 1.061 0.264 0.390 0.179 0.172

Speed Limit

45 mph Base Level

25 mph 0.051 0.982 0.541 0.220 0.830 0.361 0.419 0.225 0.446 0.093

30 mph −18.766* 68973 −0.194 0.297 0.183 0.518 0.510 0.247 0.131 0.114

35 mph −19.028* 82727 −0.567 0.439 0.587 0.460 0.330 0.300 −0.416 0.163

40 mph −18.258* 3766.9 −0.337 0.244 −1.765 0.622 −0.526 0.243 −0.928 0.114

50 mph −18.088* 5012.2 0.109 0.259 −0.530 0.554 0.006 0.260 −0.247 0.116

55 mph −0.701 0.623 −0.226 0.161 −0.609 0.266 −0.172 0.154 −0.212 0.063

Roadside Hazard Rating (Zegeer et al. 1988)

3 Base Level

4 −0.237 0.527 0.097 0.110 0.341 0.201 −0.116 0.104 0.036 0.044

5 −0.705 0.749 0.217 0.138 0.582 0.244 −0.017 0.128 0.120 0.056

6 −1.549 1.230 0.326 0.173 0.101 0.322 −0.054 0.165 0.212 0.072

7 −18.645* 3594.820 0.367 0.238 0.633 0.405 −0.495 0.266 0.220 0.103

Pavement Condition 0.044 0.089 0.027 0.017 −0.010 0.025 −0.003 0.015 −0.007 0.006

Pavement Roughness 0.014 0.012 0.000 0.002 0.003 0.003 0.003 0.002 0.001 0.001

Presence of Lighting −16.589* 2903.590 −0.483 0.219 0.418 0.323 −0.167 0.201 −0.592 0.095

Presence of Horizontal

−16.846* 4205.718 −15.196 330.239 −14.118 339.152 −1.577 0.580 0.219 0.105

K A B C PDO

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Vertical Curve

Approaching Slope −0.250 3194.766 0.077 0.211 0.042 0.310 0.216 0.184 −0.175 0.084

Vertical Curve

Leaving Slope −10.742* 2019.942 −0.072 0.165 0.345 0.346 0.067 0.139 −0.137 0.078

Grade −2.117 3194.767 −0.070 0.238 −0.367 0.425 −0.210 0.212 0.173 0.098

Curvature Degree −0.074 0.075 −0.008 0.006 −0.010 0.012 0.002 0.004 0.003 0.002

Fit Statistics

AIC 301.21 N/A 3446.6 N/A 1593.9 N/A 3713.9 N/A 10221 N/A

BIC 481.89 N/A 3627.29 N/A 1774.57 N/A 3894.63 N/A 10401.48 N/A

Table 4. Poisson regression of 750 mi (dataset 4).

Variables

K A B C PDO

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Intercept −15.751* 5.097 −6.558 0.786 −4.271 1.451 −3.059 0.670 −2.020 0.320

Ln (Length) 0.939 0.253 0.989 0.037 1.087 0.073 1.065 0.033 1.046 0.016

Ln (AADT) 1.033 0.370 0.846 0.052 0.200 0.085 0.453 0.043 0.460 0.021

Shoulder Width

8 ft Base Level

<2 ft −0.289 1.147 0.163 0.173 −0.403 0.528 0.937 0.135 0.209 0.078

≥2 ft < 4 ft −1.343 1.132 0.504 0.092 0.875 0.194 0.523 0.090 0.303 0.040

≥4 ft < 6 ft 0.583 0.594 0.121 0.101 0.367 0.213 0.575 0.091 0.258 0.042

≥6 ft < 8 ft 0.201 0.669 0.072 0.117 0.592 0.224 0.373 0.108 0.259 0.048

Lane Width

>12 ft Base Level

9 ft or less −16.465* 2043.232 0.225 0.173 0.259 0.350 0.046 0.156 0.228 0.075

9.5 ft–10.5 ft 0.476 0.593 0.017 0.099 0.021 0.193 0.124 0.086 0.064 0.042

11 ft–11.5 ft −16.412 3375.189 0.015 0.234 0.044 0.529 0.223 0.203 0.473 0.096

Speed Limit

45 mph Base Level

25 mph 1.968* 1.515 0.372 0.198 −0.429 0.505 0.766 0.183 0.136 0.087

30 mph 3.859* 1.699 0.309 0.209 0.487 0.386 0.865 0.186 −0.060 0.103

35 mph 4.421* 1.214 −0.072 0.277 1.385 0.319 0.805 0.200 −0.300 0.117

40 mph −15.287* 2356.470 −0.949 0.234 −0.674 0.388 −0.550 0.207 −1.064 0.100

50 mph −15.549* 3298.388 −0.403 0.274 −0.444 0.501 0.220 0.231 0.021 0.095

55 mph 0.181 1.121 −0.311 0.129 −0.580 0.259 −0.066 0.135 −0.295 0.055

Roadside Hazard Rating (Zegeer et al. 1988)

3 Base Level

4 3.154* 0.912 0.082 0.095 0.110 0.184 −0.067 0.087 0.036 0.039

5 2.140* 1.102 0.058 0.120 0.245 0.236 0.176 0.107 0.054 0.051

6 2.655* 1.225 −0.057 0.153 0.681 0.284 0.266 0.133 0.230 0.063

7 3.538* 1.264 −0.130 0.207 0.147 0.422 0.338 0.174 0.154 0.087

Pavement Condition 0.026 0.092 0.002 0.015 0.041 0.030 −0.012 0.013 0.012 0.006

Pavement Roughness 0.002 0.009 0.003 0.001 0.000 0.003 0.001 0.001 0.000 0.001

Presence of Lighting 0.281 1.065 −0.234* 0.197 −0.299 0.371 −0.686 0.191 −0.507 0.088

Presence of Horizontal

−17.481* 1993.639 −2.822* 1.002 −1.566 1.007 −1.416 0.451 0.182 0.102

K A B C PDO

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Vertical Curve

Approaching Slope

0.128 1.044 0.527 0.240 −0.006 0.504 0.115 0.153 −0.013 0.071

Vertical Curve Leaving

Slope

1.569 1.614 0.129 0.145 −0.211 0.394 0.078 0.131 −0.060 0.060

Grade −1.661 1.842 −0.586* 0.268 −0.035 0.558 −0.131 0.184 0.066 0.084

Curvature Degree 0.043 0.013 −0.010 0.011 −0.019 0.021 0.003 0.008 0.000 0.004

Fit Statistics

AIC 286.79 N/A 3815.9 N/A 1636.9 N/A 4357.2 N/A 9471.1 N/A

BIC 463.989 N/A 3993.09 N/A 1814.11 N/A 4534.37 N/A 9648.25 N/A

Table 5. Poisson regression of 1,000 mi (dataset 5).

Variables

K A B C PDO

Parameter

Estimate

Std.

Error

Paramete r

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Paramete r

Estimate

Std.

Error

Intercept −31.452* 1760.461 −6.809 0.630 −5.467 1.031 −2.938 0.545 −1.978 0.249

Ln (Length) 0.468 0.186 1.004 0.033 1.086 0.057 0.986 0.030 1.044 0.014

Ln (AADT) 1.330 0.342 0.821 0.046 0.542 0.076 0.385 0.039 0.481 0.018

Shoulder Width

8 ft Base Level

<2 ft −16.852* 1732.218 0.518 0.113 0.649 0.208 0.476 0.122 0.356 0.056

≥2 ft < 4 ft −0.132 0.494 0.156 0.079 0.516 0.134 0.460 0.073 0.380 0.033

≥4 ft < 6 ft −0.047 0.469 0.166 0.077 0.088 0.144 0.359 0.073 0.265 0.033

≥6 ft < 8 ft −0.515 0.612 0.011 0.093 0.316 0.156 0.007 0.092 0.234 0.038

Lane Width

>12 ft Base Level

9 ft or less 0.616 0.840 0.007 0.159 0.004 0.282 0.441 0.133 0.260 0.062

9.5 ft–10.5 ft −0.013 0.645 0.021 0.086 0.270 0.136 0.056 0.076 0.133 0.034

11 ft–11.5 ft −16.119* 2424.845 0.480 0.203 0.338 0.377 0.286 0.195 0.404 0.085

Speed Limit

45 mph Base Level

25 mph 17.524* 1760.455 0.725 0.172 0.675 0.293 0.494 0.156 0.670 0.074

30 mph −0.253 3591.022 0.597 0.173 0.927 0.277 0.423 0.160 0.370 0.081

35 mph 17.349* 1760.455 0.211 0.189 0.306 0.308 0.018 0.168 0.010 0.085

40 mph 16.745* 1760.455 −0.503 0.186 −0.922 0.350 −0.653 0.164 −0.658 0.081

50 mph 18.193* 1760.455 −0.163 0.239 −0.252 0.428 −0.151 0.208 −0.070 0.099

55 mph 16.423* 1760.455 −0.247 0.124 −0.160 0.211 −0.255 0.108 −0.006 0.053

Roadside Hazard Rating (Zegeer et al. 1988)

3 Base Level

4 0.175 0.501 0.227 0.077 0.065 0.134 0.240 0.071 0.130 0.032

5 0.376 0.682 0.267 0.094 0.122 0.166 0.232 0.089 0.207 0.040

6 1.849 0.720 0.275 0.122 0.609 0.197 0.151 0.117 0.309 0.050

7 1.050 1.230 0.245 0.169 0.405 0.282 0.638 0.142 0.377 0.067

Pavement Condition 0.031 0.079 0.012 0.011 0.010 0.019 0.008 0.010 0.002 0.005

Pavement Roughness −0.012 0.010 0.001 0.001 −0.001 0.002 −0.002 0.001 −0.001 0.001

Presence of Lighting −16.573* 1550.651 −0.163 0.153 −0.971 0.312 0.054 0.138 −0.441 0.069

K A B C PDO

Parameter

Estimate

Std.

Error

Paramete r

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Paramete r

Estimate

Std.

Error

Presence of Horizontal

Curve −16.460* 1920.232 −1.343 0.380 −0.724 0.506 −1.053 0.304 0.282 0.075

Vertical Curve

Approaching Slope −3.731* 3.897 −0.113 0.144 −0.010 0.182 −0.017 0.124 −0.044 0.053

Vertical Curve Leaving

Slope −2.798* 3.873 −0.215 0.122 0.128 0.180 −0.014 0.108 0.031 0.049

Grade 3.217* 3.986 0.206 0.163 0.028 0.230 −0.007 0.146 0.025 0.064

Curvature Degree −0.016 0.026 0.003 0.002 −0.006 0.006 0.003 0.002 0.001 0.001

Fit Statistics

AIC 431.73 N/A 3220.9 N/A 6632.4 N/A 7271.9 N/A 17936 N/A

BIC 627.60 N/A 3416.78 N/A 6828.22 N/A 7467.77 N/A 18131.8 N/A

Table 6. Poisson regression of 150 mi (dataset 6).

Variables

K A B C PDO

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Paramete r

Estimate

Std.

Error

Intercept −19.149* 10998.67 −4.694 2.139 −5.136 4.328 −1.940 1.747 −1.536 0.852

Ln (Length) 0.545 0.422 0.865 0.083 1.555 0.208 1.015 0.078 0.968 0.037

Ln (AADT) 0.533 0.996 0.695 0.170 0.428 0.329 0.395 0.138 0.413 0.067

Shoulder Width

8 ft Base Level

<2 ft −20.420* 24227.87 0.864 0.531 −15.263* 3531.042 0.687 0.560 0.714 0.262

≥2 ft < 4 ft −12.502* 18084.20 0.525 0.691 −16.908* 2784.792 1.117 0.569 0.804 0.267

≥4 ft < 6 ft 0.115* 0.865 0.275 0.172 0.735* 0.364 0.250 0.143 0.366 0.068

≥6 ft < 8 ft −17.600* 7235.989 0.518 0.196 1.162* 0.402 0.042 0.193 0.154 0.094

Lane Width

>>12 ft Base Level

9 ft or less — — — — — — — — — —

9.5 ft–10.5 ft 1.544 1.707 0.395 0.461 −0.512 1.214 −0.119 0.425 0.028 0.205

11 ft–11.5 ft −18.574* 6138.690 −0.239 0.250 −0.350 0.525 −0.299 0.216 0.013 0.101

Speed Limit

45 mph Base Level

25 mph 18.006* 10998 0.105 0.361 1.196 0.759 0.316 0.325 0.408 0.149

30 mph 1.546* 23648 1.318 0.413 1.049 1.049 0.664 0.441 0.075 0.239

35 mph −0.149* 21251 −0.228 0.763 1.068 1.223 −0.118 0.630 0.326 0.244

40 mph 0.466* 17020 −1.046 0.657 0.928* 0.992 −1.671 0.761 −0.745 0.246

50 mph −0.417* 21180 −1.302 1.051 −16.001* 2273.451 −0.491 0.645 −0.129 0.257

55 mph 17.814* 10998 −0.116 0.289 0.114 0.662 0.022 0.264 −0.107 0.123

Roadside Hazard Rating (Zegeer et al. 1988)

3 Base Level

4 0.941* 1.160 0.284 0.195 0.110 0.414 0.293 0.173 0.195 0.080

5 −15.919* 5770 0.441 0.288 −0.037 0.564 0.395 0.244 0.009 0.120

6 2.540 1.986 0.567 0.355 −0.161 0.749 0.072 0.318 0.122 0.146

7 −13.932* 13063 0.989 0.657 0.648 0.999 −0.108 0.578 0.005 0.265

Pavement Condition −0.109 0.178 0.000 0.035 −0.007 0.073 −0.011 0.029 0.005 0.014

Pavement Roughness −0.034 0.030 −0.010 0.005 0.012 0.010 −0.004 0.004 −0.001 0.002

Presence of Lighting −17.037* 10913 −0.571 0.559 −17.676* 1495.695 0.122 0.399 −0.337 0.208

K A B C PDO

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Paramete r

Estimate

Std.

Error

Presence of Horizontal

Curve −18.902* 14864 −1.721 1.009 −15.769* 1921.014 −0.347 0.516 0.146 0.189

Vertical Curve

Approaching Slope −0.729 79728 −0.125 0.501 −0.641 0.923 0.305 0.297 0.211 0.158

Vertical Curve Leaving

Slope −2.137* 8271.0 −0.312 0.459 −0.782 0.883 0.268 0.280 0.070 0.140

Grade −12.347* 9774.5 0.137 0.574 1.152 0.983 −0.431 0.381 −0.257 0.191

Curvature Degree 0.015 0.043 0.001 0.010 −0.009 0.028 0.008 0.008 0.008 0.003

Fit Statistics

AIC 112.98 N/A 1111.6 N/A 377.43 N/A 1272.8 N/A 3216.9 N/A

BIC 253.709 N/A 1252.28 N/A 518.16 N/A 1413.54 N/A 3357.64 N/A

Table 7. Poisson regression of 300 mi (dataset 7).

Variables

K A B C PDO

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Intercept −70.276* 6853.18 −5.939 1.394 −2.073 2.287 −3.565 1.169 −3.483 0.551

Ln (Length) 1.978 0.476 0.996 0.062 1.039 0.106 1.098 0.055 1.061 0.025

Ln (AADT) 2.604 0.737 0.720 0.093 0.269 0.141 0.468 0.078 0.540 0.037

Shoulder Width

8 ft Base Level

<2 ft −0.420 1.405 0.869 0.242 1.300 0.369 0.399 0.290 0.335 0.123

≥2 ft < 4 ft −19.610* 2836.41 0.409 0.154 0.232 0.260 0.582 0.130 0.474 0.062

≥4 ft < 6 ft −3.631 1.544 0.345 0.168 0.232 0.284 0.300 0.147 0.452 0.066

≥6 ft < 8 ft −1.319 1.011 0.179 0.181 −0.023 0.332 0.406 0.149 0.324 0.070

Lane Width

>>12 ft Base Level

9 ft or less −10.809* 4970.7 0.340 0.296 0.430 0.440 −0.184 0.271 0.279 0.117

9.5 ft–10.5 ft 3.161* 1.407 0.303 0.163 −0.093 0.286 −0.018 0.145 0.402 0.066

11 ft–11.5 ft 20.987* 5937.2 −10.377 438.029 −19.810 0.377 −10.505 424.481 0.620 1.031

Speed Limit

45 mph Base Level

25 mph 23.630* 6853.17 0.553 0.344 −1.287 1.088 0.212 0.276 0.435 0.142

30 mph −0.087* 12195.5 0.614 0.502 0.729 0.824 0.663 0.314 0.467 0.199

35 mph 7.959* 14121.6 0.689 0.418 0.938 0.704 −0.854 0.530 −0.013 0.206

40 mph −0.832 9903.19 −0.889 0.458 −0.826 0.801 −0.748 0.309 −1.000 0.192

50 mph 2.575* 10769.3 −0.564 0.398 −0.522 0.658 −0.705 0.331 −0.021 0.135

55 mph 18.908* 6853.17 −0.239 0.228 0.010 0.396 −0.413 0.175 −0.025 0.090

Roadside Hazard Rating (Zegeer et al. 1988)

3 Base Level

4 1.983* 1.494 0.407 0.163 0.653 0.271 −0.172 0.128 −0.101 0.061

5 3.699* 1.748 0.652 0.200 −0.071 0.372 −0.032 0.164 0.039 0.077

6 4.784* 2.314 0.565 0.279 −0.188 0.514 −0.004 0.232 −0.048 0.107

7 −22.811* 8772.52 0.380 0.395 0.431 0.700 0.232 0.330 0.134 0.145

Pavement Condition 0.637 0.269 0.006 0.027 −0.032 0.045 0.018 0.022 0.024 0.010

Pavement Roughness −0.007 0.018 −0.002 0.003 0.001 0.005 0.000 0.002 0.001 0.001

Presence of Lighting 2.598* 1.564 −0.180 0.315 −0.645 0.682 −0.813 0.337 −0.283 0.126

Presence of Horizontal

−17.738* 8177.78 −1.404 1.005 −18.823* 6979.17 −1.538 1.004 0.431 0.172

K A B C PDO

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Vertical Curve

Approaching Slope −0.179 0.638 0.109 0.274 78.738* 4871.27 −0.088 0.255 −0.103 0.115

Vertical Curve Leaving

Slope 10.850* 5.899 0.069 0.245 0.367 0.314 −0.194 0.226 −0.132 0.104

Grade −9.878* 5.974 −0.222 0.335 −78.778* 4871.27 0.181 0.299 0.098 0.136

Curvature Degree 0.101 0.030 0.000 0.009 −0.010 0.021 −0.002 0.009 −0.002 0.004

Fit Statistics

AIC 149.84 N/A 1714.8 N/A 827.88 N/A 2015.2 N/A 4742 N/A

BIC 309.704 N/A 1874.67 N/A 987.73 N/A 2175.06 N/A 4901.83 N/A

Table 8. Poisson regression of 500 mi (dataset 8).

Variables

K A B C PDO

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Intercept

−39.721*

9579.61

4 −5.897 0.867 −4.339 1.421 −2.245 0.722 −1.817 0.338

Ln (Length) 1.547 0.565 1.181 0.046 1.180 0.079 1.099 0.042 1.059 0.019

Ln (AADT) 1.474 0.874 0.740 0.064 0.617 0.108 0.409 0.056 0.461 0.025

Shoulder Width

8 ft Base Level

<2 ft

−19.103*

8881.43

5 0.547 0.137 0.691 0.247 0.676 0.141 0.294 0.069

≥2 ft < 4 ft −0.025* 1.219 0.120 0.110 −0.035 0.204 0.595 0.100 0.276 0.046

≥4 ft < 6 ft 0.559* 1.040 −0.074 0.110 0.289 0.181 0.315 0.102 0.244 0.044

≥6 ft < 8 ft −18.713* 5988.73 −0.171 0.127 0.157 0.214 0.127 0.120 0.192 0.051

Lane Width

>>12 ft Base Level

9 ft or less −16.355* 7761.93 0.417 0.193 −0.576 0.359 0.273 0.165 0.148 0.082

9.5 ft–10.5 ft 1.419* 1.179 0.192 0.111 0.019 0.193 0.110 0.103 0.080 0.047

11 ft–11.5 ft −16.400* 26043.6 0.852 0.371 0.652 0.639 −0.032 0.406 0.448 0.170

Speed Limit

45 mph Base Level

25 mph 0.027* 17044.9 0.535 0.220 1.186 0.328 0.955 0.200 0.517 0.093

30 mph −0.899* 21564.7 0.500 0.237 −0.882 0.646 0.129 0.296 −0.089 0.128

35 mph −0.009* 23983.0 0.126 0.356 −0.040 0.633 0.107 0.339 −0.614 0.197

40 mph 19.604* 9579.6 −0.544 0.266 −1.358 0.550 −0.337 0.231 −0.967 0.118

50 mph −0.361* 15763.5 −0.156 0.298 −0.245 0.473 0.066 0.263 0.023 0.106

55 mph 17.779* 9579.6 −0.123 0.160 −0.252 0.264 −0.116 0.157 −0.254 0.064

Roadside Hazard Rating (Zegeer et al. 1988)

3 Base Level

4 0.432* 1.572 −0.080 0.107 0.015 0.183 −0.009 0.101 0.089 0.044

5 1.240* 1.558 −0.052 0.134 0.400 0.236 0.217 0.124 0.129 0.057

6 −0.146* 2.414 −0.251 0.178 0.395 0.312 −0.005 0.162 0.218 0.073

7 −19.523* 10584. 0.146 0.228 0.740 0.436 0.199 0.222 0.103 0.107

Pavement Condition 0.130 0.202 0.015 0.017 −0.012 0.028 −0.019 0.014 0.005 0.007

Pavement Roughness 0.005 0.016 0.002 0.002 −0.006 0.003 0.002 0.002 0.002 0.001

Presence of Lighting 2.760* 1.848 0.071 0.204 −0.022 0.352 −0.139 0.191 −0.642 0.098

K A B C PDO

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Presence of Horizontal

Curve −16.626* 111651 −1.794* 0.710 −13.960* 354.738 −1.578 0.581 0.589 0.093

Vertical Curve

Approaching Slope −4.946* 7532.0 −0.224 0.220 0.147 0.257 0.360 0.176 −0.084 0.085

Vertical Curve Leaving

Slope −16.818* 5489.0 −0.230* 0.194 0.007 0.195 0.120 0.121 −0.117 0.073

Grade 5.606* 7532. 0.258 0.249 0.059 0.297 −0.294 0.201 0.110 0.098

Curvature Degree −0.131* 0.205 −0.001 0.005 0.004 0.008 −0.015 0.007 0.003 0.002

Fit Statistics

AIC 114.54 N/A 3299.6 N/A 1602.2 N/A 3681.8 N/A 9321.9 N/A

BIC 292.598 N/A 3477.65 N/A 1780.27 N/A 3859.90 N/A 9499.99 N/A

Table 9. Poisson regression of 750 mi (dataset 9).

Variables

K A B C PDO

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Intercept −14.361 4.822 −5.176 0.767 −4.568 1.334 −3.863 0.666 −2.368 0.306

Ln (Length) 0.600 0.212 1.071 0.039 1.080 0.072 1.032 0.035 1.033 0.016

Ln (AADT) 0.956 0.303 0.814 0.051 0.432 0.085 0.561 0.042 0.527 0.020

Shoulder Width

8 ft Base Level

<2 ft 0.791* 1.116 0.417 0.162 −0.511 0.434 0.723 0.139 0.193 0.075

≥2 ft < 4 ft −0.187 0.642 0.386 0.094 0.156 0.179 0.561 0.086 0.324 0.040

≥4 ft < 6 ft 1.619 0.503 0.337 0.097 0.299 0.176 0.420 0.090 0.313 0.040

≥6 ft < 8 ft 1.066 0.636 0.088 0.119 0.381 0.197 0.155 0.110 0.160 0.048

Lane Width

>>12 ft Base Level

9 ft or less 0.892 1.323 0.093 0.178 0.341 0.299 −0.204 0.162 0.242 0.071

9.5 ft–10.5 ft 0.684 0.582 0.182 0.095 0.237 0.175 0.094 0.086 0.141 0.040

11 ft–11.5 ft 0.259 1.662 0.279 0.220 0.186 0.440 −0.128 0.213 0.343 0.095

Speed Limit

45 mph Base Level

25 mph 2.458 0.716 0.348 0.180 0.255 0.463 0.420 0.187 0.231 0.089

30 mph −23.593* 62341.13 −0.173 0.232 1.097 0.394 0.688 0.176 0.201 0.097

35 mph 0.119 0.959 0.250 0.216 1.127 0.382 0.236 0.216 −0.237 0.117

40 mph −1.065 1.186 −0.835 0.204 −0.778 0.483 −0.368 0.174 −1.002 0.102

50 mph −21.986* 39201.42 −0.144 0.238 −1.631 1.033 −0.126 0.226 −0.085 0.103

55 mph −0.701 0.819 −0.433 0.124 0.132 0.281 −0.300 0.120 −0.150 0.055

Roadside Hazard Rating (Zegeer et al. 1988)

3 Base Level

4 −22.244* 11618.73 −0.050 0.095 0.083 0.180 −0.020 0.085 0.131 0.039

5 0.792 0.732 0.217 0.121 0.318 0.214 −0.194 0.110 0.148 0.049

6 −1.735 1.522 0.168 0.155 0.207 0.282 0.152 0.130 0.200 0.063

7 0.331 1.635 0.612 0.191 0.228 0.389 −0.063 0.181 0.460 0.081

Pavement Condition 0.119 0.098 −0.018 0.015 −0.004 0.027 −0.010 0.013 0.007 0.006

Pavement Roughness −0.022 0.012 −0.001 0.002 0.000 0.003 0.004 0.001 −0.001 0.001

Presence of Lighting 2.372 1.134 −0.553 0.217 −0.402 0.363 −0.303 0.168 −0.308 0.082

Presence of Horizontal

Curve −21.347* 25841.54 −1.179 0.452 −14.166*

325.46

−2.317 0.708 0.133 0.102

Vertical Curve

Approaching Slope 354.650* 29838.59 0.085 0.160 −0.189 0.226 −0.151 0.124 −0.069 0.069

Vertical Curve Leaving

Slope

0.002 0.644 −0.033 0.130 −0.189 0.207 0.045 0.125 −0.077 0.060

Grade −354.529* 29838.59 0.026 0.188 0.437 0.266 0.113 0.158 0.099 0.082

Curvature Degree 0.024 0.069 0.003 0.012 −0.007 0.022 0.000 0.010 −0.007 0.005

Fit Statistics

AIC 309.14 N/A 3640.7 N/A 3640.7 N/A 4090.2 N/A 9241.9 N/A

BIC 483.52 N/A 3815.08 N/A 3815.08 N/A 4264.59 N/A 9416.28 N/A

APPENDIX C. NEGATIVE BINOMIAL REGRESSION

Table 10 through table 18 contain the model estimation results for negative binomial regression on two-lane, two-way undivided segments for datasets 1 through 9.

Table 10. Negative binomial regression of 150 mi (dataset 1).

Variables

K A B C PDO

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Paramete r

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Intercept −106.430* 736 −3.374 1.926 −6.907 3.976 −4.612 2.196 −0.116 1.084

Ln (Length) 3.253 1.128 0.983 0.085 1.196 0.171 0.911 0.090 0.963 0.046

Ln (AADT) 3.766 2.058 0.487 0.154 0.898 0.332 0.397 0.167 0.334 0.082

Shoulder Width

8 ft Base Level

<2 ft −37.250* 1820 0.822 0.608 −31.793* 9653 0.856 0.694 −0.191 0.462

≥2 ft < 4 ft −2.548 1.921 0.439 0.206 −0.564 0.446 0.379 0.222 0.425 0.118

≥4 ft < 6 ft 1.471 1.458 0.290 0.186 −0.192 0.312 −0.101 0.209 0.193 0.106

≥6 ft < 8 ft −42.294* 48921 0.147 0.228 −0.725 0.450 −0.217 0.247 0.313 0.122

Lane Width

>12 ft Base Level

9 ft or less —

9.5 ft–10.5 ft −32.966* 1043 −0.018 0.471 0.105 0.938 0.141 0.616 0.292 0.257

11 ft–11.5 ft 2.608 2.532 0.091 0.220 0.021 0.410 0.035 0.258 −0.014 0.129

Speed Limit

45 mph Base Level

25 mph −1.004 98319 0.971 0.411 −0.066 0.674 1.011 0.400 0.309 0.205

30 mph −1.288 16325 1.225 0.516 −0.362 0.962 0.706 0.566 −0.128 0.317

35 mph 47.609* 736 0.427 0.702 −29.571* 2759 1.128 0.515 −0.840 0.395

40 mph −5.967* 1180 −0.253 0.599 −1.603 1.150 −1.567 0.827 −0.957 0.308

50 mph 6.154* 13855 −0.103 0.693 1.390 0.807 0.450 0.587 −0.040 0.292

55 mph 37.303* 73637 0.382 0.358 −0.134 0.500 −0.243 0.359 −0.280 0.164

Roadside Hazard Rating (Zegeer et al. 1988)

3 Base Level

4 −0.523 2.044 0.295 0.204 −0.395 0.366 0.103 0.228 0.228 0.113

5 −1.659 2.048 0.392 0.265 0.348 0.472 0.423 0.294 0.206 0.154

K A B C PDO

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Paramete r

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

6 −39.451* 54412 0.043 0.360 −0.401 0.689 0.093 0.373 0.125 0.197

7 3.745* 3.626 −0.459 0.597 −28.674* 16883 0.162 0.560 0.136 0.315

Pavement Condition 0.834 0.691 −0.017 0.031 0.013 0.059 0.037 0.037 −0.011 0.018

Pavement Roughness 0.035 0.035 −0.001 0.004 −0.007 0.009 0.001 0.004 −0.001 0.002

Presence of Lighting −39.846* 80863 0.498 0.375 −28.333* 13142 0.560 0.382 −0.624 0.254

Presence of Horizontal

Curve −33.535* 9359.0 −32.630* 3275306 −30.841* 4138 −1.242 0.762 −0.207 0.266

Vertical Curve

Approaching Slope 2.524* 48274 −0.103 0.444 1.025* 9056 −0.068 0.425 −0.060 0.143

Vertical Curve Leaving

Slope −2.270 50046 −0.271 0.413 −0.304* 98257 −0.044 0.431 0.119 0.159

Grade −21.311* 61599 0.078 0.514 −24.060* 11523 −0.142 0.519 −0.045 0.190

Curvature Degree 0.029 0.039 0.001 0.010 0.011 0.019 0.009 0.008 −0.010 0.007

Fit Statistics

AIC 98.654 N/A 1197.6 N/A 466.05 N/A 1135.5 N/A 2909.5 N/A

BIC 244.411 N/A 1343.33 N/A 611.80 N/A 1281.22 N/A 3055.24 N/A

Overdispersion 0.356 — 2.43 — 4.30 — 1.397 — 1.978 —

Table 11. Negative binomial regression of 300 mi (dataset 2).

Variables

K A B C PDO

Parameter

Estimate Std. Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Intercept −72.159* 4642 −4.967 1.415 −8.814 2.656 −2.299 1.126 −2.867 0.625

Ln (Length) 0.932 0.397 1.179 0.080 1.175 0.141 1.007 0.065 1.054 0.034

Ln (AADT) 0.410 0.533 0.648 0.102 0.379 0.169 0.520 0.084 0.627 0.045

Shoulder Width

8 ft Base Level

<2 ft 21.665* 30679.285 −0.266 0.317 −0.399 0.509 −0.315 0.264 −0.113 0.153

≥2 ft < 4 ft 21.129* 30679.285 −0.437 0.329 −0.468 0.531 −0.477 0.276 −0.164 0.158

≥4 ft < 6 ft 21.000* 30679.285 −0.321 0.328 −0.795 0.548 −0.388 0.274 −0.131 0.158

≥6 ft < 8 ft 19.801* 30679.285 −0.763 0.322 −0.823 0.519 −0.764 0.269 −0.611 0.156

Lane Width

>>12 ft Base Level

9 ft or less 20.254* 1850.0 −0.366 0.273 0.017 0.560 −0.321 0.223 −0.136 0.128

9.5 ft–10.5 ft 19.899* 1850.0 −0.634 0.310 −0.499 0.612 −0.374 0.250 −0.253 0.143

11 ft–11.5 ft 18.822* 1611.0 −24.272* 4701 −31.757* 38745 −23.525* 164053 0.680 1.060

Speed Limit

45 mph Base Level

25 mph 21.899* 2952 0.253 0.515 0.180 1.197 −0.203 0.440 0.288 0.261

30 mph −1.164 5766 −1.609 0.856 1.527 0.909 −0.839 0.515 −0.842 0.327

35 mph −0.112 3798 −0.883 0.441 −0.103 0.840 −1.224 0.394 −0.964 0.222

40 mph −0.920 3819 −0.889 0.404 −0.350 0.800 −0.555 0.314 −0.141 0.188

50 mph −0.041 4061 −0.074 0.408 0.089 0.899 −0.471 0.355 −0.046 0.204

55 mph 20.358* 2955 −0.740 0.323 −0.037 0.671 −0.813 0.263 −0.473 0.160

Roadside Hazard Rating (Zegeer et al. 1988)

3 Base Level

4 −0.413 0.830 0.072 0.171 −0.064 0.307 −0.225 0.142 0.010 0.078

5 −21.990* 11334.468 0.076 0.218 0.042 0.376 −0.036 0.179 −0.055 0.098

6 −22.723* 17061.511 0.196 0.293 −0.388 0.535 −0.239 0.253 0.138 0.127

7 −21.947* 30091.028 0.606 0.397 0.888 0.665 0.038 0.353 0.105 0.193

Pavement

Condition 0.083 0.171 0.051 0.030 0.155 0.058 0.004 0.024 0.018 0.013

Pavement

Roughness 0.023 0.019 0.000 0.003 0.001 0.005 0.002 0.003 0.003 0.001

K A B C PDO

Parameter

Estimate Std. Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Presence of

Lighting −0.407 23536 −0.714 0.374 −0.232 0.606 −0.430 0.309 −0.603 0.152

Presence of

Horizontal Curve −18.759* 2673 −0.295 0.632 −31.899* 65480 −1.719 1.020 0.295 0.206

Vertical Curve

Approaching Slope −0.819 1605 −0.400 0.254 0.060 0.280 −0.117 0.193 −0.043 0.092

Vertical Curve

Leaving Slope −17.139* 1156 −0.444 0.229 0.411 0.327 −0.008 0.193 −0.002 0.085

Grade 0.992* 16045 0.654 0.291 −0.138 0.406 0.122 0.245 0.112 0.114

Curvature Degree −0.099 0.129 0.004 0.007 −0.047 0.030 0.001 0.007 0.002 0.003

Fit Statistics

AIC 155.31 N/A 1916.5 N/A 836.23 N/A 2238.1 N/A 5603.7 N/A

BIC 326.773 N/A 2087.9 N/A 1007.6 N/A 2409.55 N/A 5775.14 N/A

Overdispersion 102 — 0.910 — 0.457 — 2.183 — 2.158 —

Table 12. Negative binomial regression of 500 mi (dataset 3).

Variables

K A B C PDO

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Parameter

Estimate

Std.

Error

Intercept −12.122* 6.385 −7.907 1.048 −2.428 1.570 −3.551 0.860 −1.760 0.449

Ln (Length) 1.071 0.323 1.007 0.055 1.134 0.101 1.008 0.049 1.022 0.026

Ln (AADT) 0.762 0.470…