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This is to certify that the
dissertation entitled

An Investigation of the Underlying Assumptions of
Quasi-Induced Exposure

presented by

Xinguo Jiang

has been accepted towards fulfillment
of the requirements for the

PhD. degree in Civil & Environmental
Engineerigg

 

glam/WA 64v 9. 4/99)

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(/7 %
Date

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2/05 c:/ClRC/DateDue.indd-p.15

 

AN INVESTIGATION OF THE UNDERLYING ASSUMPTIONS OF QUASI-
INDUCED EXPOSURE

Xinguo J iang

A DISSERTATION

Submitted to
Michigan State University
in partial fitlfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Civil and Environmental Engineering

2005

ABSTRACT

AN INVESTIGATION OF THE UNDERLYING ASSUMPTIONS OF QUASI-
INDUCED EXPOSURE

By

Xinguo Jiang

Traditionally, the measures of exposure fall into two general categories: direct and
indirect. The former includes vehicle miles traveled (VMT), number of entering vehicles
(N EV) for an intersection, and annual daily traffic (ADT). Indirect exposure is normally
referred to as induced exposure. VMT is the most commonly used exposure measure in
traffic safety/crash related analyses. However, VMT as an exposure measurement has
also aroused criticism among traffic researchers: the underlying assumptions of VMT-
based methods have been challenged. In addition, the use of VMT confronts two
fundamental drawbacks in practical applications: general availability of data and finer
disaggregation of exposure.

Quasi-induced exposure, an approach to estimate relative exposure, is capable of
overcoming those difficulties confronted by the VMT method. Quasi-induced exposure
has been employed by a number of traffic researchers and has demonstrated its strength
in a variety of practical applications. For example, it is relatively easy to use;
incorporated accident data are generally available; it is able to measure the exposure of a
specific driver cohort under specific conditions (e.g., young male on Friday night on local
streets). However, the theory of quasi-induced exposure is far fiom being perfect. A set
of issues needs to be addressed: 1) there is a lack of a systematic procedure to prepare

accident data; 2) there are problems involved with the responsibility assigning scheme; 3)

more importantly, there are few attempts to validate the underlying assumption: non-
responsible drivers in two-vehicle accidents constitute a random sample of driving
population on the road.

Two techniques have been developed to validate the underlying assumption: 1) to
compare the relative exposure derived fiom accident data using quasi-induced exposure
with the “true” exposure collected from other sources, such as VMT data, seat belt use
data, and truck volume data; 2) to compare the distributions for non-responsible drivers
derived from two-vehicle and three-or-more-vehicle accidents.

By means of addressing these three stated issues, this research aims to develop a
guideline with regard to when to, or not to, use the quasi-induced exposure technique,
and to provide a systematic procedure to manipulate accident data and assign accident

faults if the validity of quasi-induced exposure is ensured.

ACKNOWLEDGMENTS

When I am moving toward the finish line of my Ph.D research, I look back on the
several years at Michigan State University and I feel grateful to a number of people who
contributed their efforts in accomplishing this work.

I would like to express my gratitude to my academic advisor Dr. Richard W.
Lyles for his encouragement, stemness, inspiration, and persistent tutoring. I truly feel
indebted—his support to me has gone beyond the relationship between an advisor and a
student.

I would like to thank Dr. William C. Taylor for his thoughts, comments, and
suggestions in the course of this research. I feel thankful, because I can’t remember how
many times I bugged him by knocking at his door for answers. In the meanwhile, I would
like to thank the other two committee members, Dr. Karim Chatti and Dr. Dennis C.
Gilliland, for serving in my doctoral committee and for their helpfiil comments and
suggestions.

Last, I would like to thank my wife, Fenghua Lin, for her constant support and for
her loving, caring, and understanding, and to my parents for their unconditioned love and

sacrifice from the other side of the Pacific Ocean.

iv

TABLE OF CONTENTS

LIST OF TABLES .................................................................................. vii
LIST OF FIGURES ................................................................................. xi
Chapter 1 INTRODUCTION .............................................................................................. 1
Chapter 2 LITERATURE REVIEW .................................................................................... 5
2.1 Introduction ................................................................................................................ 5
2.2 Accident data ............................................................................................................. 6
2.2.1 Underreporting or incomplete observations ....................................................... 7
2.2.2 Inaccuracy of data ............................................................................................. 10
2.2.3 Inconsistency of reporting ................................................................................ 12
2.2.4 Summary ........................................................................................................... 13
2.3 Accident rates and exposure .................................................................................... 14
2.3.1 Definition of exposure ...................................................................................... 16
2.3.2 Group exposure ................................................................................................. 17
2.3.3 Related issues .................................................................................................... 23
2.4 Induced exposure ..................................................................................................... 25
2.4.1 Definition of induced exposure ........................................................................ 26
2.4.2 Quasi-induced exposure .................................................................................... 30
2.5 Summary .................................................................................................................. 44
Chapter 3 PROBLEM STATEMENT ............................................................................... 46
3.1 Development of systematic rules for preparing accident data ................................. 49
3.2 Validation of assumptions ....................................................................................... 53
3.3 Summary of problems .............................................................................................. 55
Chapter 4 SYSTEMATIC RULES FOR PREPARING ACCIDENT DATA ................... 56
4.1 Identification and elimination of bad data ............................................................... 57
4.2 Responsibility assignment ....................................................................................... 66
4.2.1 Assigning responsibility ................................................................................... 66
4.2.2 Accident data recorded by different police agencies ........................................ 72
4.3 Conclusion ............................................................................................................... 75
Chapter 5 VALIDATION OF THE ASSUMPTIONS OF QUASI-INDUCED
EXPOSURE ....................................................................................................................... 78
5.1 Validation using vehicle miles of travel data .......................................................... 80
5.1.1 Introduction ....................................................................................................... 80
5.1.2 Methodology ..................................................................................................... 82
5.1.3 Highway safety information system (HSIS) ..................................................... 82
5.1.4 Manipulation of H818 data ............................................................................... 84

5.1.5 National household travel survey (N HTS) ....................................................... 87

5.1.6 Average annual vehicle miles traveled ............................................................. 88
5.1.7 D2 distributions ................................................................................................ 93
5.1.8 Comparison of D2 and VMT estimations ......................................................... 96
5.1.9 Conclusion ........................................................................................................ 98
5.2 Validation using safety-belt use data ....................................................................... 99
5.2.1 Introduction ....................................................................................................... 99
5.2.2 Methodology ................................................................................................... 100
5.2.3 Preparation of safety-belt data ........................................................................ 101
5.2.4 Discussion of variables used ........................................................................... 104
5.2.5 Comparison of safety-belt and D2 data .......................................................... 107
5.2.6 Conclusion ...................................................................................................... 116
5.3 Validation using truck volume data (W -2) ............................................................ 1 17
5.3.1 Introduction ..................................................................................................... 117
5.3.2 Methodology ................................................................................................... 118
5.3.3 Comparison of W-2 and D2 data .................................................................... 123
5.3.4 Conclusion ...................................................................................................... 126
Chapter 6 VALIDATION USING THREE-OR-MORE-VEHICLE ACCIDENTS ....... 128
6.1 Introduction ............................................................................................................ 128
6.2 Methodology .......................................................................................................... 130
6.3 Characteristics of three-or-more-vehicle accidents ............................................... 131
6.4 Comparing D23 between two- and three-or-more-vehicle accidents .................... 137
6.5 Conclusion ............................................................................................................. 145
Chapter 7 MEASURING EXPOSURE CHAN GE—MICHIGAN GRADUATED
DRIVER LICENSING .................................................................................................... 147
7.] Michigan graduated driver licensing (GDL) ......................................................... 147
7.2 Affected young drivers and program in-effect years ............................................. 149
7.3 Exposure data analysis ........................................................................................... 151
7.4 Summary ................................................................................................................ 156
Chapter 8 DIFFICULTIES WITH QUASI-INDUCED EXPOSURE ............................. 158
Chapter 9 CONCLUSIONS ............................................................................................. 166
APPENDIX A .................................................................................................................. 174
APPENDIX B .................................................................................................................. 178
APPENDIX C .................................................................................................................. 180
BIBLIOGRAPHY ............................................................................................................ 183

vi

LIST OF TABLES

Table 2.1. D1—D2 matrix used in quasi-induced exposure .................................. 32
Table 2.2. Comparison of induced exposure and quasi-induced exposure ................ 33
Table 2.3 Actual distributions of D13 and D28 for pickups and standard auto on I-94.. 36
Table 2.4. General guidelines to use or not use quasi-induced exposure .................. 42
Table 3.1. Potential cause and description of errors in accident data ...................... 50

Table 4.1. Frequencies and percentages of drinking drivers in two-vehicle accidents. 59

Table 4.2. Cross-tabulation between hazardous action and violation indication ......... 60
Table 4.3. Percentage and frequency ofhit and run crash . 62
Table 4.4. Frequencies and percentage of unusual driver ages ............................. 62
Table 4.5. Accident types, frequencies, and percentages on I-94 ........................... 64
Table 4.6. The number of accidents and the percentages left after each step. . .. . . 66
Table 4.7. Coding menu and the frequency of different hazardous actions (first

driver) .............................................................................................. 68
Table 4.8. Cross-tabulation between hazardous action and violation indication ......... 69
Table 4.9. Crosstabulation of responsibility and violation indication (first driver). . 74
Table 4.10. Crosstabulation of responsibility and violation indicator (second

driver) .............................................................................................. 74
Table 4.1 1. Crosstabulation of responsibility and violation indicator (third

driver) ............................................................................................... 74
Table 4.12. Inconsistent and total accidents by different police agencies ................. 7 5
Table 5.1.1. Sample data fi'om Utah accident file (2000) .................................... 3 5
Table 5.1.2. Sample data from Utah vehicle file (2000) ...................................... 86

vii

Table 5.1.3. Desirable data format for a typical HSIS data record ......................... 87

Table 5.1.4. Total AVMT and percentages disaggregated by age group (MI). . . . . .. 90
Table 5.1.5. Total AVMT and percentages disaggregated by gender (MI) ............... 91
Table 5.1.6. Total AVMT and percentages disaggregated by age group (UT). . .. . 91
Table 5.1.7. Total AVMT and percentages disaggregated by gender (UT). . . . . 91
Table 5.1.8. Total AVMT and percentages disaggregated by age group (CA). . . . . 92
Table 5.1.9. Total AVMT and percentages disaggregated by gender (CA). . . . . . .. 92
Table 5.1.10. D2 gender distributions for Michigan data (2001) ........................... 94
Table 5.1.11. D2 age distributions for Michigan accident data (2001). 95
Table 5.1.12. D2 gender distributions for CA & UT data (2001) .......................... 95
Table 5.1.13. D2 age distributions for CA & UT data (2001) .............................. 95
Table 5.1.14. Gender percentage difference (VMT-D2) among different states. . . 96
Table 5.1.15. Age percentage difference (VMT-D2) among different states. . . . . . 97
Table 5.1.16. Summary of chi-square statistics and p-values ............................... 97
Table 5.2.1. Sample of survey site list ......................................................... 101
Table 5.2.2. Stratification scheme in seat belt study ......................................... 102
Table 5.2.3. Coding of site description form—1998, 2000 ................................. 102
Table 5.2.4. Coding of observation data—1998, 2001 ........................................ 103
Table 5.2.5. Coding of resultant data—1998, 2001 ........................................... 104
Table 5.2.6. Vehicle type in Michigan accident data (2001) ................................ 106
Table 5.2.7. Descriptive statistics for the 168 observation sites (2001). . . . . . . . . . . . 107
Table 5.2.8. Safety-belt versus D2 distributions for statewide ............................. 108

Table 5.2.9. Summary of chi-square statistics and p-values (safety-belt versus D2

viii

data) ................................................................................................ 1 08

Table 5.2.10. Safety-belt versus D2 distributions statewide—intersection ............... 109
Table 5.2.11. Safety-belt versus D2 distributions for stratum 1 ........................... 111
Table 5.2.12. Safety-belt versus D2 distributions for stratum 2 ........................... 111
Table 5.2.13. Safety-belt versus D2 distributions for stratum 3 ........................... 112
Table 5.2.14. Safety-belt versus D2 distributions for stratum 4 ........................... 1 12

Table 5.2.15. Summary of operational and statistical significances for each stratum... 112

Table 5.2.16. The distributions for passenger cars at different levels ...................... 114
Table 5.2.17. The distributions for the age group (30-59) at the different levels. 115
Table 5.3.1 FHWA vehicle class ............................................................... 119
Table 5.3.2. Vehicle type in Michigan accident data (2001) ............................... 1 19
Table 5.3.3. Comparing vehicle type distributions between D23 and W-2

(frequencies) ...................................................................................... 1 23
Table 5.3.4. Comparing vehicle type distributions between D23 and W-2

(percentages) ..................................................................................... 123
Table 5.3.5. Chi-square statistics and p-values ............................................... 124
Table 5.3.6. Vehicle type distributions between D23 and W-2 (regrouped) ............. 1 2 5
Table 5.3.7. Chi-square statistics and p-values (regrouped) ............................... 1 2 5
Table 5.3.8. Summary of statistical and operational significances ........................ 125
Table 5.3.9. Vehicle type distributions for I-94 and [-75 (2001-2003) .................. 126
Table 6.1. Percentages of accidents by three major locations (%) ......................... 132
Table 6.2. Percentages of accident by 10 major hours (%) ................................. 133
Table 6.3. Percentages of accidents by three major accident types (%). . . . . . . . 133

Table 6.4. Percentages of accidents at different speed limits (%) ......................... 134

ix

Table 6.5. Characteristics of D23 under two defined circumstances ...................... 136
Table 6.6. Chi-square statistics and p-values for three key characteristics ............... 136
Table 6.7. Comparison of D2 distributions for three key characteristics (CA, 2000)... 138
Table 6.8. Comparing distributions for three key characteristics (CA, 2000) ........... 139
Table 6.9. Comparison of D2 distributions for three key characteristics (ME, 2000)... 141
Table 6.10. Comparing distributions for three key characteristics (ME, 2000) ......... 142

Table 6.11. Comparison of D2 distributions for three key characteristics (MI, 2000).. 143

Table 6.12. Comparing distributions for three key characteristics (MI, 2000) ........... 144
Table 6.13. Comparison of D2 distributions for three key characteristics (UT,

2000) ............................................................................................... 144
Table 6.14. Comparing distributions for three key characteristics (UT, 2000) ........... 145
Table 7.1. The frequencies of non-responsible drivers by age (midnight-5am) .......... 151
Table 7.2. Average D23 before and after the GDL and changes (midnight-5am). . . . . 152
Table 7 .3. The percentages of non-responsible drivers (midnight-5am) ................... 153
Table 7.4. The fi'equencies of responsible drivers (midnight-5am) ......................... 154
Table 8.1. D13, D23, and IRs for fast- and slow-moving vehicles .......................... 163
Table B. 1. Seat-belt versus D2 distributions for stratum l—intersection ................ 173
Table B.2. Seat-belt versus D2 distributions for stratum 2—intersection ................ 178
Table 8.3. Seat-belt versus D2 distributions for stratum 3—intersection ................ 179
Table 3.4. Seat-belt versus D2 distributions for stratum 4—intersection ................ 179
Table C. l. Seat-belt versus D2 distributions for county—male drivers .................. 130
Table C.2. Seat-belt versus D2 distributions for county—age .............................. 131
Table C.3. Seat-belt versus D2 distributions for county—passenger car .................. 182

LIST OF FIGURES

Figure 2.1. A nonlinearity relationship between accident fiequency and exposure... 23

Figure 3.1. Exposure data sources comparable with accident data ...................... 54
Figure 4.1. Flow chart of identifying and/or eliminating bad data ....................... 65
Figure 5.1 . 1. Flow chart of manipulating Utah accident data ............................ 86
Figure 5.1.2. The process to derive average AVMT ....................................... 89
Figure 5.2.]. Sample data case in the resultant data file .................................. 104

Figure 5.3.1. Illustration of stations and major intersecting roads on 1-94 in
Michigan ......................................................................................... 122

Figure 7.1. Demonstration of different ages affected by the restricted nighttime
driving ............................................................................................. 150

Figure 7.2. The D2 percentages of the 16-year-old drivers (time-of-day
distribution) ..................................................................................... 1 5 5

Figure 8.1. D1 and D2 for passenger cars and trucks under two scenarios. . . . . 160

xi

Chapter 1

INTRODUCTION

A wide range of topics has been discussed in the context of measuring roadway
safety and/or accident risk. These include accident frequencies, accident rates, exposure,
induced exposure, and quasi-induced exposure. The analysis of accident frequency can
provide valuable insights into some highway safety problems and the effectiveness of
certain traffic countermeasures (typically in before-and-after studies). However, the
problem with using accident fiequency in traffic safety analysis is the implicit assumption
that there is no significant change of accident exposure during the analysis period.
Recognizing this limitation, traffic engineers have also been interested in knowing the
“exposure” of different driver-vehicle combinations to different driving hazards, in
addition to the frequency of accidents involving these different driver-vehicle
combinations. In this context, accident rates are generally expressed as the ratio of
accident frequency to exposure. Thus, quantification of exposure is of great importance—
it provides researchers an opportunity to make normalized comparisons between driver
groups and to accurately represent the circumstances where and/or when accidents occur.
Unfortunately, quantification of exposure, while conceptually straightforward, is difficult
in practice.

Traditionally, the measures of exposure fall into two general categories: direct and

indirect. The former includes vehicle miles traveled (VMT), number of entering vehicles

(N EV) for an intersection, and annual daily traffic (ADT). Indirect exposure is normally
referred to as induced exposure.

VMT is the most commonly used exposure measure in traffic safety/crash related
analyses. However, VMT as an exposure measurement has been criticized in some
instances. For example, Steward (1960) challenged one of the assumptions that all
driving involved the same exposure to accident hazards, by giving an example that “when
vehicles travel in a platoon at an identical speed, the leading vehicle might experience
more driving hazards than the following vehicles.” In addition, the use of VMT has two
fundamental drawbacks in practical applications: general availability of data and finer
disaggregation of exposure (Lighthizer 1989, Lyles et a1. 1991). More specifically,
general availability of data refers to the fact that computation of VMT for a driving
cohort requires traffic volume and travel distance data. Unfortunately, under most
circumstances such data are not readily available. It is virtually impossible to calculate
VMT for a specific driving cohort, disaggregated by specified spatial and temporal
parameters, e. g., young drivers on local highways on Friday nights.

In light of the theoretical and operational problems involved in using VMT,
researchers developed an alternative approach to estimate relative exposure to accidents
by using the accident statistics themselves, namely, induced exposure. Since accident
data are more readily available, exposure can be directly estimated without requiring
additional information (e.g., volume data, travel distance), which is necessary for VMT-
based methods. Another desirable attribute of induced exposure is the capability of
disaggregating exposure by specific variables of interest—cg, roadway type, on driver

age. In 1964, Thorpe developed the idea of induced exposure. However, induced

exposure theory was found to have some problems, especially in the scheme for assigning
responsibility for the accident. Haight (1971) modified Thorpe’s original work and
supplemented it with a systematic responsibility-assignment scheme. The revised method
is defined as “quasi-induced exposure.”

The basis of quasi-induced exposure is founded of two fundamental assumptions
(Lyles 1994):

1. In at least some two-vehicle accidents there is an at-fault and a not-at-fault driver.
2. Not-at-fault drivers in two-vehicle accidents are a random sample of motorists
and vehicles on the road at the time of the accident.

For the first assumption, quasi-induced exposure requires the utilization of only
two-vehicle accident data with one at-fault or responsible driver and one not-at-fault or
non-responsible driver. Accident responsibility for causation is typically assigned to one
of the drivers in a two-vehicle accident based on a police accident report (e.g., Carr 1969,
Hall 1970, and Carlson 1970). The driver-vehicle combination that is responsible for the
accident is defined as Driver-l or D1. Consistent with the above, the not-at-fault driver-
vehicle combination is defined as Driver-2 or D2. The second assumption can be
rephrased based on the terms defined: D23 are randomly “selected” by D 1 s from all
vehicles existing on the system at the time of the accident and, thus, D23 constitute a
random sample of driver-vehicle combinations and, inductively, a measure of exposure
(Lyles 1994).

Quasi-induced exposure can’t be used with confidence unless these two
assumptions have been shown to be reasonable. In this context, the research effort here

focuses on validating the firndamental premises of quasi-induced exposure from

empirical and theoretical perspectives. It incorporates 1) use of different sources of data,
serving as accident exposure “truth,” to compare with the relative exposure estimated
using the quasi-induced approach and 2) comparison of D2 distributions between three-
or-more-vehicle accidents and two-vehicle accidents. Other goals of this research are to
address several issues relevant to quasi-induced exposure on the condition that the
exposure technique is useful: developing systematic rules for preparing accident data,
assigning responsibility, and exploring its theoretical difficulties.

The next chapter is a literature review covering topics related to quasi-induced

exposure.

Chapter 2

LITERATURE REVIEW

2.1 Introduction

Under the general subject of traffic safety, considerable work has been done on
the measurement of safety and/or accident risk. This includes accident frequencies, and
rates as well as exposure, induced exposure, and quasi-induced exposure. The research
effort here is on quasi-induced exposure. The particular concern lies in how to validate
the underlying assumptions of this technique. The definition of an accident rate is the
ratio of accident fi'equency to accident exposure. Rates can be calculated for a road
section, a set of intersections of the same type, a group of vehicles having some common
features, an age cohort of drivers or some other combination of driver, vehicle, and/or
environmental features. The numerator of the ratio can be straightforwardly expressed as
accident frequency or the number of accidents. The denominator can be expressed in
several ways, including direct measures such as VMT, NEV for an intersection, vehicle
registration, and ADT, and indirect measures using induced or quasi-induced exposure.
Comparison of different exposure methods employed under different circumstances will
illustrate the strength and weakness of quasi-induced exposure. In order to investigate
quasi-induced exposure related issues, it is first necessary to understand the inherent

problems with traditional accident frequencies, accident rates, and measures of exposure.

There are three main topics to be explored here: accident data, accident rates and
exposure, and induced exposure.
2.2 Accident data

Accident data are utilized by traffic engineers and researchers to plan, establish,
and evaluate safety programs in general. The interpretation of such data may lead to a
better understanding of operational problems, be of assistance in devising
countermeasures for those problems, and, in many cases, allow the evaluation of the
effectiveness of countermeasure programs. Certainly, not all safety-related decisions are
based solely on accident data, but high reliability in both the quality and the quantity of
accident data is important. The quality of accident data refers to the accuracy, timeliness,
and completeness of the data used to address traffic problems. Quality of accident data

was defined by O’Day (1993, pp. 1):

o Completeness of coverage (ascertainment)—the degree to which the data
collection system contains all cases defined by the data collection threshold;

0 Consistency of coverage—whether the degree of ascertainment varies by
jurisdiction, time, personal characteristics, weather, or other factors;

0 Missing data—in addition to the problem of missing cases, there may be missing
data elements for cases that are reported;

0 Consistency of interpretation—whether the report elements are reported in the
same manner in different states or local jurisdictions, or by different reporting
officers;

The right data—another aspect of quality is having the right data elements;
Appropriate level of detail—this depends on the variable and on the questions
asked;

0 Correct entry procedures—all of the above factors may be compromised or
enhanced by the treatment of the data at the point of entering it into the computer;
and

0 Freedom from response error—when something was measured, was it measured
correctly?

The literature pertaining to these components is presented in the next section and
is divided into three main sub-sections: underreporting, inaccuracy of data, and
inconsistency of reporting.

2.2.1 Underreporting or incomplete observations

Underreporting refers to accidents that should have been investigated but for
which no data were collected or accidents that have been investigated but for which no
data were recorded. The data for these accidents are simply not available. Incomplete
observation refers to accidents that have been investigated but for which incomplete data
were recorded. If there are incomplete data in the dataset, the measure of interest (e. g.,
exposure of older drivers at night) may be biased because the proportion in the
incomplete or underreported data (which are unavailable) could potentially be different
from those data which are available.

In 1971, Scott and Carroll reviewed the state of completeness of accident data in
several states. They indicated that reporting completeness, which excluded missing whole
accidents and incomplete accidents, was 48 percent in Washington DC, 32 percent in
Maryland, and 30 percent in Virginia. Chipman (1983) tested the accuracy of reports on
fatal motor vehicle crashes by comparing vital statistics for Canadian provinces and
territories with police-reported traffic fatalities. She discovered that counts of police-
reported deaths were larger than the vital statistics source indicated—in one year as large
as 7 percent difference for the entire country (434 deaths). She concluded that 7 percent
underreporting or misclassification in such a statistic was unacceptable for many research

applications.

With the concern for reporting completeness recognized, researchers attempted to
determine the factors that affected the inclination to report an accident. Hauer and
Hakkert (1988) discussed 14 studies of underreporting of accidents published fiom 1971
to 1985. It seemed evident that fatal accidents were reported more fully than serious
injury accidents and that the coverage of the latter was, in turn, better than that for slight
injuries. They found, on average, police records missed 20 percent of injuries that
required hospitalization and up to half of the injuries that did not. In addition, the
probability of reporting an injury sustained in a motor vehicle accident increased with the
age of the injured person. For young children it was 20 to 30 percent, and for persons
over 60 it was around 70% (Hautzinger et al., 1985). Another factor is the number of
vehicles involved. In a report by Smith (1966), the reporting percentage for property-
damage-only (PDQ) in single-vehicle accidents was 57%; in multi-vehicle accidents the
corresponding percentage was 96%. It is also believed that underreporting is more serious
in large cities where the police are overloaded and not able to take the time required for
full reporting (O’Day 1993). In Detroit, for example, police officials announced in the
early 19703 that they would investigate accidents only when they were needed at the site.
In this context, PDO accidents are likely to be severely under-reported.

O’Day (1993) argued that it was improper to simply assume that missing data
were not biased with respect to the acquired data. It is probably better to assume the
opposite. Typical examples are inclement weather and fatal accident reporting (O’Day
1993, pp. 3):

0 During periods of inclement weather it is often not possible for the available

police to attend accidents, so that higher underreporting is associated with
weather.

o It is difficult for police officers to get all accident participants for interview when
serious crashes happen in which some occupants have been transported to a
hospital. The likelihood of injury increases with age, so that age information
might be more likely to be missing for older persons.

Another important factor in underreporting is the minimum threshold in accident
reporting (Willis 1983). A minimum threshold is a criterion established by law for
accident reporting and processing which mandates the reporting of accident only when a
specified amount of property damage is reached. It is used to prevent the flooding of
accident files with data on minor (often insignificant) collisions. Nevertheless, McKnight
(1981) argued that accident statistics must include all the accidents that occur. The reason
is: “minimum thresholds of property damage and injury are used in all accident reporting
systems to keep the system from being swamped with statistics on minor accidents that
would be of no real benefit to the practitioner or scientist.” For example, traffic engineers
will not know the characteristics of involved drivers in the accidents below the minimum
threshold. Thus, they not only are unable to identify whether certain driver cohort will be
prone to get involved in accidents below the minimum threshold, but underestimate the
total number of accidents for those drivers.

In summary, past research has indicated that underreporting and incomplete data
are two common problems in reporting and/or recording accidents. Past research has also
demonstrated that a variety of factors contribute to these problems: weather conditions,
severity of accidents, minimum threshold limitations, availability of police, and size
limitations of the accident reporting system. Therefore, it is important to assess
completeness of accident data by taking the aforementioned factors into consideration

before they are used for traffic safety related analysis. For the example of availability of

police, if special attention is given to the accidents occurring in the Detroit area or a

bigger region containing this area, it is necessary to know what accidents are frequently
underreported through either field investigations or questionnaire surveys.
2.2.2 Inaccuracy of data

The problem of underreporting is compounded by a variety of inaccuracies and
errors that creep into the eventual computerized records of the accident. Inaccuracy of
data refers to elements (of a crash) that have been recorded but with unreasonable,
unknown, or biased values for various parameters in the accident reports. Identification of
some accident inaccuracies can be achieved by comparing the police accident reports
with some external sources (like hospital reports).

In the United States, traffic accidents are usually investigated by police ofiicers
who complete a standard form designed and promulgated by a state agency. Therefore,
the quality of accident data depends at least on the performance of the police
investigators and those reviewing the data and entering them into computers. McKnight
(1981) pointed out that few police had enough training in accident reconstruction to
determine what really happened and those that had the training often lacked the time
necessary to gather and analyze the available data. Shiner et al. (1983) compared police
records of 124 accidents with detailed information collected by multidisciplinary accident
investigation teams (assumed to be correct). It was found that the police data were the
most reliable for the following six variables: location, date, day of week, and numbers of
drivers, passengers and vehicles in each accident. However, the police reports analyzed
provided very little information regarding the presence of driver factors, human
conditions, and vehicular and environmental/roadway factors and deficiencies.

Hautzinger et a1. (1985) also found inaccuracies in the reporting of accident type and

10

vehicle maneuver in 5% to 16% of the cases. Seemingly, the most conspicuous reason for
the inaccuracy in reporting is the inconsistency and insufficiency of police training.
Inaccuracy of reporting accident location is another aspect of inaccurate accident
data. Zegeer (1982) estimated the accuracy of accident location in Alabama, California,
Michigan, and Illinois. Based on a questionnaire, Zegeer (1982, pp. 2) concluded that:
A sizable portion (10 to 30 percent) of accidents cannot be located due to obvious
locational coding errors or omission of location referencing information.
Inaccuracy and incompleteness of the location descriptions problems arise

because many police agencies are understaffed and must attend to other police
duties, and thus accident report accuracy may not have a high priority.

An F HW A report (1997) recommended that all states be able to identify accident
locations to the nearest 0.1mile in rural areas and 100 feet in urban area. The report also
mentioned that police officers did not generally have portable computing devices
available to guide and facilitate data collection, thus limiting quality and productivity.
This is a problem of major importance, since the location is the principal mean for
linkage to other spatial data (e.g., roadway inventory). Carreker et a1. (2000) attempted to
assess the accuracy of the existing accident location system of the Georgia DOT (GDOT)
through a comparison of the locations of crashes based on the original crash reports and
the locations chosen by GDOT using the route and mile number system. Three types of
errors were identified that might have prevented the route and mile system from
accurately locating the crash sites (Carreker et al. 2000, pp. 2):

Type 1: route and mile numbers are incorrect, 37%;
Type 2: location is in the correct vicinity but not the correct location-the mile
number is incorrect, 23%; and

0 Type 3: invalid route number, mile number or road name, 12%.

In short, typical inaccuracy in reporting accident data includes miscoding of

driver gender, age, vehicle type, road conditions, severity of accident, and accident

11

location. This is due to the limitation of data collection tools, capability of the
investigating police officers, insufficiency of police training, and/or data inputting errors.
2.2.3 Inconsistency of reporting

Inconsistency of reporting refers to the phenomenon where accident data are
recorded, reported, or investigated in an inconsistent manner. For the same or very
similar accident facts, different state, county, or police officers have different perceptions
and definitions and, consequently, the same facts might be reflected in different ways in
accident reports. Particularly, inconsistency of reporting becomes crucial when the
attempt is made to combine and compare accident datasets from different data sources
(typically, different jurisdictions). It is not much value to use a database containing
inconsistently reported accident data, since the results might be biased, conflicting or
even erroneous.

O’Day (1993) pointed out that inconsistency existed in categorizing vehicle type
between different states or local jurisdictions. For example, one state might group pickup
trucks and small vans in a single category in accident data while another might use
separate categories for such vehicles. In the same report, O’Day also mentioned the
inconsistent identification of vehicle defects as the cause of accidents. One state might
utilize specific variables in the report to identify defective vehicles, such as tires, brakes,
steering, or lights, while another state records such information only in the narrative of
the report.

Another inconsistency problem is in reporting injury severity (O’Day 1993). The
majority of states record injury on a five-point scale often referred to as the KABCO

scale: K is “person with fatal injury,” A is “person with incapacitating injury,” B is

12

“person with non-incapacitating evident injury,” C is “person with possible injury,” and O
is “no injury.” Statistics from 23 states (1988-1990) showed that California reported only
4.9% (“A”) injuries while Illinois reported up to 23.8%. It does not seem likely that these
apparent differences in accident severity are real. Obviously, inconsistency in accident
severity definition between states is a contributing factor to this variation. Therefore, the
inconsistency of definitions of accident severity limits the development of meaningful
studies across states and prevents integration of accident data from various states.

In summary, the literature review contains three examples of inconsistent
reporting problems existing in state accident reports—different definitions of defective
vehicles, injury severity, and accident location. It illustrates the point that fusion of
accident data from different states will be a problem and, thus, developing traffic safety
studies with the use of such data should be done with caution. Furthermore, the review of
literature also revealed that no past research explored the issue of combining different
accident data from different police agencies within the same state. A later section will
address this concern.

2.2.4 Summary

To summarize the discussion of accident data quality, the issues are not whether
accident data are useful for evaluating highway safety problem nor is it argued that the
use of accident data in traffic safety analysis should be abandoned. Rather, the concerns
are with identifying those aspects of accident data that should be examined during the
process of manipulating and using accident data. The goal is to improve their reliability
and quality in order to develop more dependable and practical solutions to real-world

traffic problems.

13

2.3 Accident rates and exposure

The advantage of using accident rates and exposure in safety analysis versus
accident frequencies lies in the ability to explicitly consider the driving exposure where
accident data were collected. In this sense, high-quality accident data are necessary for a
safety analysis, but not necessarily sufficient.

The definition of an accident rate is the ratio of accident frequency to some
measure of accident exposure. Accident frequency generally refers to the number of
accidents for a driver group, vehicle group, or driver-vehicle combination. Accident
exposure refers to the measurement of total driving hazards that the particular driver-
vehicle combination confronts when it is on the road. Accident frequency can be used for
relatively simple safety analysis, often before-after analysis, to examine the effectiveness
of certain safety countermeasures. As pointed out by Lyles et al. (1993), although 1
accident frequency is useful in certain situations, the problem with using it is the lack of
consideration of opportunity for accidents to occur, for instance, it is seldom recognized
that higher traffic volume alone may lead to a difference in the fi'equency of accidents. A
common problem associated with many before-afier analyses is that it assumes that the
traffic countermeasure is the only contributing factor of the change in the magnitude of
accidents, or simply traffic and road conditions remain the same.

Accident rates, on the other hand, include consideration of a measure of the
opportunity for accidents to occur. Comparison of accident rates can assist road safety
researchers in developing safety countermeasures in ways that comparison of absolute
frequencies of accidents can not. Inherent in the concept of exposure is the idea of using

exposure data to determine accident rates which indicate the relative degree of risk or

14

danger of various road traffic situations (situations broadly include all relevant vehicle,
person, and environmental characteristics). When the discussion of accident frequency is
combined with accident exposure, it has more flexibility and capability for use in
evaluating an operational intervention, identifying potential traffic problems, and making
traffic safety policy. Seemingly, the introduction of accident exposure in safety analysis
makes a fundamental difference. The distinction is recognized in a discussion by Jovanis
et al. (1991, pp. 2):

Not considering the amount of exposure means that consideration is only given to

the characteristics of the accidents that have occurred, not the road and traffic

conditions of driving during which accidents have not occurred.

That is, safety analysis without the inclusion of accident exposure can be
incomplete. The argument is that the validity of an accident rate as a basis of comparison
is based on the ability to accurately determine the measure of exposure. In a study by
Chapman (1993), the exposure to risk of accidents was characterized in two ways: 1)
exposure and accident rates for a vehicle or road user (referred to as group exposure)
operating on the system, and 2) for particular sites or fixed objects (referred to as site
exposure) existing in the system. Group exposure is defined as the number of accident
opportunities a particular driver experiences as he/ she drives around the road network
(Hodge 1985). Site exposure is defined as the amount of opportunity for accidents
occurring at a particular site or group of sites (Hodge 1985).

For group exposure, vehicle miles traveled is the most commonly used measure.
In addition, the duration of travel, number of discrete trips, and number of crossings have
also been used as direct measurements of exposure. For site exposure, direct traffic

counts, number of traffic conflicts, sum of entering flows at intersections, cross-product

of conflicting flows at intersections or the square root of the cross-product of conflicting

15

flows at intersections are methods/measures recommended by Chapman (1973). Most of
the methods mentioned above (direct measurement) are hampered by data availability
and there is a greater difficulty in calculating sub-group exposure of road users or site
types (e.g., old drivers, small cars, collector streets).

The review of the literature on exposure starts with a definition, followed by
discussion of group exposure, and ends with discussion of some issues regarding accident
exposure and accident rates.

2.3.1 Definition of exposure

In 1942, De Silva mentioned the concept of exposure and defined it as “the
number and relative danger of the hazards he (the driver) encounters.” He noted that
general exposure to different hazards varies in terms of where, when, and how a person
drove. Dunlap (1953) stated that exposure was a measure of “the frequency of the
existence of a situation which may or may not involve an accident.” This definition
showed that the driving exposure included all the situations no matter whether there were
accidents involved in the driving, which was different from De Silva. Mathewson and
Brenner (1957) recommended a general definition of exposure as a “unit of risk in motor
vehicle accident rates.” A similar definition was proposed by Mathewson and Jacobs
(1961) who defined exposure as “the frequency of occurrence of risk situations and
circumstances associated with risk situations.” Goeller (1968) called exposure over a
given driving distance “the number of times that danger occurs.” Haight (1971) noted that
“exposure to accidents” evolved as a concept by analogy to “exposure to disease,” and
indicated continuing difficulties in giving the concept a precise meaning. Carroll (1971)

offered yet another definition “driving exposure is the frequency of traffic events which

16

create a risk of accidents,” which is very similar to Mathewson and Brenner (195 7).
Briefly, these definitions of exposure are similar in nature and generally consider
exposure as a measurement of driving hazards or driving risk. .

In 1970, Klein and Waller considered exposure as the “population at risk (in terms
of passenger or vehicle miles)” and used as a denominator in the calculation of an
accident or injury rate. In a report from Operations Research, Inc. (1971), exposure was
viewed as “a systematic process affecting the crash system that is essentially a function of
the continual interaction of driving behavior with the ever-changing environment.” The
authors of this report regarded exposure as “obviously something more than the gross
vehicle mileage for all drivers under all driving conditions, the usual proxy measure.”
The elements of exposure should include: characteristics of drivers and vehicles,
characteristics of the road system and intensity of system use and environmental
conditions (weather, light conditions). These definitions illustrate that exposure to
accident risk is a combined effect of driver, road conditions and environmental conditions
in addition to passenger or vehicle miles.

Chapman (1973) reviewed the past definitions and use of exposure measures and
provided an important reference for this field. His definition is “exposure is the number
of opportunities for accidents of a certain type in a given time in a given area.” This
exposure is defined in a more strict sense—exposure is an indicator of accident
opportunities confined to a specific tirneframe and location.

2.3.2 Group exposure
Group exposure is defined as the number of accident opportunities that a road

user experiences on the road network. Generally, the most commonly used measure for

17

drivers is vehicle miles traveled, while for pedestrians, duration of travel and number of
crossing are more frequent. The focus here is vehicle miles traveled.

VMT is an expression of how much traffic uses the road and how far this traffic
travels. VMT is the most common procedure for approximating exposure of the road user
(Carr, 1969). Carroll (1973) considered the distance traveled as the most indicative
measure of exposure. However, use of VMT implicitly assumes constant risk at all sites,
under all environmental conditions, and for each mile traveled.

In one of many attempts to estimate VMT, a study done at University of
California (1975) started with short-term traffic count surveys at numerous locations, and
continuous counts at a few sites. Then the continuous count data were adjusted for
seasonal influence, and daily or weekly traffic fluctuation. The VMT was estimated by
multiplying volume counts by the length of the road segments for which the
characteristics were assumed to be the same. For the estimation of VMT for a specific

roadway segment and a particular vehicle type, the basic formula is expressed as:

—MPi )xl:(V(1)i +:(1)i +1)]x365

 

VMT =tx(MP.
t 1+1

where:
t — the proportion of particular vehicle type;
V(l)i +1— adjusted 24-hour volume counts in “ahead” leg of count location;

V(l)i — adjusted 24-hour volume counts in “back” leg of count location;

MP1. +1 — MPi— mileage between locations; and

[(V(2)i + V(l)i + 1%} average daily traffic.

Summing over all roadway segments yields a system-wide VMT estimate for the
particular vehicle type. This report did not provide information on the magnitude of

errors associated with the calibration process for seasonal, weekly, or daily fluctuation or

18

the number of short-term counts used to estimate VMT. Thus, accuracy of the computed
VMT was unknown.

Transportation engineering agencies also show interest in measuring VMT of
specific road users at regional or national levels and on an ongoing basis. F erlis et al.
(1981) developed a procedure to estimate regional VMT through the use of sampling
techniques. They elaborated that an efficient way of estimating regional VMT with a
sample of traffic counts was to estimate the average volume in each sample stratum,
multiply the average volume by the total mileage in the same stratum, and average all the

stratum-specific VMT estimates to produce an estimate for the region. The estimate is

shown as:
__ H
VMT=ZVMTh
_— h ——
VMT}, =Mh xVOLh
Nh
VOLh =(l/Nh)x ZVOLhi
l
where:

H — the number of sample strata;
M}, — the mileage of stratum h;
N), — the number of volume counts made; and

VMT - the estimated average regional VMT during the time of interest;

VOL h — the estimated average volume in sample stratum h;

VOL h — the volume measured on count i in sample stratum h.
i

VMT h — the estimated average VMT in sample stratum h during the time of

interest;
The advantage of this model lies in the straightforward computational steps and

the disadvantage is that data errors emerging in a previous step will accumulate and

propagate to a next step.

19

In an effort to forecast personal daily VMT, Kuzmyak (1981) developed a model
incorporating individual and household composition factors that most directly affected
the individual’s travel decision making, including characteristics of the individual, the
characteristics of the individual’s household, travel-related considerations, purpose of
travel, travel destination, and residence location. The strength of Kuzrnyak’s model was
its ability to forecast personal VMT by means of existing travel data sets (if available)
while the weakness was that it didn’t consider the importance of fuel price and
availability, transportation level of service, temporal consistency, and the effects of
competing modes. On the other hand, this model is unable to perform fine-grained
analysis of behavior by trip purpose or land use, since the model was derived and
calibrated based on 1977 National Personal Travel Survey data which did not report
sample location and trip details. These factors in combination substantially weaken the
applicability of the model.

Although VMT as a measure of exposure has been widely used in traffic safety
analysis, it has also aroused disagreement among traffic researchers. Basically, the
underlying assumptions of VMT-based methods have been challenged.

The first assumption is that all driving involves the same exposure to accident
hazards. This assumption was challenged by Steward (1960), who stated that “the
concept of exposure has a more narrow meaning, one which takes account of probable
facts in one’s present, and/or immediate past environment. . .an individual has been
exposed to a disease after he has direct contact with some carriers or has had opportunity
for contact.” That is, not all driving (vehicle miles) is subject to similar driving hazards

under certain circumstances, such as vehicles traveling in a platoon at an identical speed.

20

In reality, the leading vehicles might experience more driving hazards or differently than
the following vehicles.

The next assumption is that exposure to accident hazards is always proportional to
miles driven. This assumption is really a matter of which level of accident data are
considered. Generally speaking, when the use of VMT is an estimate of exposure at the
system level, the assumption is valid. Data at this level are more aggregated and the
exposure estimation is relatively gross. When exposure needs to be estimated in a
disaggregated manner by variables of interest (e.g., roadway type, driver age), the
assumption becomes less appropriate. Exposure to accident hazards in these situations
becomes a function of traffic and personal behavior characteristics in addition to miles
driven. For instance, the same driver might confront less accident hazards on a freeway
than on a local street with identical length.

Another assumption is that the degree to which exposure is associated with miles
driven is the same for all drivers. Substantial differences exist between different drivers
in terms of driving knowledge and experience and thus drivers might respond differently
to the same type of driving hazard. Given this setting, for the same miles driven,
experienced drivers might “feel” being exposed to fewer hazards than inexperienced
drivers do, even though the hazards themselves are the same. The point is that the
objectively similar situations are not equally hazardous for different drivers.

Finally, the last assumption is that the traveling speed for groups under scrutiny is
inherently assumed to be equal. In order to illustrate the point, imagine a potential at-fault
driver waiting somewhere to encounter or interact with two innocent drivers, one

traveling for 10 miles at 30 MPH and the other for 20 miles at 60 MPH. The at-fault

21

driver will have two equal opportunities (time duration) to interact with an innocent
driver. The probability of each of these innocent vehicles being impacted by an at-fault
driver would be the same. Using the traditional VMT method would result in the vehicle
that is traveling twice as far having twice the probability of being in an accident.

Another operational-oriented criticism is leveled by Lyles et al. (1991). While
VMT appears to be widely used and acceptable on a system-wide basis, it becomes
“virtually impossible” to use VMT to measure the exposure of different types of
motorists in different types of vehicles on different roadways (and so forth). This is
related to the data availability issue of VMT. In order to compute VMT disaggregated by
the variables of interest (e.g., road type, driver age, time period), it is necessary to know
the traffic volume and average of mileage traveled under a specific circumstance (e. g.,
VMT of young drivers on local streets on Friday night). Although, theoretically, this is
possible, practically there is very limited (or even no) availability of such specific
information.

The point here is to illustrate that although VMT is the most fiequently used
exposure measurement, there are theoretical and practical difficulties stemming fiom
problematic assumptions and data unavailability. The quality of predicted or calculated
VMT data, especially at a finely-disaggregated level, has been seriously questioned.
Consequently, there is a need for an alternative approach to estimate exposure.
Seemingly, quasi-induced exposure poses a promising solution to this dilemma. Not only
are the problematic assumptions of VMT avoided, but the relative exposure is estimated
solely from the more readily available accident data. In contrast to VMT, its desirable

features include fine disaggregation of exposure by variables of interest, a simple

22

calculation process, and availability of data. The details of quasi-induced exposure will
be explored in a later section.
2.3.3 Related issues

There is also a controversy regarding the relationship between accident frequency
and accident exposure, as advanced by Hauer (l 995)——accident frequency is not linearly
proportionate to accident exposure and thus the accident rate is not constant. His
argument is based on the discussion of a nonlinearity relationship between accident
fi'equency and exposure for a road user or site group. Figure 2.1 is quoted from his study.
Note that in figure 2.1, the author states that “the shape of the function is immaterial, only
its essence.” The purpose of this figure is to show how the average number of accidents
in a specified period of time would be changing if exposure changed, while all other

conditions affecting accident occurrence remained fixed.

 

 

 

 

 

 

 

'l

 

 

 

 

0 1000 2000 3000 4000 5000 6000

Ex posu roltlm o

Aecldentsltlme

l
l
l
l
l
l
l
i
I
l
l

 

Figure 2.1. A nonlinearity relationship between accident frequency and exposure
Based on figure 2.1, the accident rate is the slope of the line joining the origin and
a point in the curve. Along the curve, the accident rate varies with the change in
exposure. In practice, traffic engineers and researchers expect that the number of

accidents for a certain road user to increase proportionally with VMT. For instance, one

23

truck accident per 10,000 vehicle miles is reasonably used to predict two truck accidents
per 20,000 vehicle miles. This type of prediction is called the “linearity conjecture.” This
assumption contradicts the tendency indicated in the curve. Hauer concluded that simple
use of the accident rate would cause an over-representation problem with increasing
exposure.

Whether the linearity conjecture can be adopted depends on whether it causes a
significant effect on the results. Although it is well argued by Hauer (1995) that accident
frequency is not proportional to the accident exposure in the curve, in some portion of the
curve, the increase in accident fiequency can still be approximately considered as
proportional to accident exposure within tolerable errors. For instance, for exposure
ranging from O to 4,000 (figure 2.1), the linearity conjecture should not be a major
problem, where the linear relationship between exposure and accident frequency can be
approximated. Outside the range (>4,000), the accident rate seems to be overestimated.
Considering this worse scenario, in typical engineering practice an overestimated
accident rate will lead to conservative countermeasures with regard to certain traffic
problems and certainly it helps to promote safety.

In a very similar study by Janke (1990), the author challenged the underlying
assumptions that there was a linear relationship between accidents per driver and driver
mileage, which was commonly used as a basis for developing traffic safety-related
studies. The author argued that for two groups of drivers who are equally competent and
prudent, the same length of highway miles offers different amounts of exposure to risk.
For example (J anke, 1990), high-mileage drivers typically accumulate mileage on

roadways with relatively high speed limits, which generally have much lower accident

24

rates (per mile) than other types of roadways. Low-mileage drivers typically make short
trips on local surface roads, which are comparatively more congested and thus offer more
opportunity for accidents. This illustrates the point that different roadways offer different
accident risk for the same mile length and consequently the relationship between
accidents per vehicle mile and driver mileage is not necessarily linear.

Since strict linear proportionality of accidents to mileage does not seem to hold,
J anke (1990) suggested that the induced exposure approach gives a more balanced
measure of risk than does the method of using accidents per mile. It also appears to
circumvent effects of the complication of the relationship between the driver mileage and
driving competence in the interpretation of accident-per-mile data.
2.4 Induced exposure

In view of the difficulties of estimating exposure by means of traditional methods
(e.g., VMT), researchers began to look for an alternative to estimate exposure and turned 1
to induced exposure. The major advantage of induced exposure is that it overcomes the
problem of data availability confronted by other exposure methods, as exposure is
estimated directly from the accident data themselves. The original idea of induced
exposure is attributable to Thorpe (1964), who suggested that by making a set of
assumptions the exposure for a specific driver-vehicle combination could be estimated
according to the numbers of single- and multi-vehicle accidents for that combination. The
basic assumption behind this idea was that the exposure for certain classes of drivers,
vehicle types, and driving environments, was proportional to the number of times that the
analysis category was an “innocent victim” in collision accidents. That is, innocent

drivers involved in the accidents are randomly impacted by accident initiators, and thus

25

innocent drivers in the accidents are a random sample of the driving population on the
road at the time and place of the accident. The following section is about the development
of induced exposure.

2.4.1 Definition of induced exposure

Although the concept of “induced exposure” was originally proposed by Thorpe
(1964), Haight (1973) was the first author who explicitly defined the concept of induced
exposure through a summary of previous work. Haight offered two definitions of induced
exposure fi'om different perspectives: “narrow-sense” and “broad-sense.” The narrow-
sense definition is (Haight 1973, pp. 2):

Exposure referred exclusively to exposure to collision with other vehicles, and,

consequently, in which all other types of mishap were conceived as taking place

not because of exposure, but for other reasons.
More broadly, the definition of induced exposure is (Haight 1973, pp. 2):

Exposure and proneness as mutually exclusive and exhaustive concepts (one

internal and one external), which suffice to account for (expected) accident

expenences.

In the narrow-sense, induced exposure is defined as a measure of driving hazards
in the traffic or road environments, while in the broad-sense, induced exposure further
considers the interaction between the driver and the external environments. The details of
these two types of exposure are explored in the next sub-section.
2.4.1.1 Narrow definition

Thorpe’s theory (1964) was categorized as the narrow definition. His theory to
estimate relative exposure for a driver-vehicle combination is based on five assumptions
(Thorpe 1964, pp. 1):

1. Single vehicle accidents are caused entirely by attributes of the driver-vehicle
combination concerned.

26

Collision accidents are caused by the first two vehicles to hit.

In each collision accident there will be a “responsible” and a “not responsible”

driver-vehicle combination.

4. The relative likelihood of a driver-vehicle combination being the “responsible”
combination in a collision accident will be the same as the relative likelihood of
that combination being involved in a single-vehicle accident.

5. The likelihood of any particular driver-vehicle combination being innocently

involved in a collision accident will be the likelihood of meeting that combination

anywhere on the road.

5”!"

Assumption 5 has been used as the operative definition of induced exposure. The
exposure, E, to an accident for a given driver/vehicle combination 1' is computed by the
formula (Thorpe 1964, pp. 2):

E.=2T.-S.
1 z I

where:
Ti — the percentage of multi-vehicle accidents for driver/vehicle combination i;

Si — the percentage of single-vehicle accidents for the same driver/vehicle

combination.

This formula is attractive to traffic researchers due to its simplistic nature in
estimating exposure. In general, induced exposure has some obvious advantages as to
cost, time, and convenience, since accident records are normally available.

Thorpe’s induced exposure theory was not mature and drew considerable
criticism either because of the underlying assumptions or the exposure formula itself.
Haight (1971) pointed out that it was possible for the exposure formula to produce
negative values. In Thorpe’s original work (1964), he seemed to realize this problem and

dismissed it as one which resulted from sampling error with small numbers, since the

exposure was sensitive to errors in Ti and Si' However, the exposure of a particular

driver-vehicle combination is correlated with factors which are in turn highly correlated

with the propensity for single-vehicle accidents, the exposure will be negative regardless

27

of the sample size. For example, suppose that young inebriated drivers drive only at night
when traffic is light and therefore a high proportion of their accidents are single-vehicle.

Then the accidents of young persons in two-vehicle crashes (Ti) would be small, but
their involvement in single-vehicle (Si) accidents would be large, consequently resulting

in a negative exposure. The negative value of the formula results from the assumption
that responsible driver-vehicle combination in single-vehicle accidents follows the same
distribution as that in two-vehicle accidents.

The same issue has been explored and criticized by several traffic researchers
(Carr 1969, Hall 1970, Carlson 1970, Joksch 1973, Brown 1982, Stamatiadis 1997). Most
of the researchers later turn to quasi-induced exposure, which will be covered in a later
section. For example, Brown (1982) argued that Thorpe’s fourth assumption was very
questionable, because a variety of personal characteristics (e. g., extraversion, aggression,
anxiety) would tend to produce greater self-induced risk exposure when other drivers
were present than when they were not. Moreover, control skill failures of drivers were
largely responsible for single-vehicle accidents, whereas both control skills and roadcraft
(capability of perceiving road hazards during driving) might be causally implicated in
multi-vehicle accidents. Therefore, the probability of being involved in different types of
accident might vary for a particular driver-vehicle combination.

More recently, Stamatiadis et al. (1997) made use of Kentucky data to suggest
that such an assumption might be erroneous. Relative involvement classified by driver
age and vehicle type was significantly different for single-vehicle and multi-vehicle
accidents. Their study showed that as drivers aged, they became progressively more

conspicuous in multi-vehicle accidents. The ratio of single-vehicle to multi-vehicle

28

accident percentages decreased fiom 1.21 (driver’s age less than 25), to 0.88 (age
between 45 and 54), to 0.31 (driver’s age greater than 75); as vehicle size increased, the
same ratio increased from 0.97 (automobile), to 1.29 (straight truck), to 1.83
(combination truck). Obviously, large trucks were overrepresented in single-vehicle
accidents. This illustrates the point that accident involvement rates insingle-vehicle and
multi-vehicle accidents for the same vehicle-driver combination should not be treated
identically.

Another shortcoming of induced exposure stems from assumption 3—only one
responsible and one not-responsible driver are involved in any accident. Based on
Thorpe’s theory, responsibility for accident causation can be identified and thus assigned
to one of the drivers in a two-vehicle accident. Certainly, responsibility is not easily and
always identifiable for all accidents. If those accident data where responsibility is not
clear or shared are included in the analysis, the estimated exposure is potentially biased.
For example, two aggressive young drivers chase each other in the freeway and cause a
“side-swipe same” type of accident. It would be reasonable to assign accident fault to
both drivers rather than one of them. Given this, to the extent possible, accidents as such
are not used in induced exposure and should be eliminated fi'om further considerations.
2.4.1.2 Broad definition

The broad definition was articulated in Koomstra’s theory (1973). His model was
not based directly on concepts of guilt and innocence in two driver/vehicle combinations,
but rather on a separation of factors into two general types: external factors (called
exposure), and internal factors (called proneness). The model was expressed as (Haight

1973):

29

D(ny) = W (x) g(xi f (91 3(9))

where:
D(x, y) — the number of accidents between driver-vehicle combination x and y;

f (x) and f (y) — the proneness of driver-vehicle combinations x and y;
g(x) and g(y) — the exposure of driver-vehicle combinations x and y; and
¢ - an interaction function.

In this model, a single-vehicle accident is treated as a two-vehicle accident where
the second vehicle belongs to a fictitious “dummy” category. Due to the general nature of
Koomastra’s model, the model is somewhat difficult to follow and much more detailed
identification of the problems is needed. The potential problems are described below
(Mengert 1982, pp. 2):

1. Imperfect mixing problem, which relates to the fact that two user groups may not
have their exposure distributed identically over time or roadway types.

2. Accident fault assigning problem, which models accident fault as pertaining to
one party or the other, or to neither party but not to both.

3. The model looks upon each accident situation as symmetric in the user groups in
that the same potential accident situation would be as likely to occur if the roles of
the user groups are interchanged. It is clearly incorrect for certain combination of
vehicle groups (e.g., vehicles of greatly different size).

4. The same proneness distribution for a user group applies in all situations. This is
similar to Thorpe’s problematic assumption 4.

2.4.2 Quasi-induced exposure

Acknowledging Thorpe’s (1964) problematic assumptions and theoretical
difficulties, other traffic researchers (Carr 1969, Hall 1970, Carlson 1970, Joksch 1973,
Cerrelli 1973) modified Thorpe’s original work and supplemented it with a systematic
responsibility-assigning scheme. Haight (1971) called this technique “quasi-induced
exposure” and defined it as “an induced exposure method to measure the relative

exposure of driver/vehicle combination to the risk of driving hazard, with a well-defined

responsibility assigning system.” Based on this definition, it seems that the difference

30

between induced exposure (generally referred to as Thorpe’s and Koomastra’s methods)
and quasi-induced exposure lies in the responsibility assignment issue. The former uses
single-vehicle accident experience to establish the “responsible” involvement of an
attribute in two-vehicle accident, while the latter assigns responsibility through more
reliable sources such as actual police reports or citations (Carr 1969 and Cerrelli 1973).

Other than the responsibility assignment issue, quasi-induced exposure theory is
developed based on two fundamentally different underlying assumptions compared to
induced exposure (Lyles 1994, pp. 2):

1. In two-vehicle accidents there is an at-fault and a not-at-fault driver.
2. Not-at-fault drivers in the two-vehicle accidents are a random sample of motorists
and vehicles on the road during the study time.

For assumption one, quasi-induced exposure requires the utilization of only two-
vehicle accident data with one at-fault or responsible driver and one not-at-fault or non-
responsible driver. Accident responsibility for causation is assigned to one of the drivers
in a two-vehicle accident based on data fiom police accident reports (e. g., Carr 1969, Hall
1970, and Carlson 1970). The driver-vehicle combination that is responsible for the
accident is defined as Driver-1 or Dl. Consistent with the above, the driver-vehicle
combination who is not-at-fault is defined as Driver-2 or D2. Based on the terms defined,
assumption two can be rephrased: D23 are randomly selected by Dls fi'om all vehicles
existing on the system and thus D23 constitute a random sample of driver-vehicle
combinations and, inductively, a measure of exposure (Lyles 1994).

According to the assumptions, a Dl-D2 matrix is constructed to calculate an
involvement ratio (IR) for a particular driver-vehicle combination. Table 2.1 is a matrix

showing sex of driver for both at-fault (D13) and not-at-fault (D23). Each row in a Dl-D2

31

matrix is the responsible driver and each column is the non-responsible driver. The
summation over each row is the total number of D1 3 and the summation over each

column is the total number of D23.

Table 2.1 D1-D2 matrix used in quasi-induced exposure

 

 

 

 

 

 

D1-D2 matrix Driver-2 (not-at-fault, D2) Dl-total
male female
2
male A 1] A12 2 A1 1
Driver-1 1' =1
(at-fault, D1) 2
female A 2 I A 22 Z A2j
J =
2 2 2 2
D2-total 2.41.1 2.41.2 A = “Z .2 A1,].
i=1 i=1 1 =11 =1

 

 

 

 

 

 

Thus, the Involvement Ratio (IR) of a driver-vehicle combination is computed as
the marginal proportions of D1 3 divided by D23 for the particular combination. This ratio
of the D1 characteristic to the D2 characteristic (e.g., sex of driver) provides a measure of
relative involvement of that characteristic in accident causation. Based on the IR value,
one is able to determine if a certain driver-vehicle combination causes disproportionately
more (IR>1) or less (IR<1) accidents. If IR is equal to 1, the driver-vehicle combination
causes accidents proportionately to their presence on the road.

As the quasi-induced exposure definition and theory indicate, it is fundamentally
different from other induced exposure methods, e.g., Thorpe or Koomastra. Further
comparison reveals that differentiations are not only in terms of the underlying
assumptions and responsibility-assigning scheme, but in the accident data and variables

used. Details are shown in table 2.2.

32

Table 2.2. Comparison of induced exposure and quasi-induced exposure

 

 

 

 

 

 

. . quasi—induced
rssue induced exposure
exposure
. . . . . . police accident
responsrbrlrty assrgnment scheme one-vehicle accrdent
report, etc.
one-vehicle accident data used? yes no
. . yes, only with a D1
two-vehicle accrdent data used? yes
and a D2
three or more accident data used? yes, first two vehicles no
measurement of exposure 2T,- ’ S,- * D2

 

 

 

 

 

"' Ti is the percentage of multiple-vehicle accidents for drivers i; Si is the percentage of single-

vehicle accident for the same of driver/vehicle combination.

With the general theory of quasi-induced exposure introduced, the following
section is an exploration of the research on and using quasi-induced exposure. It is
divided into three main topics: validation of underlying assumptions, responsibility
assignment, and applications.
2.4.2.1 Validation of assumptions

The validation of underlying assumptions of quasi-induced exposure method is an
essential step in determining whether it is an appropriate exposure measurement or a
useful analysis tool. Only when the assumptions are satisfied by accident data sets, can
quasi-induced exposure be used with confidence, otherwise it should be used with
caution or not at all. As stated earlier, quasi-induced exposure’s first assumption in terms
of accident data type, is relatively easily met.

Assumption two requires that the innocent driver-vehicle combinations in the

accident be a random sample of the driving population on the road at the time of the

33

crash. Surprisingly, the literature review indicates that few traffic researchers actually
validate this assumption before using quasi-induced exposure to calculate the relative
accident involvement ratio. Most of the researchers simply make the assumption and
develop the analysis. For example, in examining Ontario accident data for different driver
age groups, driver gender, driving experience and alcohol use, Carr (1969) simply made
the assumptions and compared the results with those fiom Thorpe’s method and
concluded that quasi-induced exposure had significant advantages over Thorpe’s, without
specific investigations of whether the assumed postulations were valid. In a similar study
using National Accident Summary Files as a data source, Cerrelli (1973) employed quasi-
induced exposure to obtain a numerical estimate of the liability and driving hazard
associated with each class of driver. Again, in this study there was no validation of
assumptions. The same problem exists in more recent studies as well (DeYoung 1997,
Stamatiadis 1998, Aldridge et a1. 1999, Kirk et al. 2001a, Chandraratna et a1. 2003, and
Hing et al. 2003).

Lighthizer (1989) seemed to be the first author who explicitly dealt with
validating the underlying assumptions of quasi-induced exposure. He proposed two
techniques. The first technique was direct observation of the values of key variables in
the field. The variables included fleet-gender combination (e.g., male driving auto or
station wagon, male driving pickup or van) and fleet mix (auto and station wagon, pickup
and van, semi-truck and truck and utility vehicles). The author employed Michigan DOT
accident data (1982-1988) and on—site collected data in southwest Michigan. He
compared the distributions of driver-vehicle combination from field observations with

those of non-responsible drivers derived from Michigan DOT accident data for three

34

levels of analysis: overall, by county, and by day. The results indicated overwhelmingly
good agreement for driver gender at the overall, county, and the daily levels, but not as
positive for the fleet rrrix. Lighthizer argued that problems were due to the inadequate
accident data for the road segment of interest. Actually, there is a firndamental problem
associated with this technique, which implicitly assumes that the exposure “truth”
collected from field observations are identical to the exposure at the time when the
accident data were collected or the accident occurred. This assumption is questionable.
Exposure computed by quasi-induced exposure is specific to driving population at the
location where and at the time when accidents occurred; exposure “truth” collected by
field observations is specific to the driving population at the location where and at the
time when traffic is observed. From the perspective of location, field observation sites
might not be representative of those where the accident occurred, even though both are
on the same route; from the perspective of time, the time when the accident occurred is
before the field observation and thus the characteristics of driving population might have
changed. Lighthizer ignored these facts and did not take appropriate actions to adjust
exposure “truth” and make it comparable with accident exposure. He aggregated six
years (1982-1987) of two-vehicle accidents occurring on I-94 in the six counties in
Michigan (Berrien, Calhoun, Jackson, Kalamazoo, Van Buren, and Washtenaw) and
compared the data directly to the field data observed in the summer of 1998. The author
did explore the issue of seasonal and annual fluctuations among the accident data by
means of analysis of variance (ANOVA) procedure, but the concern of whether the field

data and the accident data were comparable was not addressed. Factors such as a

35

differentiated grth rate of traffic volume and change of driving population should be
taken into account.

The second technique was complementary sets analysis. That is, the distribution
of non-responsible driver-vehicle combinations involved in accidents caused by driver-
vehicle combinations with certain characteristics are compared with the distribution of
non-responsible driver-vehicle combinations of accidents caused by the complement set
of driver-vehicle combinations. If they are the same, D23 represent a random sample of
the driving population; if not, D23 are not a random sample and thus the assumption is
not satisfied. The author utilized Michigan DOT accident data in the analysis of driver-
vehicle’s distribution disaggregated by gender, roadway type, and fleet mix. Based on the
results, this technique produced very encouraging results which were consistent with the
assumption for several variables examined. For example, in the following D1-D2 matrix
pickups and standard automobiles were examined (pp. 152).

Table 2.3 Actual distributions of D13 and D23 for pickups and standard auto on I-94

 

 

 

 

 

 

 

 

 

 

Dl-D2 matrix D2 . D2-total
auto prckup
D1 auto 983 (92.0) 78 (8.0) 971 (89.3)
pickup 105 (90.5) 11 (9.5) 116 (10.7)
Dl-total 998 (91.8) 89 (8Q 1087

 

 

In table 2.3, the row distributions (as well as the marginal total) appear to be
similar—within 1.5 percentage points. This suggests the similarity of the D2
distributions, which supports the assumption that D2 vehicles constitute a random sample
of the vehicles on the road.

Most recently, Kirk and Stamatiadis (2001b) utilized a trip-diary approach to

measure travel exposure (VMT) and compared these estimates to those derived through

36

quasi-induced exposure within the urban boundaries of Fayette County, KY. Since trip
diaries provided data for the specific trips taken such as time of day, day of week, trip
purpose and roadways that the individual drivers selected, it allowed for the comparison
to be developed in a disaggregated manner. The exposure estimates from the trip diary
and the quasi-induced exposure were compared for three age groups (18-34, 35-64 and
64+) disaggregated by roadway class, time of day, and day of week. The results showed
that age group (35-64) had the smallest differences (less than 4 percentage points)
between the two exposure estimates although there were a few instances where the
differences were large (as many as 15 percentage points). The authors identified that for
age group (35-64) the large sample size both in participants and in number of routes
contributed to the similaritywith quasi-induced exposure. However, for the age group
(64+), VMT exposure was consistently 2 to 3 times higher than the exposure from the
quasi-induced approach. With the exposure data in more disaggregated conditions (age,
roadway class, or time of day), the differences between the two exposure estimates
became conspicuous and significant. Although the validation was not successful at any of
the disaggregation levels, the study nonetheless produced some interesting results: 1)
there were cases where exposure estimated by each method produced similar results; and
2) differences between two exposure estimates for various age groups were significant.
An essential point is made in this study that the underlying assumptions of quasi-induced
exposure can be tested through the comparison between the VMT calculated fiom
eternally available data (a trip diary, in this case) with the exposure given by quasi-

induced exposure.

37

In 2001, Golias et al. claimed that quasi-induced exposure method “had been
tested in several occasions and its statistical validity had been verified,” citing a study by
Hodge et al. (1985). Unfortunately, the referred paper described extensively the use of
group exposure measures in the assessment of risks incurred by people within particular
population groupings and reviewed briefly the use of induced exposure measurements.
There was no statistical validation whatsoever on the underlying assumptions of the
quasi-induced exposure technique.

In summary, although underlying assumptions of quasi-induced exposure have
been known for decades, very few traffic researchers actually devote efforts to validate
them. This is important because the use of quasi-induced exposure technique hinges on
the validity of underlying assumptions. Although several authors have attempted to
validate them with different methodologies, some are not theoretically precise or
incomplete (e. g., Li ghthizer 1989). This provides motivation for this research eflort to
explore/develop different techniques to test the validity of quasi-induced exposure in a
more comprehensive and convincing manner.
2.4.2.2 Responsibility assignment

The first assumption of quasi-induced exposure requires a specific accident data
format—two-vehicle accidents with one responsible driver and one innocent driver.
Therefore, it requires a responsibility-assigring scheme to determine which driver in a
two-vehicle accident is responsible for the accident.

Suspecting the validity of Thorpe’s fourth assumption, traffic researchers begin to
assign responsibility for accident causation based on police investigators’ judgment, since

assigning and recording responsibility for accident causation is a common practice for

38

police officers in investigating accidents. A series of quasi-induced exposure-related
studies (Carr 1969, Hall 1970, Carlson 1970, Joksch 1973, Cerrelli 1973) have also
demonstrated the use of police officer’s interpretation as the standard to allocate
responsibility in an accident. For example, Cerrelli (1973) initiated a study of
determining the insurance premium rates for various driver classes based on the “hazard
index” which is similar to the concept of the relative accident involvement ratio in the
quasi-induced exposure approach. The hazard index is defined as the percentage liability
of certain driver divided by the percentage exposure of the corresponding driver. While
determining the liability of each driver involved in accidents, the author simply used the
responsibility code in the accident record and split drivers into two groups: responsible
and non-responsible.

Although reviewing recent publications pertaining to quasi-induced exposure
(Lighthizer 1989, DeYoung 1997, Stamatiadis 1998) did not specifically reveal what
technique had been used to assign responsibility, communication with these three authors
confirmed that the police’s citation was the main standard. Nevertheless, using a police
officer’s judgment in assigning responsibility in two-vehicle accidents might cause some
problems. The validity of assignment of responsibility by police was questioned by
Haight (1970) who stated that “it would, except in very well-defined circumstances, be
assuming too much if we supposed that the proportions of guilty and innocent parties
were decided by the reporting authorities.” Quasi-induced exposure emphasizes only
whether a driver’s behaviors should be responsible for the accident. When investigating
police officers issue a citation to the “responsible” driver, their judgments are not

necessarily solely based on the driver’s driving behavior but a combination of factors. For

39

example, when police officers investigate traffic accidents, there may be a sort of
"negative halo effect" (DeYoung 1997), where the investigating officers are more likely
to assign the responsibility for the accident causation to a driver once they determine that
the license status of the driver is suspended or revoked, alcohol or drug usage is involved,
or an open container is found in the vehicle, regardless of whether the driver is involved
any hazardous driving actions. If this occurs, it would inflate the involvement ratios for
the groups exhibiting these behaviors. Furthermore, with fatal and serious injury
accidents, the investigating police officers most probably will not issue a citation to the
deceased or seriously injured driver even if that driver performed hazardous actions
before the accident (DeYoung 1997). If this “under-assignment” occurs, it would
underestimate the involvement ratios for the corresponding groups.

When utilizing quasi-induced exposure technique to investigate young drivers’
(16-20) behaviors with Kentucky accident data, Aldridge et al. (1999) and Kirk et al.
(2001a) happened to address the issue of how to determine the accident fault in a crash
with the same methodology. They recommended using variables describing human
factors in each accident entry, which indicated what each driver did to contribute to the
accident. If the record shows no contributory factors present for a particular driver, then
the driver is defined as non-responsible; if any contribution to accident causation is
evident, the driver is considered to be responsible. In Kentucky accident data, the human
factors include unsafe speed, failure to yield right-of-way, improper passing, and drug or
alcohol involvement. The authors also argued that there was an inherent bias in relying

on the judgment and inclination of the police officer to assign contributing factors.

40

Therefore, the validity of solely using police officers’ citations in assigning
responsibility is suspect. It could result in over- or under- estimated involvement of
certain driver-vehicle combination in accidents. It is more appropriate to assign
responsibility by collectively considering several variables in the accident report such as,
hazardous actions, most harmful event, and violations. It is emphasized that, as far as the
quality is concerned, these variables are fundamentally identical, since these variables are
observed by the same investigating police agent. What makes the difference is that
driver’s citation status is determined according to a combination of violation phenomena
(which could be hazardous actions, drinking, or revoked/suspended license), while
driver’s hazardous action is directly collected or estimated from the accident scene.
2.4.2.3 Applications

Since Carr (1969) developed quasi-induced exposure, it has been used more
frequently than any other induced exposure formulation. Interestingly, for more than a
decade after the concept of quasi-induced exposure was first introduced, there was no real
practical application of this approach. Both Kuroda, et a1. (1985) and Maleck and
Hummer (1987) presented a similar study on investigating the relationship among driver
characteristics, vehicle size, and IR by using quasi-induced exposure method. The results
showed that relationship between driver age and vehicle size were not apparent, while
driver age appeared to affect the IR for all vehicle weight classes, especially in urban
driving conditions. However, there are some fundamental problems associated with the
study. In the event of utilizing Michigan DOT accident data, the authors simply assumed
that “accident reports were properly complete ” and treated the second vehicles in two-

vehicle accidents as the not-at-fault drivers (D23). First, it has been shown that the raw

41

accident data contain substantial data errors and the quality of accidents is questionable.
Second, in two-vehicle crashes, there were always some cases where both vehicles
involved in the same accident were responsible or non-responsible for the accidents.

Considering the problems with the use of quasi-induced exposure, Lyles et al.
(1994) summarized their experience and previous researcher’s work and recommended
some general guidelines for when/how/where to use (and not use) the quasi-induced
exposure method in the real world applications. The following table is adapted fiom the
original work.

Table 2.4. General guidelines to use or not use quasi-induced exposure

 

 

 

 

 

 

to use not to use
when relative rates are adequate when D2 distribution is biased
when accident data are available and other data are . .
not when the sample srze 13 small
when data can be “cleaned” when data are not “cleaned”
when the Dl-D2 matrix is “stable” when the ,PI'DZ matrix 13
‘unstable

 

 

In table 2.4, “relative rates are adequate” refers to the fact that quasi-induced
exposure can only produce relative exposure, and not explicit rates such as accidents per
million vehicle miles. For example, if there is a necessity to calculate an accident rate for
a driving cohort, an exposure method other than quasi-induced exposure must be used. If
it is sufficient to compare the relative accident rates between two driving-vehicle cohorts,
quasi-induced exposure is certainly a good technique. “Data can be cleaned” refers to the
fact that the data set must be capable of being “cleaned” to eliminate unreliable data, e.g.,
data from certain kinds of accidents (e.g., hit-and-run accidents) and where bias is
evident. “D1-D2 matrix is stable” means that the row distributions in the matrix are

similar or insignificantly different. In reference to table 2.3 where Lighthizer’s (1989)

42

 

“complementary sets analysis” technique is discussed, the percentage of D2 auto vehicles
(92.0%) in auto-auto accidents is close to those (90.5%) in pickup-auto accidents,
suggesting that auto vehicles are randomly impacted in two-vehicle accidents.

DeYoung et al. (1997) applied the quasi-induced exposure method to fatal crash
data to generate exposure and crash rate estimates for Suspended/Revoked (S/R) drivers
in California. Based on California fatal two-vehicle crashes (1987-1992) on the highway,
the Dl-D2 matrix showed exposure rates of 8.8% and 3.3% for S/R and unlicensed
drivers, respectively, and that, compared to valid licensed drivers, the former were
overinvolved in fatal crashes by a factor of 3.7: 1, and the latter 4.9:1. The study raised an
issue concerning the degree of accuracy of the exposure estimates of S/R drivers. Using
quasi-induced exposure, the D2 percentage for S/R drivers is 8.8%, while a random
sample of all Califomia drivers shows 5.5%. The authors noted that the former were
adjusted for S/R accidents on the highway and thus accounted for driving, while the latter
was simply a population proportion. In general, the authors argued that quasi-induced
exposure yielded a reasonable approximation of the risks posed by S/R and unlicensed
drivers and the reflected facts provided a compelling rationale for seeking more effective
methods of enforcing laws prohibiting driving without a valid license. However, the
authors fail to address the basic issue in using quasi-induced exposure—the validity of
this exposure measurement. There is no evidence to ensure that the underlying
assumptions of quasi-induced exposure are fully supported by the given accident dataset.

In a paper by Stamatiadis et al. (1998), the quasi-induced exposure technique was
used to identify potential socioeconomic factors that could contribute to the relatively

high fatality crash rates in the Southeast US and to develop preliminary relationships

43

between socioeconomic characteristics and crash trends. The authors calculated relative
accident involvement ratios for single-vehicle and multi-vehicle crash rates and
determined the real effect of one particular group and its tendency to be involved in
crashes, assuming that 1) drivers involved in single-vehicle accidents are all
“responsible” and 2) the exposure of a certain driver-vehicle combination is the total
number of corresponding non-responsible driver in two-vehicle crashes. Although the
first assertion can be reasonably assumed, the second assumption is questionable on the
grounds that there is no discussion of the validity of using quasi-induced exposure.

In two similar studies, Aldridge et al. (1999) and Kirk et al. (2001a) both used the
quasi-induced exposure technique to evaluate young drivers’ accident propensity with
three different passenger groupings (no passengers, peer, and adult or child) and four
prominent crashes (left-turn, rear-end, single-vehicle, and passing crashes), respectively.
Both studies have made improvement in addressing the issue of assigning accident fault
_ by examining the specific human factors instead of police officers’ judgment and thus
eliminated the assumption that all drivers in single-vehicle accidents are responsible for
the occurrence of accidents. The human factors found in the accident database include
unsafe speed, failure to yield the right-of-way, improper passing, drug or alcohol
involvement. However, no attention has been given to the validity of using quasi-
induced exposure, which makes the results and conclusions less convincing and
theoretically flawed.

2.5 summary
In summary, if it works, the quasi-induced exposure method has a great advantage

in being used to estimate the exposure of stratified vehicle/driver combination with

44

accident data, which can’t be achieved using the conventional exposure methods, like
VMT. The extensive review of the literature has demonstrated that there are two key
elements of quasi-induced exposure that remain unresolved or have been resolved
unsatisfactorily—-—validation of its fundamental assumptions and responsibility
assignment.

Most of the authors simply apply quasi-induced exposure in their perspective
studies without taking into account the validity of the underlying assumptions. Although
some work has been done by Lighthizer (1989), Lyles et a1. (1994), and Kirk et al.
(2001b), it is either too qualitative or theoretically imprecise.

In terms of assigning accident responsibility, except for two most recent studies
(Aldridge et al. 1999 and Kirk et al. 2001a) suggesting the use of human factors, the
majority of literature heavily relies on the judgments (or the citation in the accident
report) of investigating police. The police officers’ “verdict” for accident fault is
necessary in determining the accident responsibility, but not sufficient. Factors like a
driver who has been drinking and/or using drugs, or has an invalid driver license might
potentially lead police officers to issue citations. Certainly, this is of no help in
determining the accident propensity for a specific driving cohort of interest.

The purposes of this dissertation are to develop a systematic procedure to assign
responsibility for accident causation; to determine if the underlying assumptions of quasi-
induced exposure are valid; and, ultimately, to determine if quasi-induced exposure can
be used with confidence. If 30, guidelines will be developed to indicate at what level of

data aggregation or circumstances quasi-induced exposure is applicable.

45

Chapter 3

PROBLEM STATEMENT

The literature review revealed some of the problems with the assumptions

inherent in using traditional exposure measures in traffic safety analysis. By way of

summary, these include:

1.

All driving involves the same exposure to accident hazards (assumption one). Not all
driving (vehicle miles) is subject to similar driving hazards under certain
circumstances. For example, vehicles traveling in a platoon at an identical speed
where the leading vehicles might experience more driving hazards or differently than
the following vehicles.

Exposure to accident hazards is always proportional to miles driven (assumption
two). This assumption is really a matter of which level of accident data are
considered. When VMT is used as an estimate of exposure at the system level, the
assumption is generally valid. When exposure needs to be estimated in a
disaggregated manner by other variables of interest (e. g., roadway type, driver age),
the assumption becomes less appropriate.

The degree to which exposure is associated with miles driven is the same for all
drivers (assumption three). Substantial differences exist between different drivers in
terms of driving knowledge and experience and thus drivers might respond differently
to the same type of driving hazard. Given this setting, for the same miles driven,
experienced drivers might “feel” being exposed to fewer hazards than inexperienced
drivers do, even if the hazards themselves are the same. The point is that the
objectively same situations are not equally hazardous for different drivers.

46

4. The traveling speed for groups under scrutiny is inherently assumed to be equal
(assumption four). In order to illustrate the point, imagine a potential at-fault driver
waiting somewhere to encounter or interact with two innocent drivers, one traveling
for 10 miles at 30 MPH and the other for 20 miles at 60 MPH. The at-fault driver will
have two equal opportunities (time duration) to interact with an innocent driver. The
probability of each of these innocent vehicles being impacted by an at-fault driver
would be the same. Using the traditional VMT method would result in the vehicle
that is traveling twice as far having twice the probability of being in an accident.

It is not argued that these assumptions should not be made (certainly VMT is a
good measure of exposure “truth” in general), but to illustrate the point that use of VMT
as the measure of exposure might introduce bias into the analytical results under certain
circumstances. In addition to these assumptions, the use of VMT has one fundamental
drawback in the calculation of accident exposure in practical applications: general
availability of data. General availability of data refers to the fact that additional
information (e. g., traffic volume, length of road segment) beyond the accident data
themselves are necessary in order to compute the exposure and accident rates for certain
driver-vehicle groups. Normally, this type of information is not available. Furthermore,
limited availability of data leads to another issue—finer disaggregation of exposure.
There are problems with the use of VMT as an estimate of exposure at other than the
system level. VMT is typically unavailable for specific driver-vehicle groups under
certain conditions, for example, young drivers’ exposure in the downtown area.

In light of the theoretical and operational problems involved with using VMT,
quasi-induced exposure seemingly provides acceptable and practical solutions to at least
some of the problems. It craftily avoids the assumptions that have theoretical loopholes
through a relatively simple postulation instead—non-responsible drivers involved in

accidents are a random sample of the whole driving population on the road. Furthermore,

from the operational perspective, its attractiveness lies in the utilization of already

47

available data to calculate exposure without requiring additional information and the
capability of measuring exposure disaggregated by specific variables of interest. These
two features, if both can validated, will overcome/avoid some the fundamental problems
confionted in the most traditional exposure method (VMT), including assumptions one,
two, and three.

However, quasi-induced exposure theory is far from being mature and has its own
set of problems. It was seen in the literature review that although safety researchers have
made substantial theoretical progress with quasi-induced exposure and implemented it in
a variety of safety/crash studies, the fundamental concerns/problems with the method still
remain unresolved. There are two major problems with quasi-induced exposure:

1. The first is in the preparation of accident data to make them readily available for
use in analysis by quasi-induced exposure. This includes developing a systematic
procedure to make accident data relatively error-free and accurately assigning
responsibility for each accident.

2. The second is in validation of the underlying assumption that the collection of
non-responsible driver-vehicle combinations involved in two-vehicle accidents is
a random sample of the driving/vehicle population on the road at the time and
place of those accidents.

The first problem arises from the requirement that accident data should be
presented in a way such that:

l. Two-vehicle accident data are selected with other data being discarded and
responsibility for accident causation clearly assigned (one is at-fault and the other

is innocent). Note that word “discarded” does not imply throwing away data for

48

good, but not using it in this case. Three-or-more-vehicle accidents contain a lot

of driver-vehicle information and their use will be detailed in a later chapter.

2. The information on each driver-vehicle combination in the accidents is
sufficiently recorded such that variables of interest are not missing.

3. The information on each driver-vehicle combination is reasonable and contains
minimum miscoded data information. For example, an accident labeled as “two-
vehicle accident” should not include any one-vehicle or more than two-vehicle
information.

The second problem is the basic issue in using quasi-induced exposure. The
underlying assumption can be rephrased more specifically: non-responsible drivers (D2)
involved in accidents are a random sample of the driving population on the road when
and where accidents occur. Only when this assumption is satisfied, can quasi-induced
exposure be used with confidence.

The resolution of these two issues is the goal of this research and, eventually,
guidelines will be provided on how to use (or not use) the quasi-induced exposure
approach. Each will be discussed in more detail in the following sections.

3.1 Development of systematic rules for preparing accident data

While accident data are readily available, they are often not useful in analysis
without at least some preliminary manipulation or screening. Thus, “preliminary
screening” of accident data is the first step in using quasi-induced exposure. It is of great
importance because data errors introduced in the first stage will propagate through the
rest of the process. For quasi-induced exposure, the accident data should only include

two-vehicle accidents with clearly assigned responsibility for the accident (one is

49

responsible and the other is non-responsible). The literature review revealed that traffic
researchers often do not pay sufficient attention to these concerns when using quasi-
induced exposure. Therefore, it is worthwhile to explore the potential problems that occur
when these issues are not addressed properly or sufficiently.

Examining the whole process of how accident data are obtained will help to
reveal different types of errors hidden in the data. In terms of a sequence of events, an
accident happens, police officers investigate the accident and record driver-vehicle
information on an Accident Report (AR) according to a specific format, and, finally, the
accident report is converted into a digitized format. The following table shows the
possible errors during this process.

Table 3.1. Potential cause and description of errors in accident data

 

 

 

 

cause of errors description of errors
. . . missing descriptive information on accident,
lrrnrtatron of AR format driver(s), or vehicle (3)
. . missing information on the hit-and-run driver-
lut and run drrver(s) vehicle(s)
police officer records incomplete missing descriptive information on accident,
information in AR driver(s), or vehicle(s)

 

police officer records incorrect

. . . conflicting information between variables in AR
information 1n AR

 

missing descriptive information on accident,

ARls mcompletely digitized driver(s), or vehicle(s)

 

 

conflicting information between variables in AR or

AR 1s Incorrectly dlgltlzed in the digital form

 

 

In table 3.1, errors are combined together, which are shown in a variety of forms
in the accident data. Descriptive statistics for raw accident data confirm that the errors
such as those above occur in Michigan (using 2000 data as an example):

0 Missing information in an AR, e.g., driver gender and/or driver age information;

o Abnormal values of the variables; and

50

 

- Conflicting information between variables, e.g., some variables in the record
indicate that a particular accident involves only “one-vehicle” but data are shown
for both driver 1 and 2 characteristics.

In the context of quasi-induced exposure, missing information in an AR can lead
to incomplete description of characteristics of certain driver-vehicle combinations and/or
the assignment of fault. Eventually, these errors will affect the relative accident
involvement ratio (IR) of a specific driver-vehicle cohort in a profound manner, since
they could cause the reduction concurrently in the magnitudes of the numerator and
denominator in IR. Thus, whether the IR is underestimated or overestimated hinges on
the relative reduction proportions of the numerator and denominator.

Using quasi-induced exposure without considering the quality of the raw accident
data can result in biased, or erroneous analytical results. Since most of the raw accident
data can not be ensured error-free, a logical procedure must be developed to “clean”
accident data as much as possible before it is used, which includes specific operations
aiming at eliminating more apparent data errors.

In addition to selecting and using only accident data that are relatively error-free,
assigning responsibility is another important concern. Responsibility for accident
causation is a critical issue in using the method. After the accident data are initially
manipulated to be largely error-free, two-vehicle accident data are ready for
responsibility assignment. It is noted that responsibility might be logically assigned to
either driver in the AR, both, or neither in a two-vehicle accident. However, quasi-
induced exposure explicitly requires that for each two-vehicle accident used in the

analysis, only one driver (or driver-vehicle combination) involved be responsible (or “at-

51

fault”) and the other be non-responsible. Thus, accidents with two “responsible” or “non-
responsible” drivers cannot be used in application of quasi-induced exposure. Routinely,
responsibility can be determined in individual cases on the basis of police reports or other
supplementary investigations. The most commonly used indicator is whether the driver is
issued a ticket by the investigating police officer. Several researchers (Lighthizer 1989,
Davis et al. 1993, Stamatiadis et a1. 1995 and 1997, David et al. 1997, Aldridge 1999,
Kirk et al. 2001) using the quasi-induced exposure have simply assumed that the
determination of responsibility in a two-vehicle accident is completely dependent on
whether the driver is given a citation. When investigating police officers issue a citation
to the responsible driver, their judgments may sometimes be based on a combination of
factors. They may be more likely to assign the responsibility to a driver once they
determine an indication of a traffic violation, regardless of the hazardous driving actions.
If this occurs, it would inflate the involvement ratio for the groups containing this type of
driver.

The point here is that a “violation” alone is not necessarily sufficient to allocate
responsibility in a two-vehicle accident, and thus other variables need to be taken into
consideration. At least a partial solution to this concern is to develop a systematic
procedure for assigning responsibility to individual driver-vehicle combinations
depending on the hazardous action(s) that a driver takes right before the accident and the
violation indicator itself. Therefore, it is important that two variables be taken into

consideration in a combinatory manner when relative guilt or innocence is assigned.

52

In summary, preparation of accident data is a necessary and important step in
order to use quasi-induced exposure. It helps to screen out data errors and to assign
responsibility for accident causation in a systematic manner.

3.2 Validation of assumptions

Fundamental to quasi-induced exposure is that distributions of the characteristics
of the non-responsible driver-vehicle combinations in traffic accidents have an identical
distribution to the same driver-vehicle combination in the driving population on the road
at the time and place of the crash.

The problem still lies in how to develop practical approaches to validate this
assumption. One approach is to compare the driver-vehicle characteristics fiom the non-
responsible driver-vehicle category in accidents, with those from the driving population
on the road. If similar distributions can be routinely confirmed, quasi-induced exposure is
validated. The following two approaches are developed to address this issue:

0 Compare various D2 distributions with more conventional estimates of exposure

“truth” fi'om other sources; and

0 Compare D2 distributions derived fiom two-vehicle accidents with those fi'om
three-or-more-vehicle accidents.

As for the first approach, the idea is to compare the distributions of specific
driver-vehicle combinations (D2) from the crash data to “truth” from other data sources.
The following figure shows several exposure data sources that can provide comparisons

(albeit with differing utility) with the D2 distributions derived from accident data.

53

   
 

  

census data

(gender, age, etc) traffic volume

 
 

data
Accident Data
seat belt use /
data exposure data
(V MT)

Figure 3.1. Exposure data sources comparable with accident data

It must be noted that some of the distributions calculated fiom other data sources
can be directly compared with the accident data and some cannot (such as census data).
For instance, the distributions of non-responsible driver-vehicle combinations in the
accident can be directly compared with those of traffic volume data on condition that
those two sets of data are collected under similar or identical road and traffic conditions
(such as, the same route, time of day, and day of week). If not, some conversions and
assumptions are needed to make them comparable. Depending on whether consistent
distribution patterns can be found between accident data and other “true” data sources,
the underlying assumption of quasi-induced exposure can be validated.

As for the second approach, the basic idea is to compare the non-responsible
driver-vehicle distributions calculated from three-or-more-vehicle accidents with those
from two-vehicle accidents. Traditionally, use of quasi-induced exposure only considers
two-vehicle accident data with responsibility clearly assigned with other accident data
being discarded. However, if the non-responsible driver-vehicle combination in two-

vehicle accidents is truly a random sample of the driving population, one should expect

54

that the non-responsible driver-vehicle combinations in three-or-more-vehicle accidents
are also random samples from the driving population.
3.3 Summary of problems
As discussed, the following list summarizes the problems that this research effort
attempts to solve:
0 Data errors inherent in the accident database;
0 Responsibility assignment for accident causation; and
0 Systematic validation of the underlying assumptions of quasi-induced exposure.
The work here will concentrate on the validation of the fimdamental assertions
that non-responsible driver-vehicle combinations in two-vehicle accidents are indeed a
random sample of the driving population on the road. To the extent that the approach is
validated, the research also includes development of guidelines/rules for when and where

it is appropriate to use quasi-induced exposure.

55

Chapter 4

SYSTEMATIC RULES FOR PREPARING ACCIDENT DATA

As discussed in chapter 3, accident data are not readily usable for quasi-induced
exposure application without some preliminary manipulation or screening. Examination
of accident data reveals several associated issues:

0 Missing accident records;

0 Missing variable information in police accident reports;
0 Unreasonable values for the variables; and

o Conflicting information between variables.

In addition, when responsibility assignment is explored in the context of quasi-
induced exposure, it is necessary to determine if the accident causation assignment results
from the “negative halo effect.” If so, they will be eliminated.

It is the purpose of this chapter to develop a systematic procedure to screen the
accident data obtained from state departments of transportation (DOT) to minimize data
errors and make accident data dependable to be readily usable in quasi-induced exposure
applications. In general, ready-to-be-used accident data records are fully coded for the
variables of interest (e. g., driver age, gender), reasonable with respect to values taken for

the variables, without contradiction between different variables, and, equally important,

56

have clearly and logically assigned responsibility for accident causation. In order to
achieve the stated goal, a series of operations are developed in a stepwise manner:

1. The first step is to identify and eliminate the accident data with potential
problems and errors. This can be achieved by choosing different screening
variables corresponding to different accident data problems.

2. The second step is to logically assign responsibility for the accident to each
individual driver-vehicle combination. Accident fault is determined on the
basis of two variables, i.e., hazardous action and violation indication.

The first step is only executable on existing accident cases and does not address
the “missing record” problem. The results of the literature review have shown that the
missing record problem is attributed to factors such as weather conditions, severity of
accidents, minimum threshold limitations, and availability of police in particular
locations (e. g., Detroit area, Ml). Unfortunately, there is no reasonable solution to the
missing record problem. For example, it is known that the missing record problem in the
Detroit area is due to the lack of police and a policy of simply not reporting minor
accidents. When an analysis is developed at a statewide level, accidents occurring in the
Detroit area should be excluded. The tradeoff is that some bias could be introduced if
accidents in this area have some unique characteristics (e. g., a large percentage of young
drivers).

4.1 Identification and elimination of bad data

Taylor and Maleck (1987) identified some problems in the Michigan accident

database, indicating unreasonable variable values, conflicting information between

variables, and vehicle type misclassification. Review of recent Michigan accident data

57

(2000) has also indicated that similar problems exist in the accident database. This
includes cases with unreasonable values of variables, or conflicting information between
values of variables or combinations of them. Identification and elimination of these errors
are executed in a combinatory manner, since some cases have more than one type of error
involved. Michigan accident data from 2000 (abbreviated as Michigan 2000) are chosen
as an example to illustrate how to identify and/or eliminate problematic data.

Accident data will be classified into three categories by means of the number of
vehicles involved in the accident (numveh): one-, two- and three-or-more vehicles. Note
that the discussion here is focused on two- and three-or—more-vehicle accident data. Two-
vehicle accidents are chosen because of the specified data requirement by quasi-induced
exposure. Three-or-more-vehicle accidents are selected because they might provide an
alternative to validate the underlying assumption of quasi-induced exposure. Comparison
of the distributions for the non-responsible driver-vehicle combinations in three-or—more-
vehicle accidents with those from two-vehicle accidents may be another way to validate
the assumptions of quasi-induced exposure.

Several factors will be discussed for the purpose of minimizing errors in the
accident data and in assigning the responsibility for accident causation. These include
drinking/drug use, hit-and-run crashes, driver age, accidents with conflicting information,
and accident type.

Drinkingidrug use

“Drinking/drug use” is a responsibility assignment issue. With respect to accident

causation, and as noted in the literature review, drivers with alcohol involvement or drug

use may have a higher tendency to be issued tickets by the investigating police officers

58

regardless of what hazardous actions they took and their level of responsibility in causing
the accident. The consequence is that the involvement ratio for groups containing
drinking or drug use drivers will be inflated. However, there is a potential problem in
eliminating the accidents with drinking/drug use drivers. Commonly, young drivers are
believed to have a higher tendency to be associated with drink-and-drive accidents, and
be more prone to take dangerous actions under the influence of alcohol/drugs. If this is
so, the drinking young drivers are most likely to be the real guilty party in two-vehicle
accidents. As a result, elimination of accidents with drinking/drug use by young drivers
will reduce the number of D13 and the relative accident involvement ratio for young
drivers will be underestimated correspondingly. Therefore, there is a tradeoff in
eliminating accidents with drinking/drug use drivers.

In Michigan 2000, there is a variable drinking indicating whether any driver in the
accident has been drinking. Statistics show that approximately 4.1% of all accidents
involved at least one drinking driver, among which about 1.7% are two-vehicle accidents.
Table 4.1 presents the fiequencies and percentages of each driver in alcohol-related two-
vehicle accidents. The drinking status of each individual driver is identified by another
separate variable (v1 drink, v2drink). From the table 4.1, 5,545 first drivers in two-vehicle
accidents are involved with alcohol use and 1,824 second drivers.

Table 4.1. Frequencies and percentages of drinking drivers in two-vehicle accidents

 

 

 

 

 

 

 

 

 

 

. . . . first driver* second driver"

dnnkrng condrtron N % N %
drinking 5,545 79.2 1,824 31.0
non-drinking 1 ,460 20.8 4,058 69.0
total 7,005 100.0 5,882 100.0

 

"‘ First driver refers to the first driver-vehicle in a typical accident record, not D1;
‘”" Second driver refers to the second driver-vehicle in a typical accident record, not D2.

 

For these particular accidents with drinking driver(s), one issue is explored—how
the incidence of drinking affects the decision-making of investigating officers issuing a
citation.

Based solely on the accidents with drinking drivers, the cross tabulation between
the variables hazardous action and violation indication is shown in table 4.2. Although
drivers shown in table 4.2 are all intoxicated, drivers with no hazardous actions
consistently do not receive citations (for both drivers).

Table 4.2. Cross-tabulation between hazardous action and violation indication

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

violation indication violation indication
hazardous action (first driver) (second driver)

No Yes No Yes
none 226 0 445 0
speed too fast 0 295 0 75
speed too slow 0 l3 0 3
failed to yield 0 718 0 220
disobeyed TCD 0 427 0 92
drove wrong way 0 35 0 12
drove Lt of center 0 304 0 61
improper pass 0 61 0 l6
improper lane use 0 238 0 50
improper turn 0 l l 1 0 28
improper signal 0 8 0 4
improper backing 0 154 0 28
fail to stop ACD 0 1,273 0 311
other 0 957 0 270
unknown 103 0 39 0
reckless driving 176 0 54 0
careless/negligent 246 0 0 0
uncoded & errors 200 0 116 0
total 951 4,594 654 1,170

 

 

 

 

It suggests that drinking factors do not come in play in assigning crash
responsibility. In other words, the investigating officers seem to determine the status of

traffic violation without considering the drinking factor. When drivers commit specific

60

hazardous actions, they are issued tickets. The point is that based on Michigan data,
drinking does not appear to contribute to a negative halo effect in determining “fault” for
the accident. It is possible that drinking drivers receive two citations: one for drinking
and one for apparent hazardous action. Unfortunately, these two citations can’t be
distinguished in the Michigan 2000. In table 4.2, it needs to be pointed out that the values
in the shaded cells do not appear to be logical since the drivers’ hazardous actions are
evident and they receive no citation. This issue will be further explored in a later section.

In summary, analysis of Michigan 2000 has demonstrated that driver’s drinking
seemingly has no or little effect on the decision to issue a citation. This suggests that
when quasi-induced exposure is used, the accidents with drinking driver(s) should not be
excluded from analysis. Otherwise, young drivers as the guilty party will be
underestimated.

It is noted that accidents involved with drug usage will cause a similar problem as
those with drinking for corresponding driver-vehicle combinations. Unfortunately, in the
Michigan accident database, there is no variable specifically showing whether drivers
involved in accidents use drugs.

Hit-and-run cr_a_sl_1§s_

“Hit-and-run crashes” also present problems with respect to the responsibility
assignment issue. Once an accident occurs and one of the drivers flees, it is obvious that
the investigating police officers will generally be unable to record the accident
information correctly or completely. Moreover, the police officers may not issue a
citation to the remaining driver regardless of his/her hazardous action before the accident.

Table 4.3 shows the statistics for Michigan 2000—about 10.3 percent of all accidents

61

involve hit-and-run drivers. Because the records are incomplete, these accidents should
be removed.

Table 4.3. Percentage and frequency of hit and run crash

hit and run
no 359 38 89.7

41 13 10.3
total 400 851 100.0

 

Driver age

Examining the frequency distribution of driver age for Michigan 2000 shows that
some drivers’ age is below 15 and above 100 (table 4.4).

Table 4.4. Frequencies and percentage of unusual driver ages

 

 

 

 

 

 

 

 

 

 

 

first driver second driver third driver
age range N % N % N %
0—14 1,509 0.40 1,613 0.42 70 0.02
15-100 37,3507 99.59 379,966 99.57 423,317 99.98
>101 42 0.01 39 0.01 6 0.00
total 375,058 100.00 381,618 100.00 423,393 100.00

 

 

 

 

It can be seen from table 4.4 that 99.6% of all drivers are in the range of 15-100.
For those under 15, based on Michigan law, drivers are not issued any type of valid
driving license until the age of 14 years 9 months. It is possible that some young drivers
illegally get behind the wheel, but, more likely, the phenomenon is due to data errors. For
those above 100, some drivers’ ages are as high as 400. This is obviously attributed to the
errors during the data processing. However, since there is less than 1% driver age under
15 or above 100 in Michigan 2000, removal of accidents as such is not expected to make
a significant difference in the analytical results. All drivers outside the range of 15-100

are removed.

62

Accidents with conflicting information

“Accidents with conflicting information” is another quality of data issue. A
typical check for conflicting information that is (at least implicitly) built in the accident
data is the instance when the number of vehicles involved in an accident (numveh) is not
equal to the number of drivers identified in the record. For instance, some one-vehicle
accidents have information for the second driver (e. g., 4,596 cases or 3.2% in Michigan
2000). It is more appropriate to treat these accidents as “multiple-vehicle” than “single-
vehicle” accidents. A feasible solution is to physically count the number of vehicles and
drivers information after a problematic accident is located and to redefine the value of the
variable numveh. Since quasi-induced exposure only utilizes two-vehicle accidents,
special attention will be given to mislabeled one-vehicle accidents (approximately 1.2%
in Michigan 2000) or three-or-more-vehicle accidents (approximately 0.2% in Michigan
2000). Once these accidents are identified, they will be treated as two-vehicle accidents.
Accident type

“Accident type” is concerned with quality of data as well. Under a given road and
traffic setting, there might be a limited number of accident types that could occur. The
purpose of checking accident type is to see if there are any unreasonable accident types
under a given circumstance. For example, on a freeway section the accidents should not
consist of any types such as bicycle, dual left turn, or dual right turn, considering the
limited accessibility and nature of freeway environments. In this context, I-94 (in
Michigan) is chosen as an example to show accident types, fiequencies, and percentages

of two-vehicle accidents (table 4.5).

63

Table 4.5. Accident types, frequencies, and percentages on I-94

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

crash type N %

hit train 0 0.00
pedestrian 3 0.08
bicycle 0 0.00
hit parked vehicle 6 0.16
miscellaneous multiple vehicle 416 10.98
angle straight 275 7.26
angle turn 4 0.11
head on left turn 1 0.03
rear end straight 1,856 48.98
rear end left turn 9 0.24
rear end right turn 17 0.45
dual left turn 5 0.13
dual right turn 6 0.16
head on 63 1.66
side-swipe same 998 F 26.34
side-swipe opposite I 13 2.98
angle drive 0 0.00
rear end drive 3 0.08
other drive 0 0.00
backing 10 0.26
parking 4 0.11
total 3,789 100.00

 

The first column in table 4.5 is the list of possible accident types in Michigan
data. Since the accidents occurring on 1-94 are examined, it is logical that there are no
“hit train,” “angle drive,” and “bicycle” accidents. There are several accident types,
which are most relevant to freeway off-ramps, rest areas, or illegal use of medium
openings, including “angle turn,” “head-on left-tum,” “rear—end left-tum,” “rear-end
right-turn,” “angle straight,” “dual left-turn,” “dual right-tum,” “side-swipe opposite,”
“angle drive,” “other drive,” “backing,” and “parking.” The point is that if a study is
developed to focus on the accidents on a fieeway segment, accidents occurring at the
freeway off-ramps or rest areas should be eliminated. The identification and elimination

can be achieved based on the crash type (crshtype). In table 4.5, three shaded accidents

64

are believed to be the most commonly occurring types for two-vehicle accidents in the
freeway sections and consequently are considered for further analysis. The rest of the
accidents should be excluded for the mainline analysis.

The analytical process described above is graphically illustrated in figure 4.1:

 

I DOT accident data I

l

I Two-vehicle vehicles I

 

  

         
    

 

identifying
conflicting
information

 
    

identifying and
eliminating
hit-and-run crash

 

 

    
  
    
   
      

   
 

identifying and
eliminating selected
accident types

  
  
 

   
 

identifying and

eliminating
driver age <15 or
>100

 

l readily usable accident data

 

Figure 4.1. Flow chart of identifying and/or eliminating bad data

In summary, afier these operations are executed, accident data are expected to be
more reasonable and “cleaner” in the sense that there is less conflicting information in an
accident case, no accident with driver age falling below 15 or above 100, no hit-and-run
type of accidents, and no unreasonable accident types for a given circumstance.

A note on the issue of identifying and eliminating some accident data is the
percentage of accidents that drop out. After the stated analytical process, approximately
56.0% of the accidents are filtered out from Michigan accident database (2000).
Arguably, it is assumed that different driver-vehicle combinations are subject to the data
errors in the same manner and elimination of those data will not introduce bias to the
results. Table 4.6 shows the number of accidents and the percentages left after each step

(Michigan 2000).

65

Table 4.6. The number of accidents and the percentages left after each step

 

 

 

 

 

 

 

Steps number left Q1) percentage left (%)
1. total accidents 427,353 100.0
2. two-vehicle accidents 263,093 61.6
3. conflicting info 262,974 61.5
4. hit-and-run 226,347 53.0
5. driver age 187,845 44.0

 

 

 

 

Note that in each step, the operation is executed directly on the number of
accidents left from the preceding step. The most significant step is where accidents are
categorized based on the number of vehicles involved in an accident: about 38.4% of all
accidents are filtered out. The percentages dropped out due to hit-and-run crashes
accounting for 17.5%. The accidents shown in the last step are still not readily usable by
the quasi-induced exposure technique. For each individual driver, the status of
responsibility for accident fault is not clear at this point. How to assign responsibility will
be discussed next.

4.2 Responsibility assignment

Two topics will be covered in this section: 1) how to assign responsibility for two-
vehicle and three-or-more-vehicle accidents; and 2) whether accident data recorded by
different police agencies make any difference in terms of responsibility assignment.

4.2.1 Assigning responsibility

Responsibility assignment is a critical issue because the construction of the D1-
D2 matrix is based upon it. The literature review has indicated that several authors
(Lighthizer 1989, Davis et al. 1993, Stamatiadis et a1. 1995 and 1997, David et a1. 1997,
Aldridge 1999, Kirk et al. 2001) using the quasi-induced exposure have simply assumed
that the determination of responsibility in a two-vehicle accident is completely dependent

on whether the driver is given a citation.

66

Therefore, driver’s hazardous action is investigated to track what was happening
before the occurrence of an accident. It is argued that responsibility for accident causation
can be more reasonably and consistently assigned, if they are used in a combinatory
manner. Variables chosen for this process are:

0 The hazardous action (v1hazact, v2hazact, v3hazact), which is used to describe
the hazardous actions taken by various drivers; and

o The violation indication (v1violtr, v2violtr, v3violtr), which is used to identify
whether the driver receives a citation from the investigating police officer.

The following section will cover the responsibility assignment schemes for two-
and three-or-more-vehicle accidents.
4.2.1.1 Two-vehicle accidents

Before the responsibility-assigning scheme is developed for two-vehicle
accidents, the variables violation indication and hazardous action are examined. Based on
the coding menu, the variable violation indication takes only two values: 0 and 1. When a
driver’s violation indication is equal to 1, it means that the driver is issued a ticket by the
police officer; when 0, there is no citation. The coding for hazardous actions is more
complicated.

Table 4.7 shows the coding menu and the frequency of different hazardous
actions (first driver, 187,845 cases in total) after the accident data have been
systematically “cleaned.” Of the hazardous actions in table 4.7, many are clearly
interpreted as driving hazards while others either indicate that the first drivers have no
hazardous actions (35,277 cases) or actions are unclear or unknown. There are 8,149

accidents with the hazardous action “other” which implies some hazardous actions, but

67

the actions are not apparent and thus it is impossible to determine what they are; 3919

accidents with “unknown” hazardous action, which suggest that there might or might not

be hazardous action; and 1,904 accidents with hazardous action “uncoded and errors,”

which explicitly advises that certain (but unknown) data errors are affiliated with the

coding of hazardous action. Accidents with the hazardous action “uncoded and errors”

should be excluded from the analysis.

Table 4.7. Coding menu and the frequency of different hazardous actions (first driver)

 

 

 

 

 

 

 

 

 

 

 

 

 

description N description N description N
none 35277 drove Lt of center 1844 fail to stop ACD 53743
speed too fast 7392 improper pass 2401 other 8149
speed too slow 479 improper lane use 7360 unknown 3919
failed to yield 43807 improper turn 4955 reckless driving 265
disobeyed TCD 9484 improper signal 458 careless/negligent 1038
drove wrong way 223 improper backing 5147 uncoded & errors 1904

 

For two-vehicle accidents, the relationship between the hazardous action and

violation indication for each driver is studied. This helps to provide a general picture of

the responsibility-assigning scheme. Table 4.8 shows the cross-tabulation between

hazardous action and violation indication. Based on the information displayed in table

4.9, several important observations are made:

0 When hazardous action is “none,” the driver is not issued a ticket. There are

144,730 accidents with hazardous action “none” for second driver, while only

34,508 accidents for first driver. Comparatively, the first driver is likely to be “at-

fault” driver although it is not always the case.

0 While hazardous action is self-explanatory and specific (e.g., improper pass,

improper signal), both the first and second drivers are consistently issued

citations.

68

 

“reckless driving” or “careless/negligent,” the investigating police agent does not
issue a citation to the driver. Based on 2000-2001 Michigan Vehicle Code and Law

Related to Ownership and Use of Vehicle (Candice S. Miller, 2001), the definitions of

reckless driving and careless/negligent driving are:

occur even though the action is not clear.

issued a citation by the investigating police officers.

When a driver’s hazardous action is “other,” the driver is consistently issued a

citation by the police officers. This implies that certain specific hazardous actions

When a driver’s hazardous action is “unknown,” the driver is consistently NOT

Table 4.8. Cross-tabulation between hazardous action and violation indication

 

hazardous action

violation indication

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

first driver second driver
label no yes no yes
none 34508 0 144730 0
speed too fast 0 7349 0 2424
speed too slow 0 477 0 116
failed to yield 0 43617 0 9789
disobeyed TCD 0 9442 0 1956
drove wrong way 0 223 0 49
drove Lt of center 0 1839 0 404
imprOper pass 0 2384 0 720
improper lane use 0 7321 0 2171
improper turn 0 4927 0 1 182
improper signal 0 455 0 266
improper backing 0 5127 0 1238
fail to stop ACD 0 53534 0 12914
other 0 8091 0 2960
unknown 3898 0 3443 0
reckless driving 261 0 86 0
careless/negli gent 995 . 0 0 0
total 39662 144786 148259 36189

 

 

 

 

 

As highlighted in the shaded cells, when a driver’s hazardous action is

 

Reckless driving—any person who drives any vehicle upon a highway or other
place to the general public, including any area designed for the parking of motor
vehicles, within this state, in willful or wanton disregard for the safety of persons
or property is guilty of reckless driving (pp. 214).

Careless driving—a person who operates a vehicle upon a highway or other place
open to the general public, including an area designated for the parking of
vehicles in a careless or negligent manner likely to endanger any person or
property, but without wantonness or recklessness, is responsible for a civil
infraction (pp. 21 5).

According to the definitions, these two actions are indeed two driving hazards,
which likely triggered the occurrence of the accidents. They could be any driving
behaviors endangering the safety of persons or property (no matter intentionally or
unintentionally). Therefore, hazardous actions as such are indicative of traffic violations
and, thus, drivers with “reckless driving” and “careless/negligent driving” should be

assigned accident fault.

According to the above analyses and observations, the following scheme is
developed to assign responsibility in a two-vehicle accident:

0 When there is no hazardous action, the involved driver is not responsible for
the accident occurrence.

0 When the hazardous action is apparent, including reckless driving and
careless/negligent driving, the driver is responsible for the accident.

0 When the hazardous action is “other” (not apparent but nonetheless occurs),
the driver is responsible for the accident.

0 When the hazardous action is “unknown,” the driver is not responsible for the
accident.

Given this responsibility-assigning algorithm, each two-vehicle accident will take

one of the following three forms: one responsible driver and one non-responsible driver,

70

two responsible drivers, or two non-responsible drivers. Based on the theory of quasi-
induced exposure, the number of non-guilty parties in two-vehicle accidents with one
responsible and one non-responsible driver is the relative exposure. For the example of
Michigan 2000, 13,707 accidents are eliminated in this step, accounting for 3.2% of all
the accidents recorded, and 170,741 two-vehicle accidents remain, approximately 40% of
all the accidents in the database. Note that other accident data can be discarded: 1) for
accidents with no innocent driver, the involvement ratio will be inflated because Dls are
counted but D23 are not; and 2) for accidents with no guilty driver, the involvement ratio
will be underestimated because D23 are counted but Dls are not. Now accidents are
usable for quasi-induced exposure.

4.2.1.2 Three-or-more-vehicle accidents

Three-or-more-vehicle accidents provide an alternative to validate the underlying
assumptions of quasi-induced exposure through a comparison of the distributions for
non-responsible driver-vehicle combinations with those in two-vehicle accidents. Three-
or-more-vehicle accidents are contained in the same accident database as two-vehicle
accidents. Therefore, three-or-more-vehicle accident data are coded in the same manner
as those in two-vehicle accidents in the accident database. The responsibility-assigning
logic developed for two-vehicle accidents still applies.

An issue surfaces after the responsibility is assigned to the individual driver based
on the hazardous action: are all the three-or-more-vehicle accidents eligible for the
comparison? The answer is no. In a typical three-or-more-vehicle accident there must be
at least one responsible and one non-responsible driver, so accidents with no responsible

or non-responsible drivers will be eliminated. It is consistent with the theory of quasi-

71

induced exposure: there must be an accident initiator and an innocent victim in an
accident. However, it is possible that in a three-or-more—vehicle accident there are two or
more non-responsible or responsible drivers. The assumption that innocent driver-vehicle
combinations are randomly impacted by the guilty party in both two- and three-or-more-
vehicle accidents, lays the foundation for the stated comparison. Given this, the
distributions of all the non-responsible drivers in three-or-more-vehicle accidents are
comparable to D23 in two-vehicle accidents.

4.2.2 Accident data recorded by different police agencies

With responsibility assigned to each individual driver, one might be interested to
know whether reporting practice for different enforcement agencies makes any difference
in investigating and recording accidents in terms of assigning responsibility for accident
causation. The literature review has shown that there is a consistency issue in combining
accident data from different states in terms of different definitions of defective vehicles,
injury severity, and accident location. However, no past research has been found to
explore the issue of combining accident data fi'om different police agencies within the
same state.

It is possible that even a well-trained investigating police agent could misjudge
the accident scene and record inconsistent accident information. The degree of agreement
between a driver’s hazardous action and the violation indication will be indicative of the
performance of the particular police agency in recording the accident data.

The examination is done in a stepwise manner:

1. Determine responsibility for accident causation based on hazardous actions;

72

2. Identify accidents where drivers are responsible but not issued citations or

drivers are not responsible but issued citations;

3. Determine the frequency of inconsistency (step 2) for different law

enforcement agencies;

4. Determine the total number of accidents investigated by different law

enforcement agencies (based on total records); and

5. Calculate the percentage of inconsistency by different law enforcement

agencies, defined as the ratio of step 3 to step 4.

Conveniently, step 1 can be achieved with the procedure developed in the
previous section. In steps 2 and 3, if a driver is assigned the responsibility but not issued
a citation or not assigned the responsibility but issued a citation, his/her information has
been inconsistently recorded by the police officer. For ease of explanation, the accidents
with such information are labeled as “inconsistent” accidents. Based on the percentage of
inconsistently reported accidents, the performance of each police agency can be evaluated
by comparing it with others.

Using Michigan 2000 data as an example (without any data manipulation), three
tables (4.9-4.11) show the cross-tabulations between driver responsibility and violation
indication for the first, second, and third drivers, respectively. The highlighted cells in
tables 4.9, 4.10, and 4.1 l are the number of drivers where responsibility and violation
indication are inconsistent. Interestingly, for those inconsistent accidents, it is always the
case that drivers have hazardous actions but receive no citations. The percentages for the
first, second, and third drivers are 2.0%, 0.1%, and 0.1%, respectively. Since some

accident records contain more than one inconsistent driver, the number of accidents adds

73

up 8477 in total. This subtotal will be further allocated among different Michigan police
agencies.

Table 4.9. Crosstabulation of responsibility and violation indication (first driver)

 

 

 

 

 

 

 

 

 

 

vrolatron mdrcatron total
no yes
hazardous no 155511 0 15551 1
action yes 8208 249649 257857
total 163719 249649 413368

 

 

Table 4.10. Crosstabulation of responsibility and violation indication (second driver)

 

 

 

 

 

 

 

 

 

vrolatron mdrcatron total
no yes
hazardous no 224453 0 224453
action yes 274 51685 51959
total 224727 51685 276412

 

 

 

Table 4.11. Crosstabulation of responsibility and violation indication (third driver)

 

 

 

 

 

 

 

 

 

vrolatron mdrcatron total
no yes
hazardous no 18321 0 18321
action yes ‘ 23 ’ 323 1 3254
total 18344 3231 21575

 

 

 

Four types of law enforcement agencies collect Michigan accident data: Michigan
State Police (MSP), county sheriffs, township police, and city and other police. Table
4.13 presents the number of inconsistent accidents (step 4) and total accidents (step 5)
reported by different agencies. In table 4.13, the percentage is formulated as the ratio of
step 4 to step 5, that is, the proportion of inconsistent accidents recorded by different
police agencies. The table shows that township police officers are the most consistent,
and then sheriffs, city police, and the MSP. On the other hand, the percentages are

relatively close (within one percentage point). It is argued that, operationally there is no

74

significant difference in the quality of accident data among the four different types of

police agencies.

Table 4.12. Inconsistent and total accidents by different police agencies

 

 

 

 

 

 

police type inconsistent (step 4) total (step 5) percentage (%)
MSP 616 34228 1.8
sheriff 1070 71322 1.5
township 363 302 l 5 1 .2
city and others 6428 277603 2.3
total 8477 413368 2.1

 

 

 

 

 

 

In summary, Michigan accident data do not show a conspicuous discrepancy of
accident data among the data collected by different levels of police agencies, at least as
hazardous actions and violation indication are concerned.

4.3 Conclusion

Accident data fi'om state DOTs are a convenient data source for the use of quasi-
induced exposure, although the raw data are typically not ready for immediate analysis.
In this chapter, the attempt was made to develop a systematic procedure to make the raw
accident data relatively error-flee, with the example of Michigan accident data. The
procedure can be generalized to other states, since the accidents obtained from other
states also encompass all the necessary screening variables and information. The “rules”
to “clean” accident data are summarized as follows:

0 For drinking, the incidence of drinking does not appear to adversely affect the
decision-making of investigating officers’ issuing citations. Therefore,
accidents with drinking driver(s) should not be removed.

0 For hit-and-run crashes, the accidents are incompletely recorded. Hit-and-run

accidents are eliminated.

75

o For driver age, some accidents are identified as having drivers with unusual

ages (<15 or >100). Although the percentage is negligible, such accidents will
be removed.

The most typical accidents with conflicting information are those two-vehicle
accidents miscoded as one- or three-or-more-vehicle accidents. A feasible
solution is to count the number of drivers/vehicles after a problematic accident
is identified and to redefine the value—the number of vehicles involved in an
accident.

For accident type, special attention should be given to the fact that under a
specific circumstance, only certain types of accidents are reasonable. For
example, if a study is developed to focus on the accident on a fi'eeway
segment, accidents occurring at the freeway on- and off-ramps should be

eliminated.

Reasonable responsibility assignment is developed for two- and three-or-more-

vehicle accidents, the logic of which is summarized:

When there is no hazardous action or it is “unknown,” the involved driver is
not responsible for the accident.

When a hazardous action is apparent or hazardous action is “other,” including
reckless driving and careless/negligent driving, the driver is responsible for
the accident.

Accidents with hazardous actions “uncoded and errors” are eliminated.

In addition, it is found that there is no operational difference among the accidents

investigated by different police agencies in Michigan.

76

After this procedure is completed, the data are ready to be used in quasi-induced

exposure-related studies.

77

Chapter 5

VALIDATION OF THE ASSUMPTIONS OF QUASI-INDUCED EXPOSURE

Fundamental to quasi-induced exposure is the assertion that D23 in two-vehicle
crashes constitute a random sample of the driving population on the road at the time and
place of the crash. The goal of this chapter is to employ three externally available data
sources to validate the underlying assumptions. The data used in this chapter include
vehicle miles of travel (VMT), safety-belt use data fiom the University of Michigan
Transportation Research Institute (U MTRI), and truck volume data (W-2 data) fiom the
Federal Highway Administration.

The basic idea is to compare the D2 distributions for driver-vehicle characteristics
calculated from accident data with those derived from externally available data sources,
to see if they are the same. Note that the driver-vehicle characteristics studied include:
driver gender, age, and vehicle type. Criteria are established to determine if the difference
between two distributions is significant from operational and/or statistical (chi-square
test) perspectives. Now, the question remains how to justify the significance thresholds
for the practical and statistical differences.

As for statistical difference, a significance level of a = 0.05 is a commonly used
and accepted threshold in the scientific and engineering-related studies. Based on the chi-

square contingency table, if the p-value given by the test is greater than 0.05 (significance

78

level), the null hypothesis that there is no significant difference of D2 distributions is
accepted; otherwise it will be rejected. For practical difference, the significance threshold
(,uo) is determined by satisfying the following constraint:
P(x 6 i; —p0,,u +pojl2 0.95
where,
P is the probability function;

x is an observed percentage (distribution) for certain driver-vehicle characteristic
(i.e., driver age, gender, and vehicle type);

,1: is the average percentage (distribution) for certain driver-vehicle characteristic

under various circumstances (e.g., different functional roadways, weather
conditions, time of day, day of week, year, month, etc.);

,uo is the significance threshold for certain driver-vehicle characteristic; and

[2’— ‘ #0 a; + #0] is the confidence interval.

The statistical meaning of the constraint is that there is at least 95% probability

that a randomly observed percentage (x) falls within a specified confidence interval
(l; - 110,; + 110]). The minimum value of 110 , which satisfies the inequality, is the
significance threshold. Based on the empirical practices, the threshold (,u0 = 0.04) can

satisfy the conditions for all three driver-vehicle characteristics. Therefore, if the
difference for each characteristic is more than 4 percentage points, it is operationally
significant; otherwise it is not.

It needs to be pointed out that the “operational” results do not necessarily match
the results of the chi-square test. It would be desirable that both methods generate the
same results—that is, the difference is operationally aid statistically significant or
insignificant. However, there are always some cases that the two results differ. In
addition, in order to argue that two distributions are similar, all the driver-vehicle

characteristics examined must be consistent concurrently. For example, it is assumed that

79

male young drivers use the same vehicles as male old drivers. Since the former drives
more aggressively than the latter, it is reasonably argued that young male drivers belong
to a different driving cohort from old male drivers. Therefore, similarity of two
distributions requires the consistency of all characteristics of interest.

In next sections how to use three externally available data to validate the
underlying assumptions of quasi-induced exposure will be discussed.

5.1 Validation using vehicle miles of travel data
5.1.1 Introduction

Estimates of VMT can be used to validate the underlying assumptions of quasi-
induced exposure. Generally, VMT data are directly collected from household travel
surveys conducted by state DOTs or others, or indirectly estimated from traffic counts
observed at counting stations. VMT estimates can also be derived from statewide
gasoline consumption surveys. In theory, these data will give a true indication of the
annual rrriles of travel for a typical cohort. Comparing the calculated exposure (D23) fiom
accident data with “true” exposure (VMT) would be one test for the validity of quasi-
induced exposure.

In chapter two, several theoretical and operational difficulties in using VMT as an
exposure measurement were identified. In terms of validating the assumptions of quasi-
induced exposure, the most critical issue is unavailability or limited availability of VMT
data disaggregated by desirable variables (driver age, gender, and vehicle type). For
instance, VMT data obtainable from the Michigan DOT are disaggregated by trunkline
types. So, the fundamentally useful information is the statewide VMT. In some cases

state VMT data are calculated based on traffic counts and can be disaggregated by

80

functionally classified roadway types. Other than that, VMT data disaggregated by driver
characteristics are difficult to obtain. Fortunately, the dilemma can be partially resolved
with the aid of other data sources such as the National Household Travel Survey (N HTS).
A typical NHTS report contains detailed information on a respondent’s household,
personal characteristics, annual vehicle miles traveled, and so on. Based on census
statistics of respondents with the same characteristics (e.g., gender, age group) at the state
level, it is possible to calculate the average annual VMT (AVMT) by gender and age
group. However, the NHTS data are not usable to compute VMT for different vehicle
types. Thus, driver-vehicle characteristics examined in this section only consist of driver
age and gender.

Once average annual VMT by gender and age, serving as “true” exposure, are
indirectly calculated fi'om NHTS, they can be compared with D23 derived from accident
data. Note that accident data used in this section are obtained fi'om the Highway Safety
Information System (HSIS). HSIS is “a multistate database that contains crash, roadway
inventory, and traffic volume data for a select group of states” (HSIS website). The most
obvious advantage of using HSIS data is that they are available to the general public.
Currently, there are nine participating states in HSIS, including California, Minnesota,
Illinois, North Carolina, Maine, Ohio, Michigan, Utah, and Washington. The accident
data for most of the states contain sufficient and necessary information to satisfy the data
requirements for using the quasi-induced exposure method.

The following sections include the discussion of the methodology to compare
VMT to D23, the description of the HSIS data, and then the manipulation of the HSIS

data, followed by introduction of NHTS, the development of annual VMT estimated for

81

different driver genders and age groups, the comparisons of VMT and relative exposure
estimated by quasi-induced exposure, and conclusions.
5.1.2 Methodology

Using the NHTS data, it is theoretically possible to generate VMT data
disaggregated by variables of interest—driver age and driver gender for individual states.
Examination of the extent of agreement between relative quasi-induced exposure and
“true” exposure helps to reveal if the assumption of quasi-induced exposure will be
satisfied by accident data.

VMT data can be directly compared to the relative exposure derived from

accident data for D2 characteristics. The steps in this comparison include:

1. Calculate the percentage of “true” exposure for each state based on annual VMT
data from the NHTS, disaggregated by age and gender;

2. Calculate the relative quasi-induced exposure stratified by the same two D2
characteristics (age and gender), for each state;

3. Compute the percentage distributions of age and gender based on step 2; and

4. Compare the results fi'om step 1 with step 3 to validate D23 as a measure of
exposure.

If D2 distributions disaggregated by age and gender are consistent with those
based on VMT data, it indicates that the underlying assumptions of quasi-induced
exposure are validated for the given data stratification (e. g., the state level).

5.1.3 Highway safety information system (HSIS)
In order to improve the consistency of data across multiple states, two generic

variable tables are developed for the nine states in HSIS. The first table lists the crash-

82

related variables for each state, and the second table contains the roadway-related
variables. The basic crash-related variables are divided into three separate subfiles for
ease of computer handling: accidents, vehicles, and occupants. Each accident in the
accident file is identified by a unique case number and has only one record (observation)
per crash. The vehicle file can have multiple records per crash, depending on the number
of vehicles involved, and all vehicles in a given crash are also identified by the (same)
unique case number. Similarly, the occupant file has one or more occupants per vehicle
with all occupant records being identified with the unique case number. The accident,
vehicle, and occupant files can be linked together using the unique case number. The
roadway inventory variables describe a section of roadway and are available in a variety
of different files for different states. According to the nature of the HSIS data structure,
only the accident and vehicle files in the crash-related table are chosen. They are
sufficient for satisfying the data need in validating the underlying assumptions of quasi-
induced exposure.

Note that not all HSIS states are chosen for study. Whether a state is chosen
depends on the availability of a detailed data guidebook (that is, the accident data coding
menu) for each state. As listed in the HSIS website, guidebooks are only available for
California, Maine, Minnesota, and Utah. Although Minnesota is on the list, it is not
chosen due to its mismatched coding menu: variables in the accident data do not match
with those in the guidebook. While Michigan does not have a guidebook, the coding
menu is available fiom the Michigan DOT. As a result, accident data fiom California,

Maine, Michigan and Utah will be utilized to develop comparisons.

83

The HSIS database contains only those crashes that occur on state-maintained
roads. The reason is that the locations of these crashes are assumed to be more accurate
than the crashes occurring on the local streets and roads for a given state. In order that
VMT data are comparable with D2 data calculated from HSIS, only those accidents
occurring on corresponding parts of the system will be selected.

5.1.4 Manipulation of HSIS data

HSIS vehicle and accident data are contained in two separate files. The accident
file contains basic information on the nature of the accident, such as accident type,
location, time, environment, and number of vehicles involved. The vehicle file has
information on the characteristics of the driver(s) and vehicle(s) in the crash, such as
driver age, driver gender, and vehicle type. As mentioned earlier, there is one unique case
number in the accident file, while there are several identical case numbers in the vehicle
file depending on the number of vehicles involved in a crash. Linkage of these two files
is necessary to develop quasi-induced exposure estimations.

A problem arises in that different drivers in the same accident are coded as
different data records in the vehicle file. All driver-vehicle information in the same
accident, listed as individual records, must be reformatted as a single data record. The
resultant data are then handled by an available statistical software package (i.e., SPSS).

The combined accident records (containing accident and involved driver-vehicle
information) are not necessarily coded in an error-free manner. Simple descriptive
statistics reveal that some accidents are missing information for the variables of interest
(e. g., driver age), or have unreasonable values (e. g., other than male and female for

gender). Therefore, the systematic rules developed in an earlier chapter to prepare

84

Michigan accident data must be applied here in order to make HSIS data usable. In the
event of assigning fault, the developed responsibility assignment scheme can also be
applied here, considering the similar coding for hazardous actions and violations between
Michigan data and other states.

The objectives of the preliminary manipulation of HSIS data are to link the
vehicle and accident information, reformat all the driver-vehicles in the same accident as
a single record, “clean” the erroneous or miscoded accident data, and, finally, assign
responsibility for the accident to each driver-vehicle combination.

With Utah data chosen as an example, the following section will cover how the
HSIS accident data are manipulated in a systematic manner. The values shown in the
tables below are adapted from the original Utah accident coding as noted by HSIS. In
table 5.1.1, one accident case is coded as one row (record); while in table 5.1.2, one
driver-vehicle combination is coded as one row (record). Both of the tables contain an
identical variable which can be used to combine them into one record—accident case

number (caseno).

Table 5.1.1. Sample data from Utah accident file (2000)

 

 

 

 

 

 

 

 

caseno accident variable list
rodwycls agency weekday month hour acctype county light
200000002 08 00207 7 1 10 4 03 2
200000003 06 0000F 1 1 21 2 03 5
200000004 00 01000 2 1 12 2 l9 2
200000005 08 00100 2 1 15 7 01 2
200000006 00 01600 2 1 l 1 10 3 1 2

 

 

 

 

 

 

 

 

 

 

85

 

Table 5.1.2. Sample data from Utah vehicle file (2000)

 

case no

driver-vehicle variable list

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Vehno vehgpe contribl contrin drv’sex drv age
200000002 1 2 l . . . 0 2 50
200000003 1 32 7 ... 14 l 42
200000003 2 5 3 . . . 15 1 20
200000003 3 2 7 . . . 14 2 29
200000004 1 20 51 . . . 0 1 51
200000005 1 33 30 ... 50 1 40
200000006 1 40 1 ... 0 l 50
200000006 2 6 42 . . . 0 l 67

 

The diagram in figure 5.1.1 shows the whole process for manipulating the Utah

accident data, which consists of several “operation” modules.

 

 

 

 

 

 

 

 

 

 

 

 

Utah data from HSIS
Utah accident file Utah vehicle file
7
computer programming

 

 

linkage by case No.

 

 

T

 

 

clean accident data

 

 

v

 

 

assign responsibility

 

 

 

 

 

 

2-vehicle accidents

 

 

'\ >2 vehicle accidents

 

 

Figure 5.1.1. Flow chart of manipulating Utah accident data

In the flow chart, the “computer programming” module is specially designed to

eliminate one-vehicle accidents in the vehicle file and then split the vehicle file into two

subfiles: two-vehicle accidents and three-or-more-vehicle accidents. Each subfile is

manipulated in a way that all driver-vehicle information for the same accident is

rearranged in the same row (record). This was done using Microsoft C++ (programming

code can be found in Appendix A). The function “linkage by case No.” is to link the

86

 

accident file to the vehicle file. The systematic rules developed to select useful and
dependable accident data and assign responsibility for accident causation in chapter four
are contained in the “clean accident data” and “assign responsibility” modules,
respectively. After this is done, a typical HSIS accident data record will take the form
shown in table 5.1.3, with responsibility clearly assigned for each vehicle.

Table 5.1.3. Desirable data format for a typical HSIS data record

 

accident vehicle 1 vehicle 11 I
hour county age sex age sex I
| 20004 15 19 29 2 51 1 I

 

0386110

 

 

 

 

 

 

 

 

 

 

 

 

At this point, the work with three-or-more-vehicle accidents will not be discussed.
The details of how to use three-or-more-vehicle accidents to validate the underlying
assumptions of quasi-induced exposure will be covered in a later chapter. The following
section is about how to use NHTS data to estimate VMT disaggregated by driver age and
gender.

5.1.5 National household travel survey (N HTS)

The National Household Travel Survey (NHTS) is the nation’s inventory of daily
and long-distance travel by telephone interviews. The NHTS is a survey of the civilian,
non-institutionalized population of the United States. The survey includes demographic
characteristics of households, people, vehicles, and detailed information on daily and
longer-distance travel for all purposes by all modes. NHTS survey data are collected from
a sample of US. households and expanded to provide national estimates of trips and
miles by travel mode, trip purpose, and a host of household attributes. These data provide
planners and decision makers with up-to-date information to assist them in effectively

improving the mobility, safety, and security of the nation’s transportation systems. It

87

should be pointed out that a relatively low response rate (41%) was achieved in 2001
NHTS survey, which might result in the non-response bias, and coverage bias could have
been introduced by excluding the households without land-line telephone. The margin of
error in the survey results are assessed to be up to 10%.

In the research context here, 2001 NHTS data are utilized to derive average
AVMT information for a specified driver group on a state basis. The 2001 NHTS data are
composed of four major files: household, person, vehicle, and day trip. The person file is
of the most interest, which contains key variables that can be used as the basis for
calculating disaggregated AVMT.

Ideally, gender/age group VMT can be estimated for several different states for
which accident data are readily available (California, Maine, Michigan and Utah).
However, in the 2001 NHTS data, Maine is one of the states where household location is
not categorized individually but combined with other states having population less then
one million. In this context, respondents from Maine cannot be separated from other
states. Consequently, comparisons of VMT with D2 estimates are limited to three states:
Califomia, Michigan, and Utah.

5.1.6 Average annual vehicle miles traveled

Four key variables from the person file have been identified to be the most
valuable and relevant: state-household location, respondent age, respondent gender, and
miles respondent drove during the last 12 months. It has been found that some cases are
not usefirl because respondents refused to answer what they were asked. Appropriate
actions are necessary to screen out the unclear data. And then, based on the state-

household location, separate datasets are created for each state. In each individual state,

88

data are further disaggregated by D2 characteristics (driver age and gender in this case),
with which annual VMT is averaged over all the respondents. For an example of driver
gender, average annual VMT for male drivers is the total annual VMT by all the male
respondents divided by the number of male respondents; the same concept is adopted for
female drivers and other characteristics. The following flow chart shows the process

graphically (figure 5.1.2).

 

National Household Travel Survey
person file

f

 

 

 

   

 

household state

W

eliminat; “bad” data

1

data split by household state
Michigan California Utah

1 l I

data disaggregated by gender or age group

i 1 1

average AVMT by gender or age group

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure 5.1.2. The process to derive average AVMT

In the above process, three assumptions are implicitly made to estimate average
annual VMT:
1. the survey respondents primarily travel within his/her household state;
2. the survey respondents are a random sample of the driving population on the road;

and

89

3. the respondent can accurately estimates AVMT and each sex and each age group
makes the same average errors.

Practically speaking, the first assumption is likely to be true. For the second
assumption, since NHTS is a national survey, data collected from a nationally
representative sample of households should be reliable to derive statistically reliably
travel estimates at the national and state levels.

VMT percentages

Mathematically, the average annual VMT disaggregated by driver characteristics
(e. g., female AVMT) multiplied by the corresponding population yields total annual
VMT (e.g., total female AVMT). The population information comes fi'om state census
data which are available to the public.

The following series of tables is the presentation of total annual VMT estimates
and percentages (the distributions) disaggregated by driver gender and age group for
Michigan, Utah, and California in 2001.

Table 5.1.4. Total AVMT and percentages disaggregated by age group (MI)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

age group average census total AVMT percentage
AVMT (mi) (million) (%)
15-19 6,526 659,423 4,303 3.9
20-24 14,646 642,409 9,409 8.5
25-34 16,118 1,335,227 21,521 19.4
35-44 17,858 1,590,477 28,403 25.6
45-54 17,207 1,429,001 24,589 22.2
55-64 14,736 895,921 13,202 1 1.9
65+ 8,083 1,156,882 9,351 8.4
total 13,956* 7,709,340 110,778 100.0

 

*This number is averaged AVMT for driver age or gender; same as below.

90

Table 5.1.5. Total AVMT and percentages disaggregated by gender (MI)

 

 

 

 

 

 

 

 

 

gender average census total AVMT percentage
(age>14) AVMT (mi) (million) (%)
male 17,607 3,713,910 65,391 59.7
female 1 1,058 3,995,430 44,182 40.3
total 14,333* 7,709,340 10935733139 100.0

 

 

 

As highlighted in tables 5.1.4 and 5.1.5, the total AVMT by age group and gender
are fairly close. The estimation error, defined as the difference between two AVMT totals
divided by the arithmetic mean, is approximately 1.1%, which is small enough to be
negligible. And, a relatively small estimation error (2.6%) is also found between the
average AVMT among different age groups (13,956 miles/year) and genders (14,333
miles/year).

Table 5.1.6. Total AVMT and percentages disaggregated by age group (UT)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

age group average census total AVMT percentage

AVMT (mi) (million) (%)
15-19 5,344 190,821 1,020 4.6
20-24 12,488 229,278 2,863 12.9
25-34 15,134 339,667 5,141 23.2
35-44 19,536 287,678 5,620 25.1
45-54 14,897 246,105 3,666 16.5
55-64 17,962 147,017 2,641 1 1.9
65+ 6,639 186,648 1,239 5.6

total 13,143* 1,627,214 22,190 100.0

 

Table 5.1.7. Total AVMT and percentages disaggregated by gender (UT)

 

 

 

 

 

gender average census total AVMT percentage
(age>14) AVMT (mi) (million) (%)
male 16,866 804,152 13,563 61.2
female 10,428 823,062 8,583 38.8
total 13,649* 1,627,214 22,146 100.0

 

 

 

 

 

 

 

Compared to Michigan data, the estimation error between two AVMT totals in

UT is much smaller, less than 0.3%; but, the estimation error for average AVMT among

91

all age groups (13,143 miles/year) or genders (13,649 miles/year) is approximately 3.8%.
These errors can be ignored as well. Note that the calculated estimation error is intended
to show the internal consistency between the average vehicle miles traveled data by
driver gender and driver age. For UT and MI data, the AVMT data obtained from

different approaches are operationally close.

For CA, the AVMT totals from different age groups and genders are fairly

close—the estimation error is 0.6% (table 5.1.8). And, the average AVMT among

different age groups (12,438 miles/year) and genders (13,039 miles/year) are also

consistent, approximately 1% (table 5.1.9).

Table 5.1.8. Total AVMT and percentages disaggregated by age group (CA)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

age group average census total AVMT percentage
AVMT (mi) (million) (%)
15-19 7,049 2,368,932 16,699 5.1
20-24 15,288 2,279,533 34,850 10.6
25-34 14,187 5,028,008 71,332 21.7
35-44 15,505 5,335,260 82,723 25.1
45-54 14,049 4,354,l 18 61,171 18.6
55-64 13,088 2,665,045 34,880 10.6
65+ 7,900 3,481,862 27,507 8.3
total 12,438* 25,512,758 329,161 100.0

 

Table 5.1.9. Total AVMT and percentages disaggregated by gender (CA)

 

 

 

 

 

 

 

 

 

gender average census total AVMT percentage
(age>14) AVMT (mi) (million) (%)
male 15,603 12,488,228 194,854 58.8
female 10,475 13,024,530 136,432 41.2
total 13,039* 25,512,758 331,286 100.0

 

In general, for each individual state, the total or average AVMT for different

driver genders agree with different driver age groups, which suggests the reliability and

integrity of VMT and census data.

92

 

 

It needs to be pointed out that the VMT distributions are calculated based on the
census data. Using census p0pu1ation to replace driving population (i.e., traffic volume
data disaggregated by three key characteristics) will likely cause some age groups to be
overrepresented while others are underrepresented. For example, young drivers are
assumed to drive more frequently than their proportion in census distribution while old
drivers tend to drive less. Consequently, young drivers will be underrepresented in the
driving population, while older drivers are overrepresented. So, in order to be technically
accurate and comparable with D2 distributions, VMT distributions should be computed
based on driving population data. At this point, due to the unavailability of traffic volume
data, it is assumed that driving population is characteristic of the census population at
each state.

5.1.7 D2 distributions

Calculating the D2 distributions is straightforward and based on accident data. For
Michigan, accident data are readily available from the Michigan DOT. California and
Utah accident data are obtained from the Highway Safety Information System (HSIS).
However, California and Utah data are not complete as only the accidents occurring on
state-maintained roads are filed with HSIS. Examination of the accident guidebook for
each state reveals that accidents recorded in the HSIS system occur on mainline roadway
segments and related areas (e. g., on-ramp, off-ramp, rest areas). It has been known that
under a given road and traffic setting, there might be a limited number of accident types.
Therefore, selection of accidents on state-maintained routes could be a case-specific

process.

93

For Michigan data (tables 5.1.10 and 5.1.11), D2 distributions are developed for
three categories: all accidents (total), trunkline accidents, and non-trunkline accidents.
Trunkline accidents are distinguished from non-trunkline accidents according to the
variable “control section.” The control section is a five-digit code that identifies the
portion of the trunkline system: the first two digits are the MDOT county number and the
last three digits are the unique trunkline segment number. If the five—digit code is
composed of five zeros, the route is non-trunkline. So, the trunkline can be distinguished
fiom the non-trunkline based on the control section values.

Trunkline and non-trunkline accidents are compared to see if the D2 percentage
distributions are different. Based on the Michigan experience, one can generally
estimate/predict whether D2 percentage distributions in trunkline and non-trunkline
accidents follow the same pattern, the results of which can be reasonably presumed for
two other states: California and Utah. It has been implicitly assumed that the definitions
of the truckline are similar among the states of interest.

Table 5.1.10. D2 gender distributions for Michigan data (2001)

 

 

 

 

 

 

 

 

 

 

 

 

gender Michigan total Michigan trunkline Michigan non-trunkline
N % N % N %
male 75512 53.7 24301 55.0 51211 53.1
female 65137 46.3 19899 45.0 45238 46.9
total 140649 100.0 44200 100.0 96449 100.0

 

 

According to table 5.1.10, there is a 1.9 percentage point difference of D2 male
drivers between trunkline and non-trunkline accidents. Since this difference is
operationally small, it is argued that the D2 gender distribution on trunklines is not
significantly different from that on non-trunklines. Examination of the differences for age

groups in table 5.1.11 also reveals the same phenomenon.

94

Table 5.1.11. D2 age distributions for Michigan accident data (2001)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

age Michigan total Michigan trunkline Michigan non-trunkline
N % N % N %

15-19 14166 10.1 4109 9.3 10057 10.4
20-24 16929 12.0 5461 12.4 1 1468 l 1.9
25-34 30299 21.5 9572 21.7 20727 21.5
35-44 31357 22.3 9972 22.4 21385 22.2
45-54 24974 17.8 7940 18.0 17034 17.6
55—64 12581 8.9 3991 9.0 8590 8.9

65+ 10343 7.4 3155 7.0 7188 7.5
total 140649 100.0 44200 100.0 96449 100.0

 

Based on the Michigan experience, it is reasonable to predict that for CA and UT

accident data, the D2 driver-vehicle combinations involved in the trunkline-related

accidents are representative of those in all accidents. Tables 5.1.12 and 5.1.13 show the

D2 distributions of gender and age on trunldine roads for CA and UT.

Table 5.1.12. D2 gender distributions for CA and UT data (2001)

 

 

 

 

 

 

 

 

 

 

gender Utah trunkline California trunkline
N % N %
male 13819 57.6 12823 64.1
female 10179 42 4 7178 35.9
total 23998 100.0 20001 100.0

 

Table 5.1.13. D2 age distributions for CA and UT data (2001)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

age Utah trunkline California trunkline
N % N %
15-19 3415 14.2 1197 6.0
20-24 4290 17.9 2174 10.9
25-34 5450 22.7 4851 24.3
35-44 4589 19.1 5110 25.5
45-54 3252 13.6 3720 18.6
55-64 1704 7.1 1818 9.0
65+ 1298 5.4 1131 5.7
total 23998 100.0 20001 100.0

 

 

 

 

As shown in tables 5.1.12 and 5.1.13, the total number of accidents for CA and

UT is fairly small, compared to M1 (140,649 cases in total). Based on the CA guidebook,

95

there are about 500,000 total accidents that occur each year, and approximately 160,000
occur on the state-maintained highway system. However, for CA data, significant
percentage of accidents is filtered out and approximately 17.5% is usable by quasi-
induced exposure.

In table 5.1. 12, the percentage of D2 male drivers in CA is much larger (6.5
percentage points) than UT. Operationally, the difference is significant. In table 5.1. 13,
there is considerable difference (5-8 percentage points) for the several age groups when
D2 age distributions are compared across states.

Although the differences in D2 distributions among states are recognized, it is
more important to know whether the D2 distributions for age and gender are significantly
different from those based on VMT for each state.

5.1.8 Comparison of D2 and VMT estimations

Comparisons between D2 and VMT exposure estimates are made for Michigan,
California, and Utah and the results are evaluated with operational and statistical
methods.

Tables 5.1.14 and 5.1.15 are created from information shown in tables 5.1.4
through 5.1.13. The percentage difference is defined as the VMT percentage minus the
corresponding D2 percentage. A positive sign indicates that the VMT percentage is larger
than the D2 percentage; a negative sign shows the opposite.

Table 5.1.14. Gender percentage difference (VMT-D2) among different states

 

 

 

I gender Michigan trunkline Utah trunkline California trunkline
| male 4.7 3.6 -5.1
| female 4.7 -3.6 5.1

 

 

 

 

 

96

Table 5. 1 . 15. Age percentage difference (VMT-D2) among different states

 

 

 

 

 

 

 

 

age Michigan trunkline Utah trunkline California trunkline
15-19 -6.5 -9.6 -0.9
20-24 -3.4 -5.0 -0.3
25-34 -2.1 0.5 -2.6
35-44 3.4 ‘ 6.2 -0.4
45-54 ’ 4.6 T 2.9 0.0
55-64 3.0 ‘ ‘ 4.8 1.6
65+ 0.9 0.2 2.6

 

 

 

 

 

 

The shaded cells in tables 5.1.14 and 5.1.15 are indicative of where the percentage
difference is operationally significant. D2 gender distributions for both Michigan and
Califomia data show a disagreement with those based on VMT data; two age groups (15-
19 and 45-54) in Michigan data and four age groups in Utah data show that percentage
differences are considerable. Although there is consistency in the gender distribution for
Utah data and in the age distribution for California data, D2 distributions are claimed to
be different from VMT disaggregated by age and gender for the three states discussed.

The percentage differences by gender and age for each state are also tested using
chi-square test to see if they are statistically significant. The chi-square statistic and p-
value for each comparison are presented in table 5.1.16. Note that for driver gender and

vehicle type, the critical value 1005(1) is equal to 3.84; for driver age, the critical value

10.05 (2) iS equal to 6.00.

Table 5.1.16. Summary of chi-square statistics and p-values

 

 

 

I Michigan trunkline Utah trunkline California trunkline I
I gender 286 (000*) 64 (0.00) 219 (0.00) |
age 2969 (0.00) 1851 (0.00) 300 (0.00) ]

 

 

 

 

*p-values are shown in the parenthesis.
As shown in table 5.1.16, the p-values for gender and age given by chi-square test

are constantly equal to zero. Since p-values are less than 0.05, the null hypothesis that

97

there is no significant difference of distributions between the VMT and D23 is rejected.
Statistically speaking, the underlying assumptions of quasi-induced exposure are not
supported for Michigan, California, and Utah data.
5.1.9 Conclusion

It has been shown that quasi-induced exposure estimates are operationally and
statistically different from VMT estimates for Michigan, Utah, and California. The VMT
estimates are derived from NHTS in combination with census data. The NHTS is a
national survey and collects data from a nationally representative sample of households at
the national and state levels. Therefore, the travel estimates should be statistically reliable
and representative of individual states. However, the VMT distributions are calculated
based on the census data instead of the driving population data (i.e., traffic volume data).
The data are actually indicative of the distribution of census-population for each state.
The assumption that driving population is characteristic of the census population at each
state must not hold.

As indicated earlier, the survey results are subject to up to 10% margin of error.
Since the VMT disaggregated by driver age and gender for each individual state,
supposedly as an exposure “truth,” can not be justified, the validity of D2 data can not be
determined. Therefore, it is inconclusive whether quasi-induced exposure is a legitimate
approach to measure the relative exposure on the state-maintained routes as the accident
data represent. Further research efforts are necessary to derive more dependable and
accurate VMT estimates.

The following section will cover how to use safety-belt use data to develop a

similar analysis.

98

5.2 Validation using safety-belt use data
5.2.1 Introduction

Another source of data for validation of the quasi-induced exposure technique is a
series of direct observation surveys conducted by the University of Michigan
Transportation Research Institute (UMTRI) for the purpose of studying safety-belt use
among motor vehicle occupants in Michigan. The data were collected as part of an
evaluation of the effectiveness of Michigan’s mandatory safety-belt use law/policy and
enforcement. The safety-belt data can be viewed as scientifically sampled traffic counts
disaggregated by driver and passenger gender, age, day of week, time of day, and
observation site type (intersection or freeway off-ramp). The safety-belt data include the
information on front-outboard vehicle occupants (driver and front-seat passenger) in
eligible commercial and noncommercial vehicles (passenger car, vans/minivans, sport-
utility vehicles, and pickup trucks). In terms of the research here, driver and vehicle
information in these safety-belt data are the potentially useful elements.

The safety-belt data are systematically observed and collected following a strict
sampling plan. The sampling design plan used by UMTRI follows federal guidelines for
state observational surveys for safety-belt use as developed by the National Highway
Traffic Safety Administration (NHTSA, 1992 and 1998). A systematic sampling
procedure is employed which has been designed in a manner such that selection of
observations sites is random. Since the NHTSA guidelines are strictly followed in the
data collection, the precision of the observed data is expected to be less than 5% relative

error. The resultant data represent a random sample at the state level. Therefore, at this

99

level, the safety-belt data serve as a measure of “true” exposure of the statewide driving
population. .

The underlying assumption of quasi-induced exposure is that D23 in two-vehicle
accidents constitute a random sample of the driving p0pulation on the road at the time of
accident occurrence. Comparison of the distributions for driver-vehicle characteristics
between safety-belt data and non-responsible driver-vehicle combinations (D23) will help
to determine if D23 are really a random sample of the driving population on the road.
5.2.2 Methodology

In the attempt to validate the assumption of quasi-induced exposure, D2 data must
be comparable to the observed safety-belt use data, i.e., in terms of roadway type,
weather, day of time, and vehicle classification. In the comparison, both the safety-belt
and D2 data contain three basic characteristics of the driving population that can be
compared: driver age, driver gender, and vehicle type.

D23 are examined at the state level, where the sampling plan for the safety-belt
data is developed. Further comparison will be conducted at the stratum level (multi-
county) as defined in the UMTRI study and at the county level to see if D2 assumption
can be validated at more disaggregated levels. The following is the methodology used
here:

1. Calculate the distribution for of characteristics of the driving population at the
state level, using the UMTRI data;

2. Determine the distribution for D2 characteristics at the state level;

3. Compare the results from steps 1 and 2;

4. Disaggregate the safety-belt and D2 data into several strata;

100

5. Repeat steps 2 and 3;
6. Further disaggregate the safety-belt and D2 data into counties; and
7. Repeat steps 2 and 3.

If similarity exists between the characteristic distributions of D2 and safety-belt
data, the attempt to validate the underlying assumption of quasi-induced exposure is
successfirl at the level represented by the data.

5.2.3 Preparation of safety-belt data

Since the safety-belt data are initially targeted for another purpose, the
presentation of data is not immediately usable for purposes here. The safety-belt data are
organized in three files: a list of survey sites, individual site descriptions, and observation
data fiom each site.

The list of survey sites (see table 5.2.1 for example) contains a complete listing of
sites chosen for field data investigation. It is a descriptive table including survey site
number, the county where the site is located, the specific description of site location
(direction observed, name of intersection or fi'eeway off-ramp), the site type (intersection
or fieeway off-ramp), and the stratum number. It is noted that each observation site
belongs to a certain stratum (table 5.2.2) defined in the UMTRI study (Eby et al. 2001).

Table 5.2.1. Sample of survey site list

 

 

 

 

 

I site number county site location type stratum number J
| 002 Kalamazoo NB 34W3t. & v. Ave I 1 |
| 077 Ottawa NBR I-196 & Byron Rd ER 2 T

 

 

 

Note that the strata were constructed based on historical safety-belt use rates and
VMT for each county. Total VMT by strata are roughly equal and observation sites are

randomly assigned (Eby et al. 2001) within each.

101

Table 5.2.2. Stratification scheme in safety-belt study

 

 

 

 

 

stratum county
1 Ingharn, Kalamazoo, Oakland, Washtenaw
2 Allegan, Bay, Eaton, Gr. Traverse, Jackson, Kent, Livingston, Macomb,
Ottawa
3 Berrien, Calhoun, Genesee, Lapeer, Lenawee, Monroe, Muskegon,
Saginaw, Shiawassee, St. Clair, St. Joseph, Van Buren
4 Wayne

 

 

 

 

The description file contains the characteristics of the observation site (table
5.2.3), i.e., site number, site type, traffic control device, observation day, weather, and
observation start and end times. Most of the variables listed in table 5.2.3 are self-
explanatory, e.g., day of week, weather. The variable “interruption” refers to the total
number of minutes during which safety-belt data collection is interrupted due to some

unexpected situations, such as traffic congestions or extremely adverse weather.

Table 5.2.3. Coding of site description form—1998, 2000

 

 

 

variable name codes
site number 001 — 168 (observation site number)
site type l=intersection, 2=freeway

 

site choice

1=primary, 2=altemate

 

traffic control
device

1=traffic light, 2=stop sign, 3=none, 4=other

 

 

 

 

 

 

 

 

 

 

Date MMDD

observer number 1 — 7=observers alone, 8 — 0=observer pairs
1=Monday, 2=Tuesday, 3=Wednesday, =Thursday,

day Of week 5=Friday, 6=Saturday,7=Sunday

Weather l=mostly sunny, 2=mostly cloudy, 3=rain, 4=snow

start time HHMM — military time

end time HHMM — military time

Interruption MM — number of minutes

Median l=yes (median present), 2=no (no median present)

 

102

 

The observation file includes the characteristics of driver and/or passenger (if
available) observed at the site: site number, estimated driver age, driver gender, vehicle
type, and passenger gender and age (if available). The file information is shown in table
5.2.4.

For the variables listed in table 5.2.4, it is relatively easy to identify the driver
and/or the passenger gender and the vehicle type, but is obviously not as accurate for
driver and/or passenger age. Based on the defined age ranges, it is especially hard to tell
the ages in the upper bound of range 16-29 from those in the lower bound of range 30-59.

Table 5.2.4. Coding of observation data-1998, 2001

 

 

 

 

 

variable name codes
site number 001 — 168 (observation site number)
driver gender l=male, 2=fema1e, 9=missing
driver age 2=4-15, 3=l6-29, 4=30—59, 5=60+, 9=missing
. 1=passenger car, 2=van, 3=utility, 4=pickup,
VCthIC type 9_ issing

 

passenger gender l=male, 2=fema1e, 8=no passenger, 9=missing
l=0-3, 2=4-15, 3=16-29, 4=30-59, 5=60+, 8=No

 

 

 

passenger age . .
passenger, 9=m1331ng
. ### - each vehicle within each site is assigned a
vehlcle number .
unlque number
commercial 1=no (vehicle is not commercial)
vehicle 2=yes (vehicle is commercial)

 

 

 

 

These data are aggregated to the counties, strata, and state level. Thus, the
characteristic distributions of driving populations at the state, stratum, and county levels
can be compared with those based on accident data. The comparisons under different
aggregations can be further developed for intersections and fieeway.

The data in the three existing UMTRI files can be combined into a larger one with

several variables including site number, county, site location, site type, observation day,

103

day of week, observation time, and characteristics of the drivers and passengers (if
available). The format of this file is shown in table 5.2.5. In the context of validating the
underlying assumptions of quasi-induced exposure, some of variables are irrelevant to the
discussion at hand and are eliminated. These include the characteristics of the passenger,
median type, and traffic control devices. The final data record contains the following
variables: site number, site type, county, driver age, driver gender, and vehicle type.

Table 5.2.5. Coding of resultant data—1998, 2001

 

 

 

 

 

 

 

variable name Codes
site number 001 — 168 (observation site number)
site type 1=intersection, 2=freeway
county list of county name
driver gender l=male, 2=fema1e, 9=missing
driver age 2=4-15, 3:16-29, 4=30-59, 5=60+, 9=missing
vehicle type gassipgger car, 2=van, 3=utrllty, 4—plckup,

 

 

 

 

The following is a sample case in the resultant data file:

I site no. I I sitetype I I county I I driver age I Idriver genderI Ivehicle type]
001 l l 3 1

Oakland
Figure 5.2.1. Sample data case in the resultant data file

 

 

 

5.2.4 Discussion of variables used

The following is the discussion of how accident data were selected to match a
variety of circumstances where safety-belt data were observed. In this research context,
timeframe, driver age, driver gender, vehicle type, day of week, observation period, site

type, and weather are discussed.

104

Timeframe

Michigan 2001 accident data are selected to match the 2001 safety-belt data
obtained from UMTRI. Furthermore, Michigan accidents are also selected to reflect the
seasonal observations of safety-belt data: spring (May or June) and fall (August,
September, or October), with the aid of variable month.
Driver age

In the safety-belt data, driver age is coded as a general range (e.g., 16-29, 30-59),
since it was impossible to know the exact age of drivers during on-site observations. As
stated, they are prone to error. Errors notwithstanding, the age distributions of D23 are
also aggregated into the same ranges.
Driver ggender

Driver gender should not be an issue in this exercise, since it is relatively easy to
distinguish driver gender in the field survey.
Vehicle type

Vehicle type in the safety-belt data is classified into four categories: passenger
car, van, utility, and pickup. More specifically, the “passenger car” category includes
passenger vehicles and station wagons; the “van” consists of full-size and mini vans; the
“utility” encompasses sports utility vehicles; and the “pickup” is composed of large and
small pickup trucks. Note that other vehicles were not observed and thus not recorded. In

the Michigan accident data (2001), vehicle type has 30 categories (table 5.2.6).

105

Table 5.2.6. Vehicle type in Michigan accident data (2001)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

00 uncoded & error 11 miscellaneous commercial 22 single, hazardous
01 passenger car & 12 combo unit 23 single, tank
station wagon
02 van, motorhome 13 combo, hazardous 24 single, passenger
03 pickup l4 combo, tank 25 single, tank & haz
04 truck under 10,000 lb 15 combo, passenger 26 under 26k, hazardous
05 cycle 16 combo, double or triple 27 under 26k, passenger
06 moped l7 combo, tank & hazardous 28 under 26k, tank & haz
07 go-cart l8 combo, double or triple 29 others
tank
08 snowmobile l9 combo, double or triple hazardous
09 ORV, ATV 20 combo, double or triple tank hazardous
10 other non-commercial 21 single over 26k

 

Based on the values and descriptions listed in table 5.2.6, values do not match the
categories in safety-belt data precisely. Category 01 approximately matches the category
“passenger car” in the safety-belt data; and category 03 reasonably matches “pickup” in
the safety-belt data. The category “utility” in the safety-belt data (13.4% in total) is
captured in categories 01 and 02 in the accident data; the category “van” (14.3% in total)
can’t match the category 02 in the accident data because of the motorhome vehicles. That
means for the rest of values, there is no category (or combination) in accident data that
can match the categories “utility” and “van” in the safety-belt data. With this
classification scheme, vehicle type is divided into two classifications: passenger car and
pickup truck. The rest of the data will not be used.

Other variables

There are also some other variables to be considered in the safety-belt data, which

might affect the selection of accident data. Table 5.2.7 shows the descriptive statistics for

168 observation sites for the 2001 safety-belt use study.

106

Table 5.2.7. Descriptive statistics for the 168 observation sites (2001)

 

day of week observation period site type

Monday 15.5% 7-9 AM 11.9% intersection 76%
Tuesday 14.3% 9-11 AM 20.2% fieeway (off-ramp) 24%
Wednesday 11.9% 11-1 PM 15.5%
Thursday 17.8% 1-3 PM 20.8%
Friday 14.3% 3-5 PM 19.7%
Saturday 16.1% 5-7 PM 11.9%
Sunday 13.1%

 

 

 

 

 

 

It can be seen that the observations were fairly evenly distributed over the day of
week, while the observation periods are limited to the daytime hours. In the
corresponding accident data, only accidents occurring during the daytime hours (7AM to
7PM) will be selected with the variable hour.

Furthermore, in table 5.2.7 the safety-belt data were collected at intersections and
freeway off-ramps. However, the safety-belt data were observed in a way to represent the
statewide population; correspondingly, the accidents must be statewide numbers instead
of those occurring at intersections and freeway off-ramps.

In brief, after the systematic rules to clean accident data are applied on Michigan
data, appropriate selections are undertaken to make them comparable with the safety-belt
data in terms of timeframe (2001, fall and spring), observation period (7AM-7PM), and
site type (all locations). After the responsibility is assigned, D2 distributions for driver
gender, age, and vehicle type are calculated.

5.2.5 Comparison of safety-belt and D2 data

This section includes the comparison of safety-belt with D2 data disaggregated by
the three main driver-vehicle characteristics. As indicated in the methodology, the
comparison will be conducted at three levels: state, stratum, and county. Furthermore, an

add-on comparison is developed at intersections (state and stratum levels only), to see if

107

D2 distributions are able to fit the safety-belt data. Note that for all the tables listed in this
section, the column “difference” stands for the percentage difference between safety-belt
and D2 data in terms of different driver-vehicle characteristics. Positive values indicate
that the percentages for the safety-belt data are larger than those for D2 data.
State level

Table 5.2.8 shows the comparisons of different driver-vehicle characteristics
statewide. In table 5.2.8, the percentage of male drivers observed in the safety-belt data is
2.9 points higher than D23; the age group (30-59) has the largest difference (5.0
percentage points); and the percentage difference of passenger car is fairly large, 7.3
percentage points. Operationally, these differences are insignificant for driver gender but
significant for driver age and vehicle type (larger than 4 percentage points). In addition to
the operational analysis, the differences between D23 and safety-belt use data are also
examined with chi-square test. Table 5.2.9 shows the statistics and p-values for three key
driver-vehicle characteristics.

Table 5.2.8. Safety-belt versus D2 distributions for statewide

 

 

 

 

 

 

 

 

 

 

characteristics safety-belt accident data (D2) difference
N % N % (%)
gender male 6975 58.8 24733 55.9 2.9
female 4887 41.2 19494 44.1 -2.9
16-29 3331 28.1 13642 30.8 -2.8
age 30-59 7371 62.2 25296 57.2 5.0
60+ 1156 9.7 5289 12.0 -2.2
vehicle passenger car 6394 74.5 31557 81.9 -7 .3
type pickup truck 2184 25.5 6996 18.1 7.3

 

 

 

 

 

 

 

Table 5.2.9. Summary of chi-square statistics and p-values (safety-belt versus D2 data)

 

I gender age vehicle type J
| 32 (000*) 102(0.00) 239 (0.00) |

*p-values are shown in the parenthesis.

 

 

 

 

108

 

 

In table 5.2.9, the p-values yielded by the test are consistently equal to zero
(p<0.05). These results suggest that the differences are statistically significant for these
three characteristics.

A similar analysis is conducted for the accidents occurring at intersections. These
accidents are a subset of statewide accidents, which can be largely pinpointed by
examining the area type of each accident record (variable areacode). Accidents of
interest mainly consist of those with areacode “within intersections,” “driveway within
150 ft of intersection,” and “other intersection related.” In the safety-belt data, the
observations at intersections can be conveniently identified with the built-in variable (site
type, table 5.2.5). The comparison of the safety-belt and D2 data is presented in table
5.2. 10.

Table 5.2.10. Safety-belt versus D2 distributions statewide—intersection

 

 

 

 

 

 

 

 

 

 

 

 

characteristics safety-belt D2 . difference
N % N % (%)
gender male 4849 57.2 12218 53.2 4.0
female 3635 42.8 10792 46.7 -4.0
16-29 2299 27.1 7152 31.1 -4.0
age 30-59 5298 62.5 13057 56.7 5.8
60+ 885 10.4 2802 12.2 -l.8
vehicle passenger car 4570 74.4 16447 81.9 -7.5
type pickup truck 1572 25.6 3637 18.1 7.5

 

 

 

 

 

Shown in table 5.2.10, the percentage of male drivers in the safety-belt data is
approximately 4.0 percentage points greater than that in D2 data, right around the
significance threshold; among the three age groups, the middle-aged group has the
biggest difference: 5.8 points; compared to the differences in driver gender and age, the

difference in vehicle type is larger, 7.5 percentage points. This result is expected, since it

109

has been found that there is a disagreement of distributions for driver age and vehicle
type between the safety-belt and D2 data at the statewide level.

Given the fact that the sampling plan for the safety-belt data collection was
implemented at the statewide level, the characteristics of the driver-vehicle combinations
in the safety-belt data are supposed to represent the real driving population on the road.
However, data errors might be introduced to the driver age, since it is relatively difficult
to identify accurate driver age during the field observations, especially for the 30-59 age
group. For the vehicle type distribution, there might be some errors due to the
mismatched classification. As discussed, the passenger cars in accident data might
include some sport utility vehicles, which consequently overestimate the percentage
(81.9%).

So, driver gender seems to be the most reliable characteristic. The comparison
results demonstrate a fairly good agreement of driver gender distributions between the
safety-belt and D2 data both at the statewide and intersections levels, from the
operational perspective. In this confined context, it is safe to argue that the fundamental
assumption of quasi-induced exposure, that D23 constitute a random sample of driving
population (at least, in terms of driver gender) on the road, is validated at the state level.
That is to say, quasi-induced exposure is a generally good approach at the state level,
although more validation is needed for driver age and vehicle type.

In the following section, the research continues to explore to see if the validation
can be achieved at the stratum level. Since the data are more disaggregated at the stratum

level, the differences of distributions for three characteristics are expected to be greater.

110

Stratum level

Safety-belt data can be also aggregated to the stratum level according to the

definition in table 5.2.2. Analogous to the analysis at the state level, the percentages of

driver-vehicle characteristics for D23 will be compared with those from safety-belt data

for each stratum. Discussion is developed separately for the stratum and intersections.

The data are organized on a stratum basis with percentages disaggregated by

different driver-vehicle characteristics and displayed in the same table. The following

four tables (5.2.11, 5.2.12, 5.2.13, and 5.2.14) show the comparisons for each stratum.

Table 5.2.11. Safety-belt versus D2 distributions for stratum 1

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

characteristics safety-belt D2 difference
N % N % (%)
gender male 1970 56.5 6685 50.5 6.0
female 1518 43.5 6547 49.5 -6.0
16-29 1073 30.8 4069 30.8 0.0
age 30-59 2126 61.0 7797 58.9 2.0
60+ 289 8.3 1366 10.3 -2.0
vehicle passenger car 1855 74.1 9690 83.8 -9.6
type pickup truck 647 25.9 1878 16.2 9.6
Table 5.2.12. Safety-belt versus D2 distributions for stratum 2
characteristics safety-belt D2 difference
N % N % (%)
gender male 1328 61.1 6652 52.7 8.4
female 844 38.9 5966 47.3 -8.4
16-29 576 26.5 3970 31.5 -4.9
age 30-59 1367 62.9 7123 56.5 6.5
60+ 229 10.5 1525 12.1 -l.5
vehicle assenger car 1092 71.3 8747 79.8 -8.5
type pickup truck 440 28.7 2221 20.2 8.5

 

 

 

 

 

 

 

111

 

 

Table 5.2.13. Safety-belt versus D2 distributions for stratum 3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

characteristics safety-belt D2 difference
N % N % (%)
gender male 991 57.9 4518 50.8 7.0
female 721 42.1 4367 49.2 -7.0
16-29 426 24.9 2755 31.0 -6.1
age 30-59 1067 62.4 4953 55.7 6.7
60+ 216 12.6 1177 13.2 -0.6
vehicle passenger car 821 64.3 6101 78.1 -13.9
type pickup truck 456 35.7 1706 21.9 13.9
Table 5.2.14. Safety-belt versus D2 distributions for stratum 4
characteristics safety-belt D2 difference
N % N % (%)
gender male 2686 59.8 4920 51.8 8.0
female 1804 40.2 4572 48.2 -8.0
16—29 1256 28.0 2848 30.0 -2.0
age 30-59 2811 62.6 5423 57.1 5.5
60+ 422 9.4 1221 12.9 -3.5
vehicle passenger car 2626 80.4 7019 85.5 -5.1
type Lickup truck 641 19.6 1191 14.5 5.1

 

 

 

 

 

 

 

The comparisons of the safety-belt and D2 distributions are fundamentally the

same for each stratum. The operational and statistical significances for each comparison

are summarized in table 5.2.15:

Table 5.2.15. Summary of operational and statistical significances for each stratum

stratum

chi

chi

chi

chi

112

vehicle

.05

.05

.05

.05

 

 

 

As shown in table 5.2.15, the majority of the differences are both operationally
and statistically significant, since the percentage differences are more than 4 percentage
points and the p—values given by chi-square are less than 0.05. Although for stratum 1 the
difference for age distributions is small between the safety-belt and D2 data, 2 percentage
points, it is not sufficient to suggest that D2 data are representative of safety-belt data for.
stratum 1. The differences of distributions for gender and vehicle type at the same
stratum are found to be operationally significant. Based on the information shown in table
5.2.15, it can be concluded that for all four strata examined, there is no agreement of D2
versus seat belt data from operational or and statistical perspectives.

Similar to the comparison at the state level, some other observations are revealed
according to the data shown in tables 5.2.11, 5.2.12, 5.2.13, and 5.2.14:

1. The percentages of male drivers in safety-belt data are consistently higher than
those in D23, at least 6 percentage points.

2. The percentages of the middle-age group (30-59) in safety-belt data are always
larger. It is consistent with the discussion at the state level, which is most likely
caused by the observation errors of driver age during the safety-belt data
collection.

3. The passenger car percentages for safety-belt data are consistently smaller.
Similar to the state level, it accords with the fact that the “passenger car” category
in D2 data contains some sports utility vehicles, while the safety-belt data do not.
Comparisons are also deve10ped for the individual strata at intersections, the

results of which are represented in Appendix B. Identical observations as above can be

113

offered. At the stratum level (intersections), the differences are more conspicuous
between D23 and safety-belt data from both operational and statistical point-of-views.

In summary, the discussions have illustrated that there is a disagreement in driver-
vehicle characteristic estimates between the safety-belt and D2 data for each stratum and
intersection. That means that the validity of the underlying assumptions of quasi-induced
exposure could not be confirmed at the stratum level. At the state level, it has been shown
that D2 distributions for driver age and vehicle type are significantly different from the
safety-belt data. Therefore, it is no surprise that at the stratum level where data are more
disaggregated, the results could not show an agreement between the D23 and safety-belt
data. However, the results should not lead to the conclusion that quasi-induced exposure
is not a good exposure measurement that could be used at the stratum level, since the
safety-belt data at the stratum level can’t be proved to be “exposure truth.”

Although it has been demonstrated that the underlying assumptions of quasi-
induced exposure could not be supported using the safety-belt data at the stratum level,
there are some insights gained. Table 5.2.16 presents the distributions for passenger cars
at the levels of state, state at intersections, stratum, and stratum at intersections.

Table 5.2.16. The distributions for passenger cars at different levels

 

 

 

 

 

 

 

 

 

 

 

 

levels safety-belt D2 difference
N % N % (%)
state 6394 74.5 31557 81.9 -7.3
state at intersections 4570 74.4 16447 81.9 -7.5
stratum Q) 821 64.3 6101 78.1 -13.9
stratum (3) at intersections 446 60.1 3864 78.2 -18.1

 

 

As shown in the “difference” column, the differences in percentages for passenger
cars between the safety-belt and D2 data are consistently shown as being negative,

indicating that D2 data contain higher percentages of passenger cars at all four levels. It is

114

probably due to the fact that the “passenger car” category in D2 data encompasses some
sports utility vehicles while that in the safety-belt data does not. However, a discernible
pattern can be identified fiom the “difference” column—the differences in absolute
values become more conspicuous at increasing levels of disaggregation. The percentages
for passenger cars in the D2 data are relatively stable between different levels, while the
percentages vary considerably in the safety-belt data. Therefore, the distribution for
passenger cars in the safety-belt data is more sensitive to data aggregation than the D2
data; the increasing differences shown in table 5.2.16 are mainly due to the
frequency/percentage change in the safety-belt data (exposure data).

Similar observations can be found in the age distributions. An example is given
for the middle-age group (30-59) and the results are shown in table 5.2.17.

Table 5.2. 17. The distributions for the age group (30-59) at the different levels

 

 

 

 

 

 

 

 

levels safety-belt D2 difference
N % N % (%)
state 7371 62.2 25296 57.2 5.0
state at intersections 5298 62.5 13057 56.7 5.8
stratum (2) 1367 62.9 7123 56.5 6.5
stratum (2) at intersections 948 63.8 4691 56.1 7.7

 

 

 

 

 

 

In table 5.2.17, the differences for the age group (30-59) become more prominent
when the safety-belt and D2 data are disaggregated at the fine levels. Another important
fact is that the percentages of age group (30-59) in the safety-belt data are consistently
greater than those in D2 data. It seems that rough estimates of driver age in the safety-belt
data contribute to errors and these errors persist while the data are disaggregated. It is
possible that drivers around the upper-bound of age group (16-29) and the lower-bound
of age group (60+) are mistakme counted as age group (30-59), although some errors

might cancel out, e. g., 30-31 year-old drivers are counted as being 28-29 year-old.

115

County level

With the recognition that the differences between the safety-belt and D2 data are
more obvious with the data disaggregation, it can be predicted that the distributions of D2
data will be considerably different from the safety-belt data at the county level. The
comparisons of distributions for three key driver-vehicle characteristics are presented in
Appendix C. The results demonstrate a considerable variation (maximum 22 percentage
points) of distributions between the seat-belt and D2 data.

5.2.6 Conclusion

Analysis has been undertaken to compare the driver-vehicle characteristics
between the safety-belt and D2 data at the state, stratum, and county levels. Statistically,
the results consistently suggest that driver characteristics observed in the safety-belt data
are significantly different from D23 as derived from accident data. Practically, at the state
level, quasi-induced exposure is a generally good technique in terms of driver gender;
however, further justifications are needed for driver age and vehicle type, since there are
subject to data observation errors and mismatched vehicle classification.

At the stratum and county levels where operationally significant distribution
differences have been shown for three key characteristics, the validity of the quasi-
induced exposure can not be verified, because at these levels the safety-belt data do not
necessarily represent the “exposure truth.” Notwithstanding that, it has been observed
that with the safety-belt and accident data at the more finely-disaggregated levels, the
variation of distributions by three D2 characteristics becomes more significant. The D2
estimates yielded by quasi-induced exposure are relatively stable, while the distributions

given by the safety-belt data vary considerably. Given that, quasi-induced exposure~

116

seems less sensitive to the data disaggregation, especially at the levels such as state,
statewide intersections, stratum, and stratum-intersections.

The next section will cover how to validate the underlying assumptions of quasi-
induced exposure with truck volume data.

5.3 Validation using truck volume data (W -2)
5.3.1 Introduction

Another source that can be employed to validate the underlying assumptions of
quasi-induced exposure is vehicle classification data collected by the Federal Highway
Administration’s (FHWA) Office of Highway Policy Information (OHPI). The Vehicle
Travel Information System (VTRIS) so-called “W-tables” maintained at the F HW A’s
website. Currently, there are 14 years (1990 - 2003) of data available to the general
public.

The W-tables are designed to provide a standard format for presenting the
summary of vehicle weighing and classification efforts at truck weigh sites around the
country (FHWA website). There are six types of W-tables which contain different truck-
related information and are designed for different purposes. For example, the W-4 tables
contain “information on truck axle loadings and their effect on flexible and rigid
pavement based on 18-KIP equivalent axle loads,” which is most commonly used in
pavement designs (FHWA website). However, in the research context here, special
attention is given to the W-2 tables, which contain potentially useful information for
validating the underlying assumptions of quasi-induced exposure.

The W-2 table is a summary of vehicle counts at Weigh-In-Motion (W IM)

stations by vehicle classification. At each station, the vehicle classification data are

117

averaged for each hour and the 24—hour averages are added for the average daily count
over a year. So, fiindamentally, traffic counts in W-2 tables are Average Annual Daily
Traffic (AADT). Note that WIM stations are typically located on freeway links
demarcated by intersecting major roads.

Since W-2 data are observed directly from the freeway system, they reflect the
actual vehicle type distributions at the specific locations where the WIM sites are located.
Thus, the information that W-2 data represent can be regarded as a measurement of
exposure “truth.” In theory, comparing the exposure as measured using the quasi-induced
exposure approach with the W-2 data is a potential validation of the underlying
assumption of quasi-induced exposure. This comparison is made for selected Michigan
freeway links. However, the nature of W-2 tables and availability of W-2 data limit the
efforts. For example, in Michigan (1999) several highway routes have no W-2 tables
(e. g., USl3 l); and, for other routes, although W-2 tables are available, no traffic volume
data were collected at some WIM sites (e. g., WIM station #6069 at I-69). Given the
available data fi'om the FHWA website, three interstate routes (1-94, [-75, and I-96) and
two US routes (U S23 and US12) are chosen for analysis.

The next section covers the methodology for identifying comparable D2 and W-2
data and utilizing W-2 data to validate the underlying assumptions of quasi-induced
exposure.

5.3.2 Methodology

In order to use W-2 data, the accident data must be cleaned according to the

procedure described in chapter 4 to eliminate one- and three-or-more-vehicle accidents

and accidents with conflicting information. Further, accident data need to be selected in a

118

way to reflect the same conditions under which W-2 traffic counts were collected in
terms of timeframe, vehicle type classification, and accident locations.
Vehicle type

Considering the nature of the W-2 data, vehicle type is the only driver-vehicle
characteristic that will be used in the comparison. Due to the different vehicle-type
classification schemes used in the W-2 and D2 data, it is necessary to adjust the vehicle-
type categorizations to make them comparable. The data in the W-2 tables are broken
down by 13 vehicle types shown in table 5.3.1. The vehicle type classifications for
accident data are in table 5.3.2.

Table 5.3.1. FHW A vehicle classes in W-2 tables

 

 

 

 

 

 

1 motorcycles 2 passenger cars 3' single-unit vehicles: 2'
' ' axle, 4-tire
4 b 5. single-unit trucks: 2- 6. single-unit trucks: 3-
. uses .
axle, 6-trre axle
7. single-unit trucks: 4- 8. single-trailer trucks: 4- 9. single-trailer trucks: 5-
axle, or more axle, or less axle
10. single-trailer trucks: 6- l l. multi-trailer trucks: 5- 12. multi-trailer trucks: 6-
axle, or more axle, or less axle
13. multi-trailer trucks: 7-
axle, or more

 

 

 

 

Table 5.3.2. Vehicle type in Michigan accident data (2001)

 

 

 

 

 

 

 

 

 

 

 

 

 

00 uncoded & error 01 passenger car & 02 van, motorhome
station wagon

03 pickup 04 truck under 10,000 lb 05 cycle

06 moped 07 go-cart 08 snowmobile

09 ORV, ATV 10 other non-commercial 11 misc commercial

12 combo unit 13 combo, hazardous 14 combo, tank

15 combo, passenger l6 combo, double or 17 combo, tank &

18 combo, double or triple 19 combo, double or 20 combo, double or

tank triple hazardous triple tank

21 single over 26k 22 single, hazardous 23 single, tank

24 single, passenger 25 single, tank 26 under 26k,

27 under 26k, passenger 28 under 26k, tank 29 others

 

 

119

Comparison of tables 5.3.1 and 5.3.2 shows that although vehicles are classified

differently, five consistent vehicle types can be identified:

1.

Motorcycles. Value 05 “cycle” in the accident data is equivalent to value 1
“motorcycle” in the W-2 data.

Passenger cars. In the W-2 data, value 2 “passenger cars” includes all sedans,
coupes, and station wagons manufactured primarily for the purpose of carrying
passengers. Thus, value 01 “passenger car & station wagon” in the accident data
matches value 2 “passenger cars” in the W-2 data.

Pickups and vans. In the W-2 data, value 3 “single-unit vehicles, 2-axle, 4-tire”
includes pickups, panels, vans, and other vehicles such as campers, motorhomes,
ambulances, and minibuses. Thus, value 3 in W-2 data is equivalent to values 02
“van and motorhomes” and 03 “pickups” in the accident data. However, this fit
may not be as good as the first two types.

Bus. Values 15 “combo, passenger”, 24 “single, passenger,” and 27 “under 26k,
passenger” combined in the accident data go with value 4 “bus” in the W-2 data;
Other trucks. According to tables 5.3.1 and 5.3.2, the rest of the trucks are
categorized with different schemes. However, summation of them will belong to
the same category, which includes all kinds of trucks, exclusive of pickups.
Values 04 and 12-28 (exclusive of 15, 24, and 27) in the accident data match
values 5-13 in the W-2 data.

It is noticed that several values in table 5.3.2 do not fit in the above five

categories, including 06-1 1 and 29. In W-2 data, there is no vehicle class that can match

those values. Therefore, vehicle types 06-11 and 29 in the accident data will not be used.

120

Timeframe

For Michigan, there is great flexibility in selecting different years of Michigan
accident data and W-2 data to develop the comparisons. Currently, both accident and W-
2 data are available from 1990 to 2003.

Locations

Since all of the WIM stations are located on interstates or US routes, selected
two-vehicle accidents must occur on freeway sections. This would eliminate all accidents
on ramps, local surface roads, and intersections. Note that the accidents occurring on
(ramps are filtered out because the non-guilty drivers in these accidents, if actually on
surface roads when struck (e.g., at the end of an exit ramp), will not be representative of
the driving population on the freeway sections. Accidents on freeway sections can be
located by studying the control section and area code in the accident data. In the
meanwhile, the accident data must be selected to reflect the accident types which could
reasonably occur on freeways. Similar to the discussion in chapter four, accidents
occurring on freeway sections take forms of three major types: miscellaneous multiple
vehicle, rear-end straight, and side-swipe same. Correspondingly, the D2 data only
consist of these four accident types.

Afler the appropriate screening operations are undertaken, accident responsibility
is assigned to two-vehicle accidents. Accidents with one responsible and one non-
responsible driver-vehicle combination will be used for analysis. Thus, the accident data
are chosen to be coincident with the circumstances where and when the W-2 data were

observed. The following section describes how the W-2 data are used in the comparison.

121

An example is given for a freeway segment on I-94 in Michigan. It is ascertained
that traffic composition along a freeway may change where two major intersecting traffic
streams merge or diverge. Therefore, it is necessary to locate the major intersecting roads
along the freeway section. In figure 5.3.1, the locations of the several WIM stations and

major intersecting highways along [-94 in Michigan are depicted.

1196 WIM sites usr31 usm U823

”71: rl—HH—Bl—El—

Figure 5.3.1. Illustration of stations and major intersecting roads on I-94 rn Michigan

 

 

 

 

Two assumptions have been made in order to develop a logical comparison
between D2 and W-2 data. First, it is assumed that the traffic count observed at each
WIM station will be representative of the traffic composition along the corresponding

link (1,). For instance, the traffic count from WIM station 1 will represent the traffic

composition along link AB. Second, it is assumed that the traffic characteristics along
each link remain the same and traffic at minor intersecting roads does not affect the
traffic composition along the link. Based on these two assumptions, D28 can be compared
with W-2 data for I-94 (with reference to figure 5.3.1). The comparison is developed in a
stepwise manner:
1. Calculate the vehicle type distribution of D2s on the entire roadway segment
(AE) between I-196 and US-23;
2. Determine the average traffic counts at four weighting stations (1, 2, 3, and 4),
disaggregated by vehicle type (that will be representative of the average traffic
count on the roadway segment AE); and

3. Compare the results from steps 1 and 2 (overall comparison).

122

If similarity is found in the comparison, it can be argued that the underlying
assumption of quasi-induced exposure is validated under the given circumstances. '
5.3.3 Comparison of W-2 and D2 data

As stated, the comparisons of vehicle type distributions between the W-2 and D2
data are developed for three freeway routes and two US routes. Based on the
methodology, the vehicle type distribution for a highway (e.g., I-94) in W-2 data is
averaged over all of the available WIM stations for roadway segments in a year. The
accident data used in the analysis are reflective of the same freeway, timefiame, and the
reasonable accident types. The details of W—2 and D2 distributions by vehicle type are
presented in table 5.3.3 (frequencies) and table 5.3.4 (percentages).

Table 5.3.3. Comparing vehicle type distributions between D2s and W-2 (frequencies)

 

I-94 I—96 I-75 U823 U812

 

vehicle type W2 D2 W2 D2 W2 D2 wz , D2 W2 D2

 

motorcycle “ 1 l 2 57 0 37 4 54 0 l 0

 

Passenger 11879 941 19382 718 10006 998 15960 234 2112 62

 

 

car
P‘Ckfalfsand 2808 353 4843 260 2570 406 4270 129 911 . 24
bus . 72 A 2 60 0 98 1 55 0 8 0

 

 

 

 

 

 

 

 

 

 

 

 

other trucks 5406 100 4908 67 2155 120 4697 32 612, 8

 

Table 5.3.4. Comparing vehicle type distributions between D28 and W-2 (percentages)

 

I-94 I-96 I-75 U823 U812

 

 

“hide type W2, D2 W2 D2 W2 D2 W2 D2 W2 D2

 

motorcycle 0.1 0.1 0 2 0.0 0.2 0.3 0.2 0.0 0.0 0.0

 

passenger car 58.9 67.3 66.3 68.7 67.3 65.3 63.7 59.2 58.0 66.0

 

91°13‘33““ 13.9 25.3 16.6 24.9 17.3 26.6 17.1 32.7 25.0 25.5

 

bus 0.4 0.1 O 2 0.0 0.7 0.1 0.2 0.0 0.2 0.0

 

 

 

 

 

 

 

 

 

 

 

 

othertrucks 36.8 7.2 116.8 6.4 14.5 7.8 18.8 8.1 16.8 8.5

 

123

 

In addition, chi-square is also employed to compare the D2 and W-2 distributions

for individual routes. The chi-square statistics and p-values are summarized in table 5.3.5.

Table 5.3.5. Chi-square statistics and p-values

 

 

 

 

 

 

 

 

I 1-94 I-96 1-75 U823 U812 1
| statistics 331 113 119 81 5 |
| p-values <0.05 <0.05 <0.05 <0.05 0.28 |

 

Based on these tables, there are several observations:
There is considerable variation in the vehicle type distributions. The percentages of
“pickups and vans” in the D2 data are consistently larger than these in the W-2 data,
while the percentages of “other trucks” in the D2 data are smaller.
Operationally, there is no agreement of vehicle type distributions for the W-2 and D2
data for any of the five routes. The differences in percentage for pickups and vans (9
percentage points), and other trucks (11 percentage points) are greater than the 4-
point criterion adopted earlier.
Statistically, except for U812, the differences between the W-2 and D2 data are
significant at 0.05 significance level.
The percentages of “motorcycle” and “bus” are very low in both D2 and W-2 data,
which seems realistically true. However, for three highways (I-96, U823, and US 12)
these percentages are consistently equal to zero in D2 data. It is most likely that the
sample sizes of D2 motorcycle data are insufficient to represent the (motorcycle)
driving population.

Two approaches are used to increase the sample size: 1) regrouping the vehicle

types into two categories (passenger car and others); and 2) combining several years of

D2 data for a freeway route. For the first approach, based on tables 5.3.3 and 5.3.4, the

124

vehicle type distributions in percentage for the D2 and W-2 data are presented in table

5.3.6 and the chi-square statistics and p-values are shown in table 5.3.7 .

Table 5.3.6. Vehicle type distributions between D28 and W—2 (regrouped)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

vehicle 194 I-96 I-75 U823 US12
type W2 D2 W2 D2 W2 D2 W2 D2 W2 D2
”8:223“ 58.9 67.3 66.3 68.7 67.3 65.3 63.7 59.2 58.0 66.0
others 41.1 32.7 33.7 31.3 32.7 34.7 36.3 40.8 42.0 34.0
Table 5.3.7. Chi-square statistics and p-values (regrouped)
[ 1-94 I-96 1-75 U823 US 12 |
| statistics 38 2.7 2.6 3.4 2.4 |
| p-values <0.05 0.20 0.20 0.10 0.20 |

 

 

 

 

 

 

Based on the information displayed in tables 5.3.6 and 5.3.7, determined by the
criteria established earlier, the statistical and operational significances of differences
between the D2 and W-2 data for these five freeway routes are summarized as follows:

Table 5.3.8. Summary of statistical and operational significances

 

 

 

 

 

 

 

 

| 1-94 I-96 I-75 U823 US12 1

I statistical yes no no no no I
operatrona yes no no yes yes

I ' 1 I

 

It can be seen fi'om table 5.3.8 that by regrouping the vehicle types the differences
become statistically insignificant for four freeway routes (except for I-94); and, the
differences for two freeway routes (I-96 and I-75) turn out to be operationally
insignificant.

For the second approach, comparisons using multiple years of data (2001 -2003)
are conducted for I-94 and I—75, considering the availability of W-2 data. The vehicle
type distribution on a certain fi'eeway in the W-2 data is calculated according to the

traffic count averaged over all the WIM stations on that fieeway for the three years under

125

scrutiny (2001, 2002, and 2003). Table 5.3.9 shows the vehicle type distributions for [-94

 

 

 

 

 

 

 

 

and 1-75.
Table 5.3.9. Vehicle type distributions for I-94 and I-75 (2001-2003)
194 1-75
vehicle type W2 D2 W2 D2

N % N % N % N %

motorcycle 35 0.1 5 0.1 66 0.2 1 l 0.2
”8:21;” 34011 61.3 2723 66.2 25931 65.5 3041 67.5
P‘Ckfafsand 8110 14.6 1010 24.5 7104 17.9 1049 23.3
bus 216 0.4 4 0.1 189 0.5 3 0.1

other trucks 13070 23.6 374 9.1 6304 15.9 402 8.9

 

 

 

 

 

 

 

 

 

 

 

In contrast to the information displayed in table 5.3.4, the discrepancy for vehicle
type distributions between the W-2 and D2 data in table 5.3.9 is much smaller for both I-
94 and 1-75. For example, the percentages of motorcycles in W-2 data become equal to
those in D2 data; the difference in percentage for passenger cars is 4.9 percentage points
on I-94 with data aggregation over time, as opposed to 8.4 percentage points without.
Obviously, the change is due to the increased sample size in the D2 and W-2 data.
However, in general, the vehicle type distributions for the two sets of data still differ
significantly (e.g., for “other trucks,” the difference is as much as 14.5 percentage
points). Statistically, the p-values yielded by the chi-square test are less than 0.05 for both
[-94 and [-75, which suggests that the differences are significant as well.
5.3.4 Conclusion

Analytical results have consistently demonstrated that there are significant
differences between the W—2 and D2 data (with five vehicle type categories) for the five
freeway routes examined, although the difference is statistically insignificant for U812.

The sample size seems to play an important role in the results. With the sample size

126

increased by regrouping the vehicle types into two categories, the results become mixed
regarding whether the D2 data fit the W-2 data. For I-96 and [-75 there is no significant
difference between the D2 and W-2 data; for U823 and US 12 the difference is
statistically insignificant; and for 1-94 the differences are both statistically and
operationally significant. Using multiple years of data, notwithstanding that the
difference for vehicle type distribution remains operationally and statistically significant
for I-94 and I-75, the discrepancy is much smaller with large sample size. And, the results
suggest that quasi-induced exposure is sensitive to the sample size (data aggregation)

when it is used for freeway routes.

127

Chapter 6

VALIDATION USING THREE-OR-MORE-VEHICLE ACCIDENTS

6.1 Introduction

The previous chapter was directed to a validation of the underlying assumptions
of quasi-induced exposure through using available exposure data from other sources (i.e.,
VMT, seat belt, and W-2 data). The effort here is to develop another technique to achieve
the same goal, using internally available information fiom the accident data themselves—
specifically, three-or-more-vehicle accidents.

Generally, applications of quasi-induced exposure use only two-vehicle accident
data, discarding the accidents involving only one and three-or-more vehicles. In the
context of validating the underlying assumptions of quasi-induced exposure, three-or-
more-vehicle accident data may contain some very useful information. The basic idea is
to compare the distributions for non-responsible driver-vehicle combinations calculated
from three-or-more-vehicle accidents with those from two-vehicle accidents. The
argument is that if non-responsible driver-vehicle combinations in two-vehicle accidents
are truly a random sample of the driving population at the time of accident occurrence,
one should expect that the non-responsible driver-vehicle combinations in three-or-more-

vehicle accidents are also representative of the same driving population. Similarly, the

128

comparison can be conducted between different non-responsible drivers in three-or-more-
vehicle accidents.

As discussed in chapter 4, three-or-more-vehicle accidents that are usable must
consist of at least one responsible and one non-responsible driver. The involvement
mechanism is analogous to that used in two-vehicle accidents—a typical accident must
have one responsible driver and one non-responsible driver. Based on the responsibility
assignment scheme developed in chapter 4, there are some accidents without responsible
drivers. It is essential that those accidents should be excluded fiom the analysis here as
well. A comparison will also be made between the first non-responsible drivers (denoted
as DZ’S as opposed to D28) and the rest of the non-responsible drivers (denoted as D38) in
three-or-more-vehicle accidents. Note that D2’ and D3 denoted in this way is for ease of
explanation. Comparison of the characteristic patterns of these two non-responsible
driver-vehicle combinations could help validate the underlying assumptions of quasi-
induced exposure.

There are several advantages in utilizing three-or-more-vehicle accidents in
validating the underlying assumptions. First, three-or-more-vehicle accidents are readily
available in the accident database. There is always a variable available to
identify/separate accident cases with three-or-more vehicles involved. Second, three-or-
more-vehicle accidents are coded in the same manner as two-vehicle accidents in the
accident database. Therefore, when data are grouped or manipulated in the same way,
there should not be any consistency issues between two- and three-or-more-vehicle
accidents. In addition, the systematic rules developed for preparing two-vehicle accidents

for analysis and the responsibility assignment scheme can be conveniently applied to

129

three-or-more-vehicle accidents as well. However, there are also some issues in using
three-or-more-vehicle accidents. It is perceived that the conditions/circumstances for
three-or-more-vehicle accidents might be inherently different from those for two-vehicle
crashes. For example, three-or-more-vehicle accidents are most likely to occur during the
peak hour or under otherwise congested traffic conditions. Therefore, it is necessary to
investigate to see if the characteristics of two-vehicle accidents are indeed different where
and when three-or-more-vehicle accidents take place.

The accident data used to develop the comparisons in this section are obtained
fi'om H818 and Michigan DOT. The same three participating states are selected based on
the availability of data coding guidebook from HSIS: California, Maine, and Utah. In
addition, Michigan data are also utilized, which are available from Michigan DOT. For
each state, the variables used to depict the characteristics of driver-vehicle combinations
are fundamentally identical: driver age, driver gender, and vehicle type. Since there is
some inconsistency in vehicle type definitions from state to state, generally, the vehicle
type is simplified to cars, pickups, and other vehicles.

A stepwise procedure for validating the underlying assumptions will be discussed
first. Then, the characteristics of three-or-more-vehicle accidents will be explored. Then,
comparisons of D2 distributions between two- and three-or-more-vehicle accidents will
be conducted at the state level. Finally, a summary will cover what has been learned from
the comparisons.

6.2 Methodology
Afier the HSIS data have been manipulated as described in chapter 5, they can be

used in the quasi-induced exposure application. A number of factors need to be taken into

130

account to select the appropriate accident data, such as accident location, time of day, and

crash type. The following stepwise procedure is employed:

1.

Clean and select two-vehicle accident data, identify accidents with one
responsible and one non-responsible driver, and calculate D2 distributions for the
three key characteristics;

Clean and select three-or-more—vehicle accident data, identify accidents with at
least one responsible and at least one non-responsible driver and calculate the
distributions for the three key characteristics for a_11 non-responsible drivers in
three-or-more-vehicle accidents;

Calculate the distributions for the three key characteristics for D28 and D38 in
three-or-more-vehicle accidents; and

Examine the differences between steps 1 and 2, and D28 and D38 in step 3, to see
if they are significantly different from zero.

If no significant difference is found, the underlying assumptions of quasi-induced

exposure are validated for the basic situation that the accident data represent; otherwise,

the assumptions can’t be validated. Note that the criteria as the previous chapter are used

to determine if a difference is significant.

6.3 Characteristics of three-or-more-vehicle accidents

In order to use three-or-more-vehicle accidents to validate the underlying

assumptions of quasi-induced exposure, the validation must be firmly grounded on the

understanding of the characteristics of three-or-more-vehicle accidents. Compared to

two-vehicle accidents, the underlying causes for three-or-more-vehicle accidents may be

different—they generally occur where several (more than 2) vehicles to drive closely.

131

Three-or-more-vehicle accidents (Michigan 2001) are utilized as an example to identify
the circumstances where these accidents are prone to occur. The variables of interest
include accident location, time of day, crash type, and speed limit. The characteristics of
three-or-more-vehicle accidents are compared to those of two-vehicle accidents for
different variables.
Accident location

For Michigan data (2001), simple descriptive statistics of two- and three-or-more-
vehicle accident locations indicate that the majority of accidents occur at three mutually
exclusive locations: intersection areas, freeways, and straight surface roads. The accident
location is identified with variable “area code.” Table 6.1 presents the percentages at each
of the three major locations:

Table 6.1. Percentages of accidents by three major locations (%)

 

 

 

 

 

 

 

 

 

 

 

locations 2-vehicle accidents >2 vehicle accidents

within intersection 25.2 17.4

intersection driveway within 150 fi Of 8.2 5.9
mtersecnon

other intersection related 13.7 17.7

freeways 5.2 10.7

straight surface road 29.9 36.8

total 82.2 88.5

 

From table 6.1, it seems that for 82.2% of two-vehicle and 88.5% of three-or-
more-vehicle accidents occurring at these three locations. Approximately 47.5% of three-
or-more-vehicle accidents occur on freeway areas and straight surface roads—1 2
percentage points more than two-vehicle accidents; however, three-or-more-vehicle
accidents are less likely to take place at intersections (7 percentage points less). Based on
the criterion adopted earlier, in term of accident location the difference between two- and

three-or-more-vehicle accidents is claimed to be significant.

132

 

Time of day

The investigation of time of day shows that two— and three-or-more-vehicle
accidents are liable to take place in hours where traffic is more congested, including
morning peak hours (7-9am) and afternoon hours (12-7pm). The percentages for two-
vehicle and three-or—more-vehicle accidents in these hours are presented in table 6.2

Table 6.2. Percentages of accident by 10 major hours (%)

 

 

 

 

 

 

 

 

 

 

 

 

hour 7-8am 8-9am 11-128m 12-lpm l-2pm
2-vehicle accidents 4.9 5.0 5.6 6.9 6.3
>2 vehicle accidents 6.5 5.1 5.1 6.1 6.3

hour 2-3pm 3-4pm 4-5pm 5-6pm 6-7pm
2-vehicle accidents 7.6 9.8 9.4 9.3 6.4
>2 vehicle accidents 8.0 10.9 10.9 11.5 6.9

 

 

The percentages of accidents in these 10 hours are 71.3% for two-vehicle
accidents and 77.2% for three-or-more-vehicle accidents. For 7-9am, 11am-3pm, and 6-
7pm, the percentages of two-vehicle accidents are approximately equal to those of three-
or-more-vehicle accidents; for hours (3-6pm) including evening peak hour, the
percentages of three-or-more-vehicle accidents are consistently higher by 1-2 percentage
points. Given the small percentage variation, it is argued that three-or-more—vehicle
accidents are not different from two-vehicle accidents in terms of time of day.

Crash type

For two- and three-or-more-vehicle accidents there are three major accident types

(table 6.3), including angle straight, rear-end straight, and side-swipe same.

Table 6.3. Percentages of accidents by three major accident types (%)

 

 

 

 

 

 

 

crash type angle rear-end side-swipe total
straight straight same

2-vehicle accidents 16.8 30.3 12.3 59.5

>2 vehicle accidents 10.2 60.2 5.3 75.7

 

 

 

133

The results show that for each accident type the differences in percentage are
quite significant between two- and three-or-more-vehicle accidents. For rear-end straight,
difference is substantial, approximately 30 percentage points. It can be stated that the
predominant crash type of three-or-more-vehicle accidents is different fi'om that of two-
vehicle accidents.

Speed limit

The speed limit on roadways where accidents occur is also examined. It is found
that accidents mostly happen on roadways with speed limits from 25mph to 55mph. The
results are shown in table 6.4.

Table 6.4. Percentages of accidents at different speed limits (%)

limit 2-vehic1e accidents >2 vehicle accidents
<25 1.0 0.4

25 24.4 1 1.9
30 8.2 8.2

35 19.2 19.7
40 9.9 12.6

45 17.4 22.5
50 3.9 5.5
55 11.3 10.9
60 0.1 0.1
65 1.5 3.2
70 3.3 5.1

 

In table 6.4, the percentages of accidents are generally close between two- and
three-or-more-vehicle accidents on roads with speed limits of 30 and 35. On roadways
with speed limit of 25mph or less, the percentage of two-vehicle accidents is about 13
percentage points higher than three-or-more-vehicle accidents, which is significant; on
roads with speed limits of 40mph or more, the percentages of the three-or-more-vehicle

accidents are consistently larger (except for speed limit 55mph). It suggests that,

134

comparatively, three-or-more-vehicle accidents are prone to occur on roadways with
higher speed limits. Conclusively, three-or-more-vehicle accidents occur on roads with
different speed limits (versus two-vehicle accidents).

In summary, based on the above analyses, it has been identified that three-or-
more-vehicle accidents have several noticeable differences when compared to two-
vehicle accidents:

0 Three-or-more-vehicle accidents are prone to occur on freeway sections and
straight roads;

0 Three-or-more—vehicle accidents have three primary accident types—angle-
straight, rear-end straight, and side-swipe same; and

o Three-or-more-vehicle accidents are likely to take place on roadways with speed
limits (>40mph).

Given these differences, D28 in two-vehicle accidents must be compared to
D2’8 in three-or-more-vehicle accident only under these conditions where the latter are
more likely to occur. If there is no significant difference, D28 in two-vehicle accidents are
argued to be comparable with the non-responsible in three-or-more-vehicle accidents; if
there is difference, they are not comparable.

With the use of Michigan accident data (2001), the characteristics of D28 in two-
vehicle accidents are compared under two circumstances: three major accident types (set
one) and others (set two). Table 6.5 shows the distributions for three characteristics for

D28 under these two distinctive circumstances.

135

Table 6.5. Characteristics of D28 under two defined circumstances

 

 

 

 

 

 

 

 

 

characteristics set one set two difference
N % N % (%)
male 47959 54.0 29188 53.6 0.4
gender
female 40812 46.0 25253 46.4 -0.4
vehicle can 70220 79.1 43642 80.2 -1 .1
type prckups 13453 15.2 7818 14.4 0.8
others 5098 5.7 2981 5.5 0.2
15-19 8609 9.7 6152 11.3 -1 .6
20-29 20099 22.6 12407 22.8 -O.2
30-39 20228 22.8 11746 21.6 1.2
age 40-49 18578 20.9 1 1002 20.2 0.7
50-59 12064 13.6 6977 12.8 0.8
60-69 5288 6.0 3369 6.2 -0.2
70-79 3063 3.5 2120 3.9 -0.4
80+ 842 0.9 668 1.2 -0.3

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

In table 6.5, the column “difference” refers to the difference between the two sets
of accidents. As shown, the differences for all three characteristics are consistently
smaller than 2 percentage points. This suggests that the D2 distributions under “set one”
and “set two” conditions are operationally close.

The chi-square test was also used to test the differences for individual
characteristics. The statistics and p-values generated by the test are shown in table 6.6.

Table 6.6. Chi-square statistics and p—values for three key characteristics

 

 

 

 

 

I gender vehicle type age I
I statistics 2.3 23.4 176.4 I
I p-Values 0.20 <0.05 <0.05 |

 

 

In table 6.6, although the results show no statistical difference for driver gender,
the p-values for vehicle type and age are less than 0.05, indicating that the differences are
statistically significant between “set one” and “set two.”

Thus, it has been shown that the prevalent accident types of three-or-more-vehicle

accidents are angle straight, rear-end straight, and side-swipe same. Under these three

136

accident types, operationally D28 in two-vehicle accidents are not different. In this
context, two-vehicle accidents are arguably comparable with three-or-more-vehicle
accidents.

6.4 Comparing D28 between two- and three-or-more-vehicle accidents

The attempt to validate the underlying assumptions of quasi-induced exposure is
undertaken for California, Maine, Michigan, and Utah (2000) at the state level. The
procedures to clean accidents and assign the responsibility for accident causation
developed in chapter 4 are applied to the accident data from these four states.

For each state, two types of comparisons will be conducted:

1. The D2 distributions in two-vehicle accidents for three key characteristics are
compared to a_ll the non-responsible drivers in three-or-more-vehicle accidents.
2. In three-or-more-vehicle accidents, the D2. distributions for the three
characteristics will be compared to D38.
Qafifgmfi

Table 6.7 presents the fiequencies and percentages of D28 in two- and three-or-
more-vehicle accidents for California data.

As shown in the “difference” column, there is no difference in driver gender
between two- and three-or-more—vehicle accidents. For vehicle type, there is more of a
difference, but it is not operationally significant. The difference is a maximum of 3.4
percentage points for passenger cars. The maximum percentage difference for age groups
is 3.5 for the 20-29 group, while the differences for other age groups all fall below 2
percentage points. Operationally, the difference is less than the adopted criterion and

thus, D2 distributions between two- and three-or-more-vehicle accidents are claimed to

137

be similar. The D2 distributions are firrther compared using the chi-square test. The
statistical results show that chi-square statistics (p-values in the parenthesis) are 0.01
(p=0.92), 160.6 (p<0.05), and 90.2 (p<0.05) for gender, vehicle type, and age,
respectively. The differences for vehicle type and age are statistically significant at 0.05
significance level, while not significant for driver gender. Thus, for California data D2
distributions in two-vehicle accidents agree well with those in three-or-more-vehicle
accidents operationally albeit not statistically.

Table 6.7. Comparison of D2 distributions for three key characteristics (CA, 2000)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. . - . > . .

charactenstrcs 1: veh acc% N2 veh ace/o difference

gender male 12823 64.1 12302 64.1 0.0

female 7178 35.9 6902 35.9 0.0

vehicle .cars 13714 68.6 13831 72.0 -3.4

type prckups 4717 23.6 445 1 23.2 0.4

others 1570 7.8 922 4.8 3.0

15-19 1197 6.0 1161 6.1 -0.1

20-29 4492 22.5 4976 25.9 -3.5

30-39 51 19 25.6 4974 25.9 -0.3

age 40-49 4577 22.9 4149 21.6 1.3

50—59 2760 13.8 2412 12.6 1.2

60-69 1 189 5.9 1020 5.3 0.6

70-79 524 2.6 416 2.2 0.5

80+ 143 0.7 96 0.5 0.2

 

 

Further comparisons between D28 and D38 in three-or-more-vehicle accidents are
shown in table 6.8. The column “D2‘s” shows the characteristic distributions of the first
non-responsible driver-vehicle combinations in three-or-more-vehicle accidents; the
column “D38” shows the characteristic distributions of the rest of the non-responsible
driver-vehicle combinations. The columns “D1” and “D2” show the responsible and non-

responsible driver-vehicle combinations in two-vehicle accidents, respectively.

138

Table 6.8. Comparing distributions for three key characteristics (CA, 2000)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

characteristics >2 vehicle accidents (%L 2-vehicle accidents (%)
D2 8 D38 diff. D1 D2 diff.

gender male 64.1 64.0 0.1 66.7 64.1 2.6
female 35.9 36.0 -0.1 33.3 35.9 -2.6

vehicle cars 72.5 71.3 1.2 70.2 68.6 1.6
type pickys 22.5 24.1 - l .6 22.7 23.6 -0.9
others 5.0 4.5 0.5 7.1 7.8 -0.7

15-19 6.6 5.3 1.3 12.8 6.0 6.8

20-29 26.9 24.5 2.4 29.7 22.5 7.2
30-39 25.5 26.5 -1.0 21.9 25.6 -3.7
age 40—49 21.0 22.6 -l.6 17.1 22.9 -5.8
50-59 12.3 13.0 -0.7 9.3 13.8 -4.5
60-69 5.0 5.8 -0.8 4.7 5.9 -l.2

70-79 2.3 2.0 0.3 3.2 2.6 0.6

80+ 0.6 0.4 0.2 1.3 0.7 0.6

 

 

 

 

 

 

 

 

For all three characteristics, the differences between D2, and D3 distributions are
consistently smaller than 3 percentage points, which suggests that the differences are
practically insignificant. In other words, the distributions of first non-responsible drivers
in three-or-more-vehicle accidents are similar to the rest of non-responsible drivers. This
implies that the non-responsible drivers in three-or-more-vehicle accidents are “randomly
selected” by the responsible drivers, regardless of the order in which they are impacted.
However, the comparison among D2. and D3 and D2 with chi-square test indicates that
the distributions are significantly different.

It has been demonstrated that in table 6.7, the D28 in two-vehicle accidents follow
the same distribution as the non-responsible drivers in three-or-more-vehicle accidents; in
table 6.8, the first non-responsible drivers in three-or-more-vehicle accidents are
representative of the rest of the non-responsible drivers. Deductively, it is safe to argue

that D28 in two-vehicle accidents are randomly selected by the responsible drivers. Thus,

139

 

in this case the basic assumptions of quasi-induced exposure can be validated for
California data.

In table 6.8, D1 and D2 distributions in two-vehicle accidents are also compared.
For driver gender and vehicle type, D1 and D2 distributions are operationally close, both
below 3 percentage points. However, for driver age there is a conspicuous (operationally
significant) variation. For two young driver groups 15-19 and 20-29, the D1 percentages
are approximately 6.8 and 7.2 percentage points larger than D2 percentages, respectively;
for the old driver group (70+), D1 is greater than D2, although the difference is not
significant. The discrepancy between D18 and D28 has been expected; otherwise, the
conjecture of D1 8 and D28 being equal will lead to the conclusion that different drivers
have the same propensity for accident causation, which is not factually true.

The results suggest that young drivers (15-29) and old drivers (70+) are more
likely to be responsible for the occurrence of accidents. For age group (30-69), the D1
percentages are consistently smaller than D2 percentages, indicating that drivers in this
range cause proportionately fewer accidents than their presence on the roads.

Mair;

Maine data have also been manipulated with the same procedure as described
above. Table 6.9 is the presentation of D2 distributions for three main characteristics for
two- and three-or-more-vehicle accidents. The difference for male drivers is about 0.3
percentage point; among the three vehicle types, the maximum difference lies in pickups,
about 3.3 percentage points (which is operationally insignificant); for all the age groups,
the differences consistently fall below 1 percentage point. Thus, D2 distributions in two-

vehicle accidents show a positive agreement with those in three-or-more-vehicle

140

accidents for all the three characteristics of interest. Conclusively, overall consistency is
found between two- and three-or-more-vehicle accidents. However, the results of the chi-
square test show that there is no statistical difference for driver gender only—the p-
values is equal to 0.78 for driver gender. The p-values for vehicle type (chi-square
statistics: 44.8) and age (chi-square statistics: 136.8) are both less than 0.05, indicating
that the difference is statistically significant.

Table 6.9. Comparison of D2 distributions for three key characteristics (ME, 2000)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. . 2-veh >2 veh .

characterrstrcs N % N % drff.
gender male 9652 55.4 1455 55.1 0.3
female 7768 44.6 1 185 44.9 -0.3

vehicle cars 13783 79.1 2133 80.8 -l.7
type mickups 3282 18.8 408 15.5 3.3
others 355 2.0 99 3.8 -1.8

15-19 3470 9.1 255 9.6 -0.5

20-29 5049 20.0 539 20.3 -0.3

30-39 3848 22.1 606 22.6 -0.5

age 40-49 3801 21.8 554 21.0 0.8
50-59 2532 14.5 366 14.3 0.2

60-69 1226 7.0 187 7 .1 0.0

70-79 629 4.2 97 3.7 -0.1

80+ 335 1.3 36 1.4 0.6

 

 

 

 

 

 

 

 

 

Analogous to what was done with California data, the D2, and D3 distributions
for the three characteristics are also compared. The results are shown in table 6.10. The
percentage differences listed in the “diff.” column are constantly below 4 percentage
points, which leads to the conclusion that operationally in three-or-more-vehicle
accidents the first non-responsible drivers are representative of all the non-responsible
drivers as a whole. Consistent with California data, chi-square test also finds that D2, and

D3 and D2 distributions are statistically different.

141

It is also found that considerable variations also exist between D18 and D28 with
regard to three driver-vehicle characteristics for Maine data. Comparatively, the variation
is more conspicuous for age distributions than for driver gender and vehicle type. For
example, for age group (15-19) the difference is 7.8 percentage points; for age group (40-
49) the difference is 6.0 points. These differences are operationally significant. Another
observation is that D1 8 in young (15-29) and old (70+) driver groups are consistently
larger than D28, while it is opposite for age group (30-69). This finding is consistent with
that fi'om the California data (table 6.8).

Table 6.10. Comparing distributions for three key characteristics (ME, 2000)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

characteristics >2‘ vehicle accidents (%) 2-vehic1e accidents (%)
D2 8 D38 diff. D1 D2 diff.

gender male 54.2 56.3 -2.1 58.5 55.4 3.1
female 45.8 43.7 2.1 41.5 44.6 -3.1

vehicle cars 82.0 78.7 3.3 74.9 79.1 -4.2
type pickups 14.8 17 .4 -2.6 18.7 18.8 -0.1
others 3.2 3.9 -0.7 6.4 2.0 4.4

15-19 10.3 6.5 3.8 16.9 9.1 7.8

20-29 21.4 20.2 1.2 23.0 20.0 3.0

30—39 22.6 22.7 -0.1 17.8 22.1 -4.3

age 40-49 20.3 22.7 -2.4 15.8 21.8 -6.0
50-59 13.2 15.4 -2.2 10.9 14.5 -3.6

60-69 6.9 8.2 -l.3 6.7 7.0 -0.3

70-79 3.8 3.4 0.4 6.2 4.2 2.0

80+ 1.5 0.8 0.7 3.5 1.3 2.2

Michigan

Similarly, the comparisons of D2 distributions between two- and three-or-more-
vehicle accidents are conducted for Michigan data (table 6.11). Similar to the results in
tables 6.6 (CA) and 6.8 (MB), it is shown in table 6.11 that the differences for driver age,
gender, and vehicle type are all below 2 percentage points. This indicates that an

overwhelming consistency of D2 distributions between two- and three-or-more-vehicle

142

accidents. However, the statistical results given by the chi-square test suggest that the
differences between D2 distributions are significant at the 0.05 level for all the three D2
characteristics, because p-values are all less then 0.05.

Table 6.11. Comparison of D2 distributions for three key characteristics (MI, 2000)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. . 2-veh >2 veh .
characteristics N % N % drff.
gender male 77105 54.6 6495 56.3 -1.7
female 64157 45.4 5049 43.7 1.7
vehicle cars 101850 72.1 8404 72.8 -0.7
type pickups 37293 26.4 3025 26.2 0.2
others 2119 1.5 127 1.1 0.5
15-19 14267 10.1 1177 10.2 -0.1
20-29 28252 20.0 2355 20.4 -0.4
30-39 36304 25.7 2771 24.0 1.7
age 40-49 30230 21 .4 2436 21.1 0.3
50-59 18082 12.8 1478 12.8 0.0
60-69 8476 6.0 762 6.6 -0.5
70-79 4520 3.2 462 4.0 -0.7
80+ 989 0.7 115 1.0 -0.3

 

 

 

 

 

 

 

Similar to the exercise with CA and ME data, the D28 versus D38 distributions
are compared. The data are presented in table 6.12. It can be seen from table 6.12 that,
overall, the D2. and D3 distributions for the three basic characteristics appear to show a
generally good agreement—the differences are relatively small (all below 3 percentage
points).

The D1 and D2 distributions are also compared for Michigan data (table 6.12).
Analogous to the findings in CA and ME data, for driver gender and vehicle type, the
differences between D1 and D2 distributions are smaller than 4 percentage points. Other
similar observations are offered:

1. For the young driver group (15-29), Dl percentages are larger than D28 and

the differences are practically significant.

143

2. For the older driver group (70+), D1 percentages are also greater than D28,

but the differences are not significant.

3. However, for the middle-aged group (30-69), D1 percentages are smaller.

Table 6.12. Comparing distributions for three key characteristics (MI, 2000)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

characteristics >2vvehicle accidents (%) 2-vehicle accidents (%)
D2 8 D38 diff. D1 D2 diff.

gender male 57.6 55.1 2.5 57.5 54.6 2.9
female 42.4 44.9 -2.5 42.5 45.4 -2.9

vehicle cars 74.5 71.6 2.9 73.6 72.1 1.5
type pickups 24.8 27.1 -2.3 25.3 26.4 -l.1
others 0.7 1.3 -O.6 2.1 1.5 0.6

15-19 10.9 9.2 1.7 14.3 10.1 4.2

20-29 20.8 19.8 1.0 24.4 20.0 4.4

30-39 24.6 22.8 1.8 24.0 25.7 -1.7

age 40-49 20.7 22.9 -2.2 19.4 21.4 -2.0
50-59 12.5 14.1 -1.6 9.2 12.8 -3.6

60-69 5.5 6.7 -1.2 4.3 6.0 -1 .7

70-79 4.1 3.5 0.6 3.5 3.2 0.3

80+ 0.9 1.0 -0.1 0.9 0.7 0.2

um

Table 6.13. Comparison of D2 distributions for three key characteristics (UT, 2000)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

. . 2-veh >2 veh .

characterrstrcs N % N % diff.
gender male 13819 57 .6 4280 57.3 0.3
female 10179 42.4 3195 42.7 -0.3

vehicle cars 17879 74.5 6481 76.6 -2.1
type pickups 4968 20.7 1375 18.4 2.3
others 1 152 4.8 374 5.0 -0.2

15-19 3415 14.2 992 13.3 1.0

20-29 7373 30.7 2415 32.3 -l.6

30-39 4657 19.4 1508 20.2 -0.8

age 40-49 4177 17.4 1302 17.4 0.0
50-59 2380 9.9 703 9.4 0.5

60-69 1 181 4.9 342 4.6 0.3

70-79 629 2.6 167 2.2 0.4

80+ 186 0.8 46 0.6 0.2

 

 

 

 

 

144

 

 

Table 6.14. Comparing distributions for three key characteristics (UT, 2000)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

characteristics >2Yvehicle accidents (%) 2-vehicle accidents (%)
D2 8 D38 diff. D1 D2 diff.

gender male 56.8 57.7 -0.9 57.7 57.6 0.1
female 43.2 - 42.3 0.9 42.3 42.4 -0.1

vehicle cars 76.7 76.4 0.3 78.1 74.5 3.6
type trucks 15.5 18.7 -3.2 18.2 20.7 -2.5
others 7.8 4.9 2.9 3.7 4.8 -l.l
15-19 15.0 11.6 3.4 25.6 14.2 11.4

20-29 33.5 31.2 2.3 30.1 30.7 -0.6

30-39 18.4 21.9 -3.5 15.8 19.4 -3.6

age 40-49 16.8 18.0 -1.2 11.7 17.4 -5.7
50-59 8.8 10.0 -l.2 7.2 9.9 -2.7

60-69 4.2 4.9 -0.7 4.0 4.9 -0.9

70-79 2.4 2.1 0.3 3.6 2.6 1.0

80+ 0.9 0.4 0.5 1.9 0.8 1.1

 

 

 

 

 

 

 

 

 

The identical comparisons (D2 distributions between two- and three-or-more—
vehicle accidents, DZ’S and D38, D18 and D28 in two-vehicle accidents) are also
conducted for Utah data (2000). Due to the redundancy, the data are presented in tables
6.13 and 6.14 (shown as above). Note that similar conclusions are drawn.

6.5 Conclusion

In summary, accident data from Califomia, Maine, Michigan, and Utah have
demonstrated generally good agreements of D2 distributions between two- and three-or-
more-vehicle accidents. A similar comparison is developed in three-or-more-vehicle
accidents between D2’s (the first non-responsible drivers) and D38 (the rest of the non-
responsible drivers). The results consistently show that there is an overwhelming
agreement between D28 and D38, which suggests that the responsible drivers in three-or-
more-vehicle accidents “randomly select” the non-responsible drivers. Deductively, it can
be concluded that D28 in two-vehicle accidents are indeed randomly impacted by D18 on

the road. Overall, these observations imply that at the state level, the underlying

145

assumptions of quasi-induced exposure are supported from the operational perspective.
That is, quasi-induced exposure is a good technique to measure the exposure of specific
driver-vehicle groups of interest at the state level. However, the comparison among D2.
and D3 and D2 with chi-square test indicates that the distributions are significantly
different.

During the process of validation, the comparisons have confirmed some facts. The
distributions for D28 are significantly different from Dls in two-vehicle accidents. The
difference is especially obvious for age distributions. The results show that young drivers
(15-29) and old drivers (70+) are more likely to be responsible for the occurrence of
accidents; however, driver groups (30-69) are likely to be the non-responsible party,

because they cause proportionately fewer accidents than their presence on the roads.

146

Chapter 7
MEASURING EXPOSURE CHANGE—MICHIGAN GRADUATED DRIVER

LICENSING

Graduated Driver Licensing (GDL) is a system designed to “teach” teens to drive
responsibly by gradually increasing their driving privileges as they advance through the
system. The goal of the GDL is to reduce crashes, serious injuries and traffic-related
deaths involving teen drivers and their passengers. The GDL imposes specific rules on
certain young drivers with regard to nighttime driving—no driving is allowed from
midnight to 5 AM. Due to the nighttime restriction, it is expected that the exposure of the
affected young drivers during the restricted driving period would be drastically reduced.
The research purpose here is to examine whether quasi-induced exposure is able to
capture and then represent the exposure change due to the implementation of the GDL
program. In order to quantify the effect of the GDL program with respect to exposure, the
exposure of young drivers using quasi-induced exposure within and around the restricted
nighttime period will be compared before and after the program was put into practice.

7.1 Michigan graduated driver licensing (GDL)

The GDL program implemented in Michigan on April 1, 1997 was a three-tiered

(levels) licensing system for young drivers. The eligibility and restrictions of each tier is

detailed below. Note that the GDL ends for all teens when they are 18.

147

Level 1

Level 1 license permits the holder to operate a motor vehicle only when

accompanied by a licensed parent or legal guardian, or with the permission of the parent

or legal guardian, any licensed driver 21 years of age or older. Note that there is no

nighttime driving restriction for young drivers at level 1, i_f they are accompanied by

eligible guardians. To obtain a Level 1 license a driver must:

Level 2

be at least 14 years, 9 months of age;
complete a “Segment 1” driver education course approved by the

Michigan Department of Education;

pass a vision test and meet the physical and mental standards set by the
Secretary of State;

obtain written approval from a parent or legal guardian.

A Level 2 license permits the holder to drive unrestricted between 5:00 am. and

midnight. To obtain a Level 2 license, a driver must:

be at least age 16;

complete a “Segment 2” driver education course approved by the
Michigan Department of Education;

have no convictions/civil infractions, license suspensions or crashes
during the 90-day period immediately prior to applying for a Level 2

license;

148

0 hold a Level 1 license for six months and complete a minimum of 50
hours of behind-the-wheel driving, including 10 hours of nighttime driving
that is certified by a parent or legal guardian; and

0 pass a road test conducted by a Secretary of State approved examiner.

LLell
A Level 3 license allows the license holder unrestricted privileges. To obtain a
Level 3 license, a driver must:

0 be at least age 17;

0 hold a Level 2 license for six months;

0 complete 12 consecutive months of driving without a moving violation, an
at-fault crash that resulted in a moving violation, a license suspension, or a
violation of the graduated license restrictions.

According to the three-tiered driving licensing system, at different levels young
drivers have different driving privileges and restrictions.
7.2 Affected young drivers and program in-effect years

Based on the three-tiered licensing program, fewer and different driving
restrictions are phased in as the young drivers advance through the program. In a specific

nighttime driving period (midnight-5am) drivers with level 1 or 2 license are not allowed

 

to drive alone, in other words, they are restricted; otherwise, drivers are allowed. The
diagram below (figure 7.1) graphically illustrates how different ages will be affected by
the restricted nighttime driving (midnight to 5am) due to the three-tiered GDL program
over the first years of its existence. In this diagram, it is assumed that all young drivers

are able to advance to a higher level without any failure.

149

04/97 041/98 04(99 041/ 00 Year

 

  
 
 

 
 
  

   

Level 1 Level 2
Age 14 _
Age 15 Level 1 Level 2
Age 16 Level 1 Level 2
Level 1 -
Age 17 . . . . . .
Nighttime dnvrng restrrctron

Age 18

 

Figure 7.1. Demonstration of different ages affected by the restricted nighttime driving
As shown in figure 7.1, when the GDL program was implemented in April 1997,

drivers with different ages were examined individually. For the l4-year-old or younger
drivers, they had to wait at least one year to join the GDL program and they were
expected to have a minimum of two years of restricted nighttime driving. If the drivers
were 15- or l6-year-old when the GDL program started, they would have at least two
years of restricted nighttime driving, which depended on how they performed at the
levels 1 and 2. Considering that some drivers might fail to advance to level 2 in April
1998, the restricted nighttime driving for some drivers could be extended to period fiom
04/98 to 04/99. If the drivers were 17, they stayed in the GDL program for one year
(level 1) and then were automatically out of the program. If the drivers were 18 or older,
they were not in the program. Based on the descriptions above, the affected young drivers
were those 15, 16, and 17 years old; the GDL program was “partially” effective in the
period from 04/97 to 04/99 and year 2000 was the first year that the GDL program was

fully in effect.

150

7.3 Exposure data analysis

Six years of Michigan accident data are examined, including three years before
GDL implementation (1994, 1995, and 1996) and three years after (2000, 2001, and
2002). The main purpose is to determine the frequency shifts for young (15-17) D2
drivers during the restricted nighttime period. The Michigan accident data are screened to
make them usable for quasi-induced exposure with specific attention given to driver age,
in terms of eliminating data cases with missing and/or miscoded driver age information.
The reason is that in this exercise driver age is the only driver-vehicle characteristic that
will be examined. Table 7.1 shows the fi'equencies of non-responsible drivers,
disaggregated by driver age, in the restricted driving time period before and after the
enforcement of GDL.

Table 7.1. The fi'equencies of non-responsible drivers by age (midnight-5am)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

year drrver age total
15 16 17 18 19 20 >20

1994 2 70 l 11 164 185 168 3087 3787
1995 2 68 1 12 163 206 176 3095 3822
1996* 2 71 113 168 174 165 2932 3625
2000" 1 30 78 147 161 156 2836 3409
2001 2 24 72 129 127 145 2200 2699
2002 3 21 61 1 15 1 15 116 2265 2696

 

Note: * Michigan GDL law was effective on April 1997, so data from year 1996 and earlier did

not have GDL restrictions; " data from year 2000 and later have full GDL restrictions.

In table 7.1, the affected driver ages are highlighted with shaded cells. The total

number of D28 for 15 years old drivers is very small (1-3 accidents/year) for all six years,

and it is hard to quantify the effectiveness of the GDL program. Therefore, 15-year old

drivers are not included in the discussion. However, a noticeable reduction can be seen in

the absolute number of D28 for all ages examined along the boundary where the GDL

151

 

program was implemented. Before the GDL was implemented, the number of D28 for
each age is generally consistent within the three years examined (1994, 1995, and 1996).

However, the number of D28 shows a general trend of decreasing from 2000 to
2002. For ease of explanation, the average D28 before and after the GDL for each age and
D2 changes in fiequencies and percentages are calculated in table 7.2.

Table 7.2. Average D28 before and after the GDL and changes (midnight-Sam)

 

 

 

 

 

 

 

 

 

 

 

 

 

GDL dnve‘ age total

l6 17 18 19 20 >20
before 70 l 12 165 188 170 3038 3745
after 25 70 130 134 139 2434 2935
change 45 42 35 54 31 604 810
change (%) 64.1 37.2 21.0 28.7 18.1 19.9 21.6

 

 

 

It can be seen fiom table 7.2 that, overall, there is a considerable reduction of D28
for all ages and the total after the GDL was implemented. The total number of D28
decreases by 21 .6% for some reason (e. g., traffic safety policy or programs), which
presumably contributes, at least partially, to D2 percentages decreasing for all drivers.
Given that, the D2 change in percentage for l6-year-old drivers is still significant: 64.1%
is considerably greater than the 21.6% decrease overall. The 37.2% of D2 reduction for
17—year-old drivers is also larger than the overall decrease.

Since the total number of D28 (last column in table 7.1) varies considerably from
year to year, it is more meaningful to compare the D28 in percentages over the years
(table 7.3).

As illustrated, there is a conspicuous gap in the D2 percentages for the affected
drivers at the point where the GDL program was implemented, which is not so obvious
for other ages. D2 percentages for l6-year-old drivers before the GDL program

(averaging 1.8%) are consistently higher than those after the GDL program was initiated

152

(averaging 0.8%) by 1.0%. Although this number itself does not suggest a significant
amount, the relative proportion change, defined as the ratio of average percentage change
(1.0%) to average D2 percentage without the GDL program (1 .8%), is quite substantial,
as much as 54.4%. The results also show D2 decrease in percentage for l7-year-old
drivers (0.59%), however, the relative proportion change is less significant, 19.6%. This
analysis demonstrates that with the quasi-induced exposure technique, the exposure
reduction for 16- and l7-year-old drivers is reflected in the exposure data. Meanwhile, it
is no surprise to see some 16- and l7-year-old D2 drivers in the 2000, 2001, and 2002
data, since drivers at these ages can still drive legally between midnight to 5am with
guardians when they are at level 1 or 2. An alternative explanation is that many young
drivers will continue to drive during the curfew in spite of the law.

Table 7.3. The percentages of non-responsible drivers (midnight-5am)

 

 

 

 

 

year driver age total
16 17 18 19 20 >20

1994 1.85 2.93 4.33 4.89 4.44 81.52 100.00

1995 1.78 2.93 4.26 5.39 4.60 80.98 100.00

1996 1.96 3.12 4.63 4.80 4.55 80.88 100.00

 

2000 0.88 2.29 4.31 4.72 4.58 83.19 100.00
2001 0.89 2.67 4.78 4.71 5.37 81.51 100.00
2002 0.78 2.26 4.27 4.27 4.30 84.01 100.00

 

 

 

 

 

 

 

 

 

 

 

 

Moreover, D1 percentages for all age groups are also computed before and after
the GDL implementation. Table 7.4 shows the frequencies of responsible drivers in the
restricted driving period before and after the GDL program was implemented. Comparing
the D28 (table 7.1) to D18 (table 7.4), it can be seen that D18 are generally larger than
D28 in the corresponding year for the affected drivers (16 and 17) and several other

young drivers (18-20), no matter whether the GDL is implemented. In other words, the

153

involvement ratios for young drivers are consistently greater than 1. These results
generally confirm the fact that young drivers are indeed the more dangerous driving
cohorts in the traffic stream.

Table 7.4. The frequencies of responsible drivers (midnight-5am)

 

 

 

 

 

 

 

 

year drrver age total
16 17 18 19 20 >20
1994 125 147 211 208 151 2938 3787
1995 119 142 225 215 187 2932 3822
1996 126 138 212 162 172 2808 3625
2000 60 109 213 180 173 2672 3409
2001 44 79 151 166 138 2116 2699
2002 48 1 13 173 159 148 2051 2696

 

 

 

 

 

 

 

 

 

 

In addition, D2 percentages for the 16- and 17-year-old drivers in three hours just
before and after the restricted period are also examined. The purpose is to check if the D2
distributions of the affected drivers in the restricted driving period shift to the adjacent
non-restricted time period for the years afier the GDL program was executed. Six years
including three before the GDL implementation (1994, 1995 and 1996) and three after
(2000, 2001 and 2002) are chosen to illustrate how D2 percentages evolve with the time
of day. The results are shown in figure 7.2 for the 16-year-old drivers. It is seen from
figure 7.2 that the time-of-day D2 distribution for each year examined appears to be U-
shaped. Three D2 trendlines for years before the GDL implementation (abbreviated as
“D2 trendlines before”) and three for years after (abbreviated as “D2 trendlines after”)
are similar in nature. Although at some hours the relative position of D2 trendlines before
and after fluctuate up and down, some general trends are observed based on these two

sets of D2 trendlines:

154

p—A

 

 

 

 

 

21-22 22-23 23—24 0—1 1-2 2-3 3-4 4-5 5-6 6-7 7-8

Figure 7.2. The D2 percentages of the 16-year-old drivers (time-of-day distribution)

. In the three hours before the restricted driving period, generally, the D2 trendlines

afier fall below the D2 trendlines before. This is not expected, since the restriction of
nighttime driving should cause the affected drivers (especially those at level 2) to
drive relatively more in this period to compensate the travel scheduled between
midnight to 5am (e.g., young drivers end the midnight activities earlier). Thus, the
nighttime driving restriction pushes the affected drivers out of time period (midnight-
5am) and D2 percentages afier the GDL was implemented should be larger in the
period (9-12pm). However, the fiirther investigation of D2 distribution in the earlier
hours indicates that D2 trendline afier is generally located atop D2 trendline before. It
suggests that affected young drivers will drive relatively more outside the restricted
nighttime driving period to compensate the driving activity suppressed by the GDL

law in a long-time stretch.

155

2. In the restricted driving period, the D2 trendlines before are consistently located
above the D2 trendlines after. This is due to the implementation of the GDL program,
which does not allow the affected drivers to drive alone or without legal guardians in
the restricted period.

3. In the three hours after the restricted driving period, the D2 trendlines after show a
relatively strong ascending rate and move atop the D2 trendlines before. This
phenomenon is to be expected. The affected drivers (especially drivers at level 2)
could, alternatively, postpone the trips scheduled between midnight to 5am (e.g.,
drivers stay wherever they were after the midnight activities), due to the deterrent
effect of the GDL program.

These trends have shown that with the quasi-induced exposure approach, the D2
time-of-day distribution for l6-year-old drivers can only partially represent the
effectiveness of the GDL program. There is a shift of D2 distributions in three hours after
the nighttime driving restrictions but not before.

7.4 Summary

In summary, using several years of accident data, quasi-induced exposure could
partially pick up the exposure change resulting from the GDL implementation. It is
reflected from two perspectives: 1) the exposure is noticeably reduced for the affected
16- and 17-year-old drivers; 2) the time-of-day distribution indicates that D2 percentages
are shifted to hours after the period of midnight-5am, but not before (at least three hours
as the data present). From this point-of-view, it can be argued that quasi-induced

exposure is a legitimate approach in this instance. As a closing note, it needs to be

156

pointed out that if the results do not show the exposure change of the affected group, it

does not necessarily constitute the evidence that quasi-induced exposure is invalid.

157

Chapter 8

DIFFICULTIES WITH QUASI-INDUCED EXPOSURE

In chapter 5, it has been observed that even with large sample size, for 1-94 the D2
data differ significantly from the W2 data even with the data aggregation. While the
sample size is an issue, a question is also raised regarding potential theoretical difficulties
associated with the quasi-induced exposure technique. It is known that freeway I-94 is
especially favored by 1m truck traffic, 33% at some WIM locations. Could Lem
truck traffic be an essential element affecting the D2 measurement on I-94?

On a typical freeway, it is argued that substantial speed variation exists between
passenger cars and trucks. Based on Taylor’s study of fieeway speeds (2000), the mean
speed of automobiles and light trucks is, on average, 7 MPH higher than that of heavy
trucks. The problem arises from the fact that using quasi-induced exposure implicitly
assumes that the travel speeds are identical for different types of vehicles.

An example with passenger cars and trucks moving along an identical freeway
segment is given to illustrate how the relative accident involvement ratio for different
vehicle types can be incorrect when speed variation is evident. The relative accident
involvement ratio is expressed as the number of times that a certain vehicle type is
responsible (hits other vehicles) to the number of times that the same type of vehicle is

non-responsible (is hit by other vehicles). Mathematically

158

D1.
IR. '

=_ 8.1
1 mi ( )

where:
IR,- — the relative accident involvement ratio for vehicle type i;
i — a vehicle type;
Dl ,- — the number of times that vehicle type i is responsible; and
D2,- — the number of times that vehicle type i is non-responsible.

The formulation above is used to calculate the relative accident involvement ratio
for different types of vehicles. However, when the traveling velocity is taken into
consideration, there are problems involved with the computation of the numerator and the
denominator of the equation. The problem becomes more typical on fi'eeways where the
speed variation between different vehicles is conspicuous and it can be safely assumed
that passenger cars generally move faster than trucks. This is explained by comparing the
magnitude of the number of non-responsible and responsible drivers between two
scenarios (“no speed variation” and “speed variation”). It is achieved in a stepwise
manner, including assumptions, model development, constraints, and comparison.
Assumptions

In order to develop the proposed comparisons, three assumptions are made:

1. The symbols used in two scenarios are distinguished with a prime (’). For the

“no speed variation” scenario, the number of non-responsible and responsible
drivers are labeled as D1 and D2, respectively; for the “speed variation”
scenario, they are labeled as D1, and D2’.

2. Two-vehicle accidents are involved with only two types of vehicles: passenger

cars or trucks. Once one vehicle initiates an accident, this vehicle is

responsible; otherwise, it is non-responsible.

159

3. Speed variation between different vehicle types has no effect on the

propensity of accident occurrence between the same vehicle types. However,

it will affect the accident propensity between different vehicle types. A8

reflected in the traffic characteristics, overtaking is one of the most common

driving maneuvers to cause speed variation. Based on this deduction,

overtaking between different vehicle types is likely to cause accidents.

Model development

Under these two scenarios, the number of non-responsible and responsible drivers

is calculated based on the information shown in figure 8.1. In figure 8.1, Nu is the number

of times that vehicle 1' hit vehicle j. The subscript P stands for passenger cars and T stands

for trucks.

 

 

no speed variation

speed variation

 

 

 

 

 

 

131’: Dz’f

‘1
i v

 

Nrr

 

 

 

® -- passenger cars

-- trucks

-- passenger cars

hit trucks
0

Figure 8.1. D1 and D2 for passenger cars and trucks under two scenarios

160

Based on the denotation in figure 8.1, the number of non-responsible and
responsible drivers for passenger cars and trucks with and without considering speed
variation can be expressed as:

“no speed variationz”

D1,, =N,.,,+N,,T, Dl, =N,.,. +NTP (8.2)
D2P=NPP+NTP9D27=NIT+NPT (83)

“speed variation:”
191', = N”. + N14, 01', = NT, + N',,. (8.4)
D2}, = NH, +N'TP, D2} = N” +NI,T (8.5)

Constraints

When speed variation between different vehicle types is taken into account on
freeways, it suggests the consideration of a specific driving maneuver—overtaking
between passenger cars and trucks. However, given the “speed variation” scenario,
passenger cars move faster and will overtake trucks more than they do with no speed
variation. Thus, in the event of accident occurrences, passenger cars are more likely to be

the guilty party and trucks are the “victims.” Given this illustration, a relationship
between N P, and N 127 is established:
NP, < N}, (8.6)
The same theory applies to the event of trucks overtaking passenger cars—the
probability of overtaking is certainly less with “speed variation.” 80, another relationship
exists:

N", > N}, (8.7)

161

Comparison

Based on these two inequalities (8.6 and 8.7), other relationships can be derived

from equations 8.2, 8.3, 8.4, and 8.5:

DI, < D1,, D2,, > DZ}, (8.8)
Di, > 191,, 192, < D2, (8.9)

Inequalities 8.8 and 8.9 indicate that using quasi-induced exposure where
substantial speed variation exists will result in relative exposure being overestimated for
passenger cars and underestimated for trucks. Then, replacing the denominator and
numerator in equation 8.1 with inequalities 8.8 and 8.9, there is,

_ D1,, D1,,

 

 

 

 

IR <IR' = , 8.10

” D2,, P 192,, ( )

1R, = DIT >1R, = D1? (8.11)
192, Dz,

Inequalities 8.10 and 8.11 suggest that quasi-induced exposure results in the
overall estimation of relative accident involvement ratio for passenger cars being
comparatively lower and trucks being relatively higher, where considerable speed
variation is apparent.

Theoretically, it has been demonstrated that there are problems with quasi—
induced exposure when there is speed variation. In the following section the same issue is
explored from the practical perspective using Michigan accident data from 2001.

The basic idea is to calculate D18, D28, and IRs for fast- and slow-moving vehicles and
identify the patterns for these three variables with different speed limits. An essential
assumption behind the idea is that with a speed limit increases, the speed variation

between slowing- and fast-moving vehicles increases. Arguably, the assumption is valid,

162

because increasing the speed limit opens up more opportunities for fast-moving vehicles
to overtake slow-moving vehicles.

The current Michigan vehicle type classification is regrouped into two general
categories: fast- and slow-moving vehicles. The former includes passenger cars and
pickup trucks; the latter consists of a variety of heavy trucks and passenger vehicles with
3 or more axles. In this exercise, only two-vehicle accidents containing fast- and slow-
moving vehicles are selected. The systematic procedures developed in chapter 4 are
employed to clean the accident data and assign the responsibility. With the aid of another
variable—speed limit of the roadway where accident occurred (speedlmt), the accidents
are further classified. D18, D28, and [Rs for fast- and slow-moving vehicles under

different speed limits are presented in table 8.1, with the quasi-induced exposure

 

 

 

 

 

 

 

 

approach.
Table 8.1. D18, D28, and IRS for fast- and slow-moving vehicles
speed limit fast-moving vehicles slow-moving vehicles
D1 %) D2 (%) IR D1 (%) D2 (%) IR
<40 94.019 94.890 0.991 5.981 5.1 10 1.170
40 95.021 95.209 0.998 4.979 4.791 1.039
45 94.423 94.130 1.003 5.577 5.870 0.950
50 93.315 92.728 1.006 6.685 7.272 0.919
55 92.289 90.874 1.016 7.711 9.126 0.845
>55 91.719 89.868 1.021 8.281 10.132 0.817

 

 

 

 

 

 

 

 

 

The important information shown in table 8.1 is that for fast-moving vehicles, IRs
go up as the speed limits go up; while for slow-moving vehicles, it is the opposite. For
fast-moving vehicles, the result coincides with inequality 8.10—with lower speed limits
(where speed variation is less obvious), the values of IRs are relatively smaller; with

higher speed limits (where speed variation is more obvious), the values of IRS become

163

larger. Therefore, this phenomenon coincides with the results concluded from the
theoretical exploration.

Other information displayed in table 8.1 is that the IR of slow-moving vehicles is
sensitive to the change of D28—IRS change from 1.17 to 0.82 with 5% change of D28. It
suggests that the percentage of slow-moving vehicles in the traffic stream (supposedly
D28 for heavy trucks) is another essential factor affecting the IR, in addition to the speed
variation. Based on the last two columns of table 8.1, it is predicted that when the
percentage of slow-moving vehicles reaches 30%, the IR will be significantly reduced.
This might help to explain the significant difference between the D2 and W2 data on I-
94, which is particularly favored by heayy truck traffic; for I-96 and I-75 with less truck
traffic composition, the difference is insignificant.

However, there is a caveat in comparing the patterns of D1 8 and D28 with
inequalities 8.8 and 8.9. The problem is that the whole driving population is changed due
to different roadways with different speed limits. Specifically, the traffic stream has a
large percentage of heavy trucks (relatively slow-moving vehicles) as the speed limits go
up (i.e., from local surface roads to freeways). Therefore, it is expected that D2
percentages for fast-moving vehicles will decrease due to the change in the driving
population. It is hard to tell whether speed variation, change of driving population, or
both contribute to the D2 decreasing for fast-moving vehicles as presented in table 8.1.

It has been shown both theoretically and practically that the speed variation
between vehicles affects the relative accident involvement ratio. For vehicle types that
typically travel faster, the IRS will be underrepresented; while for vehicle types with

slower traveling speeds, the IRs will be overrepresented. Whether the [Rs are

164

significantly biased by the speed variation between vehicles also hinges on the percentage
of slow-moving vehicles in the traffic composition. The bias will become larger as the
percentage increases. This is also intuitive: when heavy trucks account for 1% of the
traffic, the errors introduced by the speed variation are negligible; when heavy trucks
reach 30% (such as I-94) of the traffic, the errors are significant.

In summary, when the sample size is sufficiently large, quasi-induced exposure is
a generally legitimate approach to measure the exposure on freeway links, although it is
admitted that substantial speed variance between different vehicles and percentage of
slow-moving vehicles compromise the measurement. When the composition of slow-
moving vehicles reaches certain amount (say, 30%), significant amount of biases will be
introduced to D1, D2, and IRs and thus, the quasi-induced exposure approach becomes
inappropriate and other exposure measurements should be pursued.

As a closing note to this section, it needs to be pointed out that the research results
can also be applied to the phenomenon whenever there are speed disparities in the traffic
stream. For example, the speed discrepancy is caused by the different drivers (e.g.,

younger and faster drivers versus older and slower drivers).

165

Chapter 9

CON CLUSIONS

This research has attempted to address two basic issues: 1) validation of the
assumptions of the quasi-induced exposure technique, essentially, that the non-
responsible driver-vehicle combinations involved in two-vehicle accidents are
representative of the driving population; and if validated, 2) present general
rules/ guidelines how and when to use quasi-induced exposure.

In the attempts to validate the underlying assumptions, two techniques have been
developed, by comparing D28 in two-vehicle accidents with three types of “true”
exposure data m the non-responsible drivers in three-or-more-vehicle accidents. The
exposure data include VMT, safety-belt use data, and truck volume data (W-2).

VMT data by driver age and gender were generally approximated fi'om NHTS in
combination with census data for a certain state. The results show that quasi-induced
exposure estimates are operationally and statistically different from VMT estimates for
Michigan, Utah, and California. The VMT estimates are derived fi'om NHTS in
combination with census data. The NHTS is a national survey and collects data fi'om a
nationally representative sample of households at the national and state levels. Therefore,
the travel estimates should be statistically reliable and representative of individual states.

However, the VMT distributions are calculated based on the census data instead of the

166

driving population data (i.e., traffic volume data). The data are actually indicative of the
distribution of census-population for each state. The assumption that driving population is
characteristic of the census population at each state must not hold. Since the VMT data
for each individual state, supposedly as an exposure “truth,” can not be justified, the
validity of D2 data can not be determined. Therefore, it is unconvincing that quasi-
induced exposure is a legitimate approach to measure the relative exposure on the state-
maintained routes as presented by the accident data. Further research efforts are
necessary to derive more dependable and accurate VMT estimates.

Safety-belt data obtained fiom UMTRI were compared with D2 data at three
levels: state, stratum, and county. Although the sampling plan for the safety-belt data
collection was implemented at the statewide level, driver age and vehicle type
distributions in the safety-belt data differ significantly from the D2 data. Data errors are
introduced to the driver age in the safety-belt data, since it is relatively difficult to
identify accurate driver age during the field observations, especially age group 30-59; for
vehicle type, there might be some errors due to the mismatched classification—the
passenger cars in accident data might include some sport utility vehicles. Practically, the
comparisons between the safety-belt and D2 data demonstrate a fairly good agreement of
driver gender distributions both at the statewide and intersections levels, from the
operational perspective. At the state level, quasi-induced exposure is argued to be a
generally good technique in terms of driver gender; however, further justifications are
needed for driver age and vehicle type, since there are subject to data observation errors

and mismatched vehicle classification.

167

At the stratum and county levels, the discussions have illustrated that there is a
disagreement in driver-vehicle characteristic estimates between the safety-belt and D2
data for three key characteristics. Notwithstanding that, it has been observed that with the
safety-belt and accident data at the more finely-disaggregated levels, the variation of
distributions by three D2 characteristics becomes more significant. The D2 estimates
yielded by quasi-induced exposure are relatively stable, while the distributions given by
the safety-belt data vary considerably. Given that, quasi-induced exposure seems less
sensitive to the data disaggregation, at the levels such as state, statewide intersections,
stratum, and stratum-intersections.

W-2 data by vehicle types are compared with D2 data in terms of different
freeway routes. Analytical results consistently demonstrate that there are significant
differences between the W-2 and D2 data (with five vehicle type categories) for the five
fieeway routes examined. The sample size seems to play an important role in the results.
With the sample size increased by regrouping the vehicle types into two categories, the
results become mixed regarding whether the D2 data fit the W-2 data. For [-96 and I-75
there is no significant difference between the D2 and W-2 data; for U823 and US 12 the
difference is shown statistically insignificant; but for I-94 the difference is both
statistically and operationally significant. With using the multiple years of data,
notwithstanding that the difference for vehicle type distribution remains operationally and
statistically significant for 1-94 and I-75, the discrepancy is much smaller with large
sample size. In general, the results suggest that quasi-induced exposure is sensitive to the

sample size (data aggregation) when it is used for freeway routes.

168

While the sample size is an issue, a question is also raised regarding potential
theoretical difficulties associated with the quasi-induced exposure technique, especially
on freeways where there is heavy truck traffic and substantial speed variance. It has been
theoretically and practically proved that the speed variation between vehicles affects the
IRS. For vehicle types that typically travel faster, the IRS will be underrepresented; while
for vehicle types with slower traveling speeds, the IRS will be overrepresented. Whether
the [Rs are significantly biased by the speed variation between vehicles also hinges on the
percentage of slower vehicles in the traffic composition. The bias will become larger as
the percentage of slower vehicles increases. Using 1-94 as an example, the results show
that the IR of slower vehicles is sensitive to the change of D28 (table 8.1). Based on the
last two columns of table 8.1, it is predicted that when the percentage of slow-moving
vehicles reaches 30%, the IR will be significantly reduced. This might help to explain the
significant difference between the D2 and W2 data on I-94, which is particularly favored
by My truck traffic; however, for I-96 and I-75 with less truck traffic composition, the
difference is insignificant.

The other technique to validate the underlying assumptions of quasi-induced
exposure is to use three-or-more-vehicle accidents. Accident data from California, Maine,
Michigan, and Utah have demonstrated generally good agreements of D2 distributions
between two- and three-or-more-vehicle accidents. A similar comparison is developed in
three-or-more-vehicle accidents between DZ’S (the first non-responsible drivers) and D38
(the rest of the non-responsible drivers). The results also consistently show that there is
agreement between D28 and D38, which indicates that the responsible drivers in three-or-

more-vehicle accidents “randomly select” the non-responsible drivers. Deductively, it

169

suggests that D28 in two-vehicle accidents are randomly impacted by Dls on the road.
Overall, these observations imply that at the state level, the underlying assumptions of
quasi-induced exposure are supported from the operational perspective. That is, quasi-
induced exposure is a good technique to measure the exposure of specific driver-vehicle
groups of interest at the state level.

Based upon the conducted comparisons, the guidelines are summarized as follows
in terms of how and when to use quasi-induced exposure:

0 Practically speaking, at the §La_te_ level quasi-induced exposure is a generally good
technique to measure the relative exposure for three driver-vehicle characteristics
considered.

0 In determining whether quasi-induced exposure can be used in a typical
application, two comparisons with accident data can be conducted:

0 comparing D2 distributions between two-vehicle and three-or-more-
vehicle accidents; and
o comparing D2’ and D3 distributions in three-or-more-vehicle accidents.
0 If validated, two procedures can be employed to make accident data usable by
quasi-induced exposure:
0 the procedure to clean accident data; and
o the procedure to assign responsibility for accident faults.
In the meanwhile, the research also reveals findings and difficulties associated
with quasi-induced exposure:
0 Quasi-induced exposure is sensitive to the sample size (data aggregation). With

data are disaggregated at more finely-disaggregated levels, the variation of

170

distributions by three D2 characteristics becomes more conspicuous/significant
both from the operational and statistical senses.

Under the circumstances when substantial speed variation exists between different
vehicles, quasi-induced exposure results in the estimation of relative accident
involvement ratio for passenger cars being comparatively lower and trucks being
relatively higher.

Overall, the empirical approach to validate the underlying assumptions of quasi-

induced exposure has shown some potential. However, during the validation process

using a variety of accident and exposure data, it has been demonstrated that there are a

number of problems inherently associated with the data themselves. Suggestions for

further research in this field include:

Require more sophisticated accident collection efforts to improve the quality of
accident data. The research has shown that a significant amount of accident data is
eliminated due to the data errors, when efforts are directed to clean the accident
data. This can be improved with the aid of advanced data collection equipments
on the accident scene (e.g., laptops equipped with GPS and GIS devices),
systematic police training, and a more informative accident form.

Improve the reliability and availability of exposure data. This research has been
greatly compromised due to the quality of the exposure data, for example, the
driver age in the safety-belt data. It would be desirable to conduct a
comprehensive statewide traveler survey to collect vehicle miles traveled data by
three key driver-vehicle characteristics under different circumstances (e.g.,

roadway type, time-of-day)

171

0 Explore the effect of speed variation between young versus old drivers on the
results of quasi-induced exposure. This could be the extension work of the

discussion on the speed variation between passenger cars and trucks (chapter 5).

172

APPENDICES

173

 

APPENDIX A

C-H- CODE TO MANIPULATE HSIS DATA

#include <stdlib.h>
#include <stdio.h>
#include <st1ing.h>

static const int line_size = 512;

int getdelirn (char "lineptr, size_t *n, int delim, FILE *stream)
{
int indx = 0;
int c;
/* Sanity checks. */
if (lineptr == NULL || 11 == NULL || stream == NULL)
return -1;

/* Allocate the line the first time. */
if (*lineptr == NULL) {
*lineptr = (char *) malloc (line_size);
if (*lineptr = NULL)
return -1;
*n = line_size;
}

/* Clear the line. */
mernset (*lineptr, '\0', *n);
do {
c = fgetc (stream);
if (c > 128 || c = 0) continue;
if (0 == EOF) {
break;
}

/* Check if more memory is needed. */
if (indx >= (*n) ) {
*lineptr = (char *) realloc (*lineptr, *n + line_size);
if (*lineptr = NULL) {
return -1;
}

174

/* Clear the rest of the line. */
memset(*lineptr + *n, '\0',1ine_size);
*n += line_size;
}
/* Push the result in the line. */
(*lineptr)[indx++] = c;
/* Bail out. */
if (c = delim) {
break;

}
} while (1);
return (c = EOF) ? -l : indx;
}

int getline (char **1ineptr, size_t *n, FILE *stream)
{

return getdelirn (lineptr, n, '\n', stream);
}

int main(int argn, char *argv[])
{
FILE *inpfile, *oupfilel, *oupfile2;
char *oldline = NULL, *newline = NULL;
char oldline_copy[4096], newline_copy[4096], saveline[40] [4096];
size_t len;
. char delim[2], delim2[2];
int dup = 0, i,j;
char oupfl [32], oupf2[32];
int read, 11;

delim[O] = ' ';
delim[l] = '\t’;
delim2[0] = '\n';
delim2[0] = '\n';

if (argn < 2) {
printf ("input file name is needed ");
exit(l);

}

strcpy (oupfl , argv[1]);

strcat (oupfl, ".outl");

strepy (oupfl, argVIIl);

strcat (oupf2, ”.out2");

inpfile = fopen(argv[ 1 ], "r");

175

oupfilel = fopen(oupfl, "w");
oupfileZ = fopen(oupf2, "w");

if (inpfile = NULL) {
printf ("input file could not be opened\n");

return 1;

}

getline (&oldline, &len, inpfile);
strcpy (oldline_copy, oldline);
strtok (oldline,delim);

while ((read = getline (&newline, &len, inpfile)) 1= -1) {
11 = strlen (newline);
strcpy (newline_copy, newline);
strtok (newline,delim);

if (dup == 0)

strcpy (saveline[O], oldline_copy);

if (strcmp (oldline, newline) == 0) {

duP ++;

strcpy (saveline[dup], newline_copy);

}

else {

if (dup == 1){
for (i=0; i<=dup; i++){
for (j=0; j<str1en(saveline[i])-l; j++)
fputc (saveline[i][j], oupfilel);

fputs ("\t", oupfilel);
}
fputs ("\n", oupfilel);
}
if (dup > 1) {
if (dup > 10)
printf ("%s\n", newline);
for (i=0; i<=dup; i++){
for (i=0; j<strlen(saveline[i])-l; j++)
fputc (saveline[i][j], oupfile2);
fputs ("\t", oupfile2);
} .
fputs ("\n", oupfile2);
}
dup = 0;

176

strcpy (oldline, newline);
strcpy (oldline_copy, newline_copY);

}

fclose (inpfile);
fclose (oupfilel );
fclose (oupfile2);

177

APPENDIX B

COMPARISON BETWEEN D2 AND SEAT-BELT DATA AT STRATUM LEVEL

(INTERSECTIONS)

Table B. l. Seat-belt versus D2 distributions for stratum l—intersection

 

 

 

 

 

 

 

 

 

characteristics seat-belt D2 difference

N % N % (%)

gender male 1265 53.9 6269 50.4 3.5
female 1080 46.1 6171 49.6 -3.5

16-29 652 27.8 3853 30.9 -3.1

age 30—59 1474 62.8 7275 58.5 4.3
60+ 219 9.4 1312 10.6 -l.2
vehicle passenger car 1 196 71.7 9124 83.8 -12.1
type pickup truck 473 28.3 1761 16.2 12.1

 

 

 

 

 

 

 

 

Table B.2. Seat-belt versus D2 distributions for stratum 2—intersection

 

 

 

 

 

 

 

 

 

characteristics seat-belt D2 difference
N % N % (%)
gender male 886 59.7 6290 52.7 7.0
female 598 40.3 5640 47.3 -7.0
16-29 373 25.2 3777 31.6 -6.4
age 30-59 948 63.8 6691 56.1 7.7
60+ 163 10.9 1462 12.3 -1.4
vehicle passenger car 748 71.3 8289 79.8 ~8.5
type pickup truck 301 28.7 2103 20.2 8.5

 

 

 

 

 

 

 

 

178

 

 

Table B.3. Seat-belt versus D2 distributions for stratum 3—intersection

 

 

 

 

 

 

 

 

 

 

 

 

 

characteristics seat-belt D2 difference
N % N % (%)
gender male 552 56.0 4337 50.9 5.2
female 433 44.0 4188 49.1 -5.2
16-29 245 24.9 2669 31.3 -6.4
age 30-59 604 61.4 4709 ' 55.2 6.2
60+ 135 13.7 1147 13.5 0.2
vehicle passenger car 446 60.1 5864 78.2 -18.1
type pickup truck 296 39.9 1637 21.8 18.1

 

 

 

 

Table 3.4. Seat-belt versus D2 distributions for stratum 4——intersection

 

 

 

 

 

 

 

 

 

 

 

characteristics seat-belt D2 difference
N % N % (%)
gender male 2146 58.5 4616 51.6 6.9
female 1524 41.5 4326 48.4 -6.9
16-29 1029 28.0 2704 30.2 -2.2
age 30-59 2272 61.9 5065 56.6 5.2
60+ 368 10.1 1173 13.2 -3.1
vehicle passenger car 2180 81.3 6627 85.6 -4.3
type pickup truck 502 18.7 1111 14.4 4.3

 

 

 

 

 

 

 

179

 

 

COMPARISON BETWEEN D2 AND SEAT-BELT DATA AT COUNTY LEVEL

APPENDIX C

Table C. 1. Seat-belt versus D2 distributions for county—male drivers

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

male driver ,
county seat-belt D2 drffe);ence
N % N % ( °)
Allegan 141 73.4 406 56.2 17.3
Bay 136 69.7 583 52.9 16.8
Berrien 157 51 606 50.9 0.1
Calhoun 28 45.9 571 49.7 -3.8
Eaton 89 66.9 458 48.2 18.7
Genesee 123 51.9 2091 49.9 2.0
Grand Traverse 47 57.3 591 52.4 4.9
Ingham 51 40.2 1937 50.8 -10.6
Jackson 149 58.2 715 52.9 5.3
Kalamazoo 634 57.4 1414 50.8 6.6
Kent 288 53.4 3503 53.3 0.1
Lapeer 117 58.8 355 56.0 2.8
Lenawee 47 68.1 401 53 .6 14.5
Livingston 150 70.8 670 52.6 18.3
Macomb 299 57 4233 53.7 3.3
Monroe 85 65.4 466 49.5 15.9
Muskegon 186 62.2 800 51.5 10.7
Oakland 616 58.3 8040 52.1 6.2
Ottawa 29 76.3 1224 54.3 22.0
Saginaw 17 63 l 169 52.1 10.9
Shiawassee 8 50 247 54.9 -4.9
St. Clair 3 30 669 52.5 -22.5
St. Joseph 60 72.3 165 50.5 21.8
Van Buren 160 58.6 241 53.4 5.2
Washtenaw 669 55.8 1793 52.2 3.7
Wayne 2686 59.8 9177 52.7 7.1

 

180

 

 

Table C.2. Seat-belt versus D2 distributions for county—age

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

16-29 30-59 60+

county seat- diff. seat- diff. seat- diff.
belt D2 (%) belt D2 (%) belt D2 (%)
Allegan 17.7 30.2 -12.5 70.8 56.7 14.1 11.5 13.1 -1.6
Bay 27.7 29.4 -1 .7 62.6 55.3 7.3 9.7 15.3 -5.6
Berrien 13.6 27.5 -l3.9 69.2 56.7 12.5 17.2 15.8 1.4

Calhoun 29.5 33.9 -4.4 57.4 52.9 4.5 13.1 13.1 0

Eaton 16.5 29.7 -13.2 69.9 59.8 10.1 13.5 10.5 3
Genesee 27 30.6 -3.6 61.2 57.8 3.4 l 1.8 11.6 0.2
Grand Traverse 19.5 29.7 -10.2 64.6 55.6 9 15.9 14.6 1.3
Ingham 33.1 36.4 -3.3 48.8 54.2 -5.4 18.1 9.4 8.7
Jackson 25 29.5 -4.5 57 57.4 -0.4 18 13.1 4.9
Kalamazoo 34.9 37.7 -2.8 57.1 51.5 5.6 8.0 10.8 -2.8
Kent 28 34.5 -6.5 64.4 56.2 8.2 7.6 9.3 -l .7
Lapeer 35.2 34.4 0.8 50.3 54.4 -4.1 14.1 1 1.2 2.9
Lenawee 24.6 31.8 -7.2 49.3 52.8 -3.5 26.1 15.4 10.7
Livingston 26.4 30.5 -4.1 64.2 58.4 5.8 9.4 11.1 -1.7
Macomb 31.8 29.8 2 59.8 57.9 1.9 8.4 12.3 -3.9
Monroe 27.7 33.6 -5.9 58.5 56.0 2.5 13.1 10.4 2.7
Muskegon 30.1 30.1 0 61.5 55.9 5.6 8.4 14 -5.6
Oakland 26.7 28.9 -2.2 64.8 61.2 3.6 8.5 9.9 -1.4
Ottawa 31.6 35.7 -4.1 52.6 52.9 -0.3 15.8 11.4 4.4

Saginaw 29.6 31.8 -2.2 55.6 54.4 1.2 14.8 13.8 1
Shiawassee 37.5 32.4 5.1 43.8 54.7 -10.9 18.8 12.9 5.9
St. Clair 30.0 31.4 -1.4 50.0 54.9 -4.9 20.0 13.7 6.3
St. Joseph 18.1 31.5 -13.4 77.1 53.8 23.3 4.8 14.7 -9.9
Van Buren 20.9 26.8 -5.9 69.2 57.0 12.2 9.5 16.2 -6.7
Washtenaw 30.3 33.0 -2.7 62.4 58.9 3.5 7.3 8.1 -0.8
Wayne 28 28.9 -0.9 62.6 58.6 4.0 9.4 12.5 -3.1

 

181

 

Table C.3. Seat-belt versus D2 distributions for county—passenger car

 

passen er car

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

county seat-belt D2 diffgence
N % N % ( °)
Allegan 86 72.3 450 75.6 -3.3
Bay 87 78.4 700 78.7 -0.3
Berrien 155 82.0 893 85.9 -3.9
Calhoun 40 88.9 789 83.1 5.8
Eaton 61 82.4 632 79.0 3.4
Genesee l 12 82.4 2814 79.6 2.8
Grand Traverse 39 70.9 758 78.8 -7 .9
Ingham 73 79.3 2749 85.6 -6.3
Jackson 133 80.6 866 77.7 2.9
Kalamazoo 615 83.6 2035 84.4 -0.8
Kent 313 80.7 4828 85.5 -4.8
Lapeer 82 82.0 370 69.0 13.0
Lenawee 29 87.9 470 76.7 1 1.2
Livingston 85 66.9 786 75.6 -8.7
Macomb 271 77.7 5319 81.6 -3.9
Monroe 49 76.6 604 75.7 0.9
Muskegon 164 88.2 1051 81.1 7.1
Oakland 541 72.1 11152 86.0 -13.9
Ottawa 17 85.0 1580 82.5 2.5
Saginaw 9 100.0 1617 83.4 16.6
Shiawassee 7 87.5 281 74.9 12.6
St. Clair 5 83.3 848 78.5 4.8
St. Joseph 34 72.3 199 74.3 -2.0
Van Buren 135 76.7 288 77.2 -0.5
Washtenaw 626 80.4 2422 85.3 -4.9
Wayne 2626 81.5 12620 86.7 -5.2

 

182

 

 

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