Accident Analysis and Prevention 42 (2010) 1805–1813
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Accident Analysis and Prevention
j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / a a p
Analyzing fault in pedestrian–motor vehicle crashes in North Carolina
Gudmundur F. Ulfarsson a,∗, Sungyop Kim b,1, Kathleen M. Booth c,2
a University of Iceland, Civil and Environmental Engineering, Hjardarhagi 2-6, IS-107 Reykjavik, Iceland
b University of Missouri–Kansas City, Department of Architecture, Urban Planning and Design, 5100 Rockhill Road, Kansas City, MO 64110-2499, USA
c Clark Construction, 110 Tampico, Suite 100, Walnut Creek, CA 94598, USA
a r t i c l e i n f o
a b s t r a c t
Article history:
Crashes between pedestrians and motor vehicles are an important traffic safety concern. This paper
Received 9 December 2009
explores the assignment of fault in such crashes, where observed factors are associated with pedestrian
Received in revised form 16 April 2010
at fault, driver at fault, or both at fault. The analysis is based on police reported crash data for 1997 through
Accepted 3 May 2010
2000 in North Carolina, U.S.A.
The results show that pedestrians are found at fault in 59% of the crashes, drivers in 32%, and both are
Keywords:
found at fault in 9%. The results indicate drivers need to take greater notice of pedestrians when drivers
Fault
are turning, merging, and backing up as these are some of the prime factors associated with the driver
Crash
being found at fault in a crash.
Pedestrian
Driver
Pedestrians must apply greater caution when crossing streets, waiting to cross, and when walking
Motor vehicle
along roads, as these are correlated with pedestrians being found at fault. The results suggest a need
for campaigns focused on positively affecting pedestrian street-crossing behavior in combination with
added jaywalking enforcement. The results also indicate that campaigns to increase the use of pedestrian
visibility improvements at night can have a significant positive impact on traffic safety. Intoxication is
a concern and the results show that it is not only driver intoxication that is affecting safety, but also
pedestrian intoxication.
The findings show in combination with other research in the field, that results from traffic safety studies
are not necessarily transferable between distant geographic locations, and that location-specific safety
research needs to take place. It is also important to further study the specific effects of the design of the
pedestrian environment on safety, e.g. crosswalk spacing, signal timings, etc., which together may affect
pedestrian safety and pedestrian behavior.
© 2010 Elsevier Ltd. All rights reserved.
1. Introduction
Fault is assigned to the party (pedestrian, driver, both, or in some
cases neither) who acted negligently or is in other ways found to
Walking, for exercise or as an alternative mode of transporta-
have caused the crash. Some studies indicate that the pedestrian,
tion, is encouraged in today’s society. Walking provides health
not the driver, is more commonly found at fault (Lee and Abdel-Aty,
benefits and decreases the use of motor vehicles. However, pedes-
2005; Preusser et al., 2002) but in a recent study drivers were more
trians share the world with motor vehicles and the resulting
likely to be found at fault (Kim et al., 2008a,b).
opportunities for conflict lead to a crash risk. The National Highway
Fault has been explored in non-pedestrian–motor vehicle
Traffic Safety Administration (NHTSA) reported a total of 68,000
crashes. For example, a young or an elderly driver is more likely to
pedestrian injuries and 4,641 pedestrian fatalities in the U.S.A. in
be found at fault than a middle-aged driver (McGwin and Brown,
2004 (NHTSA, 2005). While these numbers account for only 2% of
1999). Young males are more likely to be at fault than young
people injured in traffic crashes in the U.S.A., they represent 11% of
females, whereas the opposite holds for elderly females compared
traffic crash fatalities (NHTSA, 2005).
to elderly males (McGwin and Brown, 1999). However, relatively
few studies have focused on fault and the factors correlated with
the assignment of fault in pedestrian crashes, aside from a study in
Hawaii (Kim et al., 2008b).
Research has explored a variety of aspects relating to pedes-
∗ Corresponding author. Tel.: +354 525 4907; fax: +354 525 4632.
trian safety, including pedestrian injury severity (Kim et al., 2010,
E-mail addresses: gfu@hi.is (G.F. Ulfarsson), kims@umkc.edu (S. Kim),
2008a; Kim, 2007), effects of gender (Kim et al., 2010; Clifton et
katie.booth@clarkconstruction.com (K.M. Booth).
1
al., 2004), vehicle speed (Gårder, 2004), U.S. interstate crashes
Tel.: +1 816 235 1725; fax: +1 816 235 5226.
2 Tel.: +1 925 279 4000; fax +1 925 279 4030.
(Johnson, 1997), pedestrian age (Kim et al., 2010, 2008a; Oxley
0001-4575/$ – see front matter © 2010 Elsevier Ltd. All rights reserved.
doi:10.1016/j.aap.2010.05.001

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G.F. Ulfarsson et al. / Accident Analysis and Prevention 42 (2010) 1805–1813
et al., 1997, 2005; Zegeer et al., 1993), fault (Kim et al., 2008b),
sidering all outcomes simultaneously, e.g. odds-ratios consider the
intersections (Lee and Abdel-Aty, 2005), truck crashes (Lefler and
ratio between one outcome and one other outcome at a time.
Gabler, 2004), pedestrian behavior (McMahon et al., 1999), crash
The MNL model represents the probability of one outcome
types (Stutts et al., 1996), and crash frequency (Shankar et al., 2003)
occurring over another based upon each outcome’s propensity, Sni,
to name just a few of the areas that have been studied.
as shown in
Multiple studies have examined the pedestrian actions that
most commonly contribute to crash occurrence. Pedestrians fail-
Pni = P(maxSni ≤ Sni),
(1)
i /= i
ing to yield the right of way, disregarding traffic signals, running
into the street, stepping from between parked cars, walking while
where i, i ∈ I, and I represents the set of possible outcomes. Also,
intoxicated, or walking with traffic rather than against it are noted
n ∈ N, where N stands for all observed crashes. The propensity itself
(Preusser et al., 2002; Oxley et al., 1997; Stutts et al., 1996; Baltes,
can be represented with the linear-in-parameters form:
1998). Such behavior can be correlated with the assignment of fault.
Pedestrians are naturally not the only ones who cause crashes.
Sni = ixn + εni,
(2)
Failure to yield, excessive speed, improper backing, moving vio-
where
i is a vector of estimable coefficients specific to outcome
lations, distraction, reckless driving, and intoxication have been
i, and xn is a vector of observed variables specific to crash n. The
identified as some of the most frequent contributing factors involv-
random component, εni, is assumed to be identically and inde-
ing drivers (Stutts et al., 1996). A study of fatal hit-and-run
pendently distributed type I extreme value. This leads to the MNL
pedestrian crashes showed that drivers are less likely to leave the
model of the probability of fault outcome i conditional on crash n
scene when the pedestrian is a child or an elderly person (Solnick
having occurred (McFadden, 1974, 1981):
and Hemenway, 1995). When the pedestrian is female or a child,
it is more likely that the driver will be identified. Drivers often run
e ixn
Pni =
.
(3)
from crashes where they would be considered to be at fault (Solnick
∀
e i xn
i ∈ I
and Hemenway, 1995).
The binary assignment of fault to either driver or pedestrian in
The coefficients,
i, are estimated with the method of maximum
Hawaii has been explored (Kim et al., 2008b). Fault and the factors
likelihood (see, e.g. Greene, 2007).
affecting it have also been studied for bicycle–motor vehicle crashes
It should be reiterated that the MNL model has a strict assump-
(Kim and Li, 1996). The present study explores how observable
tion that the unobserved random component, εni, is identically and
factors associated with pedestrian–motor vehicle crashes corre-
independently distributed. This leads to the independence of irrel-
late with which party is found at fault in a multinomial fashion,
evant alternatives (IIA) property of the MNL. IIA means that adding
i.e. driver at fault, pedestrian at fault, or both at fault. The study
or deleting alternative outcomes should not affect the odds among
omits hit-and-run crashes, which are about 12% of the complete
the remaining outcomes. If this property is violated the MNL model
dataset. In many such cases, the driver and vehicle information is
results will become biased (McFadden, 1981). A statistical test of
not known and in the majority of those cases fault has been assigned
the violation of IIA is performed using the Small–Hsiao test (Small
to the driver. This may lead to an underrepresentation of intox-
and Hsiao, 1985). The test statistic is 2 distributed and if the statis-
icated drivers, since it can be speculated that intoxicated drivers
tic is larger than a 2 table value at a particular level of significance it
may be more likely to leave the scene.
is evidence to reject the null hypothesis of the IIA property holding.
The results of this study provide new information on behavior
In this study, the 0.05 level of significance is chosen.
and factors associated with being found at fault. This information
To enable focus on the most significant coefficients, coefficients
can be used to increase awareness of pedestrian and driver behavior
that are not found significantly different from zero at the 0.05 level
that contributes to crash occurrence.
of significance using a t-test (see, e.g. Greene, 2007) are removed.
To avoid artificial accuracy, the likelihood ratio statistic (see, e.g.
Greene, 2007) is used to test whether two or more coefficients
2. Methodology
on related variables (or on the same variable in different outcome
equations) are significantly different from each other at the 0.05
Numerous models exist for exploring data, predicting behav-
level of significance and if not they are constrained to be equal.
ior, and forecasting outcomes. Kim et al. (2008b) studied fault
To judge the overall model fit it is possible to compare the
in pedestrian–motor vehicle crashes using logistic regressions for
model’s log-likelihood at convergence with the log-likelihood of
each crash type. In their study there were two outcomes, pedestrian
a naïve model, e.g. a model with all coefficients set to zero (equiva-
at fault or driver at fault. For binary outcomes the logistic regres-
lent to assigning equal probability to all outcomes), or a model with
sion or odds-ratio analysis are natural methods, but other methods
only alternative-specific constants (equivalent to assigning proba-
could be used, such as discriminate analysis and analysis of variance
bility to outcomes equal to the observed share of the outcomes in
(see, e.g. the textbook by Agresti, 2002).
the dataset). The latter test is stronger. This is performed by cal-
In the present study, there are three discrete outcomes, pedes-
culating the statistic (see, e.g. the textbook by Washington et al.,
trian at fault, driver at fault, and both at fault. The fundamental
2003):
limitation of the binary methods is a lack of statistical efficiency
2
LL( )
when applied in a multinomial context, since these methods do
= 1 −
,
(4)
LL(c)
not use all the available data simultaneously as they consider
only two alternatives at once. A more statistically efficient method
where LL( ) represents the log-likelihood at model convergence,
when dealing with three or more outcomes is the multinomial
LL(c) represents the log-likelihood of a model with alternative-
logit (MNL) model (McFadden, 1974, 1981). The MNL model has
specific constants only. The
2 goes from 0 (for no improvement
been commonly used for modeling outcomes of events which
in log-likelihood) to 1 for a perfect fit. A value for 2 larger than 0.1
are partly random and partly systematic, such as crash injury
already indicates meaningful improvement.
severity outcomes (e.g. Ulfarsson and Mannering, 2004). The MNL
To facilitate the interpretation of results, the percentage change
approach is able to simultaneously estimate the effect of numer-
in probability of a fault category is calculated when each vari-
ous observed variables on the probability of multiple outcomes.
able is switched between 0 and 1, since all the variables are such
Whereas, the binary methods loose statistical efficiency by not con-
binary indicators. This has been termed the direct pseudo-elasticity

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G.F. Ulfarsson et al. / Accident Analysis and Prevention 42 (2010) 1805–1813
1807
(Shankar and Mannering, 1996) and was applied in the same way
A trend emerges when considering pedestrian injury: the
by Ulfarsson and Mannering (2004):
greater the pedestrian severity, the greater the share of crashes
P
when the pedestrian is found at fault.
EPni
ni[given xnk = 1] − Pni[given xnk = 0]
x
=
,
(5)
When considering driving speed, there are trends showing that
nk
Pni[given xnk = 0]
for the lowest speed category the driver share for at fault is greater
where xnk is the kth variable in xn. A value of 1 means a 100% change,
but for the higher speed categories the pedestrian share for at fault
i.e. a doubling of the probability when the variable is switched. This
is greater. These trends hold for the roadway types, with freeways
value is calculated and its average for all crashes in the model is
and major street types showing pedestrians more greatly repre-
used to interpret the model results. To give an example of a typi-
sented as the at fault party, but with the driver being found more
cal interpretation, since the pseudo-elasticities are percentages and
often at fault on smaller streets, and in parking areas.
indicate the change in probability, if the probability of both being
Time of day shows no strong trend but with some tendency for
found at fault is 10% in a particular crash, then a pseudo-elasticity
the pedestrian at fault share to grow later in the day. The light
of 50% means that probability is increased by 50%, thereby chang-
conditions are perhaps more telling, showing that pedestrian fault
ing to 15%. High pseudo-elasticities can therefore result only for
increases with increasing darkness.
probabilities that are small to begin with.
The negative behavioral factors related to the crash are linked
with the shares of fault as can be expected, e.g. in cases when the
3. Data description
driver was drunk, the driver is more often found at fault, and simi-
larly for drunken pedestrians. These negligent behaviors are likely
This study uses police reported pedestrian–motor vehicle crash
to have a statistical correlation with fault. The precipitating factors
data compiled from 1997 through 2000 in the state of North
are not mutually exclusive, and the number of observations indi-
Carolina, U.S.A. The data is subject to potential underreporting,
cates the number of crashes where this factor was noted. They do
although such problems are expected to be lesser when consider-
therefore not add up to the total number of observations.
ing pedestrian–motor vehicle crashes than for vehicle-only crashes,
due to either party’s interest in reporting the other party’s fault, and
4. Results
the increased likelihood of injury in crashes involving pedestrians.
Crashes where fault was not determined or neither party was found
The multinomial logit model results for the estimated effect
to be at fault have been excluded from this study (2,311 crashes,
of observed variables on the probability of fault assignment in
about 19% of the total dataset), to enable the research focus on the
pedestrian–motor vehicle crashes are shown in Table 2. Recall
assignment of fault. Also as previously noted, hit-and-run crashes
that this is a conditional model which depends on a crash having
have been omitted due to them being nearly exclusively driver fault
occurred. The average direct pseudo-elasticities for these factors
and due to lack of driver data in those cases.
are presented in Table 3.
Pedestrians are found at fault in approximately 59% of the
The Small–Hsiao test (Small and Hsiao, 1985) did not reject the
crashes, drivers in 32%, and fault is assigned to both in 9% (see first
null hypothesis of the IIA property holding valid in the resulting
row of Table 1 ). It is worth highlighting that there is a large dif-
MNL model at the 0.05 level of significance, in fact the p-values
ference in the assignment of fault between this study population
found by the test were 0.580 and 0.342, indicating strong lack of
and the one studied in Hawaii (Kim et al., 2008b). Drivers in Hawaii
statistical evidence to reject the IIA null hypothesis. The 2 statistic
are found at fault in 92% of the crashes, and pedestrians in 8% (Kim
is found to be 0.37. Here the 2 measures the improvement in model
et al., 2008b). Several reasons can explain this. The Hawaii study
log-likelihood over a model with only alternative-specific constants
data assigns fault as a binary, either driver or pedestrian, while
(no variables). This is an excellent improvement in overall model
in the present study fault can also lie with both parties. This can
goodness-of-fit.
only explain part of the difference. There may be a difference in
4.1. Pedestrian
pedestrian and driver behavior between North Carolina and Hawaii.
There may also be a difference in how fault is determined. This
Age, ethnicity, gender, and injury of the pedestrian were all
finding shows that results from traffic safety studies may not be
found to be important covariates. The correlations between fault
fully transferable between distant geographic locations, and that
and age show that children 12 years old and younger are on average
location-specific research needs to take place.
nearly twice as likely to be found solely at fault than are pedestri-
Table 1 shows descriptive statistics of the data, which are 7,088
ans older than 17. Also, 13–17 year olds are also more likely to be
observations of pedestrian–motor vehicle crashes. In Table 1, the
found solely at fault than pedestrians older than 17.
frequency counts are broken down by fault categories. In this sec-
When considering pedestrian ethnicity, African American
tion, the relative frequencies directly observed in the data will be
pedestrians are associated with a slightly greater average proba-
discussed. The statistical analysis will test all relationships for sta-
bility of being found solely or jointly at fault and correspondingly,
tistical significance and those will be discussed in Section 4.
drivers are less likely to be found solely at fault.
Clear tendencies for age are evident in Table 1. With young
Pedestrian gender is also correlated with the determination of
pedestrians overrepresented in the pedestrian fault category, and
fault, with male pedestrians being more likely to be found solely at
older drivers overrepresented in the driver fault category, where by
fault than female pedestrians.
overrepresentation it is meant that the percentage share is larger
The model shows a correlation between fatal pedestrian injury
than the average share across all observations.
and the pedestrian being found solely at fault. The lower injury
For ethnicities, the data primarily contain White and African
class, possible pedestrian injury, is associated with an increased
American individuals, other ethnicities are relatively rare. A small
probability of the driver being found solely at fault.
tendency appears, indicating relatively fewer African Americans
in the driver fault category than White individuals and, relatively
4.2. Driver
more African Americans in the pedestrian fault category than White
individuals.
The age of the driver is found to have an impact. The youngest
Male pedestrians are relatively more often found at fault than
drivers, 14–17 years old, are more likely to be found solely or jointly
female pedestrians. The pedestrian is relatively more often found
at fault, and the pedestrian is less likely to be found solely at fault.
at fault when the driver is female than male.
For older drivers, 75+ years old, there is a larger effect towards the

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G.F. Ulfarsson et al. / Accident Analysis and Prevention 42 (2010) 1805–1813
Table 1
Descriptive statistics.
Variables
Driver at fault
Pedestrian at fault
Both at fault
Assignment of fault
2,256 (31.8%)
4,168 (58.8%)
664 (9.4%)
Pedestrian
Age
≤12
163 (13.0%)
1,010 (80.6%)
80 (6.4%)
13–17
180 (25.7%)
466 (66.5%)
55 (7.9%)
18–24
294 (34.5%)
469 (55.0%)
90 (10.6%)
25–44
841 (34.8%)
1,349 (55.7%)
230 (9.5%)
45–64
558 (41.9%)
629 (47.3%)
144 (10.8%)
65–74
119 (40.6%)
135 (46.1%)
39 (13.3%)
75+
96 (42.5%)
105 (46.5%)
25 (11.1%)
Ethnicity
White
1,303 (37.2%)
1,886 (53.9%)
311 (8.9%)
African American
821 (26.5%)
1,957 (63.3%)
315 (10.2%)
Native American
9 (20.5%)
29 (65.9%)
6 (13.6%)
Hispanic
46 (23.0%)
140 (70.0%)
14 (7.0%)
Asian
17 (44.7%)
16 (42.1%)
5 (13.2%)
Other
60 (28.2%)
140 (65.7%)
13 (6.1%)
Gender
Male
1,234 (27.3%)
2,903 (64.2%)
382 (8.5%)
Female
1,022 (39.8%)
1,265 (49.2%)
282 (11.0%)
Injury severity
Fatal
80 (11.9%)
539 (80.3%)
52 (7.8%)
Incapacitating
303 (22.2%)
958 (70.1%)
105 (7.7%)
Not incapacitating
769 (29.3%)
1,614 (61.4%)
246 (9.4%)
Possible
1,063 (46.2%)
992 (43.1%)
248 (10.8%)
None
41 (34.5%)
65 (54.6%)
13 (10.9%)
Driver
Age
14–17
157 (39.8%)
191 (48.4%)
47 (11.9%)
18–24
475 (32.9%)
829 (57.4%)
140 (9.7%)
25–44
814 (28.7%)
1,761 (62.1%)
260 (9.2%)
45–64
507 (29.9%)
1,048 (61.8%)
140 (8.26%)
65–74
123 (32.4%)
210 (55.3%)
47 (12.4%)
75+
173 (53.4%)
123 (38.0%)
28 (8.6%)
Ethnicity
White
1,434 (32.7%)
2,547 (58.1%)
403 (9.2%)
African American
670 (28.6%)
1,446 (61.7%)
227 (9.7%)
Native American
14 (25.9%)
33 (61.1%)
7 (13.0%)
Hispanic
52 (40.6%)
61 (47.7%)
15 (11.7%)
Asian
15 (51.7%)
12 (41.4%)
2 (6.9%)
Other
70 (49.0%)
64 (44.8%)
9 (6.3%)
Gender
Male
1,337 (32.6%)
2,367 (57.7%)
398 (9.7%)
Female
919 (30.8%)
1,801 (60.3%)
266 (8.9%)
Driving speed
0–10 mph
1,283 (61.9%)
511 (24.6%)
280 (13.5%)
11–20 mph
293 (30.7%)
581 (60.8%)
82 (8.6%)
21–30 mph
211 (19.4%)
804 (73.8%)
75 (6.9%)
31–40 mph
212 (14.5%)
1,144 (78.3%)
105 (7.2%)
41–50 mph
144 (15.3%)
722 (76.9%)
73 (7.8%)
51–60 mph
83 (17.6%)
345 (73.3%)
43 (9.1%)
61+ mph
30 (30.9%)
61 (62.9%)
6 (6.2%)
Time and environment
Time of day
00:00–06:59
196 (30.8%)
370 (58.2%)
70 (11.0%)
07:00–09:59
330 (46.9%)
302 (43.0%)
71 (10.1%)
10:00–15:59
821 (41.1%)
988 (49.5%)
189 (9.5%)
16:00–18:59
505 (27.6%)
1,166 (63.8%)
157 (8.6%)
19:00–23:59
404 (21.0%)
1,342 (69.8%)
177 (9.2%)
Light conditions
Daylight
1,577 (38.4%)
2,160 (52.5%)
375 (9.1%)
Dawn/dusk
99 (30.2%)
195 (59.5%)
34 (10.4%)
Dark-lit
407 (28.7%)
882 (62.2%)
128 (9.0%)
Dark-unlit
173 (14.1%)
931 (75.6%)
127 (10.3%)

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G.F. Ulfarsson et al. / Accident Analysis and Prevention 42 (2010) 1805–1813
1809
Table 1 (Continued. )
Variables
Driver at fault
Pedestrian at fault
Both at fault
Roadway
Road class
Freeway
28 (18.0%)
119 (76.3%)
9 (5.8%)
US route
77 (15.2%)
400 (78.7)
31 (6.1%)
State route
303 (19.6%)
1,101 (71.1%)
145 (9.4%)
Local street
960 (26.6%)
2,333 (64.7%)
311 (8.6%)
Private/parking
888 (69.9%)
215 (16.9%)
168 (13.2%)
Road type
One way
221 (54.8%)
144 (35.7%)
38 (9.4%)
Two way, not divided
1,815 (32.5%)
3,219 (57.6%)
559 (10.0%)
Two way, divided
220 (20.2%)
805 (73.7%)
67 (6.1%)
Road Geo.
Curved
163 (34.2%)
273 (57.2%)
41 (8.6%)
Straight & level
1,680 (32.0%)
3,065 (58.4%)
500 (9.5%)
Straight & grade
413 (30.2%)
830 (60.8%)
123 (9.0%)
Traffic control
None
1,664 (29.0%)
3,534 (61.6%)
540 (9.4%)
Traffic signal
271 (36.7%)
411 (55.7%)
56 (7.6%)
Yield/stop sign
195 (43.9%)
188 (42.3%)
61 (13.7%)
Human control
72 (80.0%)
13 (14.4%)
5 (5.6%)
Other sign
54 (69.2%)
22 (28.2%)
2 (2.6%)
Crash
Intoxication
None
2,024 (35.2%)
3,199 (55.6%)
533 (9.3%)
Driver only
117 (62.6%)
41 (21.9%)
29 (15.5%)
Pedestrian only
86 (8.1%)
901 (84.4%)
81 (7.6%)
Both
29 (37.7%)
27 (35.1%)
21 (27.3%)
Speed a factor
Yes
53 (46.9%)
33 (29.2%)
27 (23.9%)
No
2,203 (31.6%)
4,135 (59.3%)
637 (9.1%)
Multiple pedestrians
Yes
134 (58.5%)
74 (32.3%)
21 (9.2%)
No
2,122 (30.9%)
4,094 (59.7%)
643 (9.4%)
Precipitating factors
Pedestrian dart/dash
12 (1.2%)
1,000 (96.8%)
21 (2.0%)
Pedestrian crossing street
476 (13.2%)
2,938 (81.5%)
193 (5.4%)
Pedestrian waiting to cross
123 (20.9%)
365 (62.0%)
101 (17.2%)
Pedestrian walking along road
162 (30.9%)
258 (49.1%)
105 (20.0%)
Driver turning/merging
271 (67.4%)
62 (15.4%)
69 (17.2%)
Driver backing up
469 (81.7%)
20 (3.5%)
85 (14.8%)
driver being found solely at fault, and with the pedestrian or both
fault, or both being found at fault is increased. During dawn/dusk
at fault being less likely. Elder drivers are according to the model,
lighting conditions the pedestrian is less likely to be found solely at
on average 47% more likely to be found solely at fault than drivers
fault. It has been previously noted that during darkness, the proba-
18–74 years old.
bility of greater pedestrian injury severity is significantly increased
Male drivers are slightly more likely to be found solely at fault.
(Kim et al., 2008a). Pedestrian behavior and visibility in darkness is
Driving speed 0–10 mph is linked with on average 51.5% increase in
an important continuing traffic safety concern.
the probability of the driver being found solely at fault, or jointly at
fault with the pedestrian. This fits the discussion of Table 1, which
showed this trend although the effects of the higher driving speeds
4.4. Roadway
did not appear statistically significant. At low speeds, the driver is
showing caution so one might have expected the opposite result.
On major roadways, where pedestrian traffic is limited or even
However, there is a reason for the low speed and it is that the crash
restricted (freeway, U.S. route, State route), the pedestrian is more
has occurred in what can be described as a pedestrian environment,
likely to be found solely at fault in a crash; especially on a freeway
such as a parking lot, driveway, etc. The effect of high speed remains
where the average pseudo-elasticity indicates a 61% increase in the
insignificant due to the stronger effect from roadway type which
average probability of the pedestrian being found solely at fault. On
will be discussed later in this section.
one way roads and undivided two way roads the pedestrian is less
likely to be found solely at fault. On curved road sections the driver
is more likely to be found solely at fault than on straight sections;
4.3. Time and environment
the probability is increased by 52.5% on average.
When considering traffic control, the driver is more likely to
The different times of days showed a small trend towards the
be found solely at fault when under traffic signal control and the
pedestrian being more likely to be found solely at fault after 4 PM in
probabilities of the pedestrian and both being at fault are reduced.
the day and until midnight. There is a stronger effect for darkness
However, under yield/stop sign control, there are large increases in
that is unlit by streetlights, where the driver is less likely to be found
the probabilities of the driver being found at fault and both being
solely at fault and the probability of the pedestrian being solely at
found at fault.

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G.F. Ulfarsson et al. / Accident Analysis and Prevention 42 (2010) 1805–1813
Table 2
Multinomial logit model results for fault in pedestrian crashes.
Variables
Driver at fault
Pedestrian at fault
Coefficient
Standard error
t-Statistic
Coefficient
Standard error
t-Statistic
Pedestrian
Age
≤12 years old
−0.704
0.152
−4.64
0.917
0.144
6.36
13–17 years old
0.720
0.119
6.03
African American
−0.318
0.072
−4.45
Male
0.334
0.075
4.48
Fatal injury
0.575
0.134
4.30
Possible injury
0.349
0.073
4.77
Driver
Age
14–17 years old
−0.286
0.147
−1.94
75+ years old
0.569
0.156
3.66
Male
0.167
0.071
2.36
Driving speed: 0–10 mph
−0.685
0.089
−7.70
Time and environment
Time: 16:00–23:59
0.377
0.072
5.25
Light
Dawn/dusk
−0.360
0.167
−2.15
Dark-unlit
−0.709
0.116
−6.10
Roadway
Freeway
1.130
0.237
4.78
US route, state route
0.505
0.090
5.61
One-way road
−0.468
0.179
−2.62
Two way, not divided
−0.380
0.108
−3.51
Curved road
0.623
0.138
4.53
Traffic signal
0.700
0.125
5.60
Yield/stop sign
−1.053
0.141
−7.45
Crash
Driver intoxicated
1.490
0.204
7.30
Pedestrian intoxicated
1.049
0.115
9.14
Both intoxicated
−0.691
0.317
−2.18
−1.231
0.347
−3.55
Speed a factor
−2.399
0.278
−8.62
Multiple pedestrians
1.208
0.177
6.82
Precipitating factors
Pedestrian dart/dash
−0.981
0.385
−2.55
0.794
0.251
3.17
Pedestrian crossing street
−1.250
0.145
−8.60
1.640
0.136
12.04
Pedestrian waiting to cross
−1.462
0.156
−9.34
−0.392
0.150
−2.61
Pedestrian walking along road
−1.230
0.154
−7.99
−0.912
0.157
−5.79
Driver turning/merging
0.489
0.187
2.61
−2.278
0.212
−10.75
Driver backing up
−2.111
0.243
−8.69
Alternative-specific constant
1.601
0.093
17.19
0.953
-0.152
6.27
Log-likelihood at constants
−6368.0
Log-likelihood at convergence
−4009.7
Number of observations
7,088
Goodness-of-fit: 2 = 0.37. “Both parties at fault” is the base case and its coefficients are restricted to zero. All coefficients are significant at the 0.05 level or better.
The data do not include information on the specifics or quality
average pseudo-elasticity is approximately 172%, indicating nearly
of the pedestrian environment. This is a limitation which would be
a tripling of the probability of the driver being found at fault. When
important to tackle in future research. For example, the presence,
the pedestrian alone is intoxicated there is a similar effect; the
width, and quality of sidewalks and pedestrian crossings, affect the
probability of the pedestrian being at fault increases. The average
safety and behavior of pedestrians. So do also signal timings and dis-
pseudo-elasticity is lower than for drivers, still a rather large 57%,
tance between crosswalks. A good pedestrian environment reduces
but that is to be expected since the average probability of fault is
chances of pedestrians resorting to unsafe behavior and keeps a safe
highest for pedestrians (see Table 3). When both driver and pedes-
separation between pedestrians and traffic.
trian are intoxicated there is a large increase in the probability of
both being found at fault, but also a notable increase in the proba-
4.5. Crash
bility of the driver being found solely at fault.
When speed is judged as a factor in the crash, there is a large
Intoxication of either driver or pedestrian has strong effects.
(301%) increase in the probability of the driver or both driver and
When the driver alone is intoxicated, naturally there is a large
pedestrian being found at fault, and a fairly large reduction in the
increase in the probability of the driver being found at fault; the
probability of the pedestrian alone being found at fault.

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G.F. Ulfarsson et al. / Accident Analysis and Prevention 42 (2010) 1805–1813
1811
Table 3
Average direct pseudo-elasticities of variables in the model.
Variables
Average direct pseudo-elasticities
Driver at fault
Pedestrian at fault
Both at fault
Pedestrian
Age
≤12 years old
−62.4%
90.1%
−24.0%
13–17 years old
−34.0%
35.7%
−34.0%
African American
−19.2%
11.1%
11.1%
Male
−17.1%
15.8%
−17.1%
Fatal injury
−28.4%
27.3%
−28.4%
Possible injury
27.4%
−10.2%
−10.2%
Driver
Age
14–17 years old
18.4%
−11.0%
18.4%
75+ years old
47.2%
−16.7%
−16.7%
Male
12.2%
−5.1%
−5.1%
Driving speed: 0–10 mph
51.5%
−23.6%
51.5%
Time and environment
Time: 16:00–23:59
−19.4%
17.5%
−19.4%
Light: dawn/dusk
23.6%
−13.8%
23.6%
Dark-unlit
−38.2%
25.5%
25.5%
Roadway
Freeway
−48.0%
61.0%
−48.0%
US route
−25.4%
23.7%
−25.4%
State route
−25.0%
24.3%
−25.0%
One way road
31.8%
−17.5%
31.8%
Two way, not divided
26.6%
−13.4%
26.6%
Curved road
52.5%
−18.2%
−18.2%
Traffic signal
61.1%
−20.0%
−20.0%
Yield/stop sign
87.2%
−34.7%
87.2%
Crash
Driver intoxicated
171.8%
−38.8%
−38.8%
Pedestrian intoxicated
−45.0%
57.1%
−45.0%
Both intoxicated
25.1%
−27.0%
149.7%
Speed a factor
301.4%
−63.6%
301.4%
Multiple pedestrians
125.6%
−32.6%
−32.6%
Precipitating factors
Pedestrian dart/dash
−67.7%
90.7%
−13.8%
Pedestrian crossing street
−78.6%
284.1%
−25.5%
Pedestrian waiting to cross
−55.2%
30.6%
93.2%
Pedestrian walking along road
−29.2%
−2.8%
142.0%
Driver turning/merging
436.7%
−66.3%
229.3%
Driver backing up
242.3%
−58.5%
242.3%
Average probability
31.8%
58.8%
9.4%
Italic indicates changes of 50% to less than 100%. Bold indicates changes of 100% or more.
In crashes involving multiple pedestrians, there is on average a
solely at fault, and a smaller decrease in the probability of both
roughly doubling of the probability of the driver being found solely
being found at fault.
at fault, and a decrease in the probability of both or the pedestrian
Crashes occurring with the pedestrian crossing a street are asso-
only being found at fault.
ciated with a large increase in the probability of the pedestrian
being found solely at fault, with an average pseudo-elasticity of
4.6. Precipitating factors
284%. This fits the pattern from Table 1, in the majority of crashes
when the pedestrian is crossing the street, the pedestrian is found
The precipitating factors are behaviors that contributed to the
solely at fault. We can speculate that this might indicate effects
cause of the crash. These are not mutually exclusive. They are there-
of jaywalking, e.g. crossing at an illegal point or against a Don’t
fore expected to be generally statistically correlated with fault
Walk signal, and that pedestrians may misjudge the safety of such
determination. Some precipitating factors are correlated to the
behavior.
point of endogeneity with the determination of fault and those have
Pedestrian waiting to cross is linked to an increase in the prob-
been omitted. For example, driver failed to yield, pedestrian failed
ability of the pedestrian being found solely at fault, or jointly with
to yield, are factors which are nearly perfectly correlated with fault
the driver. In those cases, greater caution appears expected of the
determination and are endogenous.
pedestrian. However, when the pedestrian is walking along the
When the pedestrian darted/dashed into the road it leads to a
road the probability of both driver and pedestrian being found
large increase in the probability of the pedestrian being found at
jointly at fault is increased, while the probability of either party
fault, a large decrease in the probability of the driver being found
alone being found at fault is reduced.

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1812
G.F. Ulfarsson et al. / Accident Analysis and Prevention 42 (2010) 1805–1813
Driver turning/merging or backing up are actions associated
pedestrian intoxication. It is clear that taking part in traffic while
with relatively large increases in the probability of the driver
intoxicated is a risk, whether the person is a driver or a pedestrian;
being found solely at fault and with a large increase in the
or a bicyclist for that matter (Kim et al., 2007).
probability of both driver and pedestrian being found at fault,
During darkness, in areas that are not lighted, the pedestrian is
whereas the probability of the pedestrian being found solely
more likely to be found solely at fault or jointly with the driver.
at fault is reduced. This clearly indicates the added caution
Pedestrian behavior in darkness is a continuing traffic safety issue.
expected of drivers while performing such actions, but still since
Pedestrian awareness of how difficult it is for drivers to see pedes-
the probability of shared fault is also increased, this shows that
trians after dark needs to be improved. This result, especially taken
pedestrians need to be more cautious of vehicles making such
with pedestrian injury severity results (Kim et al., 2008a), also indi-
moves.
cates that campaigns to increase the use of visibility improvements
can have a significant positive impact on traffic safety.
The great difference in the distribution of assignment of fault
5. Conclusions
between this study’s North Carolina population and Hawaii (Kim
et al., 2008b) shows that results from traffic safety studies are
The largest effects based on the average direct pseudo-elasticity
not necessarily transferable between distant geographic loca-
for each fault outcome indicate the factors that change the prob-
tions, and that location-specific safety research needs to take
ability of fault determination the most. First review a summary of
place. It is therefore recommended that a multi-state study
those effects. The largest effects associated with the driver being
would be performed to explore those geographic differences in
found solely at fault are: driver turning/merging (437%), speed is a
detail.
factor (301%), driver backing up (242%), driver intoxicated (172%),
and multiple pedestrians (126%).
Acknowledgments
The largest effects associated with the pedestrian being found
solely at fault are: pedestrian crossing street (284%), pedestrian
This research was supported in part by the U.S. National Science
dart/dash (91%), pedestrian less than or equal to 12 years old (90%),
Foundation and the U.S. Department of Defense [Grant Number
freeway (61%), and pedestrian intoxicated (57%).
EEC-0353718]. The authors gratefully acknowledge the assistance
The largest effects associated with both the driver and pedes-
of the Highway Safety Research Center at the University of North
trian being found jointly at fault are: speed is a factor (301%), driver
Carolina, which provided the data.
backing up (242%), driver turning/merging (229%), both driver and
pedestrian intoxicated (150%), and pedestrian walking along road
References
(142%).
The results indicate drivers need to take greater notice of pedes-
Agresti, A., 2002. Categorical Data Analysis. John Wiley & Sons, Inc., New Jersey, p.
trians when drivers are turning, merging, and backing up as these
691.
Baltes, M.R., 1998. Descriptive analysis of crashes involving pedestrians in Florida,
are some of the prime factors associated with the driver being found
1990–1994. Transportation Research Record 1636, 138–145.
at fault in a crash. In this particular dataset, speed was rarely noted
Clifton, K.J., Burnier, C., Fults, K.K., 2004. Women’s involvement in pedestrian–
as a factor in the crash, this occurs only in 113 crashes, and this
vehicle crashes. In: Conference Proceedings 35: Research on Women’s Issues
in Transportation, Vol. 2, Transportation Research Board, pp. 155–162.
explains in part the lack of results for speed and speeding. Another
Gårder, P.E., 2004. The impact of speed and other variables on pedestrian safety in
complication with interpreting the effect of vehicle speed is that
Maine. Accident Analysis and Prevention 36 (4), 533–542.
the higher the speed the greater the percentage of pedestrians
Greene, W.H., 2007. Econometric Analysis, 6th Ed. Prentice Hall, 1216 pp.
Johnson, C.D., 1997. Pedestrian fatalities on interstate highways. Transportation
being found at fault (Table 1). This may seem counterintuitive but
Research Record 1578, 23–29.
we speculated a link with roadway type and the speed limit. On
Kim, J.-K., 2007. Statistical methods in transportation: application of behavioral
major roadways with higher speed limits, pedestrian access is often
models for safety analysis of vulnerable groups. D.Sc. Dissertation, Washington
limited, lacking, or even illegal. In such areas, pedestrians face a
University in St. Louis, UMI Dissertation Publishing, p. 182.
Kim, J.-K., Kim, S., Ulfarsson, G.F., Porrello, L.A., 2007. Bicyclist injury severities
difficult, high-speed environment, the risk of a severe crash, and
in bicycle–motor vehicle accidents. Accident Analysis and Prevention 39 (2),
increased probability of being found at fault.
238–251.
The results indicate that pedestrians are more likely to be found
Kim, J.-K., Ulfarsson, G.F., Shankar, V.N., Kim, S., 2008a. Age and pedestrian injury
severity in motor–vehicle crashes: a heteroskedastic logit analysis. Accident
at fault when crossing a street. Although not directly indicated in
Analysis and Prevention 40 (5), 1695–1702.
the data, jaywalking is likely to be an explaining factor for this
Kim, K., Brunner, I.M., Yamashita, E., 2008b. Modeling fault among accident-involved
effect. Also, when the pedestrian is waiting to cross or walking
pedestrians and motorists in Hawaii. Accident Analysis and Prevention 40 (6),
2043–2049.
along the street, greater caution is expected of the pedestrian,
Kim, J.-K., Ulfarsson, G.F., Shankar, V.N., Mannering, F.L., 2010. A note on modeling
since pedestrians are more likely to be found at fault in those
pedestrian-injury severity in motor-vehicle crashes with the mixed logit model.
situations. This suggests a need for campaigns focused on pos-
Accident Analysis and Prevention 42, 1751–1758.
Kim, K., Li, L., 1996. Modeling fault among bicyclists and drivers involved in collisions
itively affecting pedestrian behavior, especially crossing streets
in Hawaii, 1986–1991. Transportation Research Record 1538, 75–80.
or walking along streets in combination with added jaywalking
Lee, C., Abdel-Aty, M., 2005. Comprehensive analysis of vehicle–pedestrian crashes
enforcement. Pedestrians need to be more proactively safe in traf-
at intersections in Florida. Accident Analysis and Prevention 37 (4), 775– 786.
Lefler, D.E., Gabler, H.C., 2004. The fatality and injury risk of light truck impacts
fic.
with pedestrians in the United States. Accident Analysis and Prevention 36 (2),
Roadway and pedestrian access design has an important impact.
295–304.
Although this dataset does not contain specific details about the
McFadden, D., 1974. Conditional logit analysis of qualitative choice behavior. In:
pedestrian environment, it can be readily stated that a good pedes-
Zarembka, P. (Ed.), Frontiers in Econometrics. Academic Press, New York, NY.
McFadden, D., 1981. Econometric models of probabilistic choice. In: Manski, C.,
trian environment reduces chances of pedestrians resorting to
McFadden, D. (Eds.), Structural Analysis of Discrete Data with Econometric
unsafe behavior. This goes for sidewalk and crosswalk design,
Applications. MIT Press, Cambridge, MA.
pedestrian signal timings, spacing between crosswalk or pedestrian
McGwin Jr., G., Brown, D.B., 1999. Characteristics of traffic crashes among young,
middle-aged, and older drivers. Accident Analysis and Prevention 31 (3),
access points. Good design helps keep a separation between pedes-
181–198.
trians and traffic, and further study into the details of the pedestrian
McMahon, P.J., Duncan, C., Stewart, J.R., Zegeer, C.V., Khattak, A.J., 1999. Analy-
environment is warranted.
sis of factors contributing to “walking along roadway” crashes. Transportation
Research Record 1674, 41–48.
Intoxication is a well known concern, and the results show that
National Highway Traffic Safety Administration, 2005. Traffic Safety Facts 2004. U.S.
it is not only driver intoxication that is affecting safety, but also
Department of Transportation.

---

G.F. Ulfarsson et al. / Accident Analysis and Prevention 42 (2010) 1805–1813
1813
Oxley, J., Fildes, B., Ihsen, E., Charlton, J., Day, R., 1997. Differences in traffic
Solnick, S.J., Hemenway, D., 1995. The hit-and-run in fatal pedestrian accidents:
judgements between young and old adult pedestrians. Accident Analysis and
victims, circumstances and drivers. Accident Analysis and Prevention 27 (5),
Prevention 29 (6), 839–847.
643–649.
Oxley, J.A., Ihsen, E., Fildes, B.N., Charlton, J.L., Day, R.H., 2005. Crossing roads safely:
Stutts, J.C., Hunter, W.W., Pein, W.E., 1996. Pedestrian–vehicle crash types: an
an experimental study of age differences in gap selection by pedestrians. Acci-
update. Transportation Research Record 1538, 68–74.
dent Analysis and Prevention 37 (5), 962–971.
Ulfarsson, G.F., Mannering, F.L., 2004. Differences in male and female injury sever-
Preusser, D.F., Wells, J.K., Williams, A.F., Weinstein, H.B., 2002. Pedestrian crashes
ities in sport-utility vehicle, minivan, pickup and passenger car accidents.
in Washington, DC and Baltimore. Accident Analysis and Prevention 34 (5),
Accident Analysis and Prevention 36 (2), 135–147.
703–710.
Washington, S.P., Karlaftis, M.G., Mannering, F.L., 2003. Statistical and Econometric
Shankar, V., Mannering, F., 1996. An exploratory multinomial logit analysis of single-
Methods for Transportation Data Analysis. Chapman & Hall/CRC, Boca Raton, FL,
vehicle motorcycle accident safety. Journal of Safety Research 27 (3), 183–194.
p. 425.
Shankar, V.N., Ulfarsson, G.F., Pendyala, R.M., Nebergall, M.B., 2003. Modeling crashes
Zegeer, C.V., Stutts, J.C., Huang, H., Zhou, M., Rodman, E., 1993. Analysis of
involving pedestrians and motorized traffic. Safety Science 41, 627–640.
elderly pedestrian accidents and recommended countermeasures. Transporta-
Small, K., Hsiao, C., 1985. Multinomial logit specification tests. International Eco-
tion Research Record 1405, 56–63.
nomic Review 26 (3), 619–627.

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