Journal of Transportation Technologies, 2012, 2, 213-219
doi:10.4236/jtts.2012.23023 Published Online July 2012 (
Likelihood Parameterization of Bicycle Crash Injury
Deo Chimba*, Daniel Emaasit, Boniphace Kutela
Department of Civil Engineering, Tennessee State University, Nashville, USA
Email: *
Received March 23, 2012; revised May 3, 2012; accepted May 25, 2012
This paper evaluates different factors and parameters contributing to likelihood of bicycle crash injury severity levels.
Multinomial Logit (MNL) model was used to analyze impact of different roadway features, traffic characteristics and
environmental conditions associated with bicycle crash injury severities. The multinomial model was used due to its
flexibility in quantifying the effect of the independent variables for each injury severity categories. Model results
showed that, severity of bicycle crashes increases with increase in vehicles per lane, number of lanes, bicyclist alcohol
or drug use, routes with 35 - 45 mph posted speed limits, riding along curved or sloped road sections, when bicyclists
approach or cross a signalized intersection, and at driveways. In addition, routes with a high percentage of trucks,
roadway sections with curb and gutter, cloudy or foggy weather and obstructed vision were found to have high pro-
bability of severe injury. Segments with wider lanes, wide median and wide shoulders were found to have low likeli-
hood of severe bicycle injury severities. Limited lig hting locatio ns was found to be associated with in capacitatin g injury
and fatal crashes, indicating that insufficient visibility can potentially lead to severe crashes. Other findings are also
presented in the paper.
Keywords: Bicycle Crash; Injury Severity; Multinomial Logit
1. Introduction
The av erage annu al number o f bicycle fatal crashes from
1998 to 2008 in United States was 721. In 2008, 716
pedalcyclists were killed and an additional 52,000 bicy-
clists were injured in traffic crashes. Pedalcyclist deaths
accounted for 2 percent of all traffic fatalities, and made
up 2 percent of all the people injured in traffic crashes in
2008 (NHTSA, 2008 [1]). The same report highlights
that pedalcyclist fatalities occurred more frequently in
urban areas (69%), at non-intersection locations (64%),
between 5 p.m. and 9 p.m. (28%), and during the months
of June (9%) and September (12%). This paper evaluates
factors influencing bicycle crash injury severities.
Bicycle crashes have been studied by several re-
searchers for the past decade. Cheryl et al. [2] developed
a bicycle route safety rating model based on injury seve-
rity. The model development was conducted using a lo-
gistic transformation of bicycle crash data from Jersey
City, New Jersey, for the period 1997 to 2000. The re-
sulting model met 90% confidence level by using various
operational and physical factors like traffic volume, lane
width, population density, highway classification, and
presence of vertical grades, one-way streets, and truck
routes to predict the severity of an injury that would re-
sult from a motor vehicle crash that occurred at a specific
location. In another study, Jeremy and Asad [3] exam-
ined the effect of roadway and environmental factors on
injury severity in bicycle-motor vehicle collisions. An
ordered probit model for injury severity was estimated
using the Highway Safety Information System (HSIS)
data set for two-lane roadways. The model parameters
and the marginal effects of significant variables were
used to examine the influ ence of roadw ay and crash ch a-
racteristics on injury severity of cyclists. In this study,
speed limit, straight and curved grades, fog and unlighted
darkness were found to increase injury severity, while
average annual daily traffic, an interaction of the shoulder-
width and speed-limit variables, and street lighting were
found to be associated with decreased injury severity.
Karl and Lei [4] found that bicyclists are more likely
to be attentive than motorists, and slightly less likely to
be associated with misjudgment or alcohol or drug use
than motorists. The same study found that bicyclists are
much more likely to disregard traffic controls or go the
wrong way on a street just before becoming involved in a
collision than motorists. Motorists are more likely to fail
to yield, to engage in improper overtaking, or to follow
too closely before becoming involved in a collision than
*Corresponding Aut ho r.
Copyright © 2012 SciRes. JTTs
bicyclists. Shankar and Mannering [5] found that riding
without a helmet, and under the influence of alcohol in-
creased the likelihood of a disabling injury or fatality.
The same study found that the use of alcohol, over-
speeding, and older motorcyclists were associated with
higher likelihoo d of severe injury.
Quddus et al. [6] used ordered probit model to study
how various factors, including specific characteristics of
the roadway and th e riders, can lead to different levels of
injury and damage severity. The rationale for using the
ordered probit model was due to its capability to model
categorical dependent variables. The authors dismissed
the use of unordered multinomial, nested logit, or probit
models because they do not account for the ordinal na-
ture of the injury categories and the association of inde-
pendence of irrelevant alternatives (IIA) in the multino-
mial logit (MNL) models. The ordered probit models are
known to have weakness in classification of injury seve-
rity. However they are useful when the coefficient for
each variable in the model is required to classify injury
severities category. On the other hand, unordered multi-
nomial model is appropriate for evaluating the effect of
the variables to each injury severity category. Shankar
and Mannering (1996) [5] used the multinomial logit
model to examine factors affecting injury severities.
Their findings revealed that the multinomial logit formu-
lation was a potential approach to determine significant
factors affecting severity. The main disadvantage of us-
ing the multinomial logit model was that the error term
follows a generalized extreme value (GEV) distribution,
which leads to the issue of IIA.
A review of these previous studies however indicated
plenty of methodolog ies in evaluating bicycle crashes. In
view of the methodologies used in previous studies and
their recommendations for further research, this paper
examines the use of the multinomial logit (MNL) model
in analyzing bicycle crash severity. Ordered models are
not used herewith due to their limited independent vari-
ables effect outcome probabilities, Washington et al. [7].
Based on the bicycle related statistics presented above,
it is therefore warranted to examine the factors contri-
buting to these types of crashes. Th is study complements
the desire of many all any tran sportation related agencies
and jurisdiction in ensuring the safe use of bicycle as the
mode of transportation. Understanding the factors con-
tributing to the levels of injury severity is an important
step towards making bicycle one of the safe and more
attractive modes. Furthermore, differentiating the con-
tributing factors may help establish safer bicycle mode of
2. Methods
The MNL have been used widely on injury severity stu-
dies. As an extension from the Logit model, MNL is used
for dependent variable with more than 2 categories or
indicators, Quddus et al. [5] and Mouskos, et al. [8]. The
MNL model is built based on the assumption that the
choice between any pair of alternatives of the response
variable is independent of the availability of other alter-
natives. It implies that the random part of utility function
is independent among the alternatives. The multivariate
response variable can be distinguished depending whe-
ther the variable has an ordered or unordered category.
When categories in the response variable are not ordered,
MNL regression becomes appropriate compared to other
type of regressio ns, Shankar and Mann ering [4]. Su ppose
there are J categories of the injury severity as the re-
sponse variable, then there will be J – 1 equations for
MNL as a binary logistic regression comparing a group
with the reference (base) category or comparison group.
Using the maximum likelihood, MNL simultaneously
estimates the J – 1 logit functions. The probabilities of
other members in other categories are compared to the
probability of membership in the reference category.
Suppose the utility functio n is denoted as, Washington et
al. [7]:
kik iki
where k
is the independent variable, i
is the coef-
ficient associated with each independent variable, and
is the error term. Suppose the response variable k,
is subjected to different categories of severity, 0, ···, i,
, if for
qj UUji
In this study, i = 0, 1, 2 and 3 where 0k represent
non-injury crash, 1k represent possible injury or non-
incapacitating crash, 2k
U represent incapacitating in-
jury and Uk3 representing fatal crash. From the four in-
jury categories, three equations are formed, one for each
category in relation to the reference or base category, in
this case is Uk0. The general logistic equation is given as,
Washington, et al. [6], Shankar and Mannering [4];
Pq j
The odds ratio
kj ki
PP will depend log-linearly on
, i.e.,
log kj nj i
 (3)
The interpretation of the effects of explanatory vari-
ables to the responses is based on comparing the coeffi-
cient of variable in the category modeled to the reference
(base) category. Possible or non-incapacitating injury,
incapacitating injury and fatal crash model results are
interpreted in relation to base category which is non-
Copyright © 2012 SciRes. JTTs
injury crash. The marginal effect of an independent vari-
able k
on the choice probability for alternativ e j can be
expressed as:
jk k
Pqjx P
Equation (4) depends not only on the parameter
but also on the mean of all other alternatives
Direct interpretation of the parameter estimates can be
done usi ng the log of odds ratio:
log ji
This is reduced to,
log ji
for compari-
sons with the reference category iif the coefficients
associated with the base category are set to zeros. A
positive coefficient to the variable will mean the relative
probability of injury severity J increases relative to the
probability of the same variable in the base categ ory. The
estimation can be performed by using the maximum like-
lihood (ML) method in which th e log likelihood function
is given as
log log
kj kj
 (7)
with kj = 1 if the crash record k falls into severity
category j and = 0 if otherwise.
3. Study Data
The study utilized crashes involving bicycles which oc-
curred on Florida State maintained highway s from 2004 t o
2008. A total of 10,708 bicycle related crashes were
screened, among them, 11% none injury, 28% possible
injury, 42% non-incapacitating injury, 16% incapacitating
injury, and 3% fatal crashes. The study combined the
severity into three main groups. The first group coded as
“0” (none-injury), representing bicycle crashes that re-
sulted in no injury. The second group is possible injury
and non-incapacitating injury combined together and
coded as “1” (moderate injury) representing bicycle
crashes that resulted in minor injuries. The third group is
incapacitating injury and fatal coded as “2” (severe in-
jury) representing all bicycle crashes resulted into body
disability or death occurring within 30 days after the
crash. The three categories were used in MNL model
where category 0 is pivoted as a base.
The analysis used both continuous and categorical
variables in the model. The summary of continuous va-
riables is included in Tab le 1. Categorical variables used
Table 1. Variables summary statistics.
Mean Std. Dev Min. Max.
Average Annual Daily Traffic
(AADT) 35,725 16,099 1000 161,000
Vehicle per Day per Lane 7206 2762 250 26,833
Number of Lanes 5 1 2 8
Lane Width 29 8 8 84
Shoulder Width 3 2 0 25
Medium Width 19 16 0 800
Percentage of Trucks 5 3 0 42
Age 35 21 15 100
Speed Limit 42 6 15 55
are listed in Table 2. Most of these categorical variables
were coded as binary (taking on values of 1 or 0).
Analysis showed that 25% of all crashes analyzed re-
sulted from the vehicle or bicycle making a right turn,
2% when changing lane, 9% when making left turn and
3% when slowing. For contributing causes failed to yield
right of way comprised of approximately 36% of all
crashes. With respect to land use, 24% of the bicycle
crashes occurred in residential areas while 76% occurred
in commercial or business areas. Signalized intersections
and intersection influenced crashes contributed to about
75% of the bicycle crashes. At intersection crashes are
those which are within 50 ft from the intersection or
ramp. The influenced areas are those within 250 ft from
an intersection or ramp. Alcohol and drug related bicycle
crashes comprised of about 10% of total crashes. For the
crashes that resulted from Driving under the Influence
(DUI) of alcohol, 15% resulted in fatality. General statis-
tics of some numerical variables analyzed are summa-
rized in Table 1.
4. Results
None-injury crash category (e.g. category 0) was kept as
a base in MNL model. The models developed compared
the coefficient magnitudes and signs of the independent
variables in relation to the base category. The MNL re-
sults are presented in Ta ble 3. The model result p arame-
ters are interpreted in relation to the base category as in-
dicated. It should be noted that some independent vari-
ables were significant in one injury category but insig-
nificant in other.
4.1. Curved Sections
The coefficient of the curved sections in the model is
positive in both categories. The magnitude of the coeffi-
cients increases steadily from category 1 to category 2,
indicating that crashes occurring in curved areas will
have strong probability of resulting into severe injury
Copyright © 2012 SciRes. JTTs
Copyright © 2012 SciRes. JTTs
Table 2. Coding of categorical variables.
Categorical variable Coding
Presence or absence of sloped roadway sections Coded as 1 and 0 respectively
Roadway section without or with shoulder Coded as 1 and 0 respectively
At intersection and influenced or not intersection Coded as 1 and 0 respectively
Driveways or non-driveway Coded as 1 and 0 respectively
Dusk, night, no light or dayli ght Coded as 1 and 0 respectively
Cloudy, rai n, fog or clear Coded as 1 and 0 re spectively
Curved roadway sections or straight Coded as 1 and 0 respectively
Special speed zone control or non-speed zone Coded as 1 and 0 respectively
Signal control or no control Coded as 1 and 0 respectively
Stop sign control or not Coded as 1 and 0 respectively
Vision obstructed or not Coded as 1 and 0 respectively
Urban areas or other areas Coded as 1 and 0 respectively
30 mph or less speed limi t or higher speed Coded as 1 and 0 respectively
35 - 45 mph spe e d Limit or lower sp e ed Coded as 1 and 0 respectivel y
Drug or alcohol use or none Coded as 1 and 0 respectively
Table 3. Injury severity modeling results.
Multinomial logistic regression Number of observations = 10,708
Likelihood ratio chi2 = 7363.23 Prob > chi2 = 0.0000
Log likelihood = –8082.3266 Pseudo R2 = 0.3130
Possible or non-incapacitating injury severity Coefficient Std. error Z-value
Vehicle per day per lane 9.0E–07 7.5E–08 12.03
Number of lanes 0.1530 0.061 2.49
Median width –0.0031 –0.002 1.82
Lane width –0.0287 –0.011 2.65
Shoulder width –0.0088 –0.005 1.74
Bicyclist age 0.0079 0.001 8.28
Percentage trucks 0.0089 0.006 1.42
Sloped roadway sections 0.0104 0.005 2.13
No shoulder 0.0468 0.004 10.83
At intersection of influ e n c ed 0.2249 0.064 3.49
Driveways 0.3101 0.071 4.37
Dusk, night, no lig ht 0.1010 0.048 2.1
Cloudy, rain, f og 0.1308 0.051 2.58
Curved roadway sections 0.2221 0.146 1.52
Special speed zone control 0.1607 0.071 2.26
Signal control 0.0685 0.031 2.22
Stop sign control 0.1083 0.057 1.9
Vision obstructed 0.1497 0.062 2.4
Urban areas 0 .2106 0.130 1.62
30 mph or less speed li mit –0.2057 0.103 –1.99
35 - 45 mph speed limit 0.1085 0.043 2.5
Drug or alcohol use 0.3130 0.077 4.05
Incapacitating injury or fatal
Vehicle per day per lane –2.3E–05 1.1E–05 –1.98
Number of lanes 0.4170 0.217 1.92
Median width –0.0020 0.001 –2.42
Lane width –0.0423 0.014 –3.11
Shoulder width –0.0842 0.033 –2.55
Bicyclist age 0.0248 0.003 8.56
Percentage trucks 0.0206 0.011 1.89
Sloped roadway sections 0.0499 0.022 2.22
No shoulder 0.3371 0.167 2.02
At intersection of influ e n c ed 1.1469 0.147 7.79
Driveways 1.9544 0.253 7.74
Dusk, night, no lig ht 0.8689 0.128 6.81
Cloudy, rain, f og 0.1854 0.080 2.31
Curved roadway sections 0.4855 0.196 2.48
Special speed zone control 0.4816 0.153 3.15
Signal control –0.0916 0.173 –0.53
Stop sign control 0.8683 0.248 3.5
Vision obstructed 0.1384 0.085 1.62
Urban areas 0 .8300 0.253 3.28
30 mph or less speed li mit –1.3688 0.319 –4.29
35 - 45 mph speed Limit 0.8890 0.160 5.55
Drug or alcohol use 1.7918 0.138 13.01
compared to light injury. The find ing coincides with pre-
vious study which found that higher crash rates can be
expected on curves than tangents, with rates ranging
from two to four times higher than tangents, Jeremy and
Asad [3].
4.2. Posted Speed Limit
Speed limit is a function of several roadway parameters,
sight distance and roadway co ndition. The study group ed
the speed limit into three, from 15 - 30 mph were coded
as “1” representing low speed, 35 - 45 mph coded as “2”
and 50 mph or above represen ting higher speed coded as
“0”. As it was found in curved sections, the coefficient of
high speed is positive in both models (Table 3). The
likelihood of severe injury is high at high speed com-
pared to low speed. The finding is consistent with the
previous researches which found speeding to be associ-
ated with severe injury, Jeremy and Asad [3].
4.3. Lighting
Lighting conditions is categorized in Florida crash form
into daylight, dusk, dawn, dark with street light and dark
without traffic light. These categories were grouped into
two, one coded “0” representing day light and the other
coded as “1” for limited lighting conditions, dusk, dawn
and dark which represent “limited lighting” resulted with
positive coefficient in both severe injury and fatal crash
models. Based on the results, severe injury or fatal bicy-
cle crashes will be expected at locations with limited
lighting conditions compared to locations with adequate
4.4. Traffic Volume per Lane and Percentage of
Percentage of trucks is the average proportions of trucks
to the total number of vehicles at that particular section.
The variable has positiv e coefficient in the model (Table
3). The safety problem between trucks and bicycles can
lie on the visibility of the truck drivers and smallness of
the bicycle itself. Traffic volume have strong positive
coefficient in less severe (possible or non-incapacitating)
but negative coefficient for incapacitating/fatal model
indicating crashes occurring in the congested areas will
have less severe injuries. The result related with AADT
might be different if crash frequency was the subject,
some previous studies has found increase in crash fre-
quency with increase in traffic volumes, Mouskos et al.
Copyright © 2012 SciRes. JTTs
4.5. Location
Crash location refers to location on the roadway where
the crash occurred. The location can be at the intersection,
driveways, ramps, railroad, bridges, parking lots, toll
booth and public bus stops. In modeling, the factors were
grouped into 3 categories with code “0” representing
non-intersection related crashes, “1” representing at in-
tersection or intersection influenced crashes, “2” for
driveways and “3” representing other remaining location
categories. Result shows bicycle crashes occurring at
driveways and intersections are likely to result in either
non-incapacitating, incapacitating injury, or fatal (Table
4.6. Age
Older bicyclists seem to be more vulnerable to fatal in-
jury than younger ones. The models show positive, sig-
nificant coefficient in the fatal injury category in both
models (Table 3). This finding is consistent with the
previous research which found increase in age to be as-
sociated with likelihood of severe injury crash (Shankar
and Mannering [5]).
4.7. Number of Lanes, Lane Width, Shoulder
Width and Median Width
As expected, number of lanes showed positive coeffi-
cients to injury severity, the finding which is consistent
with findings from previous studies that evaluated crashes
involving bicycle and all other vehicle types, Theodore et
al., Miao and Lump, Miao, Garber and Ehrhart [9-12]. In
multilane segments, as the number of vehicles per lane
increases, there become fewer gaps to allow lane chang-
ing, turning movements, or merging, which eventually
increases the likelihood of crashes. Median width is sig-
nificant with a n egative co efficient, indicating likeliho od
of bicycle crash injuries severity level decreases as me-
dian width increases. This is consistent with many pre-
vious studies, Milton and Mannering, Abdel-Aty and
Radwan and Lee and Mannering [13-15]. The results
show that wider lanes reduce the probability of severe
injury. Wider lanes can be used by a bicyclist as a room
for correcting errors in the situation of near crash occur-
rence. Wider shoulders have negative coefficient show-
ing its important role in reducing bicycle crash injury
severities. From a highway safety point of view, a
shoulder can be used by a bicyclist to stop in case of an
emergency or during an incident, and drivers can take
advantage of wider shoulders to avoid hitting roadside
objects. In addi tion, bicycli sts can veer to w ider shoulders
to avoid a crash.
5. Conclusion
The model results indicate that there are significant fac-
tors that influence bicycle injury severities on the high-
ways. Significance of these factors to the occurrence of
crashes varies depending on human judgment, contribut-
ing causes, environmental conditions, traffic characteris-
tics, geometrics and location on highways. The multino-
mial Logit (MNL) model was used for analysis as it al-
lows the use of one injury severity as a reference cate-
gory while analyzing others. The results showed that,
increase in number of lanes, alcohol and drug use, high
posted speed limit links, curved areas, turning move-
ments, intersection and driveways, and driving with no
adequate daylight have strong significance effects on
intensifying injury severity. In addition, the higher the
percentage of trucks and the older the bicyclist means the
more severe the injury. Regarding traffic volumes, the
study found that under congestion condition few severe
incidents occur though higher crash frequencies can be
expected. Limited lighting locations was found to be as-
sociated with incapacitating injury and fatal crashes, in-
dicating that insufficient visibility can potentially lead to
severe crashes.
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