Use of Heteroscedastic Ordered Logit Model to Study Severity of Occupant Injury: Distinguishing Effects of Vehicle Weight and Type

Abstract

A heteroscedastic ordered logit model was used to study the effects of various vehicle, environmental, roadway, and occupant characteristics on the severity of injuries sustained by vehicle occupants, conditional on the crash occurrence. As expected, the models found that heavier vehicles increased both a vehicle's crashworthiness and driver aggressiveness toward others. The models also found that if all passenger vehicles were to become 1,000 Ib heavier, crash injury outcomes would not change dramatically. However, if all passenger cars were to become light-duty trucks (i.e., minivans, pickups, and sport utility vehicles) of the same weight, incapacitating injuries and fatalities were predicted to rise by 26% and 64%, respectively. Beyond weight and vehicle type, many other factors were controlled for as well. For example, older occupants and female occupants were more likely to experience injury and death, particularly when navigating curved roadway sections with higher speed limits.

Full text

Xiaokun Wang and Kara Kockelman Page 1 of 21
Occupant Injury Severity using a Heteroscedastic Ordered Logit Model:
Distinguishing the Effects of Vehicle Weight and Type
By
Xiaokun Wang
Graduate Student Researcher
The University of Texas at Austin
6.9 E. Cockrell Jr. Hall, Austin, TX 78712-1076
wangxk@mail.utexas.edu
Kara M. Kockelman
Clare Boothe Luce Associate Professor of Civil Engineering
The University of Texas at Austin
6.9 E. Cockrell Jr. Hall, Austin, TX 78712-1076
kkockelm@mail.utexas.edu
Phone: 512-471-0210
FAX: 512-475-8744
(Corresponding Author)
Presented at the 2005 Annual Meeting of the Transportation Research Board
Forthcoming in Transportation Research Record
Word Count: 6990 + 4 figures & tables = 7990 word-equivalents
ABSTRACT
This paper uses a heteroscedastic ordered logit model to study the effects of various vehicle,
environmental, roadway and occupant characteristics on the severity of injuries sustained by
vehicle occupants, conditional on the crash occurrence. As expected, the models find that heavier
vehicles increase both a vehicle’s crashworthiness and its aggressiveness towards others. The
models also find that if all passenger vehicles were to become 1000 lbs heavier, crash injury
outcomes would not change dramatically. However, if all passenger cars were to become light
duty trucks (i.e., minivans, pickups and sport utility vehicles) of the same weight, incapacitating
injuries and the fatalities are predicted to rise by 26 and 64 percent, respectively. Beyond weight
and vehicle type, many other factors were controlled for all well. For example, older occupants
and female occupants are more likely to experience injury and death, particularly when
navigating curved roadway sections with higher speed limits.
KEY WORDS
Crash modeling, Injury severity, Heteroscedastic ordered logit, Vehicle weight, Light-duty trucks
INTRODUCTION
Since 1997, the number of injuries caused by motor vehicle crashes has declined each year in
the United States. However, during the same period, the number of fatalities has increased. In
2003, a total of 43,220 deaths were reported on United States highways, the highest since 1990
[1]. Some researchers [2] attribute this change in injury severity to the revocation of the national
speed limit in 1996. Others suggest that the rise in recent years of SUVs and pickups, which are

Xiaokun Wang and Kara Kockelman Page 2 of 21
heavier than passenger cars, may be the source of the increased fatalities, as cited by The New
York Times [3]. Of course, most automotive manufactures hold the view (at least publicly) that
heavier vehicles are safer [3]. And this opinion is supported by several studies [4,5,6].
In order to untangle the contributions of vehicle type and vehicle weight, this paper examines
crash consequences conditioned on crash occurrence (i.e., it examines crashworthiness and
aggressiveness, rather than crash frequency), while controlling for a variety of variables,
including speed limits, weather, roadway design and vehicle and occupant characteristics. Using
data from the National Automotive Sampling System’s Crashworthiness Data System (NASS
CDS), both a standard and a heteroscedastic ordered logit model are calibrated.
This paper begins with a review of related research. Then, the structure of the heteroscedastic
ordered logit model is described and an equation for calculating the marginal effects of variables
that appear in both the severity and variance equations is given. The data are then described,
along with regression results and a comparison of the standard and heterscedastic models.
PREVIOUS RESEARCH
Motivated by different purposes and relying on different data sets, researchers have applied a
variety of methods to analyze the influential factors in crash severity. Some [7,8] experimentally
tested vehicles and their restraint systems, which is a costly process and one that allows for
relatively few variations in control variables. Most studies rely on some type of statistical
analysis of police-reported crash data. Some of these approaches are rather unsophisticated,
correlating just a few variables at a time. For example, Huelke and Compton [9] simply
compared the number of unrestrained occupants with the number of belted occupants on each
injury level to illustrate the effect of seatbelt use. Shinohara et al. [10] used a Chi-square test to
compared injury severities between belted and unbelted occupants, compact cars and medium-
sized cars, and drivers and passengers.
More sophisticated approaches utilize multivariate analyses and discrete-response models for
level of injury severity. The logistic model is a very popular choice. For example, Krull et al. [11]
used a logistic model to study how driver condition, vehicle type, roadway geometrics, AADT,
speed limit and rollover involvement affect the probability of fatal and incapacitating injuries.
Bedard et al. [5] used it to analyze how driver, crash, and vehicle characteristics contribute to
driver fatalities. Toy and Hammitt [12] modeled the risk of serious injury and death as a function
of vehicle type, driver's age, gender, restraint use and the configuration of the crash in two-
vehicle crashes. As an extension to this approach, Dissanayake et al. [13] employed the
sequential binary logit (SBL) model to find how crash and injury severity are influenced in
passenger car-fixed roadside object crashes.
Though multinomial logit (MNL) and probit (MNP) models do not recognize order in injury
levels (such as fatal crashes being worse than PDO crashes) and do require far more coefficient
estimates when variables are not generic (i.e., when variables do not vary by outcome type, as is
the case with design, weather, vehicle and occupant characteristics), they do avoid certain
restrictions posed by standard ordered models. They allow variables to have opposing effects
regardless of injury order; for example, air bars may cause more injuries but fewer fatalities [14].
Thus, MNL and MNP models may still have a place in crash severity analysis. For example,
Ulfarsson and Mannering [15] used an MNL to study the effect of gender on injury severity
across different vehicle types. Yet the most frequently used model for such analyses is an
ordered logit (OL) or ordered probit (OP) model. Of these two models, the OL tends to converge
more quickly [16] while the OP has a simpler statistical form and is much more common in past

Xiaokun Wang and Kara Kockelman Page 3 of 21
studies. For example, Khattak [17,18] has used OP models to analyze the effect of adverse
weather conditions, vehicle and information technology, and driver age on injury severity.
Renski et al. [2] used it to study the effect of speed limits. Kockelman and Kweon [19]
controlled for a wide variety of factors in order to deduce the effect of vehicle type. Their later
work [20] combined crash exposure, frequency and severity models for a rather comprehensive
risk analysis of various driver and vehicle types. Abdel-Aty [21] calibrated different OP models
for injury severity, along roadway sections, at signalized intersections, and at toll plazas. Khattak
and Rocha [22] focused on SUVs.
Extensions to the OP and OL model specifications include the ordered mixed logit model
(OML), the heteroskedastic ordered probit (HOP) model and the heteroskedastic ordered logit
(HOL) model. Several crash-severity investigations have relied on these. The OML model allows
for random coefficients across observational units, while the HOP and HOL models allow the
error term’s variance to vary. Srinivasan’s [23] OML model accommodated variable, random,
and correlated injury severity thresholds. He used Chi-square tests to show that the OML model
was statistically superior to the OL model. O'Donnell and Connor’s [24] work is most closely
related to the models examined here. They applied HOP and HOL models to discern how injury
severity is affected by occupant age, seating position, use of a seat belt, blood alcohol level,
vehicle speed, type, and make and collision type. The variance in their error terms was
parameterized to be a function of occupant age, vehicle speed, vehicle year and time of accident.
They found that higher speeds and occupant age result in higher injury severity, along with head-
on crashes, travel in light-duty truck, vehicle age, being female, having a blood alcohol level
over 0.08 percent and not wearing a seatbelts. Among all these factors, they estimated seat
position to have the most significant effect, with the driver’s position being safest, a result that is
inconsistent with most other research [9,25]. Their models’ variance terms were minimized for
30-year-old occupants and crash times of 1:00 pm, and increased with travel speed.
Previous research involving vehicle type is extensive; in comparison, research distinguishing
vehicle weight from vehicle type is limited. Evans and Wasielewski [26] studied the effect of
vehicle weight on serious and fatal driver injury rates in head-on crashes. Though control
variables were limited (e.g., vehicle type was not included) and the model structure
unsophisticated, this early research was influential in later studies. Bedard et al. [5] aimed to use
vehicle weight (though not vehicle type) as a control variable but ended up relying on wheelbase
instead (since wheelbase is highly correlated with weight and gave them more precise results).
Farmer et al. [4] did control for vehicle type and weight as well as the collision partner’s type
and weight. However, their model estimated only the probability of a severe or fatal injury
outcome, using a binary logistic regression model. Toy and Hammitt [12] used the ratio of the
vehicle curb weights as an explanatory variable in their two-vehicle crash model. Thus, they
assumed that only the ratio of weights, rather than their absolute values, is what contributes to
injury severity.
This work controls for the most valuable variables used in O’Donnell and Connor [24], along
with vehicle weights, both for the primary vehicle and any collision partner. It also calibrates
distinct models for single- and two-vehicle crashes, since these are distinctive crash types. It
should be noted that multi-vehicle crashes are first divided into several two-vehicle crashes
where the collision partner is defined as the first vehicle to crash into the observed vehicle. The
following section describes the model specifications.

Xiaokun Wang and Kara Kockelman Page 4 of 21
MODEL STRUCTURE
After considering the strengths and limitations of the various models used in previous
research, this paper uses the HOL model to study a variety of factors that influence injury
severity. The general form of the HOL model can be explained via equations (1) through (8).
Let
y denote the occupant’s observed injury severity level, *y the latent (unobserved) injury
severity measure, and
(1,2,3)
j
j
µ
=
the thresholds for injury severity, such that the following
hold:
0y
= (no injury) if * 0y ≤
1y = (no visible injury, only pain reported) if
1
0*y
µ
<
≤
2y =
(non-incapacitating injury) if
12
*y
µ
µ
<
≤
3y
= (incapacitating injury) if
23
*y
µ
µ
<
≤
4y
= (death) if
3
*y
µ
>
The latent injury severity measure
*y
is obtained using a linear equation:
*'yx
β
ε
=+ (1)
where
x
is the set of factors explaining *y , with associated parameters
β
, and the error term
ε
indicates the effect of all unobserved factors on
*y . If one defines
10
,0
µ
µ
−
=−∞ = and
J
µ
=+∞, then the probability of injury severity
j
for the
th
i observation can be written as the
following [16]:
1
1
()( *)
ji j i
jj
ii
xx
Py j P y F F
µ
βµβ
µµ
σσ
−
−
−−
⎛⎞⎛ ⎞
== <≤ = −
⎜⎟⎜ ⎟
⎝⎠⎝ ⎠
(2)
where ( )F
 is the logistic distribution’s CDF and
2
i
σ
is the variance of the random contribution
of unobserved factors in the
th
i observation, parameterized so as ensure its positivity, by using an
exponential function. In other words,
() ( )
1
1 exp( )Fx x
−
=+ −
(3)
()
()
2
2
exp
ii
Z
σ
γ
= (4)
where
i
Z
is the set of variables explaining the error term variance of the
th
i observation, and
γ
is
the associated parameter set. It can be seen here that an OL model, which assumes
homoscedasticity, restricts
γ
to equal zero. For the model used in this work, the variance is
parameterized as a function of speed limit (similar to O'Donnell and Connor’s [24] use of travel
speed), vehicle type, and vehicle curb weight. The use of speed limit in the variance specification
is based on O'Donnell and Connor’s [24] use of travel speed (a variable that is missing in most
crash observations used here), and vehicle type and weight are used because a great many
unobserved vehicle features are connoted by these (including variables like stiffness and
structure). (The effects of occupant gender and age also were tested in the variance specification,
but then excluded because they were not statistically significant.) Coefficients can be estimated
using the method of maximum likelihood. For HOL, the likelihood function is [16]:

Xiaokun Wang and Kara Kockelman Page 5 of 21
1
11
ij
w
Jn
ji j i
ji
ii
xx
LF F
µβ µ β
σσ
−
==
⎛⎞
−−
⎛⎞⎛ ⎞
=−
⎜⎟
⎜⎟⎜ ⎟
⎜⎟
⎝⎠⎝ ⎠
⎝⎠
∏∏
(5)
Here
ij
w
is the weight or expansion factor for the
th
i observation (i.e., occupant)
experiencing injury severity level
j
. (Sample unit expansion factors are provided in the NASS
CDS data set, recognizing that certain crashes are relatively underreported.)
As Greene [27] indicates, in an ordered probit (or logit) model, the sign of any parameter
β
i
can only clearly determine the marginal effect of variable x
i
on the extreme probabilities (in this
case, the probability of no injury and the probability of a fatal injury). The marginal effects on all
other probabilities are ambiguous, since a shift in the distribution can cause the probability of
intermediate response types to fall or rise, depending on the positioning of the average response.
For an HOL model, this issue is complicated when the variable of interest affects not only the
latent injury severity but also the variance. In an HOL model, the marginal effect of such a
variable x
t
across the sample, for the “average observational case”, can be written as follows:
()
1 1
1
()
1
jj j j
t t
tt j j
t
xx x x
Py j
ff xf f
x
µβ µβ µβ µβ
β
γ
γµ µ
σ
σσ σ σσ
− −
−
⎛⎞⎛ ⎞
−− − −
⎛⎞⎛ ⎞ ⎛⎞⎛ ⎞
∂=
=− ⋅⋅−− − ⋅
⎜⎟⎜ ⎟
⎜⎟⎜ ⎟ ⎜⎟⎜ ⎟
⎜⎟⎜ ⎟
∂
⎝⎠⎝ ⎠ ⎝⎠⎝ ⎠
⎝⎠⎝ ⎠
(6)
where
t
x
is the variable of interest,
t
x
is its weighted average across observational units;
σ
is the
(weighted) mean variance across observations;
x
is the vector of (weighted) average values;
t
β
is the
th
t
variable’s coefficient for explaining *y ; and
t
γ
is that same variable’s coefficient for
explaining variance
2
σ
, and ( )
f
 is the probability density function for the logistic distribution:
()
()
2
exp( )
1 exp( )
x
fx
x
−
=
+−
(7)
As equation (6) suggests, the
th
t variable’s marginal effect is related not only to its own,
primary coefficient, but also to its average value and the value of it variance-specifying
coefficient. Therefore, even the marginal effect on the extreme probabilities cannot be inferred
from simply the signs of the estimated primary parameters. Equation (6) must be used when
determining the marginal effects of vehicle type, since these were used to specify the variance
relation. If the variable of interest,
t
x
, only explains the injury severity measure,
*y
, and not the
variance, then its marginal effect simplifies to equation (8). In this case, similar conclusions
about those variables’ marginal effects can be drawn as in the standard, homoscedastic OL
model.
()
t
Py j
x
∂=
=
∂
1jj
t
xx
ff
µβ µ β
β
σ
σσ
−
⎛⎞
−−
⎛⎞⎛ ⎞
−− ⋅
⎜⎟
⎜⎟⎜ ⎟
⎜⎟
⎝⎠⎝ ⎠
⎝⎠
(8)
The effects of binary variables on probabilities can best be obtained by comparing
probabilities where the variable equals 1 and where it equals 0 (i.e., the base variable is used)
with all other variables held at their average values (except in the case of other binary variables
that share the same category with the variable under evaluation; of course, these are held at 0).
For convenience, the effects of binary variables are also called marginal effects in this paper.
It can be seen from the above analysis that HOL models allow the distribution of unobserved
factors to differ, providing more flexibility and realism than an OL model. As an example,

Xiaokun Wang and Kara Kockelman Page 6 of 21
SUVs’ stiffness may help protect occupants, but their added roll-over potential can counter this
effect, resulting in more outcome uncertainty. Such vehicle types then would be expected to
exhibit higher variability in their latent injury severity measures, a feature permitted by HOL
specifications. Thanks to this feature, HOL models allow extreme probabilities to be similarly
affected (i.e., in the same direction) when variable values change.
DATA DESCRIPTION
The data set used in this paper comes from the National Automotive Sampling System’s
Crashworthiness Data System (NASS CDS) for the years 1998 through 2001. The NASS CDS
collects crash data at 24 sites (also called primary sample units, or PSUs) in 17 states in the U.S.
All crashes selected are police reported, involving property damage and/or personal injury and at
least one towed passenger car or light truck or van. Data are sampled in a stratified fashion, first
among PSUs, then among police jurisdictions, and lastly among reported crashes, and together
they represent just 0.05 percent of all police-reported crashes in the U.S, less than most other
national collected data set. Each observation in the sample data is given a population expansion
factor called a Ratio Inflation Factor (RIF), which is the inverse of the probability of selecting
that crash from crashes nationwide. This value is used as the observational weight in the
likelihood function’s (Eq. (5)) maximization.
It is important to note that CDS data are not totally unbiased. More severe crashes are more
likely to be reported and thus entered into the CDS. Weights are estimated in order to try and
account for these selection biases, but some statistical uncertainty remains. Moreover, different
PSUs have different criteria for reporting their crash data (such as a minimum crash cost or
severity). This causes some geographic heterogeneity in the data [19] . Nonetheless, among all
available data sets, the NASS CDS is the most appropriate one for this study because of its
detailed information and comparatively unbiased sample. Farmer et al. [4] and Toy and Hammitt
[12] also used the NASS CDS. Other, larger sample data sets either lack vehicle weight
information (such as the National Automotive Sampling System’s Crashworthiness Data
System’s General Estimates System (NASS GES) and Highway Safety Information System
(HSIS)), or focus on a particular crashes (such as FARS). These datasets may be preferable when
the effect of vehicle weight is not concerned. For example, White [28] and Kockelman and
Kweon [19] used NASS GES in their studies; Bedard et al. [5], Gayer [29] and Kahane [6] used
FARS.
Information on vehicles and occupants were merged in order to produce an occupant-based
dataset. There are 18,609 occupant observations for two-vehicle crashes and 7,628 for one-
vehicle crashes containing all required variables. These represent 53.6 percent and 77.8 percent
of the NASS CDS sample data for such crash occupants, respectively. The dependent variable,
injury severity, is missing in 6,036 occupant observations, accounting for a large percentage of
the invalid observations. Other variables missing in significant numbers include occupant age
and gender, seat belt usage, curb weight, seat type, and weight of collision partner.
Less severe injuries and passenger cars as collision partners are slightly underrepresented in
the data analyzed here. Bucket seat types are over-represented, in both models. Furthermore,
because the NASS CDS does not provide curb weights for the medium and heavy-duty trucks,
these are assumed to weigh 25,000 lbs here. Any overall bias in this assumption is expected to be
largely picked up by the indicator variable used for medium and heavy trucks in the model’s
specification.

Xiaokun Wang and Kara Kockelman Page 7 of 21
ANALYSIS OF RESULTS
It is necessary to compare the OL and HOL model results and select the preferred model,
before focusing on specific results for each of the explanatory variables used.
Comparison of the OL and HOL Model Results
Explanatory variables for injury severity include vehicle, weather, roadway and occupant
information. Variance is explained by vehicle type, vehicle curb weight and speed limit. Variable
statistics are presented in Table 1. As noted, the models are estimated using the method of
maximum likelihood, in LIMDEP. The results for both OL and HOL models are shown in Table
2. The existence of heteroscedasticity in one- and two-vehicle crashes are tested using
Likelihood Ratio (LR) tests, as follows [27]:
2(ln ln )
one vehicle restricted unrestricted
LR L L
−
=− −
2
5
2( 8530.5 ( 8505.4)) 50.3 20.52
χ
=− − − − = > = (9)
2(ln ln )
two vehicle restricted unrestricted
LR L L
−
=− −
2
10
2( 20265.8 ( 20099.3)) 333.0 29.59
χ
=− − − − = > = (10)
So for both type of crashes, the null hypotheses
γ
=0 are rejected at a 0.001 significance level,
suggesting that heteroscedasticity exists in both crash types. Thus, the more flexible HOL
specification is statistically preferred to the OL model.
As shown in Table 2, all explanatory variables (in both one-vehicle and two-vehicle crashes)
result in similar OL and HOL estimates. But the HOL models also produce several statistically
significant coefficients characterizing variance of the model’s error term. These suggest that
variance varies with vehicle weight, speed limit and vehicle type. Those traveling in pickups on
roads with higher speed limit experience greater variation in their injuries than others. This
added uncertainty in injury outcomes may be due to greater diversity in truck designs and more
potential for extreme crashes at higher speeds.
Table 3 further shows the difference of marginal effects in OL and HOL, using two-vehicle
collision partner vehicle type as an example. (The primary vehicle type is held at its mean value,
which means the figures presented in the table indicate an average effect of the given collision
partner vehicle type.) For the OL model, as expected, the marginal effect on the probability of no
injury has the same sign as the coefficient on the right hand side of Table 2, while the probability
of fatality has the opposite sign. In this model, all injury severity levels other than no injury
experience the same direction of change as the probability of fatality. The OL model results
suggest that SUVs, minivans and pickups are more aggressive than cars of the same weight,
everything else constant. The HOL model depicts things a little differently. Pickups are still
shown to be more aggressive than cars. SUVs are also more agressive, though the fatality
probability decreases slightly. Minivans, which are built on car frames, are no more aggressive
than cars. (While they increase the probability of overall injury for occupants in their collision
partners, the probabilities of incapacitating and fatal injuries are both lower.) This suggests that
pickups and SUVs, which have raised bodies and often have a rigid frame, are more aggressively
designed than cars and minivans, as pointed out by Newstead et al. [30] and Kahne [6], Gabler
and Hollowell [31]. Thus, recognition of heteroscedasticity due to collision partner’s vehicle type
has illuminated an interesting distinction that would not be visible in the less flexible OL model.
Effects of Vehicle Weight and Type
In addition to the effects of the collision partner vehicle type described above (since OL and
HOL results differ on this point), the effects of (primary) vehicle type and weight and of

Xiaokun Wang and Kara Kockelman Page 8 of 21
collision partner weight (in the case of two-vehicle crashes) are of great interest. Figure 1
provides charts showing the changes of injury severity probability (given that a crash has
occurred) with respect to these variables. In one-vehicle crashes, occupants in heavier vehicles
are estimated to sustain more severe injuries, but the effect of weight in one-vehicle crashes is
less dramatic than that in two-vehicle crashes. In two-vehicle crashes, increasing vehicle weight
is found to reduce all injury probabilities for occupants (also see [4]) – while raising those for
occupants of collision partners. Considering both the crashworthiness and aggressiveness effects
of vehicle weight in both crash types (where 30 percent of crashes involve just one-vehicle) and
holding all other variables at their average values, a weight increase of 1000 lbs of all U.S.
vehicles (Different from the study by Kahane [6], this vehicle weight increase occurs on all types
of vehicles − and on both primary and counterpart vehicles based on the fleet and crash-type
proportions witnessed in the NASS CDS data set.) can be estimated. The models predict that the
overall probability of injury or death will
fall by 3 percent. In it, Non-incapacitating and
incapacitating injury probabilities are predicted to fall by 1 and 5 percent, respectively, while the
probability of death is predicted to rise by 19 percent. Thus, the overall effect of increasing light-
duty vehicle weights (by 33%) is almost negligible.
In one-vehicle crashes, minivans and pickups are estimated here to be less crashworthy,
everything else constant (including weight). In contrast, SUVs are found to decrease the
probability of occupant injury, while increasing the probability of fatality. Similarly, Kockelman
and Kweon [19] found that pickups and SUVs are less safe than passenger cars in single-vehicle
crashes. White [28] found that occupants involved in single vehicle crashes are more likely to be
killed or seriously injured if they are driving a light truck rather than a car. Ulfarsson and
Mannering [15] also found that in single-vehicle accidents, pickup, SUV and minivan drivers
tend to sustain more severe injuries than passenger car drivers. In two-vehicle crashes, all light-
duty trucks (i.e., minivans, pickups and SUVs) are predicted to result in more severe injuries for
their occupants, i.e., less crashworthy – after controlling for vehicle weight. At first glance this
conclusion may appear to be at odds with work by Krull et al. [11], Kockelman and Kweon [19]
and Abdel-Aty [21]; however, such research has not controlled for both vehicle weight and type
simultaneously (nor for variables like seat type).
If all passenger cars were to become light duty trucks (based on each vehicle type’s own,
average weight and the crash-type proportions witnessed in the NASS CDS data set), the overall
probability of sustaining some kind of injury (even those that are not visible) following a crash is
predicted to increase by 3 percent. Among these, the incapacitating injury is expected to rise by
25 percent and fatalities by a startling 79 percent. The results suggest that
lighter vehicles reduce,
rather than increase, the probability of death. Of course, it is difficult to believe that lighter
vehicles are indeed safer if the only variable that changes is weight. In reality, vehicle weight is
probably correlated with design variables not controlled for here (such as bumper design and
vehicle interior padding). Thus, the results may simply be implying that vehicle design is more
important than weight. This implication is consistent with manufacturer Honda’s stated position,
though Honda is a notable dissenter in the automotive industry [3]. It also suggests that
policymakers should not be so concerned about fatality rates as a result of more stringent fuel
economy legislation; they should be concerned about vehicle design. This conclusion is
consistent with that by Greene and Keller [32].
In addition, it should be noticed that vehicle weight and type are often correlated with driver
characteristics, such as travel speed choice and other aggressive behaviors. So a vehicle’s
crashworthiness and aggressiveness, as estimated here, also may reflect driver attributes.

Xiaokun Wang and Kara Kockelman Page 9 of 21
Moreover, some vehicles may be less likely to be crash-involved, thanks to better brakes or other
design attributes; so overall risk may differ from risk conditioned on having been crash-involved.
(Kweon and Kockelman [20] present crash rate and risk estimates by vehicle and driver type.)
Finally, the variable of vehicle age was controlled for in initial models and found to be
statistically insignificant; so its results are not presented here.
Seating and Seat Belts
Vehicle equipment is important in protecting crash victims. The model results suggest that
bench-type seats with separate cushions (NHTSA [33] provides seat type details) are the least
safe, in both one-vehicle and two vehicle crashes. This may be because they are more likely to
collapse in crashes. Benches with folding backs, however, are estimated to be most protective,
perhaps because they are neither as stiff as integral seats nor as fragile as seats with separate
cushions, as suggested by Prasad et al. [34] and Burnett et al. [8]. As expected, seat belts play a
key role in protecting occupants. In two-vehicle crashes, with lap and shoulder belts working
together, the probability of being injured decreases by 36.3 percent while that of being killed
decreases by 47.3 percent, when compared with not wearing a seat belt. The effect of wearing a
lap-only or shoulder-only belt is estimated to be statistically equivalent to a lap-and-shoulder belt.
The effect of seat belts is more pronounced in one-vehicle crashes. Wearing lap and shoulder
belts is estimated to decrease the probability of being injured by a striking 90.2 percent and the
probability of being killed by 71.9 percent. (Lap-only or shoulder-only belts are estimated to
decrease the probability of being injured by 65.7 percent and the probability of being killed by
60 percent, which is still striking.) The general effect of seat belt for all crash types shows that
lap-and-shoulder belts are better than lap-only or shoulder-only belts, especially in preventing
slight injuries. This result is consistent with Huelke et al.’s [35] and others’ results.
Roadway Design and Environmental Factors
Roadway features, including speed limits, geometric characteristics and traffic safety
measures, affect injury severity by influencing the manner of the crash (such as speed and
collision type). Environmental factors, such as weather and lighting, also can play important
roles.
As expected, the results indicate that in two-vehicle crashes, roads with higher speed limits
have a higher proportion of fatal crashes. This change is clearer at higher speed limits. When the
speed limit changes from 35 mi/h to 45 mi/h, the probability of being injured increases by 0.03
(or 4.7 percent) and the fatality probability increases by 0.001 (or 86.6 percent). When the speed
limit changes from 65 mi/h to 75 mi/h, the probability changes are 0.09 (or 19.7 percent) and
0.01 (or 110.1 percent). It is interesting to find that in one-vehicle crashes, the probability of
being injured is the highest when the speed limit is 60 mi/h. Over this speed limit, the probability
of getting injured decreases. But the fatality probability keeps increasing with the speed limit.
However, the effect of the speed limit is not as significant as that in a two-vehicle crash. When
the speed limit increases from 65 mi/h to 75 mi/h, the probability of being killed increases by
only 0.0007 (or 6.1 percent). Zhang et al. [36], Krull et al. [11] and Khattak et al. [18] all found
in their works that higher speed limits are associated with more severe injuries. This work shows
results consistent with theirs. However, the speed limits are correlated with a host of design
factors that permit higher speed limits, such as wider lanes and shoulders, and less horizontal and
vertical curvature. These better design features counteract the speed limit effect, especially for
one-vehicle crashes, biasing its coefficient toward zero. Speed limits also may be associated with

Xiaokun Wang and Kara Kockelman Page 10 of 21
certain use variables, such as AADT per lane and heavy-duty truck use. Thus, it is very difficult
to estimate the true effect of speed limits, everything else constant, without controlling for all
such variables.
Adverse weather is estimated to be safer for occupants. In two-vehicle crashes, bad weather
decreases the probability of being injured by 0.09 (16.4 percent) and the probability of being
killed by 0.0007 (or 32.5 percent). In one-vehicle crashes, its effect is more significant. This can
be attributed to the more cautious driver behavior during bad weather, including lower speeds.
This conclusion is consistent with that of Khattak et al. [17]. However, Zhang et al. [36] found
that snowy weather increases severity, and Dissanayake and Lu [13] did not find weather to be
statistically significant. Lack of light shows different effects in the two types of crashes. It
decreases the severity in one-vehicle crashes, consistent with the work by Krull et al. [11], but
increases the injury severity in two-vehicle crashes. In general, the lack of light results in a
higher injury severity. This is consistent with results of Khattak et al. [18] and Abdel-Aty [21].
Ideally, one would control for degree of curve, as well as vertical grade, but these variables
are not provided in the NASS CDS data set. Nevertheless, related variables are included and
controlled for here. For example, the presence of horizontal curvature increases injury severity
risk. This is as expected, and consistent with work by Dissanayake and Lu [13] and Abdel-Aty
[21] . Evidently, a leftward curve is more dangerous than a rightward curve, in terms of any
resulting injuries. Compared to a straight road section, a leftward curve increases the fatality
probability by 56.7 percent and a rightward curve increases the fatality probability by 39.2
percent. One-vehicle crashes show similar results. While prior studies do not differentiate
between uphill and downhill grades, Dissanayake and Lu [13] find that grades are associated
with more severe injuries. Here, after distinguishing uphill/downhill and one-vehicle/two-vehicle
crashes, it is found that grade plays different roles in different circumstances. In two-vehicle
crashes, downhill grades are associated with more severe injury, increasing the injury probability
by 13.3 percent and fatality probability by 37.3 percent. While uphill grades result in less severe
injury, their effect is only half that of downhill grades. In one-vehicle crashes, however, the
results suggest that uphill and downhill grades have no practically significant effects.
Roadway dividers and medians are estimated to decrease injury severity in two-vehicle
crashes. Manufactured barriers are estimated to be the most effective, decreasing the probability
of fatality by 0.001, or 53.7 percent. Use of vegetation, water, embankments, or ravines is not
significantly better (in a practical sense) than no-division. In one-vehicle crashes (which are
largely run-off-road crashes), only manufactured barriers are estimated to decrease injury
severity, and then only slightly. Other dividers and one-way roads as both estimated to increase
injury severity, perhaps by offering little or no assistance to drivers who lose control of their
vehicles.
Occupant Characteristics
As occupant age increases, so does injury severity. However, the effect of age is not as
important as might be expected. In two vehicle crashes, 10 years’ increase in age results in about
a 2 percent increase in injury probability and 6 percent increase in fatality probability. In one-
vehicle crashes, the effect of age is a little stronger, but is also limited to only about 8 percent
and 16 percent, respectively. This may be because older people often compensate for their
fragility and slower reaction times by more cautious driving [13]. Women are more likely to
sustain severe injuries than men. In two-vehicle crashes, a female’s probability of being injured
is 0.08 (12.4 percent) higher than a male’s, and her fatality probability is 37.5percent higher. In a

Xiaokun Wang and Kara Kockelman Page 11 of 21
one-vehicle crash, the effect is more dramatic. The gender effect is about twice that in a two-
vehicle crash. Nearly all previous works [4,36,13,5,17,19,15] find that females and/or older
occupants are more prone to injury. Thus, this paper’s results are consistent with their findings. It
should be noted, however, that control variables can proxy for unobserved variables, such as
driver risk-aversion. For example, minivan drivers may differ from pickup drivers in multiple,
immeasurable ways that affect outcome severity; these effects are statistically ascribed to the
vehicle type variables, biasing their values. In the case of minivans, it may make them appear
safer than they truly are, all things constant, if the drivers and their occupants take extra
precautions.
In one-vehicle crashes, the driver’s seat seems to be the most dangerous place to sit, even
though alert drivers should have a strong self-preservation instinct. The right seat in the front row
and “other positions” (in the back of a pickup, for example), are estimated to be a little safer than
the driver’s position, but the differences are not statistically significant. In two-vehicle crashes,
because of side and rear impact crashes, the right seat in the front row and “other positions” are
slightly more dangerous than the driver’s position. In both types of crashes, the second row is
much safer than the front row. The probability of being killed while seated in the second row is
about 40 percent lower than while seated in the first row. When considering all crash types, the
driver’s position is generally the most dangerous place in a crash, consistent with Huelke and
Compton’s [9] results.
CONCLUSIONS
This study of crash severity applies a relatively novel methodology, the heteroscedastic
ordered logit, while controlling for a variety of relevant design, speed, vehicle, occupant, and
environmental variables. It empirically distinguishes a vehicle’s type from its weight for injuries
endured not just by its own occupants but also for those endured by occupants of crash partners.
Related studies, by Kockelman and Kweon [19] and Abdel-Aty [21], did not control for vehicle
weight.
The results suggest that both the revocation of the national maximum speed limit in 1995 and
the boom in sales of light duty trucks may have contributed to the higher injury severity in recent
years. In particular, SUVs and pickups are estimated to be more aggressive but no more
crashworthy than cars, once vehicle weights are controlled for. Notably, overall increases in the
weight of the vehicle fleet are not found to significantly impact crash severity. This is an
important point, since legislators, auto manufacturers and others often resist efforts to increase
fuel economy on the assumption that crash severities will increase. Of course, injury severity
also is influenced by a variety of other factors, including roadway design, environmental factors
and occupant characteristics. The many quantitative results provided here should be useful for
auto manufacturers, highway engineers, policy makers and travelers in providing, and
experiencing, safer travel.
ACKNOWLEDGEMENTS AND DISCLAIMER
The authors are grateful to Hampton C. Gabler, Zheng Li and Jianming Ma for providing
useful suggestions regarding data sets and analytical methods, and to Annette Perrone and
Liberty Lidz for editorial assistance. The authors are also grateful to anonymous reviewers and to
Wenzel Tom for their suggestions and comments on this paper.
The National Cooperative Highway Research Program (NCHRP) sponsored this research
(under contract number 17-23), but the opinions expressed here do not necessarily reflect the

Xiaokun Wang and Kara Kockelman Page 12 of 21
policy of NCHRP. The results of this work are preliminary and have not yet been approved by
the NCHRP 17-23 project panel for publication as an NCHRP report.
REFERENCES
1. National Highway Traffic Safety Administration (NHTSA). DOT Releases Preliminary
Estimates Of 2003 Highway Fatalities.
http://www.nhtsa.dot.gov/nhtsa/announce/press/pressdisplay.cfm?year=2004&filename=
FFARSrls404.html. Accessed July 1, 2004.
2.
Renski, H., Khattak, A. J. and Council, F. M. Effect of speed limit increases on crash
injury severity: Analysis of single-vehicle crashes on North Carolina Interstate highways.
Transportation Research Record No. 1665, 1999, pp.100-108.
3.
Hakim, D. Average U.S. Car Is Tipping Scales at 4,000 Pounds. New York Times May
05, 2004.
4.
Farmer, C. M., Braver, E. R. and Mitter, E. L. Two-vehicle side impact crashes: The
relationship of vehicle and crash characteristics to injury severity.
Accident Analysis and
Prevention
29(3), 1997, pp.399-406.
5.
Bedard, M., Guyatt, G. H., Stones, M. J. and Hirdes, J. P. The independent contribution
of driver, crash, and vehicle characteristics to driver fatalities.
Accident Analysis and
Prevention
34(6), 2002, pp.717-727.
6.
Kahane, C. J. Vehicle Weight, Fatality Risk and Crash Compatibility of Model Year
1991-99 Passenger Cars and Light Trucks.
http://www.nhtsa.dot.gov/cars/rules/regrev/evaluate/pdf/809662.pdf. Accessed July 1,
2004.
7.
Viano, D. C. and Arepally, S. Assessing the safety performance of occupant restraint
systems.
Society of Automotive Engineers Transactions 99 (6), 1990, pp.1913-1939.
8.
Burnett, R., Carter, J., Roberts, V. and Myers, B. The influence of seatback
characteristics on cervical injury risk in severe rear impacts.
Accident Analysis and
Prevention
36 (4), 2004, pp. 591-601.
9.
Huelke, D. F. and Compton, C. P. Effects of seat belts on injury severity of front and rear
seat occupants in the same frontal crash.
Accident Analysis and Prevention 27(6), 1995,
pp.835-838.
10.
Shinohara, K., Okazaki, J., Sakuma, H., Kumada, Y. and Matsumoto, A. A clinical
survey of motor vehicle crashes: What most influences the severity of patient's injuries?
JSAE Review 24(3), 2003, pp.357-358.
11.
Krull, K.A., Khattak, A.J. and Council, F.M. Injury effects of rollovers and events
sequence in single-vehicle crashes.
Transportation Research Record No. 1717, 2000,
pp.46-54.
12.
Toy, E. L., Hammitt, J. K. Safety impacts of SUVs, vans, and pickup trucks in two-
vehicle crashes.
Risk Analysis 23(4), 2003, pp.641-650.
13.
Dissanayake, S. and Lu, J. J. Factors influential in making an injury severity difference to
older drivers involved in fixed object-passenger car crashes.
Accident Analysis and
Prevention
34(5), 2002, pp.609-618.
14.
Washington, S., Karlaftis, M. and Mannering, F. Statistical and econometric methods for
transportation data analysis
. Chapman & Hall/CRC, Boca Raton, FL, 2003.

Xiaokun Wang and Kara Kockelman Page 13 of 21
15. Ulfarsson, G.F. and Mannering, F.L. Differences in male and female injury severities in
sport-utility vehicle, minivan, pickup and passenger car accidents.
Accident Analysis and
Prevention
36(2), 2004, pp.135-147.
16.
Alvarez, R.M. and Brehm, J. Hard Choices, Easy Answers: Values, Information, and
American Public Opinion
. Princeton University Press, Princeton, New Jersey, 2002.
17.
Khattak, A. J., Kantor, P. and Council, F. M. Role of adverse weather in key crash types
on limited-access roadways.
Transportation Research Record No. 1621, 1998, pp.10-19.
18.
Khattak, A. J., Pawlovich, M. D., Souleyrette, R. R. and Hallmark, S. L. Factors related
to more severe older driver traffic crash injuries.
Journal of Transportation Engineering
128(3), 2002, pp.243-249.
19.
Kockelman, K. M. and Kweon, Y. J. Driver injury severity: An application of ordered
probit models.
Accident Analysis and Prevention 34(3), 2002, pp.313-321.
20.
Kweon, Y.J. and Kockelman, K. M. Overall injury risk to different drivers: Combining
exposure, frequency, and severity models.
Accident Analysis and Prevention 35(4), 2003,
pp.441-450.
21.
Abdel-Aty, M. A. Analysis of driver injury severity levels at multiple locations using
ordered probit models.
Journal of Safety Research 34(5), 2003, pp.597-603.
22.
Khattak, A. J. and Rocha, M. Are SUVs ‘Supremely Unsafe Vehicles? Analysis of
rollovers and injuries with sport utility vehicles.
Transportation Research Record No,
1840, 2003, pp.167-177.
23.
Srinivasan, K. K. Injury severity analysis with variable and correlated thresholds:
Ordered mixed logit formulation.
Transportation Research Record No. 1784, 2002,
pp.132-142.
24.
O'Donnell, C.J. and Connor, D.H. Predicting the severity of motor vehicle accident
injuries using models of ordered multiple choice.
Accident Analysis and Prevention 28(6),
1996, pp.739-753.
25.
Smith, K.M. and Cummings, P. Passenger seating position and the risk of passenger
death or injury in traffic crashes.
Accident Analysis and Prevention 36 (2), 2004, pp.257-
260.
26.
Evans, L and Wasielewski, P. Serious or fatal driver injury rate versus car mass in head-
on crashes between cars of similar mass.
Accident Analysis and Prevention 19(2), 1987,
pp.119-131.
27.
Greene, W. H. Econometric Analysis, Fifth Edition. Prentice Hall, New Jersey, 2002.
28.
White, M. J. The “Arms Race” on American Roads: The Effect of SUV’s and Pickup
Trucks on Traffic Safety. http://econ.ucsd.edu/~miwhite/SUVS-finalversion.pdf.
Accessed March 1, 2005.
29.
Gayer, T. The Fatality Risks of Sport-Utility Vehicles, Vans, and Pickups.
http://repositories.cdlib.org/iber/econ/E01-297. Accessed March 1, 2005.
30.
Newstead S., Cameron, M., Watson, L. and Delaney, A. Vehicle crashworthiness and
aggressivity ratings and crashworthiness by year of vehicle manufacture.
http://www.general.monash.edu.au/muarc/rptsum/muarc196.pdf. Accessed July 1, 2004.
31.
Gabler, H. C. and Hollowell, W. T. Aggressivity of light trucks and vans in traffic
crashes.
SAE Special Publications No.1333, Airbag Technology, 1998, pp.125-133.
32.
Greene, D.L. and Keller. M. Dissent on Safety Issues: Fuel Economy and Highway
Safety.
Effectiveness and Impact of Corporate Average Fuel Economy (CAFE) Standards.
National Academies Press, Washington, D.C, 2002.

Xiaokun Wang and Kara Kockelman Page 14 of 21
33. National Highway Traffic Safety Administration (NHTSA). National Automotive
Sampling System Crashworthiness Data System 2000 Coding and Editing Manual
.
http://www-nrd.nhtsa.dot.gov/departments/nrd-30/ncsa/TextVer/AvailInf.html. Accessed
July 1, 2004.
34.
Prasad, P., Kim, A., Weerappuli, D.P.V., Roberts, V. and Schneider, D. Relationships
between passenger car seat back strength and occupant injury severity in rear end
collisions: Field and laboratory studies.
Stapp Car Crash Conference Proceedings No.P-
315, 1997, pp.417-449.
35.
Huelke, D. F., Mackay, G. M. and Morris, A. Intraabdominal injuries associated with lap-
shoulder belt usage.
SAE Special Publications No. 947, Frontal Impact Protection: Seat
Belts and Air Bags
, 1993, pp.39-47.
36.
Zhang, J., Lindsay, J., Clarke, K., Robbins, G. and Mao, Y. Factors affecting the severity
of motor vehicle traffic crashes involving elderly drivers in Ontario.
Accident Analysis
and Prevention
32 (1), 2000, pp.117-125.

Xiaokun Wang and Kara Kockelman Page 15 of 21
LIST OF TABLES
TABLE 1 Variable Definitions and Statistics
TABLE 2 Results of Ordered Logit and Heteroscedastic Ordered Logit Models
TABLE 3 Marginal Effects of Collision Partner’s Vehicle Type
LIST OF FIGURES
FIGURE 1 Probabilities of Injury by Vehicle Type and Weight

Xiaokun Wang and Kara Kockelman Page 16 of 21
TABLE 1 Variable Definitions and Statistics
One-vehicle Crash Two-vehicle Crash
Variable Variable Description
Mean Std. Dev. Mean Std. Dev.
#CURBWGT Curb weight of the vehicle, in lbs 3,170 720.9 3,047 726.3
CAR 1 if the vehicle is a passenger car; 0 otherwise Base variable for vehicle type
#MINIVAN 1 if the vehicle is a minivan; 0 otherwise 0.039 0.193 0.087 0.283
#SUV 1 if the vehicle is an SUV; 0 otherwise 0.214 0.410 0.082 0.274
#PICKUP 1 if the vehicle is a pickup; 0 otherwise 0.127 0.333 0.093 0.291
*PTNRVEHWGT Curb weight of the collision partner, in lbs 4,302 4,690
PTNRCAR 1 if the collision partner is a car; 0 otherwise Base variable for partner vehicle type
*PTNRMINIVAN 1 if the collision partner is a minivan; 0 otherwise 0.084 0.277
*PTNRSUV 1 if the collision partner is an SUV; 0 otherwise 0.116 0.321
*PTNRPICKUP 1 if the collision partner is a pickup; 0 otherwise 0.170 0.376
*PTNRMDTHDT 1 if the collision partner is a medium or heavy-duty truck; 0 otherwise 0.047 0.212
BUCKET 1 if the seat is a integral bucket; 0 otherwise Base variable for seat type
FOLDINGBUCKET 1 if the seat is a bucket with folding back; 0 otherwise 0.263 0.440 0.253 0.434
BENCHSEAT 1 if the seat of the occupant is a integral bench; 0 otherwise 0.072 0.258 0.077 0.267
SEPBENCH 1 if the seat is a bench with separate cushion; 0 otherwise 0.098 0.297 0.105 0.306
FOLDINGBENCH 1 if the seat is a bench with folding cushion; 0 otherwise 0.165 0.371 0.126 0.332
OTHERSEAT 1 if the seat is pedestal or box mounted; 0 otherwise 0.029 0.169 0.045 0.207
NOBELT 1 if the occupant does not use any belt; 0 otherwise Base variable for seat belt usage
LAPSHOU 1 if the occupant uses lap and shoulder belt; 0 otherwise 0.550 0.497 0.546 0.498
OTHEBELT 1 if the occupant uses shoulder only or lap only belt; 0 otherwise 0.204 0.403 0.316 0.465
GOODWEATHER 1 if the weather is good; 0 otherwise Base variable for weather
BADWEATHER
1 if the weather is adverse, including snowy, rainy, foggy and smoky;
0 otherwise
0.215 0.411 0.190 0.392
LIGHT 1 if the light condition is daylight; 0 otherwise Base variable for light condition
DARK 1 if the light condition is dark or dawn; 0 otherwise 0.543 0.498 0.263 0.440
#SPDLIMIT Speed limit of the site (unit: mph) 44.6 14.4 40.5 10.3
SPDLIMITSQD Square of the speed limit of the site (unit: mph
2
) 2,194 1,364 1,749 888.9
NODIVISION 1 if the roadway is two-way yet not divided; 0 otherwise Base variable for road division
NONPOSITIVEDIV
1 if the roadway is divided by vegetation, water, trees, embankments,
ravine ; 0 otherwise
0.144 0.351 0.220 0.414
POSITIVEDIV 1 if the roadway is divided by manufactured barriers; 0 otherwise 0.125 0.331 0.090 0.287
ONEWAY 1 if the roadway is a one-way road; 0 otherwise 0.070 0.254 0.050 0.219
STRAIGHT 1 if the roadway is straight; 0 otherwise Base variable for horizontal curve
CURVRIGHT 1 if the roadway curves right; 0 otherwise 0.161 0.367 0.060 0.238
CURVLEFT 1 if the roadway curves left; 0 otherwise 0.266 0.442 0.053 0.224
LEVEL 1 if the roadway is level; 0 otherwise Base variable for grade
UPHILL 1 if the roadway is uphill; 0 otherwise 0.152 0.359 0.173 0.378
DOWNHILL 1 if the roadway is downhill; 0 otherwise 0.303 0.460 0.143 0.350
AGE Occupant age (unit: year) 27.9 16.0 32.0 19.0
MALE 1 if male; 0 otherwise Base variable for gender
FEMALE 1 if female; 0 otherwise 0.384 0.486 0.513 0.500
FRONTLEFT 1 if seated in the driver seat (front left); 0 otherwise Base variable for seat position
FRONTRIGHT 1 if seated in the front passenger seat (front right); 0 otherwise 0.208 0.406 0.202 0.401
SECONDLEFT 1 if seated in the second row, left seat; 0 otherwise 0.076 0.264 0.081 0.273
SECONDRIGHT 1 if seated in the second row, middle or right seat; 0 otherwise 0.066 0.249 0.048 0.214
OTHERPOSITION
1 if seated in position other than the above and front left; 0 otherwise
(including the third row and outside the pickups) 0.008 0.091 0.011 0.103
* This variable is also used in the heteroscedasticity specification for two-vehicle crashes.
# This variable is also used in the heteroscedasticity specifications for two-vehicle and one-vehicle crashes.

Xiaokun Wang and Kara Kockelman Page 17 of 21
TABLE 2 Results of Ordered Logit and Heteroscedastic Ordered Logit Models
One-vehicle Crashes Two-vehicle Crashes
HOL OL HOL OL
Variable
Coef. t-stat. Coef. t-stat. Coef. t-stat. Coef. t-stat.
Latent injury severity measure
Constant -2.046 -59.614 2.000 -63.340 2.519 55.737 0.786 35.129
CURBWGT 1.94E-04 32.252 1.21E-04 22.221 -6.93E-04 -98.055 -2.64E-04 -94.360
MINIVAN -0.075 -0.939 0.195 3.469 0.495 30.737 0.243 37.886
SUV -0.380 -51.719 -0.216 -33.173 0.532 40.957 0.256 39.280
PICKUP 0.295 18.818 0.437 33.059 0.059 3.550 0.087 12.330
PTNRVEHWGT --- --- 2.48E-04 52.123 7.47E-05 49.906
PTNRSUV --- --- 0.596 64.880 0.311 64.635
PTNRMINIVAN --- --- 0.395 36.478 0.177 29.483
PTNRPICKUP --- --- 0.214 25.773 0.270 74.633
PTNRMDTHDT --- --- -5.539 -51.866 -1.411 -41.653
FOLDINGBUCKET 0.111 18.202 0.081 14.477 -0.128 -19.161 -0.071 -20.609
BENCHSEAT -0.570 -48.939 -0.499 -46.746 0.105 4.983 0.047 4.932
SEPBENCH 0.370 29.069 0.367 31.345 0.786 60.730 0.387 61.881
FOLDINGBENCH -0.416 -31.939 -0.309 -26.858 -0.115 -6.671 -0.082 -10.167
OTHERSEAT -0.362 -4.170 -0.345 -5.579 -0.041 -1.706 -0.026 -2.398
LAPSHOU -1.422 -228.349 -1.285 -233.341 -1.298 -153.502 -0.663 -153.988
OTHEBELT -1.026 -143.930 -0.909 -141.373 -1.526 -172.436 -0.742 -164.853
BADWEATHER -0.949 -97.003 -0.877 -100.323 -0.795 -116.375 -0.384 -116.469
DARK -0.125 -25.523 -0.078 -17.472 0.475 65.583 0.232 64.447
SPDLIMIT 0.062 57.742 0.065 64.518 -0.099 -52.035 -0.038 -38.873
SPDLIMITSQD -5.11E-04 -42.371 -5.12E-04 -46.578 1.46E-03 63.909 6.49E-04 58.161
NONPOSITIVEDIV 0.610 53.738 0.547 53.346 -0.170 -24.687 -0.099 -28.106
POSITIVEDIV -0.056 -4.939 -0.084 -8.386 -1.378 -105.902 -0.696 -115.116
ONEWAY 0.341 24.982 0.235 19.542 -0.346 -18.810 -0.228 -26.204
CURVRIGHT 0.323 31.568 0.252 27.606 0.669 48.656 0.362 58.832
CURVLEFT 0.564 69.939 0.500 70.199 0.909 76.342 0.460 86.546
UPHILL 0.071 8.176 0.047 5.828 -0.322 -41.688 -0.148 -41.358
DOWNHILL -0.169 -20.230 -0.149 -19.668 0.642 64.723 0.353 73.510
AGE 1.66E-02 77.145 1.53E-02 80.867 1.13E-02 57.163 5.79E-03 61.760
FEMALE 0.681 150.887 0.623 151.267 0.645 117.495 0.316 113.742
FRONTRIGHT -0.143 -40.959 -0.151 -47.495 0.086 14.527 0.030 9.775
SECONDLEFT -0.682 -53.686 -0.670 -58.016 -0.998 -48.286 -0.467 -49.399
SECONDRIGHT -0.630 -50.511 -0.658 -58.010 -1.042 -35.158 -0.513 -40.396
OTHERPOSITION -0.078 -0.540 -0.131 -1.255 -0.252 -7.539 -0.025 -1.602
Variance
CURBWGT -3.59E-05 -2.368 --- --- 7.18E-05 5.561 --- ---
MINIVAN 0.303 3.814 --- --- -0.006 -0.154 --- ---
SUV 0.141 3.152 --- --- -0.040 -0.988 --- ---
PICKUP 0.307 5.832 --- --- 0.104 2.491 --- ---
SPDLIMIT 3.06 E-03 3.266 --- --- 8.61E-03 9.681 --- ---
PTNRVEHWGT --- --- --- --- 3.07E-05 2.862 --- ---
PTNRSUV --- --- --- --- -0.100 -3.134 --- ---
PTNRMINIVAN --- --- --- --- -0.186 -5.089 --- ---
PTNRPICKUP --- --- --- --- 0.214 6.800 --- ---
PTNRMDTHDT --- --- --- --- -0.262 -1.085 --- ---

Xiaokun Wang and Kara Kockelman Page 18 of 21
TABLE 2 Results of Ordered Logit and Heteroscedastic Ordered Logit Models (Cont’d)
One-vehicle Crashes Two-vehicle Crashes
HOL OL HOL OL
Variable
Coef. t-stat. Coef. t-stat. Coef. t-stat. Coef. t-stat.
Threshold
0
µ
0.000 – 0.000 – 0.000 – 0.000 –
1
µ
0.713 24.422 0.642 34.920 2.257 31.208 1.118 70.526
2
µ
2.133 29.339 1.911 54.523 4.228 32.331 2.070 82.932
3
µ
5.264 26.744 4.639 41.769 11.764 26.891 5.410 44.628
Number of observations 7,628 18,609
LRI 0.237 0.235 0.257 0.251

Xiaokun Wang and Kara Kockelman Page 19 of 21
TABLE 3 Marginal Effects of Collision Partner’s Vehicle Type
Marginal Effect (Change of Probabilities Versus Cars)
Model Type Vehicle Type
No Injury Possible Injury
Non-
incapacitating
Injury
Incapacitating
Injury
Fatal Injury
Minivan
-0.0439 0.0519 0.0097 -0.0162 -0.0014
SUV
-0.0734 0.0435 0.0238 0.0068 -0.0006
Pickup
-0.0343 -0.0279 0.0093 0.0473 0.0056
HOL
HDT&MDT
0.4110 -0.2168 -0.1097 -0.0822 -0.0023
Minivan
-0.0434 0.0153 0.0141 0.0135 0.0006
SUV
-0.0767 0.0253 0.0252 0.0251 0.0011
Pickup
-0.0664 0.0224 0.0217 0.0214 0.0010
OL
HDT&MDT
0.2646 -0.1324 -0.0727 -0.0572 -0.0023
Note: Probabilities are calculated while evaluating all other variables at their average values.

Xiaokun Wang and Kara Kockelman Page 20 of 21
FIGURE 1 Probabilities of Injury by Vehicle Type and Weight.
Chart (a). Injury Likelihood in One-vehicle Crashes
by Type and Weight
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
2000
3000
4000
5000
6000
2000
3000
4000
5000
6000
2000
3000
4000
5000
6000
2000
3000
4000
5000
6000
Injury likelihood
Fatal
Incapacitating
Non-incapacitating
Possible
None
Car
Minivan SUV Pickup
Chart (c). Injury Likelihood in Two-vehicle Crashes
by Type and Weight of Collision Partner Vehicle
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
2000
3000
4000
5000
6000
2000
3000
4000
5000
6000
2000
3000
4000
5000
6000
2000
3000
4000
5000
6000
10,000
15,000
20,000
25,000
30,000
Injury likelihood
Fatal
Incapacitating
Non-incapacitating
Possible
None
Car Minivan SUV Pickup
Pickup
MDT-HDT
Chart (b). Injury Likelihood in Two-vehicle Crashes
by Type and Weight of Primary Vehicle
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
2000
3000
4000
5000
6000
2000
3000
4000
5000
6000
2000
3000
4000
5000
6000
2000
3000
4000
5000
6000
Injury likelihood
Fatal
Incapacitating
Non-incapacitating
Possible
None
Car
Minivan SUV Pickup

Xiaokun Wang and Kara Kockelman Page 21 of 21
FIGURE 1 Probabilities of Injury by Vehicle Type and Weight.
Chart (a). Injury Likelihood in One-vehicle Crashes
by Type and Weight
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
2000
3000
4000
5000
6000
2000
3000
4000
5000
6000
2000
3000
4000
5000
6000
2000
3000
4000
5000
6000
Injury likelihood
Fatal
Incapacitating
Non-incapacitating
Possible
None
Car
Minivan SUV Pickup
Chart (b). Injury Likelihood in Two-vehicle Crashes
by Type and Weight of Primary Vehicle
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
2000
3000
4000
5000
6000
2000
3000
4000
5000
6000
2000
3000
4000
5000
6000
2000
3000
4000
5000
6000
Injury likelihood
Fatal
Incapacitating
Non-incapacitating
Possible
None
Ca
r
Miniva
n
SUV Picku
p
Chart (c). Injury Likelihood in Two-vehicle Crashes
by Type and Weight of Collision Partner Vehicle
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
2000
3000
4000
5000
6000
2000
3000
4000
5000
6000
2000
3000
4000
5000
6000
2000
3000
4000
5000
6000
10,000
15,000
20,000
25,000
30,000
Injury likelihood
Fatal
Incapacitating
Non-incapacitating
Possible
None
Car Minivan SUV Pickup
Pickup
MDT-HDT