Accident Analysis and Prevention 40 (2008) 1674–1682
Contents lists available at ScienceDirect
Accident Analysis and Prevention
journal homepage: www.elsevier.com/locate/aap
Analysis of left-turn crash injury severity by conflicting pattern using partial
proportional odds models
XuesongWang∗, Mohamed Abdel-Aty
Department of Civil & Environmental Engineering, University of Central Florida, Orlando, FL 32816-2450, United States
a r t i c l e i n f o
Article history:
Received 19 October 2007
Received in revised form 24 May 2008
Accepted 2 June 2008
Keywords:
Signalized intersection  Left-turn crash  Conflicting pattern  Crash injury severity  Partial proportional odds model  Significant factor
a b s t r a c t
The purpose of this study is to examine left-turn crash injury severity. Left-turning traffic colliding withopposing through traffic and with near-side through traffic are the two most frequently occurring conflictingpatterns among left-turn crashes (Patterns 5 and 8 in the paper, respectively), and they are proneto be severe. Ordered probability models with either logit or probit function is commonly applied in crashinjury severity analyses; however, its critical assumption that the slope coefficients do not vary over differentalternatives except the cut-off points is usually too restrictive. Partial proportional odds models aregeneralizations of ordered probability models, for which some of the beta coefficients can differ acrossalternatives,were applied to investigate Patterns 5 and 8, and the total left-turn crash injuries. The resultsshowthat partial proportional odds models consistently perform better than ordered probability models.By focusing on specific conflicting patterns, locating crashes to the exact crash sites and relating approachvariables to crash injury in the analysis, researchers are able to investigate how these variables affectleft-turn crash injuries. For example, opposing through traffic and near-side crossing through traffic inthe hour of collision were identified significant for Patterns 5 and 8 crash injuries, respectively. Protectedleft-turn phasing is significantly correlated with Pattern 5 crash injury. Many other variables in driverattributes, vehicular characteristics, roadway geometry design, environmental factors, and crash characteristicswere identified. Specifically, the use of the partial proportional formulation allows a much betteridentification of the increasing effect of alcohol and/or drug use on crash injury severity, which previouslywas masked using the conventional ordered probability models.
© 2008 Elsevier Ltd. All rights reserved.
1. Introduction
Intersections are among the most dangerous locations of a roadwaynetwork. In the state of Florida, 43.1% of fatalities and seriousnjuries occurred at or were influenced by intersections (FloridaDepartment of Transportation, 2006). In the U.S., although onlyaround 10% of all intersections are signalized, in 2005, nearly 30%(2744) of intersection fatalities occurred at signalized intersections(Rice, 2007). Left-turn crashes occur frequently and they accountfor a high percentage of total crashes at signalized intersections.#p#分頁標題#e#
They are prone to be severe, possibly due to the relatively high conflictingspeeds of involved vehicles and the angle of impact. In asample of signalized intersections collected in Orange and Hillsboroughcounties in Florida, 64.2% of left-turn crashes involved injury,
∗ Corresponding author at: Department of Civil & Environmental Engineering,
University of Central Florida, Engr II, Room 301B, Orlando, FL 32816-2450,
United States. Tel.: +1 407 8234902; fax: +1 407 8234676.
E-mail address: [email protected] (X.Wang).
whereas the percentage of injury crashes was only 50.1% for allother crashes.
From 2002, a series of crash frequency studies have beenconduced in Florida to identify the crash profiles for themajor intersectiontypes (Abdel-Aty and Wang, 2006; Wang and Abdel-Aty,
2006, 2007, 2008;Wang et al., 2006). In one study,Wang and Abdel-Aty (2008) investigated conflicting flows, intersection geometricdesign features, and traffic control and operational features on leftturn
crash occurrence. Left-turn crasheswere classifiedinto distinctconflicting patterns (i.e., left-turn traffic colliding with opposingthrough traffic, or with near-side through traffic, etc.), and then thecrash frequencies of different patterns were modeled. The studiesindicate there are obvious differences in the factors which correlatedwith different left-turn collisions. However, crash frequencystudies model accumulated crash counts, which ignores the differenceof severe and minor crashes. Therefore, they are unable toinvestigate how specific features affect crash injury severity.
The left-turn crashes at signalized intersections result in a hugecost to society in terms of death, injury, lost productivity, and propertydamage. However, how the different factors affect left-turn
0001-4575/$ – see front matter © 2008 Elsevier Ltd. All rights reserved.
doi:10.1016/j.aap.2008.06.001X. Wang, M. Abdel-Aty / Accident Analysis and Prevention 40 (2008) 1674–1682 1675crash severity is still not clear. For example, traffic volume hasbeen identified as the most significant factor affecting crash occurrence
(Wang and Abdel-Aty, 2008), but it is not clear whether trafficflow affects crash severity. Left-turn phase has been identified to
be significant for left-turn crash occurrence, but no study investigatesits influence on crash severity. The purpose of this study is toinvestigate how traffic characteristics, driver attributes, vehicular
characteristics, roadway geometry features, environmental factors,and crash characteristics affect left-turn crash injury severity.In police reports, crash injury is categorized into five levelsbased on the most serious injury to any person involved in a crash:no injury, possible injury, non-incapacitating injury, incapacitatinginjury and fatal injury. Multinomial logit models were specifiedfor multiple alternatives of severity. Shankar and Mannering(1996) considered environmental, roadway, vehicular, and rider#p#分頁標題#e#
characteristics in their multinomial logit analysis of motorcycleriderseverity on single-vehicle motorcycle crashes. Carson andMannering (2001) developedmultinomial logit models to examinethe effect of ice-warning signs on crash severity for different roadwayfunctional classes. Ulfarsson and Mannering (2004) exploreddifferences in severity between male and female drivers in singleand two-vehicle collisions; separate multinomial logit models ofseverity were estimated for male and female drivers. However, thelogit model’s assumption of independent errors for each alternative
is inconsistent with the fact that the alternatives for crash injuriesare ordered.With ordered alternatives, one alternative is similar tothose close to it and less similar to those further away (Train, 2003).
Nested logit, mixed logit, or probit models can be applied toaccount for the pattern of similarity and dissimilarity among differentinjury levels. Abdel-Aty (2003) compared the multinomial
logit, nested logit, and ordered probit models for driver’s injuryseverity at toll plaza and found that nested logit model produced
the best fit. However, Train (2003) thinks such a specification doesnot actually fit the structure of the ordinal data.Considering that severe crashes are comparatively less frequent(especially fatal crashes) and also for simplicity, some researcherscollapsed the five level injury data into fewer levels. The binary logitor probit model can be used when severity is classified into twolevels. Al-Ghamdi (2002) applied the binary logit model to examinethe effect of crash characteristics on fatal and non-fatal injury andfound that crash location and cause of crashwere significant. Huang
et al. (in press) and Obeng (2007) applied the binary logit to analyzecrash injury of signalized intersections. But combining adjoiningcategories in ordered categorical regression could lose efficiency in
estimating regression parameters (Train, 2003).The main characteristic of crash injury data, from a modelingperspective, is that the responses are inherently ordered
multiple-choice variables. Ordered logit and probit models havebeen commonly applied to fit the ordinal data structure of injuryseverity. By using the ordered probit model, O’Donnell and Connor(1996) investigated how variations in the attributes of road userscan lead to variations in the probabilities of sustaining differentlevels of injury inmotor vehicle crashes. Ma and Kockelman (2004)used the ordered probit model to predict severity based on factorsincluding traffic, roadway and occupant characteristics andweather conditions at the time of a crash and type of vehicle.Khattak (2001) applied the ordered probit model to examine injuryof multi-vehicle rear-end crashes. Abdel-Aty (2003) applied theordered probit model to predict crash severity on roadway sections,signalized intersections and toll plazas by using the Florida crashdatabase. Abdel-Aty and Keller (2005) created the ordered probitmodels by using roadway attributes and crash types for crashesoccurred at the signalized intersections.#p#分頁標題#e#
Ordered probability models are straightforward because theyimpose the restriction that regression parameters (except cut-offpoints) are the same for different severity levels. This is called
parallel-lines assumption, or proportional odds assumption. However,for injury severity, it is not clear whether distances betweenadjacent injury levels are equal. It is too arbitrary to assume thatcoefficients of ordered probability models are the same exceptfor cut-off points. The parallel-lines constraint can be relaxed forall variables, but estimating more parameters than necessary willalso cause some variables to be insignificant. Considering that theassumption may be violated only by one or a few of the includedvariables, Peterson and Harrell (1990) proposed a partial proportionalodds model, where parallel-lines constraint is relaxedonly for those variables when it is not justified and allows nonproportionalodds for a subset of the explanatory variables. To have
more parsimonious layout, they used a gamma parameterizationof partial proportional odds model.
Analyzing left-turning traffic is crucial for improving intersectionoperation and safety. Left-turn crashes are not all identicalwith respect to the maneuvers of the involved vehicles (vehicle
movement and travelling direction). Left-turning traffic may collidewith many other traffic flows at signalized intersections, andleft-turn crashes have many distinct conflicting patterns in vehicle
maneuvers before collisions.Wang and Abdel-Aty (2008) classifiedleft-turn crashes into nine distinct conflicting patterns, and thenthe crash frequencies of different patterns were modeled. Pattern
5 is for those left-turn crashes of which one involved vehicle wasturning left and another vehicle was going straight on the opposingapproach. Pattern 8 is for left-turning vehicles colliding withvehicles going through fromthe near-side crossing approach. Theseare the most frequently occurring collision patterns, accounting for72.5% and 14.1% of all left-turn crashes, respectively, and they are
prone to be severe.
In summary, there have been numerous studies analyzing crash
injury severity. However, only limited studies examined crash
injury severity at signalized intersections (Abdel-Aty, 2003; Abdel-
Aty and Keller, 2005; Huang et al., in press; Obeng, 2007), and in
previous studies, crashes were not located to the exact sites they
occurred. Therefore, the previous approach is unable to associate
crash injury to features of related approaches. There is no study
investigating injury severity for left-turn crashes specifically. In
addition, most severity analyses depended on crash data in which
most intersection attributes are not available (i.e., turning movements,
signal phase, left-turn offset, etc.). However, these are the
only viable factors traffic engineers have some control over. In
this study, left-turn crash injury severity for Patterns 5 and 8, and#p#分頁標題#e#
total left-turn crashes are investigated using partial proportional
odds models. Left-turn crashes are located to the crash sites where
they occurred, which enables researchers to specify the effect of
attributes of intersection geometric design features, traffic control
and operational features, and traffic characteristics on crash
severity.
2. Methodology: partial proportional odds models
Crash injury severity is categorized into five levels in increasing
of severity and coded as: 1 = no injury, 2 = possible injury, 3 = nonincapacitating
injury, 4 = incapacitating injury, and 5 = fatal injury.
Note that level j = 1 is defined as the minimum value of the variable,
no injury. Let Yi denotes the recorded crash injury for crash i.
Ordered logit and probit models can be derived based on the level
of an unobserved variable (Train, 2003; Washington et al., 2003).
A critical assumption of the ordered probability models is that the
slope coefficients do not vary over different alternatives except the
cut-off points. This parallel-lines assumption could be violated in
many cases. A generalized ordered logit model can be specified to1676 X. Wang, M. Abdel-Aty / Accident Analysis and Prevention 40 (2008) 1674–1682
relax parallel-lines assumption for all variables and the probability
of crash injury for a given crash can be specified as
P(Yi > j) = g(X
iˇj) =
exp(?j − X
iˇj)
1 + exp(?j − X
iˇj)
, j= 1, 2, 3, 4 (1)
where Xi is a p×1 vector containing the values of crash i on the
full set of p explanatory variables, ˇj is a p×1 vector of regression
coefficients, ?j represents cut-off point for the jth cumulative logit.
The only difference between this model and the ordered logit model
is that ˇ is not fixed across equations.
Considering that the parallel-lines assumption may be violated
only by one or a few variables, a partial proportional odds model
can be specified, for which one or more ˇs differ across equations
and others can be the same for all equations. Peterson and Harrell
(1990) proposed a gamma parameterization of partial proportional
odds model with logit function as below:
P(Yi > j) = g(X
iˇj) =
exp[?j − (X
iˇj + T
ij)]
1 + exp[?j − (X
iˇj + T
ij)]
(2)
where Ti is a q×1 vector, q≤p, containing the values of crash i
on that subset of the p explanatory variables for which the proportional
odds assumption is not assumed, and j is a q×1 vector
of regression coefficient associated only with the jth cumulative
logit. In the model, each explanatory variable has one ˇ coefficient,
k−2 coefficients, where k is the number of alternatives (in this
study, k = 5). There are k−1? coefficients reflecting cut-off points.#p#分頁標題#e#
The  coefficients represent deviations from proportionality. This
gamma parameterization combines all the features of the traditional
ordered models while allowing for non-proportionality in
some or all of the variables in the model. If all the gammas are equal
to zero, it is actually a proportional odds model. The gammaparameterized
partial proportional odds model with a probit function can
be expressed as
P(Yi > j) = g(X
iˇj) = ?[?j − (X
iˇj + T
ij)] (3)
Partial proportional odds models can be fitted by a user-written
program gologit2 (Williams, 2006). It should be cautious for interpreting
the coefficients of intermediate categories. The sign of ˇ
does not always determine the direction of the effect of the intermediate
outcomes (Washington et al., 2003; Wooldridge, 2002).
The marginal effects are useful for interpretation of the variables.
In Stata (2005), for continuous variables, the derivative is calculated
numerically; for dummy variable, a difference rather than
the derivative is computed. Ordered probability models and partial
proportional odds models with different functions (logit or probit)
are not nested. Pseudo R2 measure R2 =1−(ln L/ln L0) and Akaike’s
information criterion AIC =−2 lnL+2p are applied to evaluatemodels’
performance, where ln L and ln L0 are the log-likelihood in the
fitted and intercept-only models, and p is the number of parameters
estimated. Pseudo R2 coincides with an interpretation of linear
model R squared (Cameron and Trivedi, 1998). Smaller AIC indicates
a better-fitting model (Stata, 2005).
3. Data preparation
Information on intersection geometry design features, traffic
control and operational features, traffic flows, and crashes from
2000 to 2005were obtainedfor 197 four-leggedsignalizedintersections
from Orange and Hillsborough counties in the Central Florida
area. Geometric design features for the intersection approach
include the number of through lanes, the number of left-turn lanes
and whether theywere exclusive, the presence of median, whether
it had exclusive right-turn lanes, the types of left-turn lane offset
(negative, zero, or positive offset), the direction of each intersection
roadway, and the angle of intersecting roadways. Traffic control
and operational features were retrieved by inspecting signal plans
provided by the county traffic engineering departments. The types
of left-turn control include “permissive”, “compound” (“permissive/
protected” or “protected/permissive”), and “protected”. The
key factors for signal phases, i.e., yellow time, and all-red time for
through and left-turn (if protected)movementswere retrieved. The
speed limit for each approach was also obtained.#p#分頁標題#e#
In both counties, the approachmovements (right-turn, through,
and left-turn) for both morning and afternoon peak hours were
counted for a year during the study period. The approach daily
turning movementswere derived fromthe approach AADT and the
proportion of approach turning movements. The real traffic volume
in the hour of collision is not available currently for signalized
intersections in the state. Instead, left-turn, through, and right-turn
movements in the crash hour of each approach were converted
from approach daily turning movements considering daily,weekly,
monthly variations, and the growth rates over the study period.
The Crash Analysis Reporting (CAR) system maintained by the
Florida Department of Transportation (FDOT) Safety Office was
used to retrieve the crash data for the selected intersections. There
were a total of 13,218 collisions for the selected intersections over
the 6-year period. The crash site location (e.g., at intersection),
the initial crash type (e.g., left-turn), the vehicle movement (e.g.,
straight ahead, making left-turn), the direction of travel (e.g.,west),
and the contributing cause (e.g., failed to yield right-of-way, disregarded
traffic signal) for both at-fault and innocent vehicles/drivers
are stored in the crash database. Left-turn crashes in this study are
defined as the crashes that occurred at the intersection when atleast
one involved vehicle was turning left before the collisions.
Only vehicular crasheswere considered. Other variables fromcrash
database include driver’s age, gender, estimated speed, impact
point, ejection, crash safety equipment usage, light condition for
both left-turning vehicle and another vehicle (might go through,
turn left, or turn right).
Of the 13,281 collisions at the selected intersections, 3098 were
left-turn collisions. This accounts for 23.4% of all police reported
vehicle collisions at the selected intersections. These collisions can
be classified into nine different patterns (Wang and Abdel-Aty,
2008). Patterns 5 and 8 are the most frequently occurring collision
types, accounting for 72.5% and 14.1%of all left-turn crashes, respectively,
and they contributed all 32 left-turn fatal crashes as shown
in Table 1, which summarized left-turn crash severity for Patterns
Table 1
Left-turn crash injury severity distribution by conflicting patterns for the selected intersections
Injury severity levels Pattern 5 crashes Pattern 8 crashes All left-turn crashes
None 694(31.18%) 126(28.90%) 1129(35.90%)
Possible 547(24.57%) 96(22.02%) 730 (23.21%)
Non-incapacitating 651(29.25%) 130 (29.82%) 845(26.87%)
Incapacitating 313(14.06%) 73(16.74%) 409(13.00%)
Fatal 21(0.94%) 11(2.52%) 32(1.02%)
Total 2226(100.00%) 436(100.00%) 3145(100.00%)X. Wang, M. Abdel-Aty / Accident Analysis and Prevention 40 (2008) 1674–1682 1677#p#分頁標題#e#
Fig. 1. Collision diagramand data arrangement for Patterns 5 and 8 left-turn crashes.
5 and 8 and entire left-turn crashes. Based on vehicle movements
(e.g., straight ahead, making left-turn) and direction of travel of both
involved vehicles, left-turn crashes were assigned to the approach
from which the left-turning vehicles turned. The approach level
intersection-related explanatory variables were arranged as entering,
near-side crossing, far-side crossing, and opposing approaches
as illustrated in Fig. 1 for Patterns 5 and 8. All of the crash related
data were assembled with intersection related data.
4. Estimation results
Partial proportional odds models with both logit and probit
functions were developed for Patterns 5 and 8, and total left-turn
crash injury severity. Partial proportional odds models were fitted
by a user-written program gologit2 (Williams, 2006). For comparison,
ordered logit and probit models were also fitted.
4.1. Pattern 5 left-turn crashes
The ordered logit model had better performance than the
ordered probit model (AIC = 5935.64 vs. 5941.97). Parallel-lines
assumption for each variablewas tested using a series ofWald tests
to see whether its coefficients differ across equations. The variable,
crash alcohol/drug involved, violated parallel-lines assumption
(p-value = 0.0066). Partial proportional odds models with both
logit and probit functions were fitted with this variable changing
across equations while other variables were imposed to have their
effects meet parallel-lines assumption. The partial proportional
odds model with a logit function performed better than that with
a probit function (AIC = 5931.86 vs. 5934.54; pseudo R2 = 0.0466 vs.
0.0454). The estimations for the ordered logit model and the partial
proportional odds model with logit function are presented in
Table 2, and the marginal effects are reported in Table 3.
The estimated partial proportional odds model had one beta
coefficient for each variable, three gamma coefficients for the
variable violating parallel-lines assumption, and four alpha coefficients
reflecting the cut-off points. The gamma coefficients for
Gamma 2 throughGamma 4were highly significant; p-valueswere
0.023, 0.051, and 0.005, respectively. The Gamma 2 value for the
variable crash alcohol/drug involved (0.3359) was added to beta
estimate (0.0618) to yield the value for the coefficient of this
variable in the second equation. The same process was used to
get the coefficient in the third equation (0.5215 = 0.4597 + 0.0618)
and in the fourth equation (0.9532 = 0.8914 + 0.0618). Therefore,
the estimated coefficients were increasing, which was
masked using the ordered probability models as shown in
Table 2. The marginal effects also showed that alcohol or drugs#p#分頁標題#e#
had positive effects on severe and fatal crashes (0.0299 and
0.0243).
Traffic volume was identified to be the most significant factor
for crash occurrence. In this study, the different forms of traffic
volume were tested for investigating their effect on crash injury
severity, which include traffic of the entire intersection, traffic of
entering approach, traffic of opposing approach, left-turning traffic,
and opposing through traffic. The results showed that having
heavy opposing through traffic, specifically in the hour of collision,
Pattern 5 crashes tended to be more severe (Coef. = 0.0148;
p-value = 0.0055). These results were confirmed by the positive
marginal effects for serious, severe, and fatal injuries as shown in
Table 3. From the crash data, 81.6% of Pattern 5 crashes were leftturning
vehicles at-fault. Generally, more opposing through traffic
meant shorter gaps for left-turn vehicles and therefore there was
less time and space after crash occurred for both vehicles to react
to reduce injury severity.
Among the geometric design features, left-turn lane offset was
identified to be significant (Coef. =−0.1813; p-value = 0.02). Providing
positive offset will mitigate the sight restriction for vehicles
turning left from opposing left-turn lanes (Joshua and Saka, 1992;
McCoy et al., 1992). With better visibility, both drivers would be
better able to react and to lower crash severity.
Protected left-turn phase was associated with less severe
crashes (Coef. =−0.1169); however, compound phase was not significant
and it was combined with permissive phase. One obvious
reason is that at a compound signal left-turning and opposing
through traffic is usually higher than that for a permissive signal. In
addition,compound is themostcomplicated phasing. Crash records
indicated that left-turn crashes occurring under protected left-turn
phases typically resulted as left-turn vehicles were not cleared
from the intersection upon the onset of the opposing through
vehicle’s green signal. Of these crashes, left-turn vehicles collided
with vehicles which just entered intersections and therefore the
through vehicles’ speeds were low, while under permissive left1680 X. Wang, M. Abdel-Aty / Accident Analysis and Prevention 40 (2008) 1674–1682
Table 6
Models for total left-turn crashes
Variables Ordered logit estimates Generalized ordered probit estimates
Coef. z Coef. z
Beta
Left-turn crash conflicting pattern (base: Pattern 6)
Pattern 5 1.5535 0.3613 0.8858 0.1943
Pattern 8 1.9124 0.3794 1.1122 0.2056
Patterns 1–4, 7 and 9 0.8874 0.3667 0.4942 0.1969
Conflicting vehicle types (base: other combination)
Both vehicles in large size −0.3482 0.1120 −0.1951 0.0655
Motorcycle involved 0.8471 0.2750 0.5057 0.1637#p#分頁標題#e#
Lighting condition: dark with street light vs. others −0.2610 0.0757 −0.1474 0.0444
Maximum of speed ratios (estimated speed/speed limit) of two involved vehicles 0.1729 0.0865 0.1029 0.0509
Driver ejected (vs. no) 0.6871 0.2851 0.3882 0.1618
Safety equipment in use (vs. not used) −0.4669 0.1038 −0.2656 0.0613
Crash alcohol/drug involved (vs. no) 0.6982 0.2503 0.0618 0.1717
Point of impact of entering left-turning vehicle (base: front and front right)
Back right −0.6947 0.1014 −0.4053 0.0602
Back −1.3157 0.2265 −0.7727 0.1290
Back left −0.9233 0.1960 −0.5543 0.1169
Front left −0.2208 0.1032 −0.1371 0.0607
Other −0.7372 0.1961 −0.4989 0.1202
Point of impact of another vehicle (base: front and front left)
Front right −1.0130 0.0980 −0.6053 0.0576
Back right −0.5116 0.0885 −0.2907 0.0522
Back and back left −1.8358 0.2056 −1.0473 0.1181
Other −1.0140 0.1350 −0.5900 0.0798
Driver age of left-turning vehicle (base: age≥25)
Very young (≤19) −0.4238 0.0963 −0.2446 0.0566
Young (20≤age≤24) −0.2225 0.0955 −0.1503 0.0565
Driver age of another vehicle (base: 20≤age≤64)
Very young (≤19) −0.2271 0.1028 −0.1441 0.0611
Old (≥65) 0.2473 0.1421 0.1500 0.0843
Gamma 2
Crash alcohol/drug involved vs. no – – 0.3359 0.1174
Point of impact of another vehicle: other vs. base case – – 0.1607 0.0974
Gamma 3
Crash alcohol/drug involved vs. no – – 0.4597 0.1869
Point of impact of another vehicle: other vs. base case – – 0.4342 0.1632
Gamma 4
Crash alcohol/drug involved vs. no – – 0.8914 0.2726
Point of impact of another vehicle: other vs. base case – – 0.4342 0.1632
Alpha
Constant 1 −0.4553 – −0.3155 0.2076
Constant 2 0.6766 – 0.3766 0.2081
Constant 3 2.2959 – 1.3606 0.2080
Constant 4 5.1588 – 2.7590 0.2200
Summary statistics
Number of observations 3145 3145
Log likelihood at convergence −3962.19 −3956.88
AIC 7978.38 7977.75
Pseudo R2 0.0816 0.0829
Note: dash (–) indicates data not applicable or unavailable.
on the occupants of involved vehicles when they collided. The
variable speed ratio of through vehicle was marginally significant
to increase crash injury (Coef. = 0.1849; p-value = 0.0850), which is
consistent with the previous studies (Kweon andKockelman, 2003).
The result also showed that using the seat belt would reduce crash
severity significantly (Coef. =−0.6672; p-value <0.0001).
4.2. Pattern 8 left-turn crashes
There were 436 Pattern 8 left-turn crashes, which account for#p#分頁標題#e#
14% of total left-turn crashes, while more than 30% of left-turn fatal
crasheswere fromthis pattern. The partial proportional odds model
with logit function had better performance (AIC = 1248.74). The
estimates and the marginal effects are presented in Tables 4 and 5,
respectively. The variable crash alcohol/drug involved was identified
to have varying coefficients for different injury levels.Near-side
crossing through traffic in the crash hour, zero or positive left-turn
lane offset of entering approach, and crashes with drivers ejected
were also identified to be significant.
4.3. Total left-turn crashes
The total number of left-turn crashes was 3145 for the selected
intersections over the period of study. Both crash alcohol/drug
involved and point of impact of another vehicle were identified toX. Wang, M. Abdel-Aty / Accident Analysis and Prevention 40 (2008) 1674–1682 1681
violate parallel-lines assumption, with p-values 0.003 and 0.041
in the Wald test, respectively. Partial proportional odds models
with either logit or probit function were fitted with these two factors
differing across injury levels. The p-value of the Wald test for
parallel-lines assumption for the final model was 0.8120, which
indicated that the final model did not violate the parallel-lines
assumption. The partial proportional odds model with probit function
had better performance with the largest Pseudo R2 (0.0829)
and the smallest AIC (7977.75) as shown in Table 6.
Results showed that Pattern 5 was more severe than Pattern
6 (conflicting with opposing right-turn vehicle. Coef. = 0.8858),
and Pattern 8 was the most severe left-turning conflicting pattern
(Coef. = 1.1122). Crashes occurred at night but with street
light and safety equipment in use will reduce crash injury level,
Coef. =−0.1474 and −0.2656, respectively. Crashes involved motorcycle,
with drivers ejected from vehicle, and higher speed ratio of
involved vehicle tend to produce more severe left-turn crashes,
Coef. = 0.5057, 0.3882, 0.1029, respectively. For both involved vehicles,
the front is the most dangerous impact point. Previous studies
showed that young drivers were more likely involved in crashes,
however, the negative coefficients −0.2446 and −0.1441 indicated
that they were less likely to be injured.
5. Summary and discussion
This paper presents a series of crash injury severity models
for left-turn crashes. Crash injury severity is categorized into five
levels in increasing of severity. The literature suggests that the
logit model’s assumption of independent errors for alternatives
is inconsistent with the fact that the crash injuries are ordered.
The parallel-lines assumption (or proportional odds assumption)
of commonly applied ordered probability models is usually too#p#分頁標題#e#
restricting. This assumption may be violated only by one or a few
of the included variables. A partial proportional odds model where
the parallel-lines constraint is relaxed only for those variableswhen
it is not justified is applied in this study.
Partial proportional odds models were developed for leftturning
traffic colliding with opposing through traffic (Pattern 5)
or with near-side through traffic (Pattern 8), and all of the left-turn
collisions that occurred at 197 signalized intersections in the Central
Florida area over 6 years. A massive data collection effort was
undertaken for these intersections including intersection approach
geometric design features, traffic control and operational features
(with signal plan), traffic characteristics (with turningmovements),
and crash data. Left-turn crashes were located to the crash sites
where they occurred, which enables the researchers to specify
the effect of attributes of intersection approach features on crash
severity. The partial proportional odds models perform consistently
better for Patterns 5 and 8, and total left-turn crashes. By using
partial proportional odds models, the interpretation of the parameters
yields greater insight concerning contributing factors, i.e., it
revealed the increasing crash injury severity due to alcohol and/or
drugs.
Of traffic characteristics, the estimated opposing through traffic
and the near-side crossing through traffic in the hour of crash are
identified to be significant for Patterns 5 and 8 crash injury, respectively.
Traffic volume has been identified as the most significant
factor influencing crash occurrence. This study found that neither
the total approach volume, nor the entire intersection volume, but
rather the specific vehicle movements affected crashed injury significantly.
With the real traffic volume at the time of crash available
in the future, a more realistic relationship can be established.
Of intersection geometric design features, left-turn offset has
been identified to be significant for both Patterns 5 and 8. Of
traffic control and operational features, protected left-turn signal
and all-red time on opposing through movements have significant
influences on Pattern 5 crash injury. Crashes occurred at night at
intersections with street lights are associated with lower left-turn
crash injury level. All these are viable factors that traffic engineers
have some control over. Therefore, based on these findings more
efficient countermeasures can be developed to mitigate left-turn
crash severity. Many crash related variables were identified to be
significant whichinclude: alcohol/drug use, vehicle type, driver age,
impact point, speed ratio, safety equipment, and driver ejection.
Acknowledgements
The authors wish to acknowledge the financial support of#p#分頁標題#e#
the Florida Department of Transportation. And the authors also
acknowledge the help they received fromOrange and Hillsborough
Counties’ traffic departments for sharing the valuable data used in
this study.
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