a joint analysis of secondary collisions and injury...
TRANSCRIPT
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Xie, Ozbay and Yang
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A Joint Analysis of Secondary Collisions and Injury Severity Levels 2
Using Structural Equation Models 3
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Kun Xie, Ph.D. Candidate 6 *Corresponding author 7
Graduate Research Assistant 8
Department of Civil and Urban Engineering 9
Center for Urban Science and Progress 10
Urban Mobility and Intelligent Transportation Systems (UrbanMITS) Laboratory 11
New York University 12
1 MetroTech Center, Brooklyn, NY 11201, USA 13
E-mail: [email protected] 14
Phone: +1-646-997-0547 15
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Kaan Ozbay, Ph.D. 18 Professor 19
Department of Civil and Urban Engineering 20
Center for Urban Science and Progress 21
Urban Mobility and Intelligent Transportation Systems (UrbanMITS) Laboratory 22
New York University 23
1 MetroTech Center, Brooklyn, NY 11201, USA 24
E-mail: [email protected] 25
Phone: +1-646-997-0552 26
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Hong Yang, Ph.D. 29 Assistant Professor 30
Department of Modeling, Simulation & Visualization Engineering 31
Old Dominion University 32
4700 Elkhorn Ave, Norfolk, VA 23529, USA 33
E-mail: [email protected] 34
Phone: +1-757-683-4529 35
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Word Count: 5500 (Text) +3 Figures+5 Tables=7500 words 37
Abstract: 224 38
Submission Date: Aug. 1, 2015 39
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Prepared for Presentation at the 95th TRB Annual Meeting 41
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ABSTRACT 1 This study aims to investigate the contributing factors to secondary collisions and the effects of 2
secondary collisions on injury severity levels. Manhattan, which is the most densely populated urban 3
area of New York City, is used as a case study. In Manhattan, about 7.5% of crash events get 4
involved with secondary collisions and as high as 9.3% of those secondary collisions lead to 5
incapacitating and fatal injuries. Structural equation models (SEMs) are proposed to jointly model 6
the presence of secondary collisions and injury severity levels. This study contributes to the 7
literature by fully exploring the determinants of secondary collisions such as speeding, alcohol, 8
fatigue, brake defective, limited view and rain. To assess the temporal effects, we use time as a 9
moderator in the proposed SEM framework and results indicate that it is more likely to sustain 10
secondary collisions and severe injuries at night. The parameter estimates of the proposed SEM are 11
further compared with those of the standard probit models which estimate the presence of secondary 12
collisions and injury severity independently. Results show that standard probit models overestimate 13
the safety effects of confounding variables (i.e. variables that can affect both secondary collision 14
occurrence and injury severity) by mixing the direct and indirect effects. In addition, it is found that 15
the standard probit models significantly overestimate the effects of secondary collisions on injury 16
severity propensity by 127.6% for daytime crashes and by 121.2% for nighttime crashes, since the 17
endogeneity of the presence of secondary collisions is ignored in the estimation. Understanding the 18
causes and impacts of secondary collisions can help the transportation agencies and automobile 19
manufacturers develop effective injury prevention countermeasures. 20
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Keywords: Safety Analysis, Secondary Collisions, Injury Severity, Endogeneity, Structural Equation 23
Model, Urban Area 24
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Xie, Ozbay and Yang
INTRODUCTION 1 A secondary collision in this study is defined as any collision or non-collision event (e.g. overturn) 2
that occurs after the initial collision in a traffic crash event. It should be distinguished that the 3
secondary “collisions” are different from the secondary “crashes” defined in the previous studies 4
such as (1, 2). A secondary crash is an induced crash event that occurs due to influence of the 5
previous one, whereas a secondary collision along with the initial collision can be regarded as 6
different phases of a single crash event. Common examples of secondary crashes include the ones 7
which occur as a consequence of the queues induced by the primary crashes. Examples of secondary 8
collisions include, but are not limited to, one vehicle striking another two vehicles consecutively, 9
one vehicle hitting another vehicle first and then a pedestrian/bicyclist/fixed object and one vehicle 10
overturning after striking another vehicle. Secondary collisions are not rare events and are among the 11
most injurious phases in crash events (3, 4). For instance, in Manhattan, New York City, about 7.5% 12
of crash events include secondary collisions and as high as 9.3% of those secondary collisions lead 13
to incapacitating and fatal injuries according to the historical crash data we collected. 14
New York City mayor launched the Vision Zero Action Plan in 2014, which targets at 15
reducing injuries and fatalities caused by traffic crashes. To improve traffic safety, the investigation 16
of contributing factors to secondary collisions and safety impacts of secondary collisions are both of 17
great importance to transportation agencies. It is expected that rational and effective injury 18
prevention countermeasures could be developed by understanding the causes and impacts of 19
secondary collisions. Manhattan, the most densely populated urban area of New York City, is used 20
as a case study. New York City’s open data policy makes detailed crash data available to the public 21
and enables data-driven safety analysis. The objectives of this study are to explore the determinants 22
of secondary collisions and to investigate the effects of secondary collisions on injury severity using 23
a robust quantitative method. Statistical models are proposed to capture the structural relationship 24
between the contributing factors, presence of secondary collisions and injury severity levels. 25
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LITERATURE REVIEW 27 There are a few studies on secondary collisions in the literature. Bryden and Fortuniewicz (1986) (5) 28
examined a total of 3,302 barrier crashes in New York State, and found that secondary collisions 29
were present in about 25% of all cases and accounted for nearly 90% of the fatalities. Ray et al. 30
(1987) (4) collected the barrier crash data from the New York State and North Carolina State and 31
investigated the impacts of secondary collisions on injury severity. They found that occupants often 32
suffered from severe injuries in secondary collisions after their vehicles being redirected from the 33
longitudinal barriers and the risks of severe injuries were nearly three times greater when second 34
collisions were present. More recently, Gabauer (2010) (3) examined the risk of secondary collisions 35
following an initial barrier impact, based on 12-year crash data from National Automotive Sampling 36
System and Crashworthiness Data System. Two binary logistic regression model were used to 37
predict the presence of secondary collisions and severe injuries, respectively. Vehicle type and 38
barrier penetration were found to be significantly associated with the involvement of secondary 39
collisions, and secondary collisions were expected to increase the risk of severe injuries by a factor 40
of 3.53, close to the safety effect of seat belt use. In a following study by Gowat and Gabauer (2015) 41
(6) which used a similar data source and statistical methods, barrier lateral stiffness, post-impact 42
vehicle trajectory, vehicle type and pre-impact tracking condition were found to influence the 43
occurrence of secondary collisions significantly, and secondary collisions were predicted to raise the 44
likelihood of severe injuries by a factor of 6.98 versus crashes without secondary collisions. 45
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However, these previous studies are limited to the cases where secondary collisions occurred 1
after striking longitudinal barriers as the first objects. Contributing factors to other types of 2
secondary collisions (e.g. one vehicle hitting another two vehicles consecutively or one vehicle 3
hitting another vehicle and then a pedestrian) haven’t been fully explored. In addition, previous 4
studies didn’t account for the endogeneity of the presence of secondary collisions in explaining 5
injury severity. In econometrics, the endogeneity occurs when an explanatory variable is correlated 6
with the error term (7). Endogeneity can arise as a result of various causes such as omitted variable, 7
measurement error and simultaneity (8). In this study, the presence of secondary collisions is likely 8
to be endogenous to the injury severity due to the possible existence of confounding variables (e.g. 9
speeding, alcohol and fatigue) which can impact both secondary collisions and injury severity levels. 10
Ignoring the endogeneity may lead to an overestimated effects of secondary collision on injury 11
severity. 12
Addressing the endogeneity issue is gaining increased attention in studies on traffic safety 13
modeling. Rana et al. (2010) presented a detailed literature review on a variety of crash injury 14
severity models with consideration of endogeneity. In this study, we focus on the case that 15
endogeneity is caused by uncontrolled confounding variables (either observed or unobserved)1. To 16
account for this type of endogeneity, a structural model specification is generally suggested. Kim et 17
al. (1995) (9) treated crash type as an exogenous variable when modeling injury severity. Ye et al. 18
(2008) (10) advanced the joint model of crash type and injury severity by including random 19
variables representing unobserved heterogeneity. Their results confirmed the presence of unobserved 20
variables that influenced both crash type and injury severity. In the study by Eluru and Bhat (2007) 21
(11), the endogeneity effects of seat belt use on severity were examined, since unbelted drivers are 22
likely be intrinsically unsafe drivers, who are prone to a high risk of severe injuries. It was found that 23
observed variables such as gender, alcohol and vehicle type and unobserved variables could 24
significantly affect both seat belt use and injury severity. In a recent study by Abay et al. (2013) (12), 25
the joint model of seat belt use and injury severity was extended in a multivariate response structure. 26
A different finding was presented on the endogeneity effects of seat belt use that belted driers tended 27
to drive more aggressively due to the increased safety they perceived by belting up. Additionally, the 28
endogeneity effects of aggressive driving behavior (13), passenger characteristics (14) and the use of 29
airbags and antilock brakes (15) were investigated in safety literature. In this study, to address the 30
endogeneity issue, we jointly model the presence of secondary collisions and severity injury levels 31
using structural equation models (SEMs), which haven’t found widespread use among transportation 32
research. 33
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CRASH DATA AND DESCRIPTIVE ANALYSIS 35 Three-year crash record data (05/01/2008~04/30/2011) was obtained from the New York State 36
Department of Transportation2 (NYSDOT). Information pertaining to crashes is recorded in three 37
related files. The first file provides event information such as location, time, and weather. The 38
second file presents the information of crash parties (including vehicles, pedestrians and bicyclists) 39
such as the vehicle type, age and gender. Contributing factors to crashes such as speeding, alcohol 40
and fatigue can be obtained from the third file. All crashes which result in death, injury or property 41
damage over one thousand dollars are considered as reportable. Reportable crashes have complete 42
1 Another common cause of endogeneity simultaneity - at least one explanatory variables are simultaneously influenced
by the response variable – is not discussed in this study. 2 Source: http://www.dmv.ny.gov/stats.htm
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information on events, parties and contributing factors, and thus a total of 43,149 reportable crashes 1
were selected and used for safety analysis in this study. 3,245 crash events (involving 7,586 parties) 2
got involved with secondary collisions, accounting for about 7.5% of the total. Secondary collisions 3
recorded include collisions with motor vehicles, bicyclists, pedestrians and fixed objects after the 4
initial ones, and non-collision events such as overturned. Figure 1 presents the frequencies by 5
secondary collision type. Secondary collisions with motor vehicles (5,328) and fixed objects (1,810) 6
account for about 94.1% of the total. 7
8 Figure 1 Frequencies by secondary collision type. 9
10
Regarding injury severity, crashes were classified into five types: no injury (39.0%), possible 11
injury (45.8%), non-incapacitating injury (9.8%), incapacitating injury (5.0%) and fatality (0.3%). 12
From Figure 2, the proportion of serious crashes (including incapacitating injuries and fatalities) is 13
5.0% when secondary collisions are not present, and the proportion increases sharply to 9.3% when 14
secondary collisions are present. Empirically, secondary collisions tend to raise the likelihood of 15
severe injuries in crash events. 16
17
18 (a) (b) 19
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Figure 2 Proportions of serious crashes for (a) without secondary collisions present and (b) 21
with secondary collisions present. 22 23
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Driver, vehicle, road and environmental features with the potential to affect the occurrence of 1
secondary collisions and injury severity were extracted from the crash record files. Driver features 2
mostly describe the risky driving behaviors such as speeding, following closely, driving under the 3
influence of alcohol, and using cell phones while driving. Vehicle features include the brake 4
defective, oversized vehicle and the vehicle types get involved in collisions. Road features provide 5
the information mainly about the pavement, traffic control and the location where each crash 6
occurred. Environmental features include the weather (e.g. cloudy, rain and snow) and the time 7
period (e.g. nighttime or daytime). The descriptions and descriptive statistics of data are listed in 8
Table 1. 9
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1
Table 1 Descriptions and Descriptive Statistics of Key Variables (N=43,149 Crashes) 2 Variable Description Mean S.D.
Injury severity 1 for no injury; 2 for possible injury; 3 for non-incapacitating injury;
4 for incapacitating injury; 5 for fatality 1.82 0.83
Secondary collision 1 for crashes involving secondary collisions; 0 for others 0.08 0.26
Driver
Alcohol 1 for crashes with drivers involving alcohol; 0 for others 0.01 0.11
Drugs 1 for crashes with drivers involving drugs; 0 for others 0.00 0.03
Backing 1 for crashes caused by backing unsafely; 0 for others 0.02 0.13
Inattention 1 for crashes caused by driver inattention; 0 for others 0.17 0.38
Inexperience 1 for crashes caused by driver inexperience; 0 for others 0.02 0.14
Yield 1 for crashes caused by failure to yield right of way; 0 for others 0.06 0.24
Sleep 1 for crashes caused by drivers asleep; 0 for others 0.00 0.05
Follow closely 1 for crashes caused by following too closely; 0 for others 0.08 0.26
Illness 1 for crashes caused by driver illness; 0 for others 0.00 0.04
Passenger
distraction 1 for crashes caused by passenger distraction; 0 for others 0.01 0.08
Passing improperly 1 for crashes caused by passing improperly; 0 for others 0.03 0.17
Pedestrian error 1 for crashes caused by pedestrian errors; 0 for others 0.04 0.19
Control
disregarded 1 for crashes caused by disregarding the traffic control devices; 0 for others 0.03 0.17
Turning
improperly 1 for crashes caused by turning improperly; 0 for others 0.03 0.18
Speeding 1 for crashes caused by speeding; 0 for others 0.03 0.18
Lane changing 1 for crashes caused by unsafe lane changing; 0 for others 0.03 0.18
Fatigue 1 for crashes caused by driver fatigue; 0 for others 0.00 0.05
Cell phone 1 for crashes caused by using cell phones; 0 for others 0.00 0.04
Failure right 1 for crashes caused by failure to keep right; 0 for others 0.00 0.07
Rage 1 for crashes caused by aggressive driving; 0 for others 0.01 0.11
Vehicle
Brake defective 1 for crashes involving vehicles with brake defects; 0 for others 0.01 0.08
Oversized vehicle 1 for crashes involving oversized vehicles; 0 for others 0.01 0.07
Pedestrian
involved 1 for crashes involving pedestrians; 0 for others 0.19 0.39
Bike involved 1 for crashes involving bikes; 0 for others 0.07 0.25
Motorcycle
involved 1 for crashes involving motorcycles; 0 for others 0.02 0.16
Truck involved 1 for crashes involving trucks; 0 for others 0.07 0.25
Bus involved 1 for crashes involving buses; 0 for others 0.03 0.18
Road
Pavement defective 1 for crashes occurring at roads with pavement defects; 0 for others 0.03 0.16
Road surface 1 for crashes occurring at roads with adverse surface condition; 0 for others 0.17 0.38
Limited view 1 for crashes occurring at roads with limited view; 0 for others 0.01 0.09
Intersection 1 for crashes occurring at intersections; 0 for others 0.62 0.49
Traffic signal 1 for crashes occurring at roads with traffic signal; 0 for others 0.44 0.50
Stop sign 1 for crashes occurring at roads with stop sign; 0 for others 0.02 0.13
Environmental
Cloudy 1 for crashes occurring during cloudy days; 0 for others 0.11 0.32
Rain 1 for crashes occurring during rain; 0 for others 0.11 0.31
Snow 1 for crashes occurring during snow; 0 for others 0.01 0.11
Glare 1 for crashes caused by sun glare; 0 for others 0.00 0.05
Time 1 for crashes occurring during nighttime (7 pm-6 am);
0 for crashes occurring during daytime (6 am-7 pm) 0.33 0.47
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STRUCTURAL EQUATION MODEL (SEM) 1
Model Specification 2 The conceptual framework of the proposed SEM is shown in Figure 3. Secondary collision 3
propensity is a function of driver, vehicle, road and environmental features. A secondary collision is 4
predicted to occur once the secondary collision propensity is over a certain threshold. The presence 5
of secondary collisions as well as driver, vehicle, road and environmental features are used to 6
estimate the injury severity propensity which is associated with injury severity outcome. To assess 7
the temporal effects, the variable time (0 for daytime and 1 for nighttime) is used as a moderator in 8
the proposed SEM framework. Crash events are classified into the daytime and nighttime groups. 9
The model parameters including the coefficients of explanatory variables and thresholds can be 10
constrained to be the same or allowed to vary between groups. The types of constraints we used are 11
described in the section of “Modeling Results”. 12 13
14 Figure 3 Conceptual framework of the proposed structural equation model (SEM). 15
16
The formulation for the proposed SEM is expressed as: 17
* '
*
* '
1 *
1, , 0,
,
i i i
i i i
i i i i
k k
i i
sc
sc if sc sc otherwise
y sc
y k if y
α z
βx (1) 18
where ( 1, 2, ..., )i i N is an index for crashes, *
isc is the latent secondary collision propensity in 19
crash i , isc is the secondary collision indicator with 1 indicating the presence of secondary 20
collisions, iz is a (M×1) vector of exogenous variables that explains the presence of secondary 21
collisions in crash i , α is a (M×1) vector of coefficients corresponding to iz , i is a normally 22
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distributed error term with mean 0 and variance 2
, is the threshold corresponding to the 1
presence of secondary collisions, *
iy is the latent injury severity propensity for crash i , iy is the 2
observed injury severity level (1 for no injury, 2 for possible injury, 3 for non-incapacitating injury, 3
4 for incapacitating injury, and 5 for fatality) for crash i , ix is a (N×1) vector of exogenous 4
variables that affects the injury severity propensity, β is a (N×1) vector of coefficients 5
corresponding to ix , is the effect of the presence of secondary collisions on the injury severity, i 6
is a normally distributed error term with mean 0 and variance 2
, ( 1, 2, ..., )k k K is an index to 7
represent injury severity outcome, and k is the upper threshold corresponding to the injury severity 8
outcome k (with 0 1 5... ,
0 , 5 ). 9
Mean- and variance- adjusted weighted least squares (WLSMV) estimator is robust for the 10
estimation of models with ordered-categorical response variables (16). Therefore, we used the 11
WLSMV estimator to estimate the parameters of the proposed SEMs. 12
13
Model Assessment 14
A set of statistical indices can be used to assess the performance of the SEMs. Chi-square (2 ) tests 15
are widely used to indicate the model goodness of fit. The null hypothesis of a chi-square test is that 16
the proposed model can fit the data, so insignificant results are desired. However, the chi-square tests 17
always tend to be statistically significant for models with large sample size (16). The chi-square 18
difference statistic (2
D ) measures the statistical significance of the decrement/improvement in 19
model overall fit as free parameters are eliminated/added (16). It is appropriate to use chi-square 20
difference statistics to compare two hierarchical SEMs estimated with the same data, even if the 21
sample size is large. 22
Another widely-used measure of model fit is the root mean square error of approximation 23
(RMSEA). The RMSEA is computed based on the chi-square statistic, but it considers the model 24
complexity by including degrees of freedom. The RMSEA is given by: 25
2
( 1)
M M
M
dfRMSEA
df N
(2) 26
where 2
M is the chi-square statistic for the proposed model M , Mdf indicates the degrees of 27
freedom and N is the number of samples. The RMSEA ranges from 0 to 1, with smaller value 28
indicating a better fit. Generally, a model with RMSEA less than 0.05 is favored (16). 29
The comparative fit index (CFI) and Tucker Lewis index (TLI) measure the relative 30
improvement in the fit of the proposed model over that of a baseline model (null model with no 31
explanatory variables) (16). The CFI and TLI penalize model complexity using 2
M Mdf and 32
2 /M Mdf , respectively. The CFI and TLI are given by: 33
2
21 M M
B B
dfCFI
df
(3) 34
2 2
2
/ /
/ 1
B B M M
B B
df dfTLI
df
(4) 35
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Xie, Ozbay and Yang
where 2
B and Bdf are the chi-square statistics and degrees of freedom for the baseline model, 1
respectively. A CFI/TLI above 0.9 indicates a good fit to the data (17). 2
3
MODELING RESULTS 4 The SEM framework in Figure 3 is used to model the presence of secondary collisions and injury 5
severity levels. To test parameter constraints over groups, three SMEs were developed with equal 6
thresholds (the threshold estimates are constrained to be the same for the daytime crash model and 7
the nighttime crash model), equal regressions (the regression coefficients are constrained to be the 8
same for the daytime crash model and the nighttime crash model) and no constraint (the thresholds 9
and regression coefficients of the daytime and nighttime crash models are set to be different). Only 10
the explanatory variables with statistically significant effects are used in the final models. Each SEM 11
has the same selection of explanatory variables so effective model comparison can be performed. 12
Statistical indices of those three SEMs are reported in Table 2. 13
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Table 2 Statistical Indices of Structural Equation Models (SEMs) with Equal Thresholds, 15
Equal Regressions and No Constraint 16
Structural Equation Models (SEMs)
Equal Thresholds Equal Regressions No Constraint
Chi-square statistics Chi-square 417.710 432.345 344.922 Degrees of freedom 23 49 20
P-value 0.000 0.000 0.000
RMSEA 0.028 0.019 0.027
CFI 0.969 0.970 0.975
TLI 0.895 0.952 0.901
17
Considering the great number of samples (N=43,419) used for model development, the 18
significant results of chi-square tests can be ignored. All the SEMs have RMSEAs less than 0.05, 19
suggesting a good fit to the data. Additionally, the CFIs and TLIs of all the SEMs are greater than 20
0.9, except the TLI for the SEM with equal thresholds (0.895) which is slightly lower than the 21
acceptance criteria. Chi-square difference tests were conducted to compare the three SEMs 22
developed. The SEM with no constraint can result in a smaller chi-square at the expense of lower 23
degrees of freedom. The chi-square of the SEM with no constraint is 72.788 (417.710-344.922) less 24
than that of the SEM with equal thresholds, with degrees of freedom decreasing by 3 (23-20). The p-25
value of the chi-square difference statistic is greater than 0.99 (2 (72.788, 3) 0.99 ), and it 26
indicates that the SEM with no constraint has a significantly smaller chi-square and a better fit than 27
the SEM with equal thresholds. Similarly, it is found that the SEM with no constraint outperforms 28
the SEM with equal regressions by presenting a significantly lower chi-square (p-value=29 2(87.423, 29) 0.99 ). 30
Due to its better performance, the SEM with no constraint is used for variable interpretation 31
and its estimates of parameters are presented in Table 3. To evaluate the endogeneity effects, 32
standard probit models were also developed and the estimation results are reported in Table 4. 33
Statistic indicator p-value was used to test the significance of explanatory variables. All the 34
explanatory variables were regarded as statistically significant at 95% level (p-values<0.05) in the 35
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proposed SEM, whereas the variables sleep and limited view were found to be insignificant in the 1
standard probit model for the nighttime secondary collisions. 2
3
Table 3 Estimates of the Structural Equation Model (SEM) with No Constraint 4
Daytime Nighttime
Secondary Collision Injury Severity Secondary Collision Injury Severity
Estimate P-value Estimate P-value Estimate P-value Estimate P-value
Secondary collision - - 0.243 0.000 - - 0.217 0.000
Driver
Alcohol 0.866 0.000 0.370 0.000 0.593 0.000 0.407 0.000
Drugs 0.800 0.001 0.800 0.000 0.657 0.037 0.399 0.049
Inattention 0.236 0.000 0.061 0.001 0.156 0.000 0.080 0.003
Inexperience 0.431 0.000 - - 0.384 0.000 - -
Yield - - 0.061 0.035 - - 0.139 0.001
Sleep 0.486 0.019 - - 0.555 0.015 - -
Illness - - 1.668 0.000 - - 1.192 0.000
Control
disregarded 0.290 0.000 0.456 0.000 0.328 0.000 0.405 0.000
Speeding 0.730 0.000 0.374 0.000 0.637 0.000 0.318 0.000
Fatigue 0.436 0.034 0.502 0.002 0.450 0.034 0.480 0.002
Cell phone - - 0.507 0.000 - - 0.480 0.043
Vehicle
Brake defective 0.574 0.000 0.473 0.000 0.673 0.000 0.405 0.004
Motorcycle
involved - - 1.265 0.000 - - 1.144 0.000
Bike involved - - 1.498 0.000 - - 1.232 0.000
Pedestrian
involved -0.498 0.000 1.496 0.000 -0.666 0.000 1.329 0.000
Road
Pavement
defective 0.470 0.000 0.178 0.000 0.396 0.000 0.229 0.000
Intersection - - 0.149 0.000 - - 0.080 0.000
Limited view 0.426 0.001 - - 0.361 0.027 - -
Environmental
Rain 0.124 0.001 - - 0.101 0.017 - -
Threshold
1 - - 0.246 0.000 - - 0.028 0.117
2 - - 1.899 0.000 - - 1.605 0.000
3 - - 2.599 0.000 - - 2.243 0.000
4 - - 3.922 0.000 - - 3.420 0.000
1.441 0.000 - - 1.219 0.000 - -
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Table 4 Estimates of the Standard Probit Models 1
Daytime Nighttime
Secondary Collision Injury Severity Secondary Collision Injury Severity
Estimate P-value Estimate P-value Estimate P-value Estimate P-value
Secondary collision - - 0.553 0.000 - - 0.480 0.000
Driver
Alcohol 0.848 0.000 0.487 0.000 0.592 0.000 0.482 0.000
Drugs 0.809 0.001 0.913 0.000 0.625 0.037 0.473 0.028
Inattention 0.238 0.000 0.102 0.000 0.143 0.000 0.106 0.000
Inexperience 0.441 0.000 - - 0.369 0.000 - -
Yield - - 0.060 0.038 - - 0.128 0.002
Sleep 0.433 0.033 - - 0.339 0.164 - -
Illness - - 1.581 0.000 - - 1.092 0.000
Control
disregarded 0.220 0.001 0.510 0.000 0.246 0.000 0.450 0.000
Speeding 0.761 0.000 0.471 0.000 0.682 0.000 0.390 0.000
Fatigue 0.495 0.016 0.615 0.000 0.469 0.027 0.605 0.000
Cell phone - - 0.502 0.000 - - 0.473 0.050
Vehicle
Brake defective 0.592 0.000 0.558 0.000 0.671 0.000 0.474 0.000
Motorcycle
involved - - 1.286 0.000 - - 1.175 0.000
Bike involved - - 1.537 0.000 - - 1.275 0.000
Pedestrian
involved -0.505 0.000 1.416 0.000 -0.662 0.000 1.229 0.000
Road
Pavement
defective 0.503 0.000 0.261 0.000 0.446 0.000 0.280 0.000
Intersection - - 0.166 0.000 - - 0.103 0.000
Limited view 0.278 0.025 - - 0.261 0.117 - -
Environmental
Rain 0.133 0.001 - - 0.109 0.011 - -
Threshold
1 - - 0.286 0.000 - - 0.077 0.000 2 - - 1.954 0.000 - - 1.668 0.000 3 - - 2.659 0.000 - - 2.312 0.000 4 - - 3.992 0.000 - - 3.498 0.000
1.587 0.000 - - 1.403 0.000 - -
2
3
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DISCUSSION 1
Variable Interpretation 2 The contributing factors to severe injuries have been fully explored in the literature, but limited 3
studies are available on the determinants of the secondary collisions. According to Table 3, 13 4
explanatory variables are found to contribute to the presence of secondary collisions and 16 affect 5
the injury severity of crashes. The effects of driver, vehicle, road and environmental features on 6
secondary collisions and severe injuries are discussed in the following paragraphs. 7
Drivers under the influence of alcohol are more likely to get involved with secondary 8
collisions relative to those who are sober, presumably because the alcohol would affect the judgment, 9
reasoning and reaction of drivers. It is also found that drinking alcohol may lead to aggressive 10
driving and thus severe injuries, consistent with the earlier studies such as (9, 11, 12, 18). Similar to 11
the impact of alcohol, taking drugs would make drivers lose consciousness and result in more 12
secondary collisions and severe injuries. Consistent results have been obtained in the previous 13
studies such as (9, 18). For crashes caused by driver inattention, the likelihoods of secondary 14
collisions and severe injuries are expected to be higher. David and Linda (2008) (19) found a higher 15
likelihood of severe injuries for passengers of teenage drivers when their drivers were distracted by 16
devices or passengers. Zhu and Srinivasan (2011) (20) also found driver distraction was associated 17
with higher severity levels. Inexperienced drivers are prone to a higher risk of secondary collisions, 18
possibly due to their inability to control the vehicles after the initial collisions. Injury severity levels 19
rise substantially for drivers who suffer from illness, since they are in vulnerable situations. The 20
impact of illness was considered in the study by Zhu and Srinivasan (2011) (20), but no significant 21
relation were found between illness and severe injuries because of the missing data issue. If drivers 22
fail to yield the right of way, the risk of getting severely injured would increase. It is intuitive that 23
drivers who fall asleep can lead to more chances of secondary collisions since they couldn’t react in 24
time even after the initial collisions. If the drivers disregard the traffic control devices, more likely 25
the secondary collisions and severe injuries would occur. Speeding is predicted to increase the 26
likelihood of secondary collisions, presumably because speeding vehicles couldn’t be slowed down 27
immediately and have higher possibility to strike multiple objects. Speeding is also found to be 28
associated with greater severe injury propensity, a result observed in the previous studies such as (21, 29
22). Fatigued drivers are prone to higher risks of secondary collisions and severe injuries, possibly 30
because they are unable to make a quick reaction. The safety effect of fatigue was investigated in the 31
study by Zhu and Srinivasan (2011) (20). Although variables related to the fatigue turned out to be 32
insignificant predictors of injury severity, they stated the possible reason that the effect of fatigue 33
could be partially captured by variables such as time of day and crash type. In addition, the use of 34
cell phone would lead to a high risk of severe injuries. According to the study by McEvoy et al. 35
(2005) (23), cell phone use caused a fourfold increase in crash injuries resulting in hospitalization. 36
David and Linda (2008) (19) found that teenage drivers had an increased likelihood of severe 37
injuries if distracted by cell phones. 38
Vehicles with brake defects tend to be exposed to secondary collisions and severe injuries, 39
since those vehicles couldn’t stop fast enough. Khattak et al. (2003) (18) and Chen and Chen (2011) 40
(24) found defective truck brakes were significantly associated with severe injuries. It is found that 41
pedestrian crashes are less likely to have secondary collisions. Crashes involving motorcycles, bikes 42
and pedestrians are prone to a higher risk of severe injuries, since motorcyclists, bicyclists and 43
pedestrians are vulnerable road users relative to vehicle occupants. Chang and Wang (2006) (25) 44
stated that motorcyclists, bicyclists and pedestrians received less protection and were expected to 45
have a greater likelihood of severe injuries compared with the automobile drivers. Valent et al. (2002) 46
12
Xie, Ozbay and Yang
(26) found crashes involving motorcyclists, bicyclists and pedestrians were associated with high 1
death risk. 2
Regarding the road features found significant, secondary collisions are more likely to happen 3
at the roads with pavement defects and limited view. Pavement defects can also increase the risk of 4
severe injuries. Chang and Wang (2006) (25) found injury severity had a serious correlation with the 5
pavement condition. Milton et al. (27) found increasing pavement friction leaded to more severe 6
injuries. However, opposite finding is stated in the study by Clifton et al. (2009) (28). Furthermore, 7
crashes occurring at intersections tend to be involved with severe injuries in comparison with those 8
occurring at road mid-blocks. The study by Yamamoto and Shankar (2004) (29) suggested a lower 9
driver injury risk at intersections for vehicle-fixed object crashes, because of the lower driving speed 10
and more attention by drivers when approaching the intersections. However, in this study which 11
considers all types of crashes, head-on and right-angle crashes are far more likely to occur at 12
intersections than mid-blocks, and these crash types are associated with a high risk of severe injuries 13
(10). 14
Furthermore, in rainy days, more secondary collisions are found to happen due to the slippery 15
roadway and affected view. However, no weather feature is found to significantly impact the injury 16
severity in this study. Different results were obtained in the literature on the safety impacts of 17
weather. Eluru (2008) (30) found crashes occurring under adverse weather conditions increased the 18
likelihood of fatally injured. On the contrary, Abdel-Aty (2003) (22) found drivers were less likely 19
to experience severe injuries under adverse weather condition, because drivers tended to slow down 20
and kept a safe distance from other vehicles. 21
Considering the temporal effects, the parameter estimates of the daytime and nighttime 22
models are compared. Explanatory variables including sleep, control disregarded, fatigue, brake 23
defective and pedestrian involved have greater impacts on the secondary collision propensity during 24
the nighttime compared with the daytime. On the other hand, the effects of explanatory variables 25
including alcohol, inattention, yield and pavement defective on the severity injury propensity are 26
found to be greater during the nighttime compared with the daytime. According to the threshold 27
parameters ( ) which map the secondary collision propensity to the observed secondary collision 28
occurrence, the smaller threshold value in the nighttime secondary collision model implies that 29
secondary collision are more likely to occur during the nighttime. Similarly, the threshold for each 30
injury severity level (k ) is lower for nighttime crashes than that of the daytime crashes, indicating 31
that it is more likely to sustain severe injuries at night. The study by Abdel-Aty (2003) (22) also 32
revealed an increased severity risk for crashes occurring at night. Kockelman and Kweon (2002) (31) 33
found later-night driving on Friday, Saturday and Sunday exhibited a high likelihood of severe 34
injuries. 35
36
Comparison of the SEM and the Probit model 37 The parameter estimates of the SEM with no constraint (presented in Table 3) are further compared 38
with those of the standard probit models (presented in Table 4) which estimate the presence of 39
secondary collisions and injury severity independently. The percentage difference of parameter 40
estimates are presented in Table 5. According to Table 5, most coefficient estimates of secondary 41
collision determinants in the proposed SEM are similar to those in the standard probit models, except 42
a few variables such as control disregarded and limited view. On the other hand, the effects of 43
confounding variables including the variables alcohol, inattention, speeding, fatigue and pavement 44
defective on injury severity are estimated quiet differently in the SEM and the standard probit 45
13
Xie, Ozbay and Yang
models. The standard probit models overestimate the safety effects of those confounding variables 1
by mixing the direct effects and indirect effects which are mediated by the presence of secondary 2
collisions in the SEM. For instance, according to SEM estimates in Table 3, the direct effects of 3
drinking alcohol on injury severity propensity during daytime is 0.370, and meanwhile drinking 4
alcohol contributes to severe injures indirectly by increasing the secondary collision propensity by 5
0.866. However, according to Table 4, the effects of drinking alcohol on severity propensity during 6
daytime is estimated to be 0.487 by the standard probit models which cannot distinguish the direct 7
and indirect effects of drinking alcohol. Most importantly, the standard probit models significantly 8
overestimate the effects of secondary collisions on injury severity propensity by 127.6% for daytime 9
crashes and by 121.2% for nighttime crashes because endogeneity effects are ignored in the 10
estimation. The endogeneity issue is caused by the fact that secondary collisions are associated with 11
risk factors such as speeding, alcohol and fatigue which contribute to severe injuries. On the other 12
hand, the estimates of the SEM present the “pure” effects of secondary collisions on injury severity 13
by accounting for its endogeneity effects. 14
15
Table 5 Percentage Difference of Parameter Estimates between the Structural Equation Model 16
(SEM) with No Constraint and the Standard Probit Models 17
Daytime Nighttime
Secondary Collision Injury Severity Secondary Collision Injury Severity
Estimate Difference Estimate Difference Estimate Difference Estimate Difference
Secondary collision - 127.6% - 121.2% Driver
Alcohol -2.1% 31.6% -0.2% 18.4% Drugs 1.1% 14.1% -4.9% 18.5% Inattention 0.8% 67.2% -8.3% 32.5% Inexperience 2.3% - -3.9% - Yield - -1.6% - -7.9% Sleep -10.9% - -38.9% - Illness - -5.2% - -8.4% Control
disregarded -24.1% 11.8% -25.0% 11.1% Speeding 4.2% 25.9%* 7.1% 22.6% Fatigue 13.5% 22.5%* 4.2% 26.0% Cell phone - -1.0% - -1.5%
Vehicle Brake defective 3.1% 18.0% -0.3% 17.0%
Motorcycle
involved - 1.7% - 2.7% Pedestrian
involved 1.4% -5.3% -0.6% -7.5% Bike involved - 2.6% - 3.5%
Road Pavement
defective 7.0% 46.6% 12.6% 22.3% Intersection - 11.4% - 28.8% Limited view -34.7% - -27.7% -
Environmental
Rain 7.3% - 7.9% -
14
Xie, Ozbay and Yang
SUMMARY AND CONCLUSIONS 1 This study investigates the contributing factors to secondary collisions and the effects of secondary 2
collisions on injury severity levels using the crash data from Manhattan. Structural equation models 3
(SEMs) are proposed to jointly model the presence of secondary collisions and injury severity levels. 4
To assess the temporal effects, the variable time is used as a moderator in the proposed SEM 5
framework. Three SMEs were developed with equal thresholds, equal regressions and no constraint 6
for the daytime and nighttime crash groups. The results of chi-square difference test indicate that the 7
SEM with no constraint outperforms the others by presenting a significantly lower chi-square 8
statistic. 9
Due to its better performance compared with other models, the SEM with no constraint is 10
used to investigate the effects of driver, vehicle, road and environmental features on secondary 11
collisions and severe injuries. 13 explanatory variables are found to contribute to the presence of 12
secondary collisions, including alcohol, drugs, inattention, inexperience, sleep, control disregarded, 13
speeding, fatigue, brake defective, pedestrian involved, pavement defective, limited view and rain; 14
while 16 were expected to increase the risk of severe injuries, including the presence of secondary 15
collision, alcohol, drugs, inattention, yield, illness, control disregarded, speeding, fatigue, cell phone, 16
brake defective, motorcycle involved, bike involved, pedestrian involved, pavement defective and 17
intersection. Considering the temporal effects, the parameter estimates of the daytime and nighttime 18
models are compared, and the results indicate that it is more likely to sustain secondary collisions 19
and severe injuries at night. In addition, the parameter estimates of the proposed SEM are further 20
compared with those of the standard probit models which estimate the presence of secondary 21
collisions and injury severity independently. The standard probit models are found to overestimate 22
the safety effects of confounding variables by mixing the direct and indirect effects. It is found that 23
the standard probit models significantly overestimate the effects of secondary collision on injury 24
severity propensity by 127.6% for daytime crashes and by 121.2% for nighttime crashes because 25
endogeneity effects are ignored in the estimation. 26
This study contributes to the literature by fully investigating the contributing factors to 27
secondary collisions and estimating the safety effects of secondary collisions after adjusting for the 28
endogeneity effects. Understanding the causes and impacts of secondary collisions can help the 29
transportation agencies and automobile manufacturers develop effective injury prevention 30
countermeasures. In addition, this study shows the potential of using SEMs in exploring the 31
structural relationship between risk factors and safety indicators, regarding that SEMs haven’t been 32
widely exploited in the traffic safety research. For future study, we will attempt to use multilevel 33
SEMs to accommodate the hierarchy of crash data (e.g. with crash characteristics being the first 34
level of dataset, vehicle characteristics being the second level and driver characteristics being the 35
third level). 36
37
ACKNOWLEDGMENTS 38 The work is partially funded by Urban Mobility & Intelligent Transportation Systems (UrbanMITS) 39
laboratory, Center for Urban Science and Progress (CUSP) and Department of Civil and Urban 40
Engineering at New York University (NYU). The authors would like to thank the New York State 41
Department of Transportation for providing data for the study. The contents of this paper reflect 42
views of the authors who are responsible for the facts and accuracy of the data presented herein. The 43
contents of the paper do not necessarily reflect the official views or policies of the agencies. 44
45
46
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