Transportation Security, Environmental Protection, and Sustainable Development

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Analysis of Factors Affecting Traffic Accident Severity Based on Heteroskedasticity
Ordinal Logit
Zhangcun Yan1; Xiaozhao Lu2; and Wanxin Hu3
1Key Laboratory of Road and Traffic Engineering of the Ministry of Education, Tongji Univ.,
Shanghai 201804. E-mail: 1950141244@qq.com
2School of Transportation and Logistics, Southwest Jiaotong Univ., Chengdu 610031. E-mail:
18815285292@163.com
3College of Computer Science, South-Central Univ. for Nationalities, Wuhan 430074
ABSTRACT
In order to identify causational information for accidents, propose preventive
countermeasures, and reduce the number of accident casualties, statistical models and
econometric models are prevalently employed to analyze the historical accident data. However,
due to certain factors including the complexity of accident data and the limitations of models,
many problems remain to be explored in accident analysis. Based on previous research findings,
this study conducted a crash severity analysis by the following steps: the classification of road
accident severity, identification of miscellaneous factors (e.g., driver, vehicle, roads,
environment, and management), introduction of covariance theory to analyze the interaction
effects among factors. Methodologically, this study used the heteroskedasticity ordinal logit
(HORL) model to investigate road traffic accident data, which also utilized T test, information
criterion test, likelihood ratio test, chi-square test, and pseudo chi-square test to test parameter
estimation and model fit. The accident data were sampled from 5,023 crash records in the HSIS
(Highway Safety Information System) database housed in North Carolina, which verified the
statistical methodology employed herein. The research found road accident data has
heteroskedasticity, and orthogonalization processing and independent distribution processing can
avoid heteroskedasticity. The fixed-variance logit model has better applicability to this. HORL is
specific to the treatment of accident data with variable variance, which can effectively capture
factor heterogeneity and tap into more potential latent variables.
Keywords: safety control, traffic accident severity, Heteroskedasticity Ordinal Logit model
1 INTRODUCTION
With the societal economy rapidly growing, the transportation safety in China has been
substantially improved in recent decades, but compared with most of developed countries a
phenomenal gap still exists in the research area of roadway safety. Roadway accident data from
the National Bureau of Statistics reveal that the total number of roadway accidents in China
decreased by 50.25% from 2006 to 2015, the total number of accidents and injuries decreased by
53.64%, the number of roadway accident deaths decreased by 35.14%. Sex has decreased, but
the total number of road traffic accidents in China is still high compared to developed countries.
In 2015 alone, the total number of roadway accident deaths amounted to 58,022, accounting for
87.67% of the total number of nationwide accident casualties in that year, traffic safety issues
have become a critical factor which retards the development of transportation industry.
Therefore, it is imperative to boost safety research which can explore the factors contributory to
the accident severities, understand the causational mechanism for accident occurrences,
implement effective management countermeasures, alleviate accident casualties and property
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damages, and subsequently enhance the safety level of transportation infrastructure systems.
2 RELEVANT STUDIES
With different research purposes and distinctive data sets, the research community resorts to
a myriad of statistical models, econometric models and other nonparametric models to identify
significant factors which influence the roadway accident severities usually in terms of property
damage only (PDO), injury and fatality. For example, Ma Zhuanglin et al used neural network
method, Ordered Logit (ORL) model and generalized ordered Logit model to establish a
highway tunnel accident severity prediction model, which analyzed time, tunnel environment
and traffic dynamics to traffic accidents. It is found that the ratio of ADT to AADD and the ratio
of large vehicles have the greatest impact on the accident severity. The weather, line shape, slope
and accident location have a significant impact on the severity of the accident; Lu G et al
researched the severity of road median crossover accidents based on the accident data of 2001-
2007 in Wisconsin, and the Ordinal Logistic and Ordinal Probit severity models were
established. It was found that the use of alcohol and drugs, road alignment, road surface
conditions, speed limit and other factors have significant impacts on severities; Hu et al. used the
Ordinal Logistic model to study the impact of driver, vehicle, and environmental factors on the
severity of the accident, and based on the data from the North Carolina North Rollover accident
data from 2010 to 2014, It was found that the impact of seat belts, road conditions and road
alignment on rollover accidents was significantly greater than 95%; To study the internal
correlation of collision accidents, Dissanayake[8] established a binary Logit regression model to
determine the seriousness of driver injury and the severity of vehicle collision in order to
determine the factors affecting the severity of injuries among elderly drivers in collision with
fixed objects. High degree of integration and strong predictive ability; Sullman used a two-item
Logit regression model to analyze the impact of risk factors such as truck driver's personal
characteristics and abnormal driving behavior on the accident. Young used a two-entry Logit
regression model to analyze the effects of wind-related factors (including wind speed, wind
direction, etc.) on vehicle rollover accidents; GF Ulfarsson used Multinominal Logit Model
(MNL) to study the effect of gender on the severity of injury in different vehicle types. It is
found that there are important behavioral and physiological differences between male and female
drivers; P Penmetsa used the MNL model to study the influence of pavement features on the
severity of accidents; Z Zeng proposed a generalized nonlinear MNL model to capture The
relationship between the unobserved and variable variance variables affecting the severity of the
accident.
In summary, the Logit model can be widely used in roadway accident analysis and
prediction. The multinomial model is commonly used for multi-class unordered variables, and
the ordered model is more suitable for multi-classes with different degrees. However, there are
certain idealized assumptions underlying the models, and misuse of models would reduce their
explanatory powers. One assumption is about error term
i

in the MNL and the ORL model: the
variance is assumed to be constant. Due to the influence of data type and data error, the error
term variance is difficult to be accurately represented by a constant value. An oversimplified
application of such a model will compromise the validity and accuracy of the modeling results.
As a research effort to patch this modeling hole, this paper invited a variable variance model to
identify the significant factors which affect the severities of roadway accidents.
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3 MODEL STRUCTURE
The ORL model of variable variance introduces the heteroscedasticity into the error term of
selected utility alternatives, so the cross elasticity between the selected alternatives is inconstant.
This step structurally modifies the independent and identical distribution (IID) assumption of the
fixed-variance MNL and ORL models, which makes the models more realistic as to the data and
have stronger interpretation. The model assumes that the severity level of the accident is y, and
various factors affecting the severity are denoted by X, and coupling relationship can be
expressed as:
*T
i i i
yB

X
(1)
where :
12
, , , , , ; 1, , ; 1,
T
i i i ik N K
X X X X i N k K  X
: Observed value vector for the
predictor variable;
 
01
, , , , ,
kK
B
   
  
: To interpret the variable corresponding parameters;
ik
X
: Observed for the
i
influencing factor of the k accident；
N : The total number of accident samples observed;
K : The number of influencing factors for each accident;
i

: Random error term represents the sum effect of other factors which are difficult to
observe, quantify but have impacts on the severities of accidents.
it is assumed that the variances of the random error terms
i

of all observations are constant and
equal. Differently, the HORL model assumes the variance of the random error term
i

of each
observation varies, but the variances are still assumed to be independent.
The HORL model assumes that
i

in the equation (1) obeys the double exponential
distribution with the parameter
 
,

, and its variance satisfies the following formula (2):
   
2
2
i i i
Var exp Z
  



(2)
where :
2
i

is the i-th variance of the unobservable error term which affects severity；
i
Z
is a set of variances of the error terms which is connected with certain explanatory
variables of the i-th observation;

represents a collection of related parameters;
HORL has the probability density function in terms of:
     
2
exp / 1 exp
i
f X X

   


.
Its cumulative distribution function is
   
,
i i i
F E Z
  

and the probability that the i-th
accident has a severity of j is formulated in (3):
1
*
1
Pr( ) Pr( ) j i j i
jj
ii
xx
y j y F F


  
 



   
     
   
   
(3)
It is parameterized by an exponential function explicitly, and its expression is (4):
   
1
1
Fx exp x

(4)
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3.1 Model calibration
The maximum likelihood estimation method is used to estimate the coefficient

of each
influencing factor, and the maximum value of the log-likelihood function is obtained to obtain
the likelihood function expression (5):
1
11
ij
W
Jn j i j i
ji ii
xx
L F F
   





   


   
   


(5)
where :
ij
W
is a weight or other factor regarding the damage level j of the i-th observation object
(such as a passenger); Get the parameter estimate
 
01
, , , ,
jJ
   
   Γ
and
 
01
, , , ,
jJ
   
  B
.
After solving the model through MLE method, the variable screening method is used to filter
the explanatory variables, and the significant variables are gradually eliminated until a
parsimonious regression model is obtained.
3.2 Model validation
The HORL model uses the z test to perform variable screening. The information criterion is
used to test the model goodness-of-fit, the likelihood ratio test, the chi-square test, the pseudo R-
square test are used for parameter estimation test.
1. The Z test
The Z test is mainly used to test the influence of explanatory variables on the explanatory
variables. Assume any parameter
0 0 1 0
Η : ,Η :
   

among them
 
0,1,2,3, ,
iip


, test
statistic z value :
 
~1Z n p  
i
i
i
β
ZSeβ
(6)
Where:
ˆ

Se
is the standard error of the regression coefficient estimator
i
β
sampling
distribution.
When it given significance level
α
, the critical value of the rejection domain
 
2
1Z n p


and the statistic p value are determined according to the degree of freedom
1np
, and if
 
2
1Z Z n p

  
or
pα
, the null hypothesis is rejected, indicating that the regression
coefficient
i
β
is significant, There is a clear linear relationship between
i
X
and Y.
2. Pseudo
2
R
test
In linear regression: the ratio of the squared error of the regression to the sum of the squares,
which is used to describe the ratio of the sum of the squares of the residuals of the fitted model to
the number of likelihood functions. The pseudo is expressed as:
 
0
0
22
2
s
LL LL
LRI LL
  

(7)
Similar to
2
R
, LRI ranges from 0 to 1, and LRI indicates that the independent variable is
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completely uncorrelated with the dependent variable; as the LRI gradually approaches, it
indicates that the model fitting effect is more significant.
3.3 Marginal effect analysis
The marginal effect of the HORL is more complicated than the ORL because the explanatory
variables not only affect the severity but also the variance. The marginal effect of the explanatory
variable
t
X
in the HORL model is Equation (8):
 
11
t1
( 1) 1
j j j j
tt
t j j
t
x x x x
py f f x f f
x
       

  
     


   

      

         
       
   
         
(8)
where :
t
X
represents the observed value of the explanatory variable;
t
X
represents the average of the observed values of the explanatory variables;

represents the mean of the variance of the explanatory variables;
X
represents the mean vector of the explanatory variable;
t

represents the coefficient of the explanatory variable
t
X
when the severity level is y;
γt
represents the coefficient of the same explanatory variable of variance.
It can be seen from Equation (8) that the marginal influence of the t-th explanatory variable is
not only related to its own coefficient, but also related to its mean value and norm variance
coefficient value. Therefore, even the marginal effects of extreme probabilities cannot be derived
from simple parameter estimates. When the explanatory variable
t
x
is only used to explain the
accident severity y, its marginal effect can be reduced to (9), and the marginal influence of the
explanatory variable can be reduced to the ORL model of the same variance.
 
1
1jj
t
t
xx
py ff
x
    
  


   


  

   
   

   

(9)
4 DATA DESCRIPTION
The 2010-2014 accident data of North Carolina were obtained from the US HSIS (Highway
Safety Information System) database, and the bicycle accident with collision fixtures is selected
as the research object. The HSIS Accident data were collected according to accident information,
driver information, vehicle information, and road information. There are nearly 300,000 data
samples per year. Here, through VBA programming, the four types of data are integrated by
accident number (caseno), and 5023 complete crash fixture bicycle accident data are extracted,
screened, cleaned and analyzed as a study case to test the subject model. The spatial distributions
of the accidents are shown in Figure 1.
4.1 Collision fixture accident variable selection
Referring to the North Carolina Data Guide [18], the road accident severity level is the
explanatory variable, and the 26 variables, based on traffic participants, driving vehicles, roads,
environment and traffic management, are selected as explanatory variables. Explanatory
variables and human related factors are: driver's injury severity, alcohol concentration, gender,
age, physical state of the accident, number of passengers in the accident vehicle; car related
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factors are: vehicle type, vehicle service life, vehicle damage before the accident Degree, road
related factors are: road grade, road geometry, road function type, pavement material, road
width, road type, central isolation type, midline width, number of vehicles, truck line type (North
Carolina restricts the route of large trucks), right side shoulder type, etc. environmental related
factors are: topographic factors, weather, light type, etc. traffic management related factors are
control type, speed limit, whether to carry out hazardous chemicals detection, etc. the specific
description of the variables and value processing see Table 1 shows.
Figure 1 Distribution of bicycle accidents in North Carolina collision fixtures from 2010 to
2014
4.2 Collision fixture accident variable processing
The types of raw data are complex, including discrete, continuous, qualitative, and
quantitative variables. In order to adapt to the model for analysis, it is necessary to segment the
continuous variables, introduce the dummy variables, and introduce the corresponding dummy
variables in combination with the qualitative variable categories. Divide the hazmat, drv_sex,
sob_test, rdsurf, light, rd_char1, trf_cntl, trk_rte, surf_typ, med_type, 0-1, which are two
opposite results, such as: pavement type, 0 is a dry road for driving , 1 is not conducive to
driving, there is water, rain and snow. The continuous variables such as age, number of lanes,
and speed limit are segmented, and dummy variables are introduced to discretize them. The
process is shown in the table 2.
5 SEVERITY ANALYSIS
Firstly, the variables such as the degree of vehicle damage, the degree of driver injury, and
the total number of passengers are removed. These variables are directly related to the severity of
the accident, but they do not make much sense. The results of the correlation analysis of the
explanatory variables are shown in the attached table. By preliminary screening, the variables
with correlation p values less than 0.05 were excluded, and the correlation analysis excluded the
variable hazmat. When using the HORL model, the variance variable test should be performed
on the explanatory variables. The principle of the test is: firstly, the explanatory variable has
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variable variance for parameter estimation, and the significance is tested. If the p value is large,
the original hypothesis is rejected, and the variable has no variation. On the contrary, there is a
varied variance. The explanatory variables are filtered using the backward deletion method. The
modeling process is shown in Table 4.
5.1Variable variance ORL accident severity analysis model
Using the HORL model for regression, a vicious accident was selected as a reference
accident. First, the variance-related variable is selected, and the initial regression fitting is
performed on both variables simultaneously with the variance and the variable variance. In the
results, the two types of estimation parameters are basically the same, but the parameter
estimation is significantly different. For example, the variable sob_test determines the variance
test parameter significance test p value is 0.312, the variance value p value is less than 0.0001;
the trk_rte constant variance p value is 0.373, The variance p value is 0.009, and such variables
are significant variables in the non-significant variable variance regression under the assumption
that the error term variance is constant. When the HORL model performs successive regressions,
it is necessary to consider both fitting results at the same time, and then eliminate the variables.
The regression test results of the first step can be seen that the variable med_type is more than
0.7 in both types of parameter estimation tests, and the significance is less than 30%, which is
eliminated. The second regression was determined by regression: the variables hazmat
(p=0.544), rdsurf (p=0.348), drv_bac3 (p=0.627), spd_limt3 (p=0.899), and the variable rdsurf in
the variance regression results (p=0.715) , drv_bac2 (p=0.934), spd_limt2 (p=0.58), the
correlation between these variables and other explanatory variables is small, and the non-
significant further regression removes them. After 8 regressions, the 95% confidence model was
obtained with significant significance, the significant variable road feature type (p=0.015), driver
safety measures (p=0.011), hazardous chemicals detection p=0.000), driver age ( p=0.001),
vehicle type (p=0.006), road centerline width (p=0.009), road function level (p=0.0000),
shoulder type (p=0.004).The parameter estimation is shown in Table 3. The HORL model
regression excavated two factors, namely the shoulder type and the midline width of the road,
which are not identified by the ORL and the MNL model, and the influence of the two factors on
the severity of the accident is more in line with the cognition.
5.2 Model checking
The obtained fitting results are tested to ensure the accuracy of the obtained model and
enhance the persuasiveness of the model. Here, the built-in test method is used to test the model
goodness of fit, parameter estimation and prediction accuracy. The test results are shown in the
attached table 4.
The results of regression fitting of the HORL model were tested, including the model statistic
test and the model goodness-of-fit test. The statistic test found that as the model is continuously
streamlined, the test statistic AIC and BIC values are continuously reduced. Small, indicating
that the accuracy of the model is increasing; the chi-square statistic significance test
Prob>chi2=0.000, so the original hypothesis is rejected: the parameters of all explanatory
variables are 0, so at least one of all coefficients is significantly non-zero, indicating the model
parameters. The effect is excellent. The LRchi2 test is equivalent to the -2L test. The smaller the
value, the better the adaptability of the model. It is learned from the test schedule 7 that the test
value is continuously decreasing during the successive regression process, indicating that the
model adaptability is explained. The streamlining of variables is constantly improving; the
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decreasing PseudoR2 indicates that the model fitting effect is more significant.
Table 1 Explanation of the explanation of the severity of bicycle accidents in collision
fixtures
SQLCode
Variable name
Variable interpretation
Independent variable definition / data
distribution range
amount
Proportion
severity
Accident severity
Fatal Injury is a serious accident, Class A / B / C
Injury is a serious accident, and No Injury is a
minor accident.
1: minor accident
3437
68.43
2: Serious accident
1391
27.69
3: a vicious accident
195
3.88
drv_bac
Alcohol concentration
>=20mg/ml, <80mg/ml for driving after drinking;
>=80mg/ml for drunk driving.
0: Normal (bac concentration <0.02)
34
0.68
1: Drinking and driving
846
16.84
2: drunk
4143
82.48
drv_sex
Driver gender
Driver gender
0: male
3783
75.31
1: female
1240
24.69
drv_age
Driver age
The age of 18 years and older is legally
referenced to the impact of the accident, and the
age is divided into 7 age groups;
1:0-17 years old
61
1.21
2:18-24 years old
1565
31.16
3:25-35 years old
1578
31.42
4:36-46 years old
882
17.56
5:47-57 years old
671
13.36
6:58-68 years old
230
4.58
7:69-90 years old
36
0.72
physcond
Driver's physical
condition
Driver's physical condition at the time of the
accident
0: normal state
284
5.65
1: sick / taking medicine / sickness
4696
93.49
2: fainting unconscious
43
0.86
vehtype
Vehicle type
Vehicle type involved IN
0: small bus
3981
79.26
1: minivan
39
0.78
2: sports car
791
15.75
3: van / school bus / middle passenger
134
2.67
4: Truck / Trailer / Tractor / Semi-trailer
78
1.55
rd_char1
Road characteristics
The road where the accident is located
0: straight road
2928
58.29
1: curvilinear road
2095
41.71
rodwycls
Road grade
The roads are divided into two categories: urban
and township. These two types include high-
speed and ordinary roads;
1: City Highway
307
6.11
2: City Road
1286
25.60
3: Township high speed
183
4
4: Township Highway
3247
65
medwid
Midline width
The width of the central divider of the road where
the accident is located, in ft
1: Zeroft
4275
85
2:1-30ft
296
6
3:30-60ft
326
6
4:>60ft
126
3
surf_wid
Pavement width
Cross section width: including roadway,
sidewalk, central barrier width, without curb
green belt
1:0-20ft
2594
52
2:21-40ft
1603
32
3:>40ft
826
16
func_cls
Road function type
The main service objects and functions of the
road at the accident site
1:Township intercontinental road
354
7
2: Roads in townships and towns
3069
61
3: Intercontinental roads in urban areas
524
10
4: Urban roads within the city
1076
21
trk_rte
Truck line type
Is the road at the accident point the designated
truck line?
0: Unspecified truck line
4282
85.25
1: designated truck line
741
14.75
surf_typ
Pavement type
Accident point road pavement material type
0: type of gravel, clay, gravel or stone
3244
65
1: Surface treatment of asphalt, concrete, etc.
1779
35
no_lanes
Number of lanes
Number of roadways at the accident point road
0: 2 lanes
4200
84
1:3-5 lanes
672
13
2:>6 lanes
151
3
rshl_typ
Right shoulder type
Accident point shoulder type
0: There are herbaceous vegetation
3956
79
1: crushed stone / hard object
891
18
2: Asphalt paving
34
1
3: guardrail
142
3
med_type
Central isolation type
Accident point road central isolation belt type
0: no separation
4274
85
1: physical separation
749
15
rdsurf
Pavement type
Pavement conditions affected by the weather
environment at the accident site
0: dry road surface
4017
79.97
1: rain / water / ice and snow
1006
20.03
light
Light
Accident point road lighting conditions
0: Good daylight
1225
24.39
1: dusk,darkness,poor lighting
3798
75.61
terrain
terrain
Topography and topography around the road at
the accident point
1: plain terrain
1626
32.37
2: Hilly terrain
2914
58.01
3: Mountainous terrain
483
9.62
spd_limt
Speed limit
Vehicle passing speed at the point of accident
1:30-40
458
9.12
2:40-50
946
18.83
3:51-60
3277
65.24
4:61-70
342
6.81
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SQLCode
Variable name
Variable interpretation
Independent variable definition / data
distribution range
amount
Proportion
hazmat
Carry dangerous goods
The traffic control department checks whether it
carries flammable and explosive dangerous
goods.
0: no dangerous goods
5021
99.96
1: Carrying dangerous goods
2
0.04
sob_test
Chemical testing
The traffic control department checks whether
the driver is taking drugs
0: no detection
4959
98.73
1: There is detection
64
1.27
drv_rest
Safety measures
Safety measures taken by the vehicle involved in
the event of an accident
1: No action taken
92
1.83
2: Use seat belts
4653
92.63
3: Other measures
278
5.53
trf_cntl
Road control type
Road traffic management measures at the
accident site, including traffic signals, signs,
markings, etc.
0: No traffic control
1600
31.85
1: Facilities such as signs, markings, signal
lights, reminders and warning signs
3423
68.15
Table 2 Dummy variables for speed limit at the accident point
Speed limit section
Dummy variable
spd_limt1
spd_limt2
spd_limt3
spd_limt4
1 : 30-40km/h
1
0
0
0
2 : 40-50km/h
0
1
0
0
3 : 51-60km/h
0
0
1
0
4 : 61-70km/h
0
0
0
1
Table 3 Collision Fixation Accident Severity HORL Model Parameter Calibration Results
Interpret variable
parameter
Standard
deviation
z
p>|z|
[95%confidence interval]
/cut1
-0.6699
0.8304
-0.8100
0.4200
-2.2975
0.9578
/cut2
0.4619
0.3703
1.2500
0.2120
-0.2639
1.1878
sob_test
1.0950
0.2509
4.3600
0.0000
0.6033
1.5868
rd_char1
0.1658
0.0657
2.5200
0.0120
0.0370
0.2945
trk_rte
-0.4239
0.2022
-2.1000
0.0360
-0.8202
-0.0276
drv_age1
-0.4989
0.3810
-1.3100
0.1900
-1.2456
0.2478
drv_age2
0.0632
0.0937
0.6700
0.5000
-0.1204
0.2468
drv_age3
0.1312
0.0933
1.4100
0.1590
-0.0516
0.3140
drv_age5
0.1182
0.1135
1.0400
0.2980
-0.1044
0.3407
drv_age6
0.5731
0.1677
3.4200
0.0010
0.2444
0.9018
drv_age7
0.4859
0.3423
1.4200
0.1560
-0.1849
1.1568
vehtype2
0.1757
0.3137
0.5600
0.5750
-0.4391
0.7906
vehtype3
0.1549
0.0820
1.8900
0.0590
-0.0059
0.3157
vehtype4
-0.0412
0.1914
-0.2200
0.8290
-0.4164
0.3339
vehtype5
0.4936
0.1750
2.8200
0.0050
0.1506
0.8365
drv_rest2
-0.5990
0.1624
-3.6900
0.0000
-0.9173
-0.2808
drv_rest3
-0.2810
0.1975
-1.4200
0.1550
-0.6681
0.1060
rodwycls2
-0.3655
0.3228
-1.1300
0.2570
-0.9982
0.2672
rodwycls3
-0.9289
0.8942
-1.0400
0.2990
-2.6815
0.8237
rodwycls4
-1.2247
0.8552
-1.4300
0.1520
-2.9009
0.4516
medwid4
0.5076
0.3265
1.5500
0.1200
-0.1323
1.1474
medwid3
-0.5442
0.3049
-1.7900
0.0740
-1.1417
0.0533
medwid2
0.0534
0.2519
0.2100
0.8320
-0.4403
0.5471
func_cls4
-1.1838
0.8297
-1.4300
0.1540
-2.8100
0.4424
func_cls3
-1.7329
0.8447
-2.0500
0.0400
-3.3885
-0.0773
func_cls2
-0.4767
0.2350
-2.0300
0.0430
-0.9374
-0.0160
rshl_typ1
1.0591
0.2964
3.5700
0.0000
0.4782
1.6399
rshl_typ2
1.0102
0.3124
3.2300
0.0010
0.3978
1.6225
rshl_typ3
0.9029
0.5270
1.7100
0.0870
-0.1301
1.9359
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Table 4 HORL model fitting effect test and parameter estimation accuracy test Results
Test statistics
Types
HORL model test parameters N=5023
A-1
A-4
A-5
A-8
Model fitting statistic
AIC
6962.873
6943.916
6954.363
6976.234
BIC
7582.442
7413.485
7397.844
7289.28
Parameter test
LRchi2
674.44
647.4
628.95
567.08
Prob>chi2
0.0000
0.0000
0.0000
0.0000
Likelihood ratio
-3386.4364
-3399.9582
-3409.1813
-3440.1172
PseudoR2
0.0906
0.0869
0.0845
0.0761
6 RESULT DISCUSSION
The results of the variance Logit model and the variable variance Logit model are compared,
and the marginal effects of each factor are calculated. The analysis is based on five categories of
predictors (independent variables): driver, vehicle, road, environment and management.
6.1 Driver factor
The regression results show that the driver characteristics have a significant impact on the
severity of bicycle accidents in collision fixtures, especially the driver's gender, age, physical
status and other factors. The driver age variable HORL model has higher significance level, and
the drv_age1 (0-17 years old) variable shows a high degree of significance, and its p=0.031. The
driver of this age group has a higher risk than the middle-aged person. The marginal effect
results show that minors who do not meet the legal driving age will increase the probability of
serious collisions with accidents by 10.37%.
6.2 Vehicle factors
The vehicle type variable is highly significant in the regression model. In the HORL model,
the minor accident is the response variable, and the significance test of the vehtype5 in the
regression result is 0.006. This type of vehicle has a significant impact on the accident severity.
The marginal effect results show that the large vehicle has a minor accident, a serious accident
and a malignant accident. The effects of probability are -49.33%, 13.96%, and 35.37%,
respectively. It can be seen that the type of vehicle has a very important impact on the severity of
accidents in collision fixtures, especially for large vehicles such as trucks, trailers and tractors.
The impact of accidents on passengers is more serious, and the possibility of serious and serious
accidents is also very high. Because the large vehicles traveling at the same speed have a larger
weight, the inertia is larger, and the smaller braking time of the vehicle is longer.
6.3 Road factors
Ten explanatory variables were initially selected, after successive regression, the significant
variables obtained are road material type, road type, large truck route, road surface shape, road
function level, midline width, shoulder type, and visible road factors for traffic accidents.
The road linear factor is significantly higher in the regression model. In the HORL model,
the variance and heteroscedasticity fitting tests are performed on the road alignment respectively.
It is found that the significance test of the variance has a p-value greater than the variance,
indicating that the error term has no variation. Both values are less than 0.05 to satisfy the
significance test, but the variable variance fitting parameters are not stable enough in the
successive regressions.
The road function level variables are more significant in the MNL and HORL models. In the
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MNL, the inter-town inter-continental roads are used as reference variables. In the regression, the
three types of roads in the township, the inter-urban road, the urban road and the urban road are
compared with each other. The result is found func_cls2. And func_cls3 have a significant
impact on the severity of the accident. The p-values of the significance test are 0.0047 and
0.0181, respectively. For the generalized model of minor accident/malignant accident, the
regression parameter of func_cls3 is 0.9678, indicating that the inter-continental road in urban
area may have a minor accident compared with the inter-continental road in the town. Higher,
the func_cls2 parameter is 0.317, indicating that roads in townships and towns may be slightly
more likely to have minor accidents than inter-town roads. For the generalized model of serious
accidents/malignant accidents, the regression parameter of func_cls3 is 1.3681, which indicates
that the intercontinental roads in urban areas are more likely to have serious accidents than the
intercontinental roads in towns and towns. The regression parameter of func_cls2 is 0.8853,
indicating that the roads in townships and towns are seriously worse than the intercontinental
roads in towns and towns. The probability of accidents is higher. Through the marginal effect, it
can be seen that the probability of minor accidents on township roads compared with township
inter-continental roads will be reduced by 10.27%, the probability of serious accidents will
increase by 11.28%, and the probability of vicious accidents will decrease by 1.01%. The
possibility of a minor accident in the urban intercontinental road compared to the inter-
continental road in the township will be reduced by 7.51%, the probability of a serious accident
will increase by 9.04%, and the probability of a vicious accident will be reduced by 1.53%. It
shows that the probability of minor accidents and vicious accidents in collisions with fixed
objects on towns and towns is higher than that of the other three types. The probability of serious
accidents in roads on towns and towns and on intercontinental roads in urban areas is higher.
Two reasons: First, the inter-continental roads in towns and towns are subject to the unfavorable
roads caused by the geographical form of North Carolina. The road management in township
areas is inferior to the urban roads, which leads to accidents. Second, the intercontinental roads
are mostly long-distance vehicles, and the speed of vehicles Higher, the possibility of a serious
accident is higher.
Regression found by variable variance found that the width of the central barrier and the type
of shoulder of the road will have a serious impact on the severity of the accident. In the
regression, the width of medwid1 is chosen as the reference variable, and the results show
medwid3 (30-60ft) and medwid4 (>60ft). There is a significant impact on the severity of
accidents in collision fixtures. The p-values of the significance tests are 0.009 and 0.43,
respectively. It is found in successive regressions that the significant changes in the midline and
road grades of the variables are significant, indicating the correlation between the variables.
Larger. Compared with no central isolation belt, the probability of a minor accident will increase
by 7.04%, the probability of a serious accident will decrease by 5.01%, and the probability of a
serious accident will decrease by 2.02. %, the study found that the ideal width of the central belt
is 63ft to 80ft. When the central isolation width is 30-60 ft, the driving comfort increases with
the increase of the width, the probability of serious accidents and malignant accidents decreases,
the road function level increases, the traffic environment becomes more complicated, and slight
accidents such as scratches and collisions occur.
The right shoulder type variable is also significant in successive regressions, with a
significance of 98% confidence level. The right shoulder types are: rshlt1 with herbaceous
vegetation, rshlt2 broken stones or hard obstacles, rshlt3 asphalt matting, rshlt4 guardrail. Here,
the rshlt4 guardrail is selected as the reference variable.The marginal effect shows that hard
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obstacles can reduce the probability of minor accidents by 6.15%. The two types of shoulders
reduce the probability of serious accidents by 3.8% and 3.19% respectively. However, the impact
on malignant accidents is large, resulting in a 3.5% increase in the probability of vicious
accidents. 9.34%, it can be seen that the accident severity of the collision fixture has a direct
relationship with the type of shoulder. Collision objects are mainly road edge objects, stationary
objects on the road, etc., so the collision objects are different and have different severity.
6.4 Traffic management
The results show that traffic management related variables affecting the severity of collision
fixtures include: chemical detection, driver safety measures, and speed limit of road sections.
Among them, the chemical detection and driver safety measures use the model to perform the
regression regression significance test p value is less than 0.0001, which has a significant impact
on the accident severity of the collision fixture. The marginal effect map of chemical detection
shows that the management of chemical detection can effectively reduce the probability of minor
accidents, but it has no effective prevention for serious accidents and serious accidents, but it is
more serious because chemical detection is mainly for drivers. The test content includes alcohol
and drugs.
Driver safety measures such as the use of safety belts and safety suits are significantly more
prominent in the models, which have a significant impact on the severity of the accident. The
marginal effect shows that taking safety measures will effectively reduce the occurrence of
serious accidents and serious accidents. In the HORL model, drv_rest3 uses no safety measures
compared with safety clothing, and the probability of serious accidents and serious accidents is
reduced by 16.16% and 34.12%, respectively.
7 CONCLUDING REMARKS
The data of accident samples from 5023 crash fixtures in North Carolina were used to verify
the Logit regression method of variable variance. The research found road traffic accident data
has heteroskedasticity, and orthogonalization processing and independent distribution processing
can avoid the occurrence of heteroskedasticity. The fixed-variance Logit model has better
applicability. HORL is limited compared to the fixed-variance model. Less, it applies to the
treatment of accident data with variable variance, which can effectively capture factor
heterogeneity and tap into more potential latent variables.
For the road design and construction industry, traffic safety design and safety assessment
should be improved. The reasonable layout of the road line type is of importance, as well as the
ratio of the circular curve, the straight line and the easing curve. If the straight line is too long,
the driver will have a safe illusion and gradually reduce the vigilance level. The curve is too long
and easy to produce fatigue, which is not conducive to driving safety and reasonable ratio to
driving. As to road design, the width of the central isolation belt matters to safety. It is found that
the central separation belt is the most safe from 19.29m to 24.38m. Therefore, the width of the
central isolation belt should be considered when designing the cross section of the road. Road
design should also consider the type of shoulder, shrub vegetation shoulder and hard stone
shoulder all of which have a significant impact on the accident severity of collision fixtures.
Large trees and hard stone shoulders should be avoided when designing the road, and asphalt
hardening or planting vegetation with good visibility should be a noticeable factor too.
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