Correlation Analysis on Accident Injury and Risky Behavior of Vulnerable Road Users Based on Bayesian General Ordinal Logit Model

Abstract

Crashes involving vulnerable road users (VRUs) are types of traffic accidents which take up a large proportion and cause lots of casualties. With methods of statistics and accident reconstruction, this research investigates 378 actual traffic collisions between vehicles and VRUs in China in 2021 to obtain human, vehicle, and road factors that affect the injury severity. The paper focuses on risky behaviors of VRUs and typical scenarios such as non-use of the crosswalk, violation of traffic lights, stepping into the motorway, and riding against traffic. Then, based on the Bayesian General Ordinal Logit model, influencing factors of injury severity in 168 VRU accidents are analyzed. Results demonstrate that the probability of death in an accident will rise when the motorist is middle-aged and the VRU is an e-bicycle rider; the probability of death in an accident will greatly decrease when the VRU bears minor responsibility. Therefore, middle-aged motorists and e-bicycle riders should strengthen safety consciousness and compliance with regulations to prevent accident and reduce injury for VRUs. In addition, helmet-wearing will help to reduce riders’ injuries. This research may provide ideas for intelligent vehicles to avoid collisions with risky VRUs.

1. Introduction

In the field of traffic collision research, pedestrians, bicycle and e-bicycle users, and road users without safety protections, are classified as vulnerable road users (VRUs (VRU: vulnerable road user, road users without safety measures, including pedestrians, bicycle riders, e-bicycle riders, and users of other non-motor-vehicles)) [1]. These road users are more likely to be hurt compared to car drivers. For this reason, identification of characteristics of such accidents and the reduction of casualties is of great significance, and study on collisions involving VRUs is the core of traffic accident research [2]. In order to improve the traffic safety of VRUs, research on patterns and characteristics and the corresponding preventive measures has become a popular topic in recent years.

Zhang Shibo et al. [3] looked at 181 actual fatal accidents of pedestrians in the National Automobile Accident In-Depth Investigation System (NAIS), and carried out a statistical study on data of location, time, weather, motorists, pedestrians, vehicles, collision status, accident consequences, and so on. On this basis, fishbone analysis of the pedestrian, the driver, the vehicle, the road, and the environment was applied, the causation mechanism of death was analyzed, and seven characteristics of traffic accidents were summarized. Tan Zhengping [4] obtained 46 kinds of basic scenarios from pedestrian accidents in the NAIS, analyzed the characteristics of pedestrian collisions in China, and collected detailed descriptions of 16 typical vehicle-pedestrian collision scenarios using methods such as cluster analysis. His research provided application scenarios for the development and testing of autonomous vehicles. Dong Aoran [5] used 6101 vehicle-pedestrian accidents in one city as the research object and selected 19 variables from aspects of the human, the vehicle, the road, and the environment. After that, the partial odds ratio model was applied to establish the modeling of pedestrian injury severity analysis, and the impact of significant variables was analyzed quantitatively with elastic analysis. Twelve variables that greatly affect the severity of pedestrian injury in vehicle-pedestrian collisions were obtained. The model presented by Šarić, Ž [6], who collected accident data in the Republic of Croatia from 2015 to 2018, could be seen as an alternative solution for heterogeneity issues and dealing with determinants, and might provide useful insights into reducing the pedestrian injury severity in vehicle-pedestrian collisions. Bajada T et al. [7] collected vehicle-pedestrian accidents in Malta from 2004 to 2018 and determined the characteristics of pedestrian accidents and the risk of injury. Firstly, they used Multiple Correspondence Analysis (MCA) to determine the characteristics and then classified the results by cluster analysis. Natarajan P [8] also used MCA to study vehicle-pedestrian accidents from the Road Accident Data Management System (RADMS) database in 2016 in Chennai, summarizing patterns and correlations leading to accidents. Tanvir Chowdhury et al. [9] carried out a survey of 1020 Bangladesh workers in Dhaka to identify the characteristics of vulnerable road users. Moreover, Lei Yang et al. [10] performed a comparative analysis of different models using Bayesian Optimization for pedestrian fatality prediction, trying to improve traffic safety of pedestrians from the approach of machine learning.

Studies on bicycle accidents are also emerging, for bicycle-related mortality made up a large part of traffic deaths [11]. Han Dashuang [12] used the traffic accident database of a city in Jiangsu province and the NAIS database to screen 116 vehicle-cyclist accidents, extracted seven accident scenarios using a classification tree, and generated a set of test conditions for each scenario according to the road and environment parameters. He eventually established an evaluation model of vehicle-cyclist collision using the Analytic Hierarchy Process (AHP) and the fuzzy comprehensive evaluation method. Han Yong [13] collected 200 accident videos of two-wheeled vehicles on the Internet and counted the data on accident scenarios, the rider’s emergency posture, the kinematic trajectory, and the human-ground impact characteristics. The results played an important role in making safety countermeasures, cutting down accidents, and reducing injuries. Helmer T [14] used the German In-Depth Accident Studies (GIDAS) and the national database to evaluate and analyze the trends of accident scenarios, statistics, and characteristics in terms of frequency and contributing factors. Scenario analysis illustrated that the safety measure of vehicles—whether active or passive—can have a vital effect on accidents of cyclists and pedestrians, as well as the consequences. Matsui Y [15] investigated the rate of death of cyclists by gender, age group, vehicle speed, and the source of fatal injury (collided with a vehicle or with the ground) data from 2009 to 2013, which showed that head injuries were the most common cause of death in vehicle-bicycle accidents. The result also showed that the percentage of deaths caused by hip injuries was significantly higher for women than for men, and the death rate for cyclists over 65 was significantly higher than those of younger ages. Hertach P [16] investigated 3658 e-bicycle riders in Switzerland in 2016 and analyzed the risk of collision and injury severity with the logistic regression model. Hu L [17] used single-vehicle collisions in the Chinese In-Depth Accident Study (CIDAS) as sample cases and conducted scene reconstruction by PC-CRASH software with the collision information obtained. Then, the statistical distribution of accident parameters was analyzed in-depth, and the influence of the mass ratio, the bumper size, the collision type, and the speed, on the severity of the cyclist’s injury were studied through logistic regression analysis.

Some scholars have made comparative studies of pedestrian accidents and bicycle (e-bicycle) accidents. Jin N [18] compared the risk of death in pedestrians and cyclists in urban transportation by analyzing actual accidents in China. Yuan Quan et al. [1] conducted statistical and comparative research on traffic accidents of pedestrians, bicycles, and e-bicycles, and determined differences in characteristic variables of the three types of accidents. The logistic regression model illustrated that nighttime, intersection, elderly VRUs, and high vehicle speed increased the severity of accidents. The same method was applied to specifically analyze the contributing factors of injury severity in e-bicycle accidents [19], and it was found that the injury severity increased when riders were elderly and the e-bicycle was making a turn. Some scholars further considered accidents at intersections. Angus E. Retallack and Bertram Ostendorf [20] studied the correlation between traffic volume and accidents in intersections in Australia. They found a linear relationship at low traffic volumes and a quadratic relationship at high traffic volumes. An influencing factor of rain was also considered in their study. R. Marzoug et al. [21] studied the relationships between different contributing factors and accidents at intersections, and illustrated them with a two-lane cellular automata model. They found the probability of collision increased as the lane-changing probability increased, and the influence of inflow was more complicated.

Statistics are the major research method used in the aforementioned research. Nowadays, the General Ordinal Logit/Probit Model has been widely applied in statistics of traffic accident modeling. In existing representative studies, this method has been used to explore related factors of motorist injury [22], highway accident casualty [23], the severity of pedestrian and cyclist injury [24], and passenger injuries in vehicle side-crash accidents [25], in which valuable results have been obtained. However, the application in VRU related research is limited. This paper refers to the aforesaid research findings, uses 378 actual traffic accidents involving VRUs in 2021 as research objects, and utilizes the General Ordinal Logit Model to conduct a statistical analysis. The purpose is to find the correlation between characteristic variables of VRUs’ risky behavior and accident injury severity.

2. Materials and Methods

2.1. Data Source

This research adopts data from 378 actual accidents that happened in a large northern city in China in 2021, which were collision accidents between vehicles and VRUs. VRUs includes pedestrians, riders of bicycles, riders of e-bicycles, and users of other non-motor vehicles; vehicles include sedans, SUVs, medium and small passenger cars, trucks, etc. The severity of an accident is classified as no injury, light injury, serious injury, and death. Data covers time, type of VRUs, the injury severity, location, and whether the VRU violated regulations (against traffic, not slowing down to turn or to avoid pedestrians, not walking/riding in a designated road, jaywalking, violating traffic lights, etc.).

2.2. The General Ordinal Logit/Probit Model

In order to analyze the relationship between different factors and the injury severity, a discrete choice model, the General Ordinal Logit/Probit Model, is used. The Traditional Ordinal Logit/Probit Model has a shortcoming, which is that its thresholds are constants. To overcome this defect and to make the model more widely applicable, scholars have come up with the General Ordinal Logit/Probit Model [24]. The two are similar in structure, but the parameters ${\mathsf{\mu }}_1,{\mathsf{\mu }}_2,\cdots {\mathsf{\mu }}_{\mathrm{k}-1}$ of the latter changed from constants to variables ${\mathsf{\mu }}_{\mathrm{n},1},{\mathsf{\mu }}_{\mathrm{n},2},\cdots {\mathsf{\mu }}_{\mathrm{n},\mathrm{k}-1}$:

To ensure the ordinal of thresholds ${\mathsf{\mu }}_{\mathrm{n},1},{\mathsf{\mu }}_{\mathrm{n},2},\cdots {\mathsf{\mu }}_{\mathrm{n},\mathrm{k}-1}$, we define the neighboring thresholds as follows [24]:

$${\mathsf{\mu }}_{\mathrm{n},\mathrm{k}}={\mathsf{\mu }}_{\mathrm{n},\mathrm{k}-1}+\exp \left({\mathsf{\alpha }}_{\mathrm{k}}{\mathrm{Z}}_{\mathrm{n},\mathrm{k}}\right).$$

(1)

In this formula, ${\mathrm{Z}}_{\mathrm{n},\mathrm{k}}$ is the observed vector of the $\mathrm{k}$th related factor for incidence $\mathrm{n}$, and ${\mathsf{\alpha }}_{\mathrm{k}}$ is the vector consisting of the corresponding regression coefficients (including constants).

As in this paper, the casualty tendency ${\mathrm{y}}_{\mathrm{n}}$ (which represents the injury severity) is defined as in Equation (2), where $\mathsf{\beta }$ is a coefficient. By comparing ${\mathrm{y}}_{\mathrm{n}}$ and thresholds ${\mathsf{\mu }}_{\mathrm{n},1},{\mathsf{\mu }}_{\mathrm{n},2},\dots {\mathsf{\mu }}_{\mathrm{n},\mathrm{k}-1}$, the injury severity ${\mathrm{Y}}_{\mathrm{n}}$ can be classified as Equation (3) [24].

$${\mathrm{y}}_{\mathrm{n}}={\mathsf{\beta }\mathrm{X}}_{\mathrm{n}}+{\mathsf{\alpha }}_{\mathrm{k}},$$

(2)

$${\mathrm{Y}}_{\mathrm{n}}=\{\begin{array}{cc}1,& {\mathrm{y}}_{\mathrm{n}}\le {\mathsf{\mu }}_{\mathrm{n},1}\\ \mathrm{k},& {\mathsf{\mu }}_{\mathrm{n},\mathrm{k}-1}<{\mathrm{y}}_{\mathrm{n}}\le {\mathsf{\mu }}_{\mathrm{n},\mathrm{k}}\\ \mathrm{K},& { \mathrm{y}}_{\mathrm{n}}>{\mathsf{\mu }}_{\mathrm{n},\mathrm{K}-1}\end{array}, \mathrm{k}=2,3,\cdots ,\mathrm{K}-1,$$

(3)

For the General Ordinal Logit Model, the probability of severity $\mathrm{k} \left(\mathrm{k}=1,2,\cdots ,\mathrm{K}-1,\mathrm{K}\right)$ is calculated as follows (without loss of generality, let ${\mathsf{\mu }}_{\mathrm{n},1}=0$) [24]:

$${\mathrm{p}}_1=\frac{\exp \left(-{\mathsf{\beta }\mathrm{X}}_{\mathrm{n}}\right)}{1+\exp \left(-{\mathsf{\beta }\mathrm{X}}_{\mathrm{n}}\right)},$$

(4)

$${\mathrm{p}}_{\mathrm{k}}=\frac{\exp \left(-{\mathsf{\beta }\mathrm{X}}_{\mathrm{n}}\right)\exp \left[{\sum }_{\mathrm{j}=2}^{\mathrm{k}-1}\exp \left({\mathsf{\alpha }}_{\mathrm{j}}{\mathrm{Z}}_{\mathrm{n},\mathrm{j}}\right)\right]\left\{\exp \left[\exp \left({\mathsf{\alpha }}_{\mathrm{k}}{\mathrm{Z}}_{\mathrm{n},\mathrm{k}}\right)\right]-1\right\}}{\left\{1+\exp \left[{\sum }_{\mathrm{j}=2}^{\mathrm{k}}\exp \left({\mathsf{\alpha }}_{\mathrm{j}}{\mathrm{Z}}_{\mathrm{n},\mathrm{j}}\right)-{\mathsf{\beta }\mathrm{X}}_{\mathrm{n}}\right]\right\}\left\{1+\exp \left[{\sum }_{\mathrm{j}=2}^{\mathrm{k}-1}\exp \left({\mathsf{\alpha }}_{\mathrm{j}}{\mathrm{Z}}_{\mathrm{n},\mathrm{j}}\right)-{\mathsf{\beta }\mathrm{X}}_{\mathrm{n}}\right]\right\}}, 1<\mathrm{k}<\mathrm{K},$$

(5)

$${\mathrm{p}}_{\mathrm{K}}=\frac{1}{1+\exp \left[{\sum }_{\mathrm{j}=2}^{\mathrm{K}-1}\exp \left({\mathsf{\alpha }}_{\mathrm{j}}{\mathrm{Z}}_{\mathrm{n},\mathrm{j}}\right)-{\mathsf{\beta }\mathrm{X}}_{\mathrm{n}}\right]}.$$

(6)

In the General Ordinal Logit/Probit Model, factor ${\mathrm{x}}_{\mathrm{m}}$ might have a significant impact on casualty tendency ${\mathrm{y}}_{\mathrm{n}}$ and thresholds ${\mathsf{\mu }}_{\mathrm{n},1},{\mathsf{\mu }}_{\mathrm{n},2},\cdots {\mathsf{\mu }}_{\mathrm{n},\mathrm{k}-1}$ at same time, i.e., ${\mathrm{x}}_{\mathrm{m}}$ can exist in both ${\mathrm{X}}_{\mathrm{n}}$ and ${\mathrm{Z}}_{\mathrm{n},\mathrm{j}} \left(\mathrm{j}=2,\cdots ,\mathrm{K}-1\right)$ in Equations (4) and (5). In order to illustrate relationships of factor ${\mathrm{x}}_{\mathrm{m}}$ and the probability of each injury severity, a calculation of the marginal effect is introduced. If a factor makes the marginal effect of the probability of certain severity increase, we say the factor has close correlation with the corresponding injury severity. In this paper, we consider accidents with injury severity 3 ($\mathrm{K}=3$), and perform the corresponding formulas for the marginal effect; more precisely, the marginal effect of continuous variable ${\mathrm{x}}_{\mathrm{m}}$ in the General Ordinal Logit Model is calculated as follows:

$${\mathrm{ME}}_{\mathrm{m},1}={\mathsf{\beta }}_{\mathrm{m}}{\mathrm{p}}_1\left(1-{\mathrm{p}}_1\right),$$

(7)

$${\mathrm{ME}}_{\mathrm{m},2}={\mathsf{\alpha }}_{\mathrm{m}}{\mathsf{\mu }}_{\mathrm{n},2}{\mathrm{p}}_3\left(1-{\mathrm{p}}_3\right)+{\mathsf{\beta }}_{\mathrm{m}}{\mathrm{p}}_2\left({\mathrm{p}}_1-{\mathrm{p}}_3\right),$$

(8)

$${\mathrm{ME}}_{\mathrm{m},3}=\left({\mathsf{\beta }}_{\mathrm{m}}-{\mathsf{\alpha }}_{\mathrm{m}}{\mathsf{\mu }}_{\mathrm{n},2}\right){\mathrm{p}}_3\left(1-{\mathrm{p}}_3\right).$$

(9)

In the above formulas, ${\mathsf{\alpha }}_{\mathrm{m}}$ is the coefficient of the corresponding contributing factor ${\mathrm{x}}_{\mathrm{m}}$ in ${\mathsf{\alpha }}_2$.

As we can see from Equations (7) and (9), the introduction of alterable thresholds makes signs before ${\mathrm{ME}}_{\mathrm{m},1}$ (effect on the lightest severity) and ${\mathrm{ME}}_{\mathrm{m},3}$ (effect on the highest severity) are not always opposite. It eases the limit of influence on injury severity by risk factors, and then increases the fitting prediction of the model.

3. Descriptive Statistics and Classification

3.1. Accident Classification

The statistic of traffic accidents involving VRUs in 2021 is listed in

Table 1. Classification of 378 accidents involving VRUs.

Variable	Classification	Quantity (n = 378)	Chi-Square Value
Time	Daytime (7:00–19:00)	262 (69.31%)	56.39
	Nighttime (19:00–7:00)	116 (30.69%)
Vulnerable road users	Pedestrian	102 (26.98%)	80.10
	Cyclist	276 (73.02%)
Accident injury severity	Injury	317 (83.86%)	173.38
	Death	61 (16.14%)
Location	Intersections	89 (23.55%)	105.82
	Others	289 (76.46%)
Illegal behavior	Yes	215 (56.88%)	7.15
	No	163 (43.12%)

. Among 378 accidents, 262 happened during the daytime. Although there is less traffic at night, due to lighting/visibility and so on, 116 accidents still happened at night. As for the classification of VRUs, 102 cases involved pedestrians and 276 involved cyclists; for accident casualties, 61 accidents resulted in death, demonstrating the vulnerability of VRUs to serious damage in traffic accidents. As for the location of accidents, intersections were the most accident-prone sections.

According to the Chi-square values in Table 1, the distribution is relatively even on illegal behavior; whereas, distributions of accident injury severity and location are extremely different.

Table 2. Comparison of 378 pedestrian and cyclist accidents.

Variable	Classification	Number of Pedestrians (n = 102)	Number of Cyclists (n = 276)	Chi-Square Value
Time	Daytime (7:00–19:00)	72 (19.05%)	190 (50.26%)	0.11
	Nighttime (19:00–7:00)	30 (7.94%)	224 (22.75%)
Accident injury severity	Injury	74 (19.58%)	243 (64.29%)	13.21
	Death	28 (7.41%)	33 (8.73%)
Location	Intersections	17 (4.50%)	72 (19.25%)	3.67
	Others	85 (22.49%)	204 (53.97%)
Illegal behavior	Yes	56 (14.81%)	159 (42.06%)	0.22
	No	46 (12.17%)	117 (30.95%)

shows the comparison of statistics of pedestrian and cyclist accidents. The Chi-square value illustrates the correlation between using a non-motor-vehicle and each variable. The accident injury severity has the largest Chi-square value, which is far higher than that of the others, indicating that “whether a non-motor-vehicle is used” is closely associated with accident casualty. As for other variables, the correlation is not evident.

3.2. Classification and Reconstruction of Typical Risky Scenarios

Risky/illegal behaviors of pedestrians and non-motorized cyclists are counted based on actual accidents (

Table 3. The proportion of risky/illegal behaviors of pedestrians and cyclists.

Behaviors	Number of Pedestrians (n = 102)	Number of Cyclists (n = 276)
Riding against traffic		33 (8.73%)
Not slowing down when turning, or giving way to pedestrians		13 (3.44%)
Not walking/riding on a designated road	2 (0.53%)	8 (2.12%)
Jaywalking	22 (5.82%)	14 (3.70%)
Illegal behavior while walking/riding on the road	4 (1.06%)	36 (9.52%)
Violation of traffic light	5 (3.78%)	28 (7.41%)
Drinking	0 (0%)	9 (2.38%)
Others	23 (6.08%)	18 (4.76%)
Total	56 (14.81%)	159 (42.06%)

), among which, violation of traffic lights, riding against traffic, and not walking/riding on the designated road are major reasons for accidents.

Typical collision scenarios are selected, and scene reconstructions are conducted with PC-Crash (Figure 1). It shows the similarities and differences between risky behaviors of VRUs in vehicle-pedestrian and vehicle-bicycle accidents.

4. Modelling Statistical Analysis

To further analyze accidents involving VRUs and explore the characteristics of contributing factors of accident injury severity, 164 cases from the aforementioned collision types with complete data are selected, which include 56 cases of pedestrians, 41 cases of bicycles, and 67 cases of e-bicycles. The Bayesian General Ordinal Logit model is used for modeling and statistical analysis. After the consideration of unobserved heterogeneity [26,27], the definition of characteristic variables and their values of samples in this study are shown in

Table 4. Definition and value of characteristic variables in sample cases.

Variables	Description and Value
Motor vehicle type (MVT)
Coach	Bus (reference item)
Truck	Truck
Motorcycle	Motorcycle
Gender of driver (GD)	1 for male/0 for female
Age of driver (AD)
AD_young	≤25
AD_mature	26–45 (reference item)
AD_middle	46–55
AD_old	>55
Vulnerable group (VG)
Bicycle	Bicycle
E-bicycle	E-bicycle
Pedestrian	Pedestrians (reference item)
Gender of vulnerable group (GVG)	1 for male/0 for female
Age of vulnerable group (AVG)
AGV_young	≤25
AGV_mature	26–45
AGV_middle	46–55
AGV_old	>55 (reference item)
Responsibility (RES)
VRU_major	VRU: major and full responsibility
VRU_minor	VRU: minor responsibility, driver: major responsibility
VRU_none	VRU: no responsibility, driver: full responsibility (reference item)
Same	Equal responsibility
Weekend or workday	1 for weekend, 0 for workday
Time of day
Before dawn	0 a.m.–6 a.m.
Morning	6 a.m.–12 a.m. (reference item)
Afternoon	12 a.m.–6 p.m.
Evening	6 p.m.–0 a.m.

.

The estimation of significant variables based on the Bayesian General Ordinal Logit model is shown in

Table 5. Significant variables estimation.

Covariates	Beta Latent Propensity	t-Value	p-Value	Alpha Threshold ${\mathit{\alpha }}_{\mathit{k}}$ [28]	t-Value	p-Value
Truck	−5.049 (1.845) a	2.736	<0.01	−1.216 (0.275)	4.421	<0.01
AD_middle	4.921 (2.514)	1.957	0.05	0.5979 (0.2327)	2.569	0.01
E-bicycle	4.545 (2.019)	2.251	0.02	\
GVG_male	−3.838 (1.461)	2.626	0.01	−0.4526 (0.1586)	2.854	<0.01
AVG_young	\			0.7186 (0.2887)	2.489	0.01
VRU_minor	\			1.978 (0.9002)	2.197	0.03

^a: average (standard deviation).

. The vehicle type: truck; the age of driver: AD_middle; the vulnerable group: e-bicycle; the gender of the vulnerable group GVG_male; the age of vulnerable group: AVD_young; and the responsibility: VRU_minor are significant parameters among all variables. Unobserved heterogeneity is not considered to affect the prediction very much.

Thereinto, the marginal effect of significant variables is shown in

Table 6. The marginal effect of significant variables.

Covariates	Property Loss (%)	Injury (%)	Death (%)
AD_middle	−3.9	−36.7	40.5
AVG_young	0	27.5	−27.5
GVG_male	5.7	25.4	−31.1
VRU_minor	0	28.1	−28.1
E-bicycle	−5.3	−26.8	32.1
Truck	15.9	4.1	−19.9

.

Validation: 40 new cases are randomly selected to validate the model, and significant variables are shown in

Table 7. The validation of marginal effect variables.

Covariates	Property Loss (%)	Injury (%)	Death (%)
AD_middle	−5.0	−49.0	44.8
AVG_young	2.5	55.1	−42.5
GVG_male	7.5	57.4	−35.0
VRU_minor	−2.5	49.6	−47.3
E-bicycle	−5.1	−32.4	62.7
Truck	82.5	17.5	−52.5

.

Comparing Table 6 and Table 7, deviation of data is observed whereas the predictions are the same. Since the major characteristic of the Bayesian General Ordinal Logit model is its variability of the threshold value, one should not evaluate or verify the model with accurate numbers. As long as ranges of results are rational, the model established in this study can be considered effective.

5. Discussion

According to the marginal effect of the Bayesian General Ordinal Logit model, influences of different variables on accident injury severity are analyzed. The results show that in motor vehicle accidents involving VRUs, when the driver’s age is between 46 and 55, the probability of death increases substantially, compared to other age intervals; the risk of death is significantly increased when the VRU is riding an e-bicycle compared to walking and cycling. Moreover, a VRU under 26, male, bearing minor responsibilities, and involving trucks will greatly reduce the probability of fatal injury, compared to accidents involving older VRUs, female, other responsibilities, and other motor vehicle types.

Given the above results, the following suggestions are made to improve traffic safety for VRUs: (1) Most of the motorists in accidents are aged between 46 and 55, have a lot of driving experience, and are more likely to overlook traffic risks. Therefore, they should be especially alert to VRUs such as pedestrians and non-motor vehicles. (2) In general, speed of an e-bicycle is faster than that of an ordinary bicycle on the road, and helmets are usually not worn by riders, which is likely to result in serious injuries and accidents. Therefore, the helmet-wearing issue needs to be strictly supervised and improved. (3) For young male VRUs, and VRUs who bear minor responsibility in accidents (i.e., VRUs’ illegal behaviors are relatively minor), the probability of serious injury will decrease. Thus, complying with regulations is beneficial to ensure safety for VRUs or to reduce the injury severity.

Different accidents illustrate the differences of various VRUs’ risky factors [19]. According to research of actual traffic accident cases, pedestrian accidents happen mostly at intersections or on the road [29], and most of the cases are collisions with vehicles (including motor vehicles and non-motor vehicles). The reasons are various. Sometimes the pedestrian suddenly crosses the road when the vehicle is approaching, without confirming safety; sometimes the motorist is absent-minded or distracted while driving, failing to notice the pedestrian in time; sometimes both sides misjudge that the other side will give way, and may miss the best avoidance timing [30]; sometimes a pedestrian appears in the blind spot of a motor vehicle and the motorist cannot avoid it. Other reasons include pedestrians entering motor lanes, urban expressways, or highways.

Accidents between non-motor vehicles and motor vehicles are also common at intersections or on the road. The causes of accidents on the road usually include cyclists riding against traffic, turning violently, entering the motor lane [19], or speeding (for e-bicycles); the causes of accidents at intersections usually include the violation of a traffic signal, riding against traffic, cutting-in to queued motor vehicles, and turning without avoidance [31]. In addition, non-motor vehicles with power plant assistance (such as e-bicycles and motorized wheelchairs) that can reach high speeds also put users at high risk of injury [32].

On one hand, the road safety administration department should reinforce relevant publicity and education and keep strictly enforcing regulations. Moreover, since most pedestrians and non-motor vehicle users have not received professional and systematic traffic safety training, their traffic safety awareness should be of long-term concern. Motor vehicle drivers were trained with systematic and professional driving skills and safety issues during the process of obtaining their driver’s license; since motor vehicles dominate the position in traffic accidents, the regulation and management of motor vehicle drivers should be even more strict. Furthermore, electric two-wheeled, three-wheeled, and four-wheeled vehicles that meet the characteristics of motor vehicles running on the road [33] should be strictly regulated and punished according to the law; enterprises and individuals that produce, sell, or transport illegal vehicles should be punished according to law as well.

On the other hand, as intelligent transportation systems are being developed and smart cars are being updated, the results of this paper can provide scenario data for intelligent vehicles to identify risky behaviors of VRUs. For instance, intelligent vehicles could use radar or visual technologies to avoid typical scenarios in order to reduce injury severity in accidents, or even prevent accidents.

We would expect that, in the foreseeable future, as pedestrians and non-motor vehicle users constantly improve their road safety consciousness, more non-motor vehicles obey the traffic rules, more motor vehicle drivers develop the habit of avoidance, and as a higher degree of vehicle autopilot is developed, pedestrians and non-motor vehicle users will increase their self-protection awareness and casualties in traffic accidents will be reduced. Nevertheless, the research of 378 accidents in one northern city has its limitations in region, time, and geographical features. In the meantime, limitation due to the size of data is not verified. Although the model has been validated, heterogeneity of unobserved factors cannot be excluded, which is also one limitation. It is hoped that subsequent researchers would carry out extensive and in-depth research on this basis.

6. Conclusions

This study, using the statistical modeling analysis, carries out an in-depth analysis on variables of 378 typical accidents involving VRUs such as pedestrians and non-motorized cyclists, and draws the following conclusions:

• According to the statistics on illegal behaviors of pedestrians and non-motorized cyclists, the main risky behaviors leading to accidents are the violation of traffic lights, riding against traffic, and not walking/riding on the designated road.
• The Bayesian General Ordinal Logit modeling analysis is applied to 168 cases of real accidents, and the effect of different variables on accident injury severity is obtained according to marginal effect analysis. Results indicate that when the driver is middle-aged and the VRU party is riding an e-bicycle, the probability of death in the accident will rise significantly, which highlights the importance of wearing a helmet. Additionally, for young male VRUs, for VRUs undertaking minor responsibility, and for the motor vehicle type being a truck, the probability of death will decrease remarkably.
• The above data analysis results show that accident prevention and injury reduction for VRUs should be implemented. Middle-aged motorists and e-bicycle cyclists should pay more attention to safe driving and accident prevention. Compliance with laws and regulations and wearing helmets for cyclists are more conducive to VRUs to reduce possible injuries.
• Results can provide scenarios for intelligent vehicles to identify illegal/risky behaviors of VRUs, to help prevent and avoid particular scenarios utilizing radar or visual technologies, and eventually reduce the injury severity of VRUs or avoid accidents.