Assessing the Impact of Different Population Density Scenarios on Two-Wheeler Accident Characteristics at Intersections

Abstract

Examining 1192 intersection car and two-wheeled vehicle collision accidents from the China In-Depth Accident Study (CIDAS) database, this study employs population density heat maps for precise assessment of surrounding population densities at accident sites. The K-Medoid clustering algorithm and silhouette coefficient were used to classify accidents into two distinct groups based on population density. Subsequent application of the random parameter logit model revealed key contributing factors to these accidents in varying population densities. The results show notable differences in factors such as collision direction of two-wheeled vehicles, types of accident conflict, road conditions, and traffic flow, depending on the population density. Based on these conclusions, the research can inform differentiated risk prediction for two-wheeled vehicle accidents at intersections and provide insights for intersection design in various population density scenarios.

1. Introduction

The insufficient passive safety performance of two-wheeled vehicles increases the risk of serious injuries to riders in collisions between vehicles and two-wheelers [1]. According to the 2023 Global Status Report on Road Safety by the World Health Organization, accidents involving two-wheeled and three-wheeled vehicles account for 21% of total road traffic deaths globally [2]. As per the annual data from China’s National Bureau of Statistics in 2023, there were 48,518 motorcycle, 36,701 non-motorized vehicle, and 3315 bicycle accidents in 2022, constituting 34% of total traffic accidents [3]. Researchers have applied numerous analytical models, aiming to reduce the occurrence and severity of two-wheeled vehicle accidents through multidimensional perspectives [4,5].

Intersections, as critical nodes in traffic systems, experience a significant increase in vehicular flow compared to other road segments and are characterized by diverse traffic patterns, leading to a higher probability of accidents. This is particularly true for two-wheeled vehicle accidents, as intersections often involve complex maneuvers like turning and merging, which increase the risk for these less protected road users. Furthermore, the high interaction between two-wheeled vehicles and other forms of transportation at intersections amplifies the potential for conflicts and accidents. The causes of road traffic accidents are generally attributed to four main categories: driver factors, vehicle factors, road design factors, and environmental factors, where an imbalance in any of these can lead to accidents [6]. In recent years, accidents at intersections have become a focal point of research [7,8,9]. Lin et al. developed multiple prediction models for intersections using machine learning algorithms to identify significant environmental variables that impact the severity of traffic accidents [10]. Fan Van applied the cumulative logistic regression model to analyze sedan accidents at intersections and established a probability prediction model for the severity of these accidents [11]. Pathivada and others used binary logistic regression models to analyze the factors influencing driver behavior in dilemma zones under mixed traffic conditions [12].

Accidents involving two-wheeled vehicles at intersections are closely related to factors such as population density, and the numbers of vehicles, bicycles, and lanes [13]. Razzaghi and others proposed that population density and GDP have positive and negative impacts, respectively, on the number of road traffic fatalities [14]. Research by Ashraf and colleagues indicates a high correlation between population density and accident frequency, with lower population densities leading to more accidents [15]. Conversely, Guerra and others suggested that fewer collision accidents occur in densely populated communities [16]. Retallack and others found that under low-traffic volume conditions, the relationship between traffic volume and accident frequency is approximately linear, with a relatively lower proportion of accidents causing injuries or fatalities [17].

Addressing the intricacies of intersection environments and the heightened collision risks between vehicles and two-wheeled vehicles, this study pioneers an innovative methodology. It amalgamates the China In-Depth Accident Study (CIDAS) database with population density heat maps. This amalgamation fills a critical void in comprehending the causative factors of accidents across diverse population densities. It facilitates an accurate assessment of population density proximate to accident locations, subsequently categorizing these sites into distinct population density scenarios. The employment of the random parameter logit regression model is crucial within this framework. It aids in pinpointing the primary causative factors and their incremental impacts on accidents involving vehicles and two-wheeled vehicles at intersections. This method not only highlights the variability in these accidents’ causative factors across different population densities but also elucidates the complex dynamics in such urban settings. By integrating accident data with demographic insights, this approach contributes to differentiated risk predictions for two-wheeled vehicle accidents at intersections and informs intersection design across various population density scenarios. The research flowchart is as shown in Figure 1.

2. Data Acquisition and Processing

2.1. Basic Accident Data

This study is based on the China In-Depth Accident Study (CIDAS) database; extracting national accident data from 2015 to 2020. After screening and eliminating cases with unreasonable or missing key data, a total of 1192 intersection vehicle-to-two-wheel vehicle collision cases were selected for this study. The accidents are categorized based on the highest Abbreviated Injury Scale (AIS) score of the rider’s injuries, dividing them into minor injury accidents (MI), serious injury accidents (SI), and fatal accidents (FI). Accidents with a maximum AIS value of 1–2 are considered minor injury accidents, 3–5 as serious injury accidents, and cases where the victim loses vital signs at the scene or cannot be resuscitated are classified as fatalities. In this study, the proportions of minor injury, serious injury, and fatal cases are 71.8%, 16.6%, and 11.6%, respectively.

2.2. Population Density Information

2.2.1. Population Density Heatmap

The WorldPop Hub provides global population density data for sharing, available for download in Geotiff format for researchers [18]. The resolution of these population density heat maps is 100 m, utilizing the random forest Dasymetric method for redistribution and mapping, with each pixel value corresponding to the total population in the area. In the heat maps, low population density scenarios are represented in blue, gradually transitioning to red as the population density increases.

This study uses population density heat maps for China from 2015 to 2020. It is important to note that the CIDAS database, on which this research is based, includes accident data from multiple cities such as Ningbo, Foshan, and Changsha. However, for the purposes of this study, only the population cloud map and accident pinpointing for Ningbo city are visually presented. The left side of Figure 2 shows the population density distribution in the southeast coastal region of mainland China in 2020, while the right side depicts a localized view of Ningbo city’s population distribution.

2.2.2. Extraction of Population Density Information around Accident Sites

In extracting the geographic coordinates of each accident site, the ArcGIS 10.2 software was utilized to build a geographic coordinate system. The latitude and longitude (XY) data of the accident sites were imported, ensuring accurate correspondence between the accident coordinates and the coordinate system. Each accident location was then marked on the population density heat map. Although the WGS84 geographic coordinate system performs well in aligning accident points with the population density heat map, its measurement of length information is limited, necessitating a conversion to the Mercator projection coordinate system.

To ensure the completeness of the sampling, a 200 m buffer zone was established around each accident point. This buffer zone was used to intersect with the population density heat map, extracting population density data within a 200 m radius of each accident site. The data were then exported according to the accident numbers and aligned with the basic accident data. Taking the city of Ningbo as an example, the left side of Figure 3 shows the local road network information (partial), while the right side (Figure 3) displays the matching of accident points with population density information. The figure clearly shows that most accident points are located at road intersections, with precise marking positions.

2.3. Clustering and Categorization of Population Density Data

To study the causes of accidents in different density intervals and summarize their differences, it is essential to cluster the collected population density data. Commonly used clustering algorithms include K-means and K-medoid, among others.

K-medoid is an improved version based on the K-means algorithm. Unlike the K-means algorithm, the k-medoid algorithm uses actual data points as the cluster centers rather than the averages [19]. Given that the population density data are continuous and exhibit a notably unbalanced distribution, after conducting K-means clustering, significant disparities emerge between the different levels. Such disparities can compromise the scientific integrity and validity of subsequent research. Consequently, this study opted for the K-medoid clustering algorithm for the clustering process.

The computational mechanism of the K-medoid clustering algorithm is outlined below:

(1)

An accident dataset D is constructed from the population density values of the 1192 traffic accident cases analyzed in this study, $D=\{d_1,d_2\dots d_{1192}\}$. Various cluster counts denoted as M (medoid) are taken into account, $M=\{m_2,m_3,m_4\}$.

(2)

Compute the absolute distance between each pair of sample points;

$$\begin{array}{c}d\left(d_i,d_j\right)=\left|d_i-d_j\right|\end{array}$$

(1)

(3)

Allocate each data point to its nearest medoid:

$$\begin{array}{c}{C}_j\left(d_i\right)={argmin}_{mj\in M}\left|d_i-m_j\right|\end{array}$$

(2)

(4)

For each cluster Ci, select a new medoid that minimizes the aggregate distance to all other points within the cluster:

$$\begin{array}{c}{m}_i^{\prime }={argmin}_{d_k\in C_i}{\sum }_{d_l\in C_i}\left|d_k-d_l\right|\end{array}$$

(3)

(5)

Iteratively perform steps 3 and 4 until the medoids stabilize and no longer shift.

The silhouette coefficient is a commonly used evaluation metric to measure the quality of clustering results, specifically used to gauge the compactness and separation of the clusters [20]. It integrates both the closeness of samples within a cluster and the separation between samples of different clusters, with a value range between [−1, 1]. A higher silhouette coefficient indicates better clustering results, characterized by a higher degree of compactness within clusters and better separation between clusters. We conducted the aforementioned clustering analysis on the population density data corresponding to the accident cases and categorized them into 2, 3, and 4 classes, respectively. We then compared the silhouette function size for each clustering result and analyzed the sample count within each interval for different numbers of clusters. After comprehensive consideration, we selected the optimal solution. The silhouette coefficients and classification details under different clusters are displayed in

Table 1. Different scenarios under each clustering target number.

Number of Clusters	Number of Samples in Each Interval	Silhouette Coefficients
2	label0 = int:701; label1 = int:491	0.57
3	label0 = int:576; label1 = int:394; label2 = int:222	0.53
4	label0 = int:402; label1 = int:326; label2 = int:290; label3 = int:174	0.51

.

In determining the optimal clustering scheme by dividing all accident samples into different numbers of clusters, experiments were conducted with 2, 3, and 4 clusters. From Table 1, it can be seen that the silhouette coefficients for clustering into 2, 3, and 4 classes are 0.57, 0.53, and 0.51, respectively. Comparative analysis of various metrics for these cluster counts revealed a gradual decrease in the internal balance within each cluster as the number of clusters increased. Such imbalance could lead to significant errors in the construction of subsequent random parameter models, impacting the accuracy of study results. Based on the definition of the silhouette coefficient, when the number of clusters is 2, the samples have higher compactness within their cluster and better separation from other clusters. Moreover, the number of cases contained in each cluster is the most reasonable. Therefore, the optimal number of clusters is determined to be two, which are, respectively, coded as “High Population Density Scenarios” and “Low Population Density Scenarios” (HPDS and LPDS). Subsequent analyses were be performed separately on these two classes to observe the differentiated impacts of population density on accident causation.

2.4. Descriptive Statistical Analysis

To comprehensively analyze the causes of vehicle-to-two-wheeled vehicle accidents, this study selects a total of 17 accident parameters, considering factors related to personnel characteristics, vehicle accident characteristics, and environmental features.

Table 2. Descriptive statistics for different options in accident data.

Scenario	HPDS	LPDS	Scenario	HPDS	LPDS
TW collision position			TW velocity
Front	150 (0.32)	256 (0.36)	<20 km/h	166 (0.35)	209 (0.29)
Side	285 (0.6)	405 (0.56)	20–40 km/h	224 (0.47)	272 (0.38)
Rear	37 (0.08)	59 (0.08)	>40 km/h	82 (0.17)	239 (0.33)
Accident conflict types			Cyclists gender
Frontal collision	67 (0.14)	108 (0.15)	Female	157 (0.33)	193 (0.27)
Rear-end collision	45 (0.1)	88 (0.12)	Male	315 (0.67)	527 (0.73)
Side collision	343 (0.73)	506 (0.7)	Vehicle avoidance measures
Special	17 (0.04)	18 (0.03)	no measures	132 (0.28)	201 (0.28)
Driver gender			Steering	129 (0.27)	184 (0.26)
Female	72 (0.15)	100 (0.14)	Speed up/down	211 (0.45)	335 (0.47)
Male	400 (0.85)	620 (0.86)	Vehicle collision velocity
Helmet-wearing condition			<10 km/h	105 (0.22)	118 (0.16)
No helmet	80 (0.17)	127 (0.18)	10~30 km/h	206 (0.44)	230 (0.32)
With helmet	392 (0.83)	593 (0.82)	30–50 km/h	136 (0.29)	240 (0.33)
Cyclists weight			>50 km/h	25 (0.05)	132 (0.18)
Light	155 (0.33)	168 (0.23)	Traffic flow situation
Medium	237 (0.5)	404 (0.56)	Very few	59 (0.13)	107 (0.15)
Heavy	80 (0.17)	148 (0.21)	Fewer	233 (0.49)	436 (0.61)
Cyclists age			More	173 (0.37)	173 (0.24)
[<25]	61 (0.13)	61 (0.08)	Congested	7 (0.01)	4 (0.01)
[25–50]	237 (0.5)	327 (0.45)	Accident time
[50<]	174 (0.37)	332 (0.46)	Dawn	76 (0.16)	131 (0.18)
Vehicle steering			Morning	87 (0.18)	159 (0.22)
Not turned	211 (0.45)	299 (0.42)	Midday	103 (0.22)	135 (0.19)
Turn right	165 (0.35)	212 (0.29)	Afternoon	137 (0.29)	215 (0.3)
Turn left	96 (0.2)	209 (0.29)	Night	69 (0.15)	80 (0.11)
Vehicle mass			Road conditions
Light	13 (0.03)	17 (0.02)	Dry	411 (0.87)	644 (0.89)
Medium	281 (0.6)	395 (0.55)	Damp	19 (0.04)	35 (0.05)
Heavy	178 (0.38)	308 (0.43)	Wet	42 (0.09)	41 (0.06)
TW classification			Accident weather
Bicycle	43 (0.09)	48 (0.07)	Rainfall	94 (0.2)	104 (0.14)
Electric assist bicycle	281 (0.6)	323 (0.45)	Heavy rainfall	65 (0.14)	98 (0.14)
Motorcycle	114 (0.24)	287 (0.4)	No precipitation	313 (0.66)	518 (0.72)
Special	34 (0.07)	62 (0.09)

presents the specific distribution of these independent variables. From a proportional perspective, high-speed accidents in LPS exceed those in HPDS. Notably, compared to low-speed accidents, high-speed accidents result in more severe injuries. The table reveals that the distribution of some accident parameters varies across different population density scenarios, indicating the need for an in-depth analysis of the data to uncover the mechanisms by which population density scenarios influence the causes of accidents.

Figure 4 illustrates the monthly variation in the number of accidents at intersections involving two-wheeled vehicles. The data indicate that the likelihood of accidents is highest in May and June, gradually decreases starting in August, and maintains the lowest level from January to April, annually. This trend could be attributed to multiple factors. In the cold weather of winter, the reduced use of two-wheeled vehicles leads to fewer accidents; conversely, in the favorable weather of May and June, increased two-wheeled vehicle usage results in a higher rate of accidents [21]. The variation in monthly accident numbers suggests that accidents involving two-wheeled vehicles are susceptible to environmental and weather influences. Therefore, risk assessments of vehicle-to-two-wheeled vehicle accidents should take into account both seasonal and weather-related factors.

Figure 5 compares the severity of vehicle-two-wheeled vehicle accidents at intersections in different population density scenarios. It reveals that accidents in low-population-density scenarios are generally more severe than those in high-population-density scenarios, with a significant increase in the proportion of fatal accidents. This phenomenon further exposes the potential impact of various population density scenarios on accidents at intersections involving vehicles and two-wheeled vehicles. To delve deeper into the specific patterns of how different population density scenarios affect these accidents, this study will employ statistical methods to analyze accident data in each scenario. The objective is to uncover the potential correlations and heterogeneity between various population density scenarios and the causes of accidents. This approach aims to provide a more detailed understanding of the relationship between population density and the occurrence and severity of vehicle-to-two-wheeled vehicle accidents at intersections.

3. Methodology

To date, researchers have employed various models to analyze the factors affecting road traffic accidents. Traditional multinomial logit models, ordered logit models, and ordered probit models do not allow for changes in individual variables [22]. However, in traffic accidents, the impact of different accident factors on the dependent variable (accident severity) varies. When analyzing accident causation, it is easy to overlook unobserved factors. Ignoring the impact of these accident factors may likely lead to biases in the analysis results. The random parameters logit model is the most widely used analytical method to address unobserved heterogeneity in traffic accident analysis [23].

The random parameters logit model is an extension of the multinomial logit model, allowing researchers to adjust some or all parameters within the model to consider the potential impact of unobserved heterogeneity on accident analysis results [24]. In this study, based on two population density scenarios, two sets of random-parameter logit models that might exhibit heterogeneity were established. This approach will enable researchers to gain a deeper understanding of the heterogeneity in accident causation across different population density scenarios.

When constructing a multinomial logit regression, the Nlogit 6.0 software can only recognize binary variables. For a predictor with S categories $(S>2)$, we need to introduce $(S-1)$ dummy variables [25]. For instance, the predictor “vehicle turning direction” is trichotomous, indicating no turn, right turn, or left turn. In this case, two dummy variables are required.

$$\begin{array}{c}{s}_1={\{}_{0,\hspace{1em} \mathrm{O}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}}^{1,\hspace{1em} \mathrm{N}\mathrm{o} \mathrm{T}\mathrm{u}\mathrm{r}\mathrm{n}\mathrm{i}\mathrm{n}\mathrm{g}};\hspace{1em}{s}_2={\{}_{0,\hspace{1em} \mathrm{O}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}}^{1,\hspace{1em} \mathrm{T}\mathrm{u}\mathrm{r}\mathrm{n}\mathrm{i}\mathrm{n}\mathrm{g} \mathrm{R}\mathrm{i}\mathrm{g}\mathrm{h}\mathrm{t}}\end{array}$$

(4)

When $s_1=s_2=0$, it indicates that during the current accident, the vehicle’s turning direction is to the left.

Based on previous research, the first step is to establish a multinomial logit model, with the utility function defined as follows [26]:

$$\begin{array}{c}{S}_{ij}={\beta }_i{X}_{ij}+{\epsilon }_{ij}\end{array}$$

(5)

In the formula, ${\beta }_i$ represents the vector of estimated parameters, while $X_{ij}$ signifies the selection of the $j$-th accident variable under the $i$-th severity level of the rider’s injury. Additionally, ${\epsilon }_{ij}$ denotes the error term, which is assumed to follow a generalized extreme value distribution [27].

To account for the unobserved heterogeneity of accident parameters under different population density scenarios, a variable $\beta$ needs to be introduced. This variable is assumed to follow a series of density functions: $Prob\left({\beta }_j=\beta \right)=f\left(\beta \right|\phi )$ where $\phi$ represents a series of parameters used to precisely describe the characteristics of this function, such as location and scale parameters.

Given the above settings, the probability formula for different degrees of accident severity in the multinomial logit model is [28]:

$$\begin{array}{c}{P}_i\left(t\right)=\int \frac{EXP\left({\beta }_j{X}_{ij}\right)}{\sum _{y}EXP\left({\beta }_j{X}_{ij}\right)}f\left(\beta |\phi \right)d\beta \end{array}$$

(6)

In the formula, $f\left(\beta \right|\phi )$ represents the density function of $\beta$. The parameter vector $\phi$ describes the statistical characteristics of this density function, such as mean and variance. Other related terms are defined earlier in the text.

The random-parameter logit model is estimated using the maximum likelihood method, with Halton sampling. Previous studies have demonstrated that Halton sampling is more effective than random sampling. Based on past research, 500 iterations of Halton sampling are chosen to ensure the accuracy of parameter estimation, hence this sampling scheme is adopted in this study [22].

4. Results and Analyses

This section summarizes the main results of the study.

Table 3. Model Estimation Results.

Variable	HPDS					LPDS
	Paramete	T-Ratio	Marginal Effects			Paramete	T-Ratio	Marginal Effects
			MI	SI	FI			MI	SI	FI
Random parameters
[FI]TW Collision position2 (1 side, 0 else)	−2.68	−1.76	−0.0026	−0.0004	0.00295
Standard deviation	2.57	2.00
[SI]Traffic flow situation2 (1 Less vehicles, 0 else)						−3.75	−2.16	0.01145	−0.0164	0.00497
Standard deviation						4.18	2.02
Personnel characteristics
[FI]Cyclists Gender0 (1 female, 0 else)	−1.35	−2.41	0.0138	0.00202	−0.0158
[FI]Driver Gender0 (1 Female, 0 else)						−0.71	−1.68	0.00606	0.00084	−0.0069
[FI]Helmet condition1 (1 No wearing, 0 else)	1.57	2.21	−0.0129	−0.0028	0.01573
[SI]Cyclists weight1 (1 Light weight, 0 else)	−0.93	−2.56	0.02185	−0.0242	0.0023
[SI]Cyclists weight2 (1 Medium weight, 0 else)	−0.61	−2.17	0.03072	−0.0331	0.0024
[FI]Cyclists age1 (1 [<25], 0 else)						−1.33	−2.11	0.00438	0.00068	−0.0051
Vehicle accident characteristics
[FI]Vehicle steering2 (1 no steering, 0 else)	−0.99	−2.04	0.01216	0.00279	−0.015
[FI]TW Collision position1 (1 Fount, 0 else)						−0.64	−2.05	0.01841	0.00314	−0.0216
[FI]TW Collision position2 (1 side, 0 else)						−0.77	−2.94	0.03554	0.00708	−0.0426
[FI]Vehicle mass1 (1 Light weight, 0 else)						1.29	2.04	−0.0040	−0.0007	0.00471
[SI]TW Classification2 (1 Electric assist bicycle, 0 else)						−0.61	−1.97	0.01655	−0.0202	0.00369
[FI]TW velocity1 (1 [<20 km/h], 0 else)	−1.47	−3.03	0.0173	0.00464	−0.0219	−1.37	−4.61	0.02943	0.00514	−0.0346
[MI]TW velocity2 (1 [20–40 km/h], 0 else)	1.13	4.43	0.05509	−0.0331	−0.0220	1.24	5.00	0.05557	−0.0255	−0.0301
[FI]TW Classification1 (1 Bicycle, 0 else)	2.19	2.87	−0.01553	−0.00207	0.01761
[FI]TW Classification3 (1 Motorcycle, 0 else)	−2.00	−2.42	0.00861	0.00206	−0.0107
[MI]Accident conflicts types2 (1 Rear impact, 0 else)	−0.77	−1.98	−0.0133	0.00985	0.00345	0.77	2.34	0.0123	−0.0055	−0.0068
[FI]Vehicle avoidance measures1 (1 No measures, 0 else)						−0.75	−2.28	0.01064	0.00129	−0.0119
[FI]Vehicle collision velocity1 (1 [<10 km/h], 0 else)						−1.21	−4.21	0.02427	0.00455	−0.0288
[SI]Vehicle collision velocity2 (1 [10–30 km/h], 0 else)						−0.82	−2.22	0.01464	−0.0165	0.00186
Environmental characteristics
[SI]Traffic flow situation1 (1 Fewer vehicles, 0 else)						−1.47	−2.64	0.02739	−0.034	0.00658
[FI]Traffic flow situation2 (1 Less vehicles, 0 else)	−0.75	−1.68	0.01165	0.00231	−0.014	0.66	2.69	−0.0399	−0.0053	0.04519
[SI]Traffic flow situation3 (1 More vehicles, 0 else)						−1.64	−2.94	0.03993	−0.0463	0.00637
[FI]Accident time1 (1 Before dawn, 0 else)						1.08	3.95	−0.0234	−0.007	0.03031
[FI]Accident time3 (1 Moon, 0 else)	−2.11	−2.30	0.00649	0.0005	−0.00699
[SI]Accident time1 (1 Before dawn, 0 else)						0.76	2.04	−0.00944	0.01432	−0.00487
[SI]Accident time2 (1 Morning, 0 else)	−0.87	−2.00	0.01053	−0.0113	0.00078
[SI]Accident time3 (1 Moon, 0 else)	−1.03	−2.40	0.01371	−0.014	0.00024
[SI]Road conditions3 (1 dry, 0 else)	−0.64	−2.53	0.05137	−0.0555	0.00413	1.05	2.02	−0.07012	0.08621	−0.01609
[FI]Accident weather2 (1 Heavy rainfall, 0 else)						−0.68	−1.70	0.00593	0.00109	−0.007

presents the estimation results of the random-parameter logit model for two different population density scenarios. This includes the observed random parameters, parameter coefficients, T-test values, and the marginal effects of each accident parameter. The abbreviations inside the parentheses (MI, SI, FI) indicate that the selection of each accident parameter has a significant impact on the severity of injuries (minor, serious, or fatal) sustained by riders. The subsequent discussion will detail the estimated results of the accident variables according to population density scenarios.

4.1. Random Parameters

According to the model’s calculation results, there are two random parameters that follow a normal distribution: the direction of two-wheeled vehicle collisions in high-population-density scenarios and the size of traffic flow at intersections in low-population-density scenarios.

In highly populated scenarios, side collisions of two-wheeled vehicles significantly impact fatal injuries to riders, following a normal distribution (−2.68, 2.572). The analysis shows that in 85.1% of intersection accident samples in densely populated scenarios, side collisions between vehicles and two-wheeled vehicles are less likely to cause fatal accidents; whereas, in the remaining 14.9% of the data, such collisions are more likely to result in fatalities.

In low-population-density scenarios, the lower traffic flow at intersections significantly affects the severity of injuries to riders, with the random parameter fitting a normal distribution (−3.75, 4.182). The results indicate that in 81.6% of intersection accidents in low-population-density scenarios, reduced traffic flow does not tend to cause serious injuries; however, in 18.4% of the accidents, low traffic flow increases the probability of serious injuries to riders.

4.2. Personal Characteristics

In high-population-density scenarios, the risk of fatal accidents decreases when the rider is female (marginal effect: −0.01581), possibly due to women’s more conservative and cautious driving style, characterized by lower speeds. The likelihood of fatal accidents increases when riders do not wear helmets (marginal effect: 0.01573), indicating that helmet usage significantly reduces the severity of two-wheeled vehicle accidents, in line with traffic regulations and existing research [29]. Light- and medium-weight riders face a reduced risk of serious injury (marginal effects: −0.02415 and −0.03311, respectively).

In low-population-density scenarios, the risk of fatal accidents decreases for female drivers or riders under 25 years of age (marginal effects: −0.00689 and −0.00505, respectively), which aligns with findings from existing research [30,31,32].

4.3. Vehicle Accident Characteristics

In high-population-density scenarios, the risk of fatality for riders involved in side-impact collisions at intersections significantly increases (marginal effect: 0.00295). This is attributed to the structural characteristics of two-wheeled vehicles and the direction of their fall, which makes side collisions more impactful and increases the risk of fatal injuries to the rider. Conversely, the probability of rider fatality decreases when a vehicle collides head-on with a two-wheeled vehicle (marginal effect: −0.015). The type of two-wheeled vehicle also significantly affects the outcome of the accident: the probability of rider fatality is higher in bicycle accidents than in motorcycle accidents (marginal effects: 0.01761 and −0.0107, respectively), likely because motorcyclists typically wear better safety equipment [33]. Two-wheeled vehicle accidents occurring at speeds within the [0–40 km/h] range tend to result in minor rather than fatal injuries (marginal effect: 0.05509), aligning with previous research on the relationship between speed and accident severity.

In low-population-density scenarios, the probability of fatality decreases for two-wheeled riders involved in both head-on and side-impact collisions (marginal effects: −0.02155 and −0.04263, respectively), possibly reflecting the reduced risk of severe accidents due to lower traffic density. For types of two-wheeled vehicles, electric-assist bicycles are less likely to be involved in serious accidents (marginal effect: −0.0202). As for the speed of two-wheeled vehicles, the findings are largely consistent with those in high-density scenarios, reflecting the consistency of this parameter (marginal effects: −0.0346 and 0.05557). Collisions involving light and heavy vehicles with two-wheel vehicles are more likely to result in fatalities (marginal effect: 0.00471). When collisions occur without specific evasive actions, the probability of fatalities for two-wheel riders decreases (marginal effect: −0.0119). This might be due to drivers in less densely populated scenarios being less attentive and unable to take proper evasive actions when accidents occur, leading to more severe injuries for riders. Additionally, when vehicles collide with two-wheel vehicles at speeds of 10–30 km/h, the probability of severe injuries to riders decreases, indicating that lower collision speeds are safer for riders, in line with existing research.

Additionally, some parameters exhibit heterogeneity between different population density ranges, showing opposite marginal effects. For example, in high population density scenarios, rear-end collisions are less likely to result in minor injuries (marginal effect: −0.0133), whereas in low-population-density scenarios, the probability is reversed (marginal effect: 0.0123). This phenomenon indicates that certain accident parameters impact accidents differently in various population density scenarios, suggesting that intelligent vehicles navigating through intersections of varying population densities should adopt differentiated warning strategies.

4.4. Environmental Characteristics

In high-population-density scenarios, the probability of serious injuries to riders increases when there is less traffic flow (marginal effect: 0.00231), consistent with previous studies [34]. Accidents occurring in the morning or on dry road surfaces reduce the risk of serious injuries to riders (marginal effects: −0.01131 and −0.0555, respectively); while accidents occurring at noon are less likely to result in serious injuries or fatalities (marginal effects: −0.01395 and −0.00699). The variation in the severity of two-wheel vehicle accidents at intersections during different times of the day may be attributed to several factors. Different periods of the day correspond to varying traffic flows and driving speeds. Accidents occurring in the morning and at noon are less likely to have severe consequences, potentially related to the physical condition of drivers and riders. Both morning and noon are times when individuals are likely to be in a better mental state, positively influencing the severity of accidents that occur.

In low-population-density scenarios, the dawn period is more prone to serious or fatal accidents (marginal effects: 0.01432 and 0.03031), aligning with previous research [35]. This increased risk during the dawn period can be attributed to both riders and drivers being in a suboptimal mental state, which can lead to more hazardous accidents. Under dry road conditions, the risk of serious injuries to riders increases. This may occur as the speed of two-wheel vehicles tends to increase on dry roads, leading to a higher risk of severe injury for riders. When traffic flow is not congested, the probability of serious injuries to riders decreases (marginal effects: −0.03397, −0.01641, and −0.0463); whereas fewer vehicles increase the risk of rider fatalities (marginal effect: 0.04519). The decrease in traffic flow can paradoxically increase the risk of serious injury to riders, possibly due to drivers being less attentive when there are fewer vehicles and tending to drive faster, thereby increasing the likelihood of severe accidents. During heavy rain, the probability of rider fatality decreases, in line with existing studies [36].

The impact of road surface conditions (dry) and traffic flow (few vehicles) on the risk of serious injuries to riders has opposite marginal effects in different population density scenarios. This could be due to the influence of road conditions on the riding speed of two-wheel vehicles, indirectly affecting the severity of accidents. Moreover, when traffic flow decreases, serious injury accidents are more likely to occur at intersections in high-population-density scenarios, while in low-population-density scenarios, the probability of such risks decreases.

5. Conclusions

This study, utilizing the CIDAS accident database and China’s population density heat maps, applies the K-medoid algorithm to categorize intersection vehicle-to-two-wheel vehicle accidents into two distinct population density scenarios. Through the development of random parameter logit models for each scenario, and the calculation of the marginal effects of significant accident factors, it aims to provide a nuanced risk prediction for vehicle-two-wheel vehicle accidents at intersections, taking into account varying population densities. Conclusively, the research highlights significant differences in the causes of two-wheel vehicle accidents at intersections across diverse population density scenarios, underscoring the importance of incorporating population density considerations in accident analysis and prevention planning.

Building on the conclusions already demonstrated in previous studies, this research compares the marginal effects of accident causation in different population density scenarios and finds heterogeneity in the impact of certain accident causes: rear-end collisions at busy intersections are more likely to lead to serious accidents compared to those in low-population-density scenarios; whereas, in low-population-density scenarios, low traffic flow and dry road conditions are more likely to result in serious or fatal accidents. The heterogeneity in the causes of two-wheel vehicle accidents identified in different population density scenarios by this study can provide adaptive safety warning strategies for intersections in varying population densities. Specifically, the results of this study can enable intelligent vehicle safety warning systems to dynamically adjust driving strategies and safety warning parameters for two-wheel vehicle accidents by conducting real-time analysis of population density around intersections, in conjunction with high-precision maps, thereby significantly reducing the frequency and severity of such accidents. Additionally, the findings of this research can also inform urban intersection layout strategies and risk warning systems for different intersections.

The study, while providing valuable insights into two-wheel vehicle collision accidents, acknowledges certain limitations. Firstly, due to the lack of exhaustive national accident data, the database used in this study encompasses only the traffic accidents recorded nationwide, thus limiting the ability to conduct detailed frequency analysis of accident data and leaving room for improvement in terms of completeness of the study. Secondly, the accuracy of some data recorded in the accident database is not rigorously assured due to a lack of precision in recording. For instance, the database includes parameters like the ‘familiarity with the accident location,’ but due to the subjective nature of such data and variability in reporting, the reliability of these parameters is inconsistent, leading to their exclusion from this study. Future research could address these limitations by supplementing such data types, collecting comprehensive accident data from various cities, and conducting more thorough and rigorous analyses using uniform metrics to quantify each accident parameter.