Investigating Factors Influencing Crash Severity on Mountainous Two-Lane Roads: Machine Learning Versus Statistical Models

Abstract

Due to poor road design, challenging terrain, and difficult geological conditions, traffic accidents on mountainous two-lane roads are more frequent and severe. This study aims to address the lack of understanding of key factors affecting accident severity with the goal of improving mountainous traffic safety, thereby contributing to sustainable transportation systems. The focus of this study is to compare the interpretability of model performances with three statistical models (Ordered Logit, Partial Proportional Odds Model, and Multinomial Logit) and six machine learning models (Decision Tree, Random Forest, Gradient Boosting, Extra Trees, AdaBoost, and XGBoost) on two-lane mountain roads in Yunnan Province, China. Additionally, we assessed the ability of these models to uncover underlying causal relationships, particularly how accident causes affect severity. Using the SHapley Additive exPlanations (SHAP) method, we interpreted the influence of risk factors in the machine learning models. Our findings indicate that machine learning models, especially XGBoost, outperform statistical models in predicting accident severity. The results highlight that accident patterns are the most significant determinants of severity, followed by road-related factors and the type of colliding vehicles. Environmental factors like weather, however, have minimal impact. Notably, vehicle falling, head-on collisions, and longitudinal slope sections are linked to more severe accidents, while minor accidents are more frequent on horizontal curve sections and areas that combine curves and slopes. These insights can help traffic management agencies develop targeted measures to reduce accident rates and enhance road safety, which is critical for promoting sustainable transportation in mountainous regions.

1. Introduction

According to statistics, accidents on secondary and lower-level roads in China account for the largest proportion of all traffic incidents, reaching up to 70%. Fatalities from these accidents account for nearly 50% of the total. Traffic accidents on mountainous two-lane roads alone make up more than 15% of all road incidents [1]. To prevent and reduce the severity of road accidents in mountainous areas, and to construct a safe and sustainable transportation environment locally, identifying the key factors that contribute to the severity of accidents on different mountainous road segments has become a crucial focus of accident analysis and prevention research [2,3,4,5,6,7]. Previous studies on the causes of mountain traffic accidents [2] have typically considered accident severity as the response variable and factors related to personnel, vehicles, roads, and the environment as explanatory variables. Statistical models or machine learning algorithms have been employed to fit the relationships among these variables [8,9,10]. These studies have identified key factors that are highly correlated with the severity of accidents in mountainous areas, and have analyzed the marginal effects of these variables on changes in accident severity. The findings from these studies provide evidence for relevant departments to prevent mountain traffic accidents by altering factors related to drivers, vehicles, roads, and the environment.

However, there are three main deficiencies in past research. First, although previous research has compared the performance of statistical analysis models and machine learning models in identifying the causes of traffic accidents, their focus has primarily been on highways and urban roads. In contrast, mountainous two-lane roads, due to their open environment, present unique accident causes, such as collisions with wildlife. Moreover, the variables and research focus in mountain road accident analysis differ significantly from other environments. For example, the road alignment design of highways is typically more standardized and smoother, focusing on efficient and safe high-speed travel [11,12]. However, the alignment of mountainous two-lane roads is more complex, with sharp curves, steep slopes, and often a combination of interacting topographical factors (such as sections with both curves and slopes) [4,6]. These complex road conditions not only affect driving behavior but may also amplify the impact of certain accident causes on crash severity. Therefore, reassessing the applicability of statistical analysis models and machine learning models in this specific context is particularly important. Second, some studies have overlooked the issue of imbalanced accident data distribution on mountain roads, ignoring the fact that minor accidents far outnumber severe ones [13], which may introduce bias into the modeling results. Third, there is still a lack of comprehensive understanding regarding the impact of human, vehicle, road, and environmental factors on accidents of varying severity levels on mountain roads. Addressing these gaps is critical not only for improving traffic safety but also for supporting sustainable mobility by developing targeted interventions that minimize the risk of severe accidents. Accordingly, this study, building on statistical analysis and machine learning models that have been extensively validated in other road environments, compares their performance in analyzing the causes of accidents on mountain roads, in order to more accurately analyze the causes of accidents and formulate effective counter-measures to reduce the frequency and severity of accidents on mountain roads.

To address these three deficiencies, we collected over 5000 accident records from the past decade on a two-lane mountain road in Yunnan Province, China. This study evaluates the severity of accidents on mountain roads, considering both casualties and property damage. We applied various statistical models (Ordered Logit, Partial Proportional Odds, and Multinomial Logit) and machine learning models (Decision Tree, Random Forest, Gradient Boosting, AdaBoost, Extra Trees (Extremely Randomized Trees), and XGBoost) to explore the key factors contributing to accident severity, and compared their performance in terms of accuracy and interpretability.

The main contributions of this paper are as follows: First, we introduced the Synthetic Minority Over-sampling Technique (SMOTE) to address the issue of data imbalance. We then compared this method with Random Over-Sampling and Random Under-Sampling to demonstrate the superiority of SMOTE. By resampling the training set, we improved the accuracy of identifying causative factors. Second, we compared various statistical and machine learning models, thoroughly evaluating their accuracy and interpretive results. Third, this study focuses on analyzing the accident factors leading to traffic accidents of different severity levels and found that the impact of the same accident factor is significantly different for accidents of varying severity levels, and compares these findings with conclusions from previous studies. The structure of this paper is as follows: Section 2 reviews the literature on factors contributing to accident severity and identifies research gaps. Section 3 introduces the theoretical basis of the statistical and machine learning models used in this study. Section 4 presents the data overview, variables, and SMOTE technique. Section 5 compares the performance of various models. Section 6 selects the best model to analyze the factors leading to accident severity. The final section summarizes the main findings and discusses their implications for accident prevention.

2. Literature Review

Previous analyses of the causes of traffic accidents in mountainous areas can be categorized into two main types: one type focuses on specific conditions (such as vehicle type or collision scenario) [14,15,16], and the other type is a comprehensive analysis that examines multiple influencing factors [17,18]. These studies have identified a range of factors that are significantly related to the severity of traffic accidents, primarily concentrating on four key areas: personnel, vehicles, roads, and the environment. Detailed information is provided in

Table 1. Summary of recent studies on accident modeling in mountainous areas.

Literature	Model	Dependent Variables	Event-Related				Road Condition-Related			Temporal
			WR	AP	CVT	DR	RA	VCT	RSC	TE	HY
Alrejjal et al. (2022) [14]	Random Parameter Logit Model	Risk of rollover	√	/	√	√	/	√	√	√	√
Wang et al. (2021) [19]	Layered Bayesian Logistic Model	Severity of driver injury	/	√	√	√	/	/	/	√	/
Haq et al. (2020) [20]	A hierarchical Bayesian logical model	Severity of driver injury	√	√	√	√	√	√	√	√	√
Wen et al. (2023) [6]	PLM, RPLM, CRPLM	Severity of passenger injuries and property damage	/	√	√	√	√	√	√	√	√
Chen and Chen (2013) [21]	Mix Logit Model	Severity of driver injury	√	√	√	√	/	/	√	√	/
Wen and Xue (2020) [5]	REGOP	Severity of driver injury	√	√	√	√	√	/	√	√	/
Huang et al. (2018) [22]	CART	Severity of driver injury	√	√	√	√	√	√	√	√	/
Song et al. (2023) [7]	GOL, RTRPGOL, MNL, RPLHMV	Severity of driver injury	√	√	√	√	√	√	√	√	√
Hyodo and Kenta (2021) [23]	Ordered Logit Model.	Severity of driver injury	√	√	√	√	√	√	√	√	/
This study	Three statistical analysis models and six machine learning models	Severity of passenger injuries and property damage	√	√	√	/	√	√	√	√	√

Note: (1) “√” indicates that the study considered this variable, “/” indicates that the study did not consider this variable; (2) “PLM”: Polynomial Logit Model; “RPLM”: Random Parameter Logit Model; “CRPLM”: Correlated Random Parameter Logit Model; “REGOP”: Random Effects Generalized Ordered Probit Model; “CART”: Classification and Regression Tree Model; “GOL”: Generalized Ordered Logit Model; “RTRPGOL”: Random Threshold Generalized Ordered Logit Model; “MNL”: Multinomial Logit Model; “RPLHMV”: Random Parameter Logit Model with Heterogeneity in Means and Variances. (3) “Three statistical analysis models and six machine learning models”: Ordered Logit Model, Partial Proportional Odds Model, Multinomial Logit Model; Decision Tree, Random Forest, Gradient Boosting, AdaBoost, Extra Trees, XGBoost. (4) “WR”: Weather; “AP”: Accident Pattern; “CVT”: Collision Vehicle Type; “DR”: Driver-related Factors; “RA”: Road Alignment; “VCT”: Vertical Curve Type; “RSC”: Road Surface Condition; “TE”: Time (Day/Night); “HY”: Holiday (Holiday/Non-holiday).

.

2.1. Contributing Factors

When analyzing the causes of traffic accidents, factors are typically classified into three main aspects: event-related, road condition-related, and time-related. Event-related factors include weather conditions, vehicle types, and speeding. Previous studies have found these factors to be critical influencers of accident risk. For example, Alrejjal et al. [14] found that speeding, along with the involvement of SUVs and pickup trucks, significantly increased the risk of rollovers. Haq et al. [20] showed that mountainous terrain and adverse weather conditions often exacerbate injury severity. Hyodo and Hasegawa [23] discovered that high temperatures and reduced visibility increase the likelihood of severe multi-vehicle and fatal accidents. Driving behaviors, including speeding and fatigued driving, are among the most crucial factors affecting injury severity [22]. Wang et al. [19] found that driver age, vehicle registration status, and alcohol consumption influence traffic fatality rates, with inexperienced drivers and heavy vehicle reducing fatality risk. Haq et al. [20] noted that in certain truck-related collisions, older and female drivers/passengers are more likely to suffer severe injuries, while male and middle-aged drivers face higher severe injury risks in other collisions.

Road condition-related factors also significantly impact accident occurrence. Hyodo and Hasegawa [23] found that icy and snowy road conditions are associated with less severe accidents. Chen and Chen [21] discovered that the combination of curves and slopes greatly affects injury severity, with medium-radius curves and moderate slopes increasing the likelihood of moderately severe collisions. Song et al. [7] noted that installing guardrails on curved road sections can reduce the risk of severe injuries, while using cable barriers may increase the risk.

Time-related factors are also linked to accident severity. Huang et al. [22] found that speeding in the afternoon or evening, as well as speeding on large curves and straight sections in the morning, noon, or night, increases the likelihood of severe accidents. Basu and Saha [24] found that collision frequency on certain one-way roads is lower during the day and higher at night. Wang et al. [13] studied traffic accidents in long downhill tunnels on mountain roads and identified peak accident periods as 4:00–6:00, 13:00–16:00, 17:00–19:00, and 23:00–1:00, accounting for 54.38% of total accidents.

In summary, the severity of traffic accidents is influenced by factors related to the incident, road conditions, and time of occurrence. Among incident-related factors, speeding, fatigued driving, excessive alcohol consumption, and adverse weather conditions are the primary contributors to accidents. For road-related factors, icy surfaces, curves, and slope combinations are the main causes. As for time-related factors, driving in the afternoon, evening, and at night is associated with higher accident frequencies. However, as shown in Table 1, many studies have not conducted a comprehensive analysis of the factors contributing to accidents. A thorough understanding of these influences is crucial for developing targeted traffic safety measures.

2.2. Modeling Methods

Table 1 shows that statistical analysis models are widely adopted in the causal analysis of mountain traffic accidents due to their strong explanatory power. The Ordered Logit model is favored for its ability to evaluate the statistical significance of multiple accident factors and the relative probability changes in accident severity [23,25,26]. Despite its excellent performance in analyzing accident severity, the Ordered Logit model has inherent limitations, including the assumption of homogeneity across different severity levels and the constraints of the parallel lines assumption, which limit the consideration of unobserved heterogeneity [5]. Researchers have attempted various optimizations to overcome these limitations, such as the Mixed Logit model [27], the Random Parameters Ordered Probit model [14,27], the Multinomial Logit model [7,28], and the Random Effects Generalized Ordered Probit model [5,29]. These models serve as important supplements to traditional models. Additionally, the Partial Proportional Odds model has been widely applied in accident causal analysis due to its advantages in significance testing and prediction accuracy [30,31].

Machine learning has become increasingly important in the causal analysis of traffic accidents, and has been widely applied in recent years, although less so in mountainous scenarios. In other road scenarios, models such as Artificial Neural Networks (ANN) [32,33] and Decision Trees [34] have been widely adopted. Recently, the use of interpretive tools like SHAP (SHapley Additive exPlanations) has enhanced the practicality and interpretability of machine learning models in traffic accident analysis, promoting their application in this field [35,36]. Researchers have also begun comparing machine learning models with traditional statistical analysis models to find the optimal analytical approach. For example, Iranitalab and Khattak [37] compared four statistical and machine learning methods, finding that machine learning models exhibited better predictive performance in forecasting more severe collision accidents. Fernández-Delgado et al. [38] also demonstrated that machine learning algorithms surpass statistical analysis methods in overall predictive accuracy.

3. Methodology

Previous studies on the classification of accident severity have mainly focused on the extent of injuries to occupants, with relatively few studies simultaneously considering both property damage and injury severity [6]. Moreover, as analyzed in the previous section, past research has often focused on comparing the predictive performance of statistical analysis models and machine learning models, with less attention given to comparing the differences in analysis results between these two types of models. To provide a more comprehensive analysis of accident causation, this study comprehensively considers these two factors and employs both statistical analysis methods and machine learning models for causal analysis.

As shown in Figure 1, the workflow of this study is divided into three main parts. First, more than 5000 raw accident records were collected from a two-lane mountain road in Yunnan Province. These records were rigorously validated and screened, and, based on previous studies, eight independent variables related to event characteristics, road conditions, and time factors were extracted from the screened data. The dependent variable was accident severity, classified based on casualties and direct property damage. Subsequently, the data underwent multicollinearity testing and were split into 80% training and 20% testing sets. The training set was processed using SMOTE, and then tested using the testing set.

Secondly, three statistical models and six machine learning models were used to analyze the relationship between the independent variables and accident severity. The performance and analysis results of these models were comprehensively compared to determine the best model for detailed causal analysis.

Finally, SHAP analysis was conducted on the results of the optimal model. SHAP summary plots displayed the distribution of Shapley values for each independent variable to determine their importance. Additionally, SHAP dependence plots illustrated the impact of each independent variable on accident severity.

3.1. Statistical Models

The Logit model has been widely applied in studying the causal factors of mountain traffic accidents [23,25,26,27]. It provides easily interpretable coefficients that reflect the odds ratios of the log changes in variables influencing the likelihood of accidents. This offers researchers an intuitive method to assess the contribution of various factors to traffic accident risk. However, previous studies [14,21,23,39] have typically used a single logit model, lacking cross-model comparisons to evaluate performance. This approach may overlook potential model limitations, thereby affecting the comprehensiveness and accuracy of research findings. This study considers five models from two categories of model, with mathematical formulas and differences between models shown in

Table 2. Comparison of statistical analysis models.

Model Category	Subtype	Mathematical Model		Differences
Ordered Models	Ordered Logit Model	$\begin{array}{l}P(Y_i\le j)={\displaystyle \frac{\exp (a_j-{\displaystyle {\sum }_{k=1}^K{\beta }_k{X}_{ik}})}{1+[\exp (a_j-{\displaystyle {\sum }_{k=1}^K{\beta }_k{X}_{ik}})]}},\\ j=1,2,\dots ,J=1\end{array}$	(1)	Suitable for ordered categorical dependent variables
	Partial Proportional Odds Model	$\begin{array}{l}P(Y_i\le j)={\displaystyle \frac{\exp (a_j-{\displaystyle {\sum }_{k=1}^K{\beta }_{jk}{X}_{ik}})}{1+[\exp (a_j-{\displaystyle {\sum }_{k=1}^K{\beta }_{jk}{X}_{ik}})]}},\\ j=1,2,\dots ,J=1\end{array}$	(2)	Relaxes the odds ratio in the ordered Logit model
Multi-category Model	Multinominal Logit Model	$\begin{array}{l}P(Y=j)={\displaystyle \frac{\exp ({\beta }_j{X}_i)}{{\displaystyle {\sum }_{j=1}^J\exp ({\beta }_j{X}_i)}}},\\ j=1,2,\dots ,J=1\end{array}$	(3)	Applicable to nominal scale multi-category
	Conditional Logit Model	$\begin{array}{l}P(Y=j)={\displaystyle \frac{\exp ({\gamma }_j{X}_{ij})}{{\displaystyle {\sum }_{j=1}^J\exp ({\gamma }_j{X}_{ij})}}},\\ j=1,2,\dots ,J=1\end{array}$	(4)	Dealing with grouped or matched data
	Mixed Logit Model	$\begin{array}{l}P(Y=j)={\displaystyle \frac{\exp ({{\gamma }^{\prime }}_j{X}_i+{{\beta }^{\prime }}_j{Z}_i)}{{\displaystyle {\sum }_{j=1}^J\exp ({{\gamma }^{\prime }}_j{X}_i+{{\beta }^{\prime }}_j{Z}_i)}}},\\ j=1,2,\dots ,J=1\end{array}$	(5)	Combining fixed and random effects

Note: ① In Equation (1) $a_j$ represents the intercept for category j, $X_{ik}$ is the k independent variable of the i-th observation, ${\beta }_k$ is the regression coefficient for the k-th independent variable, K is the total number of independent variables, and j is the number of corresponding variable categories; ② in Equation (2), the regression coefficients for each category are different, and ${\beta }_{jk}$ represents the regression coefficient for category j and the k-th independent variable; ③ in Equation (3), ${\beta }_j$ is the regression coefficient vector for category j, and $X_i$ is the independent variable vector for the i-th observation; ④ in Equation (4) ${\gamma }_j$ is the regression coefficient vector for category j, and $X_{ij}$ is the independent variable vector for the i-th observation under category j; ⑤ in Equation (5), ${{\gamma }^{\prime }}_j$ is the regression coefficient vector for the fixed effects part, $X_i$ is the independent variable vector for the i-th observation, ${{\beta }^{\prime }}_j$ is the regression coefficient vector for the random effects part, and $Z_i$ is the independent variable vector for the random effects part.

.

In the category of ordered models, this study not only utilizes the commonly used ordered logit model but also employs the partial proportional odds model. The ordered logit model operates under the proportional odds assumption, meaning that the same independent variable has identical regression coefficients, ${\beta }_k$, across different categories. In contrast, the partial proportional odds model relaxes this assumption, allowing the regression coefficients of the same variable to differ across categories ${\beta }_{jk}$. This flexibility is particularly important when the proportional odds assumption does not hold, enabling more accurate data modeling.

For multinomial models, although conditional logit and mixed logit models can incorporate item-specific attributes, the analysis of traffic accident causality primarily focuses on individual attributes. Therefore, this study selected the multinomial logit model to more accurately capture the contributions of different factors to accident risk.

Regarding the dependent variable, ordered models are based on ranking by severity, while multinomial models only require the dependent variable to be categorical. When the dependent variable is accident severity, theoretically, an ordered model should be used for analysis. However, some researchers still opt for the multinomial logit model [40]. This is because the multinomial logit model offers greater flexibility in handling unordered categorical dependent variables. While it cannot reflect the ordinal nature of the dependent variable, it can capture the independent effects of different factors on various levels of accident severity, aiding the comparison and validation of model results. Therefore, by comparing the performance of the ordered logit model, partial proportional odds model, and multinomial logit model, a more comprehensive understanding of how causal factors influence accident severity can be achieved.

3.2. Machine Learning Models

In recent years, machine learning models have gained increasing attention in traffic accident causation analysis due to their superior model fitting capabilities and advancements in interpretive methods [41,42]. Santos et al. [43] reviewed 56 studies on collision injuries and found that Decision Trees are the most widely used model, while Random Forests are often considered the best model. However, the Random Forest model has a slower training speed and higher computational cost. To address this issue, Extra Trees can reduce computational cost and mitigate overfitting problems through more random feature selection. Chen and Wang [44] found that the AdaBoost model performed best in their study. Therefore, this study selected six commonly used machine learning models and briefly introduced the theoretical basis and common hyperparameters of each model, summarizing their advantages and disadvantages (see

Table 3. Comparison of six ML models.

ML Models	Brief Description	Advantage	Disadvantage	Common Hyperparameters
Decision Tree	A simple, intuitive classification algorithm that models decisions as a tree.	High interpretability and ease of understanding Fast construction and prediction Not sensitive to small changes in data Can handle both categorical and continuous features	Prone to overfitting Susceptible to noise and outliers Requires expertise to choose tree depth and structure	max_depth min_samples_spilt min_samples_leaf
Random Forest	An ensemble learning algorithm that combines multiple decision trees to improve predictive performance.	High accuracy and robustness Resistant to overfitting Effective with high-dimensional data	Parallelizable across trees Computationally expensive Lower interpretability compared to single decision trees	n_estimators max_depth min_samples_split min_samples_leaf
Gradient Boosting	An iterative technique that sequentially builds decision trees, with each tree correcting the errors of the previous one.	Powerful predictive performance Excellent generalization capabilities Handles various data types well	Requires extensive hyperparameter tuning Sensitive to outliers	n_estimators learning_rate max_depth min_samples_split min_samples_leaf
AdaBoost	An algorithm that combines weak classifiers to form a strong classifier by focusing on the mistakes of previous classifiers.	Significant performance improvement with weak classifiers Applicable to small datasets Customizable weak classifiers	Prone to overfitting Sensitive to noise and outliers	n_estimators learning_rate
Extremely Randomized Trees (Extra Trees)	An algorithm that builds decision trees using random subsets of features, aiming to improve performance and reduce overfitting.	Fast training speed More random feature selection compared to RF Can be processed in parallel	Higher model complexity Less interpretable than a single decision tree	n_estimators max_depth min_samples_split min_samples_leaf
XGBoost	An efficient gradient boosting framework that uses tree-based models to optimize objective functions and prevent overfitting.	High computational efficiency Handles large-scale datasets well Regularization features to prevent overfitting Offers extensive hyperparameter options for tuning	Lacks interpretability compared to simpler models May not be optimal for small datasets	learning_rate n_estimators max_depth

).

4. Data Profile

This study focuses on a typical mountainous road segment in Chuxiong Prefecture, Yunnan Province, specifically the Yuan-Shuang Highway from K0+000 to K87+422 (including both basic road sections and intersections). This road is a two-way, two-lane highway with a total length of 87.42 km, a design speed of 60 km/h, and a roadbed width of 8.5 m. There are 159 curves along the route, with a minimum curve radius of 125 m, and the curved sections account for 46.14 km, or 52.54% of the total length. At the same time, more than 5000 traffic accident records and road alignment data from 2012 to 2022 were collected from local traffic management departments. The original accident data primarily include a brief description of the incident, time of occurrence, day of the week, kilometer marker, weather conditions, road surface, accident type, lighting conditions, vehicles involved, number of fatalities, missing persons, injuries, and direct property damage. As traffic accident data are often manually recorded, some entries may lack critical information or be unclear in their descriptions. Therefore, invalid information was excluded, and key information was extracted from the original data for classification. After filtering, 3183 traffic accident data points were extracted from this road section, forming a database for analyzing the causes of collisions in mountainous areas based on road alignment characteristics.

Additionally, in accordance with the Ministry of Public Security of China’s “Notice on Revising the Standards for the Classification of Road Traffic Accidents” and the “Interim Provisions on Traffic Accident Statistics” by the Traffic Management Bureau of China, specific classification standards for the severity of road collisions were defined (see

Table 4. Criteria for classifying accident severity.

Number of Injured Persons (B)/Number of Fatalities (C)		Property Damage Amount (A) in Yuan
		A < 200	200 ≤ A < 1000		1000 ≤ A < 30,000	30,000 ≤ A < 60,000	A ≥ 60,000
Non-motorized Vehicle Accidents		Minor accidents (1)	General accidents (2)
Motor Vehicle Accidents (No Fatalities)	B = 0	Minor accidents (1)				General accidents (2)	Major accidents (3)
	1 ≤ B ≤ 2	Minor accidents (1)		General accidents (2)		Major accidents (3)
	3 ≤ B ≤ 5	General accidents (2)				Major accidents (3)
	B > 5	Major accidents (3)
Motor Vehicle Accidents (With Fatalities)	1 ≤ C	Major accidents (3)

). Traffic accidents are categorized into three levels based on the extent of personal injury and property damage: minor accidents, general accidents, and major accidents.

This study analyzes mountain road traffic accidents from a technical system perspective. Based on a literature review and the calculation of the Variance Inflation Factor (VIF) for collinearity testing, the analysis results are shown in

Table 5. Variance inflation factor (VIF) analysis table.

Variable	VIF	1/VIF
RSC	1.05	0.951645
WR	1.05	0.954810
CVT	1.04	0.964906
VCT	1.03	0.974198
RA	1.02	0.976964
AP	1.02	0.977916
TE	1.02	0.979570
HY	1.00	0.998491

. Generally, when the VIF value is higher than 10, it indicates high multicollinearity among variables. However, in this study, the VIF values of the selected variables are all close to 1, indicating very low multicollinearity. Finally, eight independent variables were used for causality analysis of mountain vehicle collision severity: weather (WR), accident pattern (AP), road surface condition (RSC), collision vehicle type (CVT), time (TE), road alignment (RA), vertical curve type (VCT), and holiday (HY). Additionally, data were extracted, including start and end kilometer markers, road segment units, unit length (meters), accident occurrence frequency, number of accidents, left deflection angle (°), right deflection angle (°), horizontal curve radius (meters), horizontal curve length (meters), and vertical curve length (meters). Using a slope threshold of |2.5|%, the road segments were divided into straight and gradient sections. According to the “Highway Route Design Code (JTG D20-2017)” issued by the Ministry of Transport of China, the minimum design limit for horizontal curve radii should be 150 m. However, in the dataset used in this study, the minimum radius of horizontal curves was 125 m, and a significant number of accidents occur on extremely curved sections where the radius falls between 125 and 150 m. Therefore, road segments with a horizontal curve radius of less than 150 m are classified as curved sections, while those with a radius greater than 150 m are classified as straight sections. The variable descriptions are shown in

Table 6. Variable descriptions.

Variable	Value	Minor Accidents		General Accidents		Major Accidents		Total
		Number	Percentage	Number	Percentage	Number	Percentage
WR	Sunny-1	1861	66.14%	812	28.85%	141	5.01%	2814
	Rainy and snow-2	125	72.25%	42	24.28%	6	3.47%	173
	Cloudy-3	130	66.33%	57	29.08%	9	4.59%	196
AP	Collision with fixed object-1	202	78.90%	40	45.63%	14	5.47%	256
	Rollover-2	146	59.84%	87	35.66%	11	4.51%	244
	Vehicle falling-3	3	27.27%	1	9.09%	7	63.64%	11
	Side collision-4	777	63.33%	411	35.94%	39	3.18%	1227
	Rear-end collision-5	654	81.55%	139	17.33%	9	1.12%	802
	Head-on collision-6	47	40.87%	46	40%	22	19.13%	115
	Collide with pedestrian-7	135	56.96%	74	31.22	28	11.81	237
	Other collisions-8	136	50.75%	106	39.55%	26	9.70%	268
	Scratch-9	16	69.57%	7	30.43%	0	0	23
RSC	Dry-0	2039	66.31%	885	28.78%	151	4.91%	3075
	Wet-1	77	71.30%	26	24.07%	5	4.63%	108
CVT	Vehicle-pedestrian accident-1	145	57.54%	79	31.35%	28	11.11	252
	Single vehicle accident-2	192	81.70%	30	12.77	13	5.53%	235
	Multiple vehicle accident-3	1779	65.98%	802	29.75%	115	4.26%	2696
TE	Daytime-0	1577	68.56%	641	27.87%	82	3.57%	2300
	Nightime-1	539	61.04%	270	30.58%	74	8.38%	883
RA	Horizontal curve section-1	208	61.72%	112	33.23%	17	5.04%	337
	Longitudinal slope section-2	179	71.60%	61	24.40%	10	4.00%	250
	Straight road section-3	1426	65.26%	647	29.61%	112	5.13%	2185
	Combination of curved and sloping sections-4	303	73.72%	91	22.14%	17	4.14%	411
VCT	Flat-1	1240	65.23%	554	29.14%	107	5.63%	1901
	Convex-2	381	70.17%	142	26.15%	20	3.68%	543
	Concave-3	495	66.98%	215	29.09%	29	3.92%	739
HY	Weekday-0	1530	66.55%	658	28.62%	111	4.82%	2299
	Public holiday-1	586	66.29%	253	28.62%	45	5.09%	884

Note: WR (weather), AP (accident pattern), RSC (roadside conditions), CVT (collision vehicle type), TE (time), RA (road alignment), VCT (vertical curve type), and HY (holiday); “Other collisions” in AP include collisions with wildlife, electric vehicles, and other special forms of incidents.

.

In the dataset comprising 3183 instances, minor accidents accounted for 66.5%, general accidents constituted 28.6%, while major accidents only represented 4.9%. This imbalance may cause machine learning models to favor the prediction of the majority class, thereby overlooking the minority class, leading to significant bias in the analysis results. To address this issue, it is essential to handle data imbalance prior to model training, ensuring that the model accurately reflects the characteristics of each class and minimizes prediction bias.

There are two primary techniques for handling imbalanced data: under-sampling and over-sampling. Under-sampling techniques include random under-sampling and ensemble under-sampling methods (e.g., random under-sampling and balance cascade), which balance the dataset by reducing the number of majority class samples. However, these methods risk discarding valuable information. On the other hand, over-sampling techniques include random over-sampling and synthetic minority over-sampling techniques (e.g., SMOTE, ADASYN, and Borderline-SMOTE), which balance the dataset by increasing the number of minority class samples.

Numerous studies have demonstrated that SMOTE, among over-sampling methods, exhibits superior performance in addressing data imbalance issues in the field of traffic accident causality analysis [45,46,47]. SMOTE (Synthetic Minority Over-Sampling Technique) generates new synthetic samples by interpolating between existing minority class samples, thereby expanding the minority class and reducing the risk of overfitting. This study employed SMOTE to process the training set (with 80% of the accident data used for training and 20% for testing). Additionally, commonly used methods such as Random Over-Sampling and Random Under-Sampling were applied, and the data processed by these three different methods were input into the XGBoost model with default hyperparameters. By comparing the accuracy across these methods, the superiority of SMOTE was validated. The specific process of running SMOTE is as follows:

• For each sample in the minority class, compute the Euclidean distance to all other samples in the minority class and identify the k-nearest neighbors;
• Set the sampling rate N and randomly select a number of k-nearest neighbors of x;
• Construct a new sample using the following formula:

$$x_{new}=x+\mathrm{rand}(0,1)\times \left|x-x_n\right|$$

(6)

Here, $x_{new}$ represents the newly generated synthetic sample, x is an original minority class sample, and $x_n$ is a k-nearest neighbor sample of x, which is a sample close to x in the feature space.

5. Model Comparison

This section aims to comprehensively examine the performance of the selected models and interpret their results. First, the training set data were used to test the statistical analysis models (Ordered Logit model, Multinomial Logit model, and Partial Proportional Odds model) to check whether the data met the model assumptions.

Second, the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) were used for statistical models, while the F1 score and AUC value were used for machine learning models. Additionally, the prediction accuracy of all models was calculated and compared. Finally, the causal analysis results of all models were compared and thoroughly analyzed. To ensure robust results, the formulas for the metrics used to compare the statistical analysis models were as follows:

$$\mathrm{AIC}=2k-2\ln (\hat{L})$$

(7)

$$\mathrm{BIC}=\ln (n)k-2\ln (\hat{L})$$

(8)

In Equation (7), k represents the number of estimated parameters in the model, and $\hat{L}$ is the maximum likelihood estimate of the model. In Equation (8), n denotes the number of samples; k is the number of estimated parameters in the model, and $\hat{L}$ is the maximum likelihood estimate of the model.

The metric formula used for comparing machine learning models is as follows:

$$\mathrm{Accuracy}={\displaystyle \frac{TP+TN}{TP+TN+FN+FP}}$$

(9)

$$\mathrm{Precision}={\displaystyle \frac{TP}{TP+FP}}$$

(10)

$$\mathrm{Recall}={\displaystyle \frac{TP}{TP+FN}}$$

(11)

$$\mathrm{F}1={\displaystyle \frac{2\times \mathrm{Precision}\times \mathrm{Recall}}{\mathrm{Precision}+\mathrm{Recall}}}$$

(12)

In the formula, TP represents the number of true positive classifications, FN represents the number of false negative classifications, FP represents the number of false positive classifications, and TN represents the number of true negative classifications.

5.1. Hypothesis Testing of Data and Comparison of Statistical Models

To ensure robust results, this study used random sampling, selecting 80% of the total accident data as the training set, and the remaining 20% as the test set for validation. The models used in this section were executed in Stata.

Before applying statistical analysis models, it was crucial to verify whether the data met the assumptions of the models. The fundamental assumption of the ordered logit model is that the odds ratio of the independent variables remains constant across the ordered response categories. This means each independent variable has a uniform impact on the transition between response categories. Therefore, the Brant test was used to assess this assumption for the Ordered Logit model. The Partial Proportional Odds model extends the Ordered Logit model, allowing certain variables to violate the proportional odds assumption, thus eliminating the need for this test. The Multinomial Logit model requires that the data satisfy the IIA (independence of irrelevant alternatives) assumption, which means that the addition or removal of categories of the dependent variable should not affect the probability of choosing other categories.

The Brant test was used to evaluate whether the Ordered Logit model met the proportional odds assumption. As shown in

Table 7. Brant test for the ordered logit model.

Independent Variable	${\mathit{x}}^2$	p-Value	Degrees of Freedom
ALL	31.00	0.000	8
WR	0.27	0.602	1
AP	0.38	0.539	1
RSC	0.56	0.456	1
CVT	11.40	0.001	1
TE	9.35	0.002	1
RA	0.52	0.472	1
VCT	1.68	0.194	1
HY	0.11	0.746	1

, the p-values for collision vehicle type and time were less than 0.1, indicating that the results were not significant at the 90% confidence level, meaning the proportional odds assumption was not met. The Multinomial Logit model requires that the data meet the IIA assumption, which means that deleting or adding categories of the dependent variable does not affect the probability of choosing other categories. The test results are shown in

Table 8. IIA test.

Omitted	Chi2	df	p > Chi2
2	3.061	9	0.962
3	0.497	9	1.000
1	−7.984	9	---

. The IIA assumption requires a chi-square value greater than 0. If the chi-square is less than 0, the model does not meet the asymptotic assumption, indicating that the data do not meet the IIA assumption.

In the Partial Proportional Odds model, less significant variables were gradually removed to make the model analysis more accurate. As shown in Figure 2, as the number of variables decreased, the model’s overall performance was optimal when the number of variables (including sub-variables) was 13.

Subsequently, a horizontal comparison of the three statistical analysis models was conducted based on AIC and BIC. The comparison results are as follows:

As shown in Figure 3, the Partial Proportional Odds model had the lowest AIC and BIC values, indicating better model performance. In contrast, the Ordered Logit model and the Multinomial Logit model had poorer fit performance due to the data not meeting the model’s assumptions.

5.2. Comparison of Machine Learning Models

Before conducting a comprehensive evaluation of the Machine Learning model’s performance, this study applied three different resampling methods—SMOTE, Random Over-Sampling, and Random Under-Sampling—to the originally imbalanced accident dataset. The processed datasets were then input into an XGBoost model with default parameters for prediction. The decision to use the XGBoost model with default parameters was made to provide a baseline reference, allowing for an initial assessment of the effectiveness of the data imbalance handling methods without involving complex hyperparameter tuning. Additionally, XGBoost has demonstrated excellent performance in handling non-linear data and high-dimensional features, offering strong generalization capabilities and inherent advantages in dealing with imbalanced data, making it a suitable model for evaluating these resampling methods. Furthermore, the study utilized the Optuna framework to iteratively optimize the specific parameters for each resampling method, including determining the precise number of samples generated for each accident severity level and identifying the optimal value for k-neighbors in the SMOTE method. Optuna is an efficient automated hyperparameter optimization framework based on Bayesian optimization, which intelligently selects the most appropriate parameter combinations by constructing a probabilistic model of the objective function. The data generated for each category under different resampling methods after iteration are shown in the table below (

Table 9. Data distribution by different imbalance handling methods.

Method	Minor Accidents	General Accidents	Major Accidents	k-Neighbors
SMOTE	2844	930	581	5
Random Over-Sampling	2419	1150	694	-
Random Under-Sampling	202	92	14	-

).

After balancing the dataset using these three methods, the original unbalanced dataset was also input into the XGBoost model with default hyperparameters for prediction. The prediction accuracies obtained are shown in Figure 4.

As shown in Figure 4, over-sampling methods are more suitable for the dataset used in this study compared to under-sampling methods. Among all the evaluated approaches, the XGBoost model performed best when trained on data processed with SMOTE, showing an approximate 24.23% improvement in accuracy compared to the original unbalanced data. Therefore, SMOTE was selected for data balancing.

To further evaluate the performance of the machine learning models, the F1 score and AUC value were introduced for a comprehensive comparison of the six selected models, with the results presented in Figure 5 and Figure 6. Additionally, the Optuna method was employed to search for the optimal hyperparameters for each model, which are listed in

Table 10. Variance inflation factor (VIF) analysis table.

Model	Hyperparameter	Value
Decision Tree	max_depth	14
	min_samples_split	2
	min_samples_leaf	1
Random Forest	n_estimators	800
	max_depth	9
	min_samples_split	11
	min_samples_leaf	1
Gradient Boosting	n_estimators	200
	learning_rate	0.028
	max_depth	8
	min_samples_split	4
	min_samples_leaf	3
AdaBoost	n_estimators	200
	learning_rate	0.217
Extra Trees	n_estimators	200
	max_depth	20
	min_samples_split	4
	min_samples_leaf	1
XGBoost	n_estimators	200
	learning_rate	0.134
	max_depth	5

.

The F1 scores for Decision Tree, Random Forest (RF), Gradient Boosting (GB), AdaBoost, Extra Trees, and XGBoost were 0.7538, 0.7540, 0.7403, 0.6183, 0.7543, and 0.7585, respectively. From Figure 5, it can be observed that the F1 score of the AdaBoost model was significantly lower than that of the other models, while the differences among the other machine learning models were relatively small, with XGBoost performing slightly better.

To provide a more comprehensive comparison, ROC curves were introduced to further evaluate the machine learning models’ performances (Figure 6). Before plotting the ROC curves, the multiple classification variables were converted into binary variables (indicating the presence or absence of each feature), and ROC plots were drawn for each type of traffic accident. Finally, the three ROC curves were combined. When it was difficult to determine which ROC curve represents better performance, the AUC value was used for judgment.

As the false positive rate increased, the true positive rate for different types of accidents also increased. A horizontal comparison of ROC curves for different accident types shows that the increase in the true positive rate is most apparent for major accidents, with the ROC curves being highly consistent. This indicates that the machine learning models constructed in this study are most sensitive to capturing major accidents, demonstrating strong specificity in model discrimination. Conversely, for minor and moderate accidents, the curves show a slower increase in the true positive rate as the false positive rate rises, indicating lower specificity compared to major accidents. Gradient Boosting and XGBoost models exhibit more importance analysis results, both showing excellent analysis capabilities for major accidents (with AUC values of 0.96 and highly consistent fitting curves). For general accidents, XGBoost shows better applicability. For minor accidents, although Gradient Boost demonstrated superior fitting performance compared to all other machine learning models when the false positive rate reached around 0.2, it was generally still outperformed by XGBoost.

5.3. Comparison of Model Fitting Ability

After comparing the statistical models and machine learning models in the previous sections, this study found that the partial proportional odds model in the statistical analysis models, and the XGBoost model in the machine learning models, performed the best. In this section, accuracy was selected as the metric to conduct a horizontal comparison between the two types of model to identify the optimal model for analyzing the causes of traffic accidents. The comparison is illustrated in Figure 7.

From Figure 7, it can be observed that most machine learning models exhibit stronger fitting performance, while statistical analysis models are limited by their linear construction, resulting in weaker predictive capabilities. The accuracies of Decision Tree, Random Forest (RF), Gradient Boosting (GB), AdaBoost, Extra Trees, and XGBoost models were 75.73%, 75.73%, 74.27%, 61.84%, 75.73%, and 79.25%, respectively. XGBoost had the highest prediction accuracy at 79.25%, whereas AdaBoost had the lowest accuracy at 61.84%. This could be due to the limitations of AdaBoost in feature selection and weight allocation, reducing its ability to leverage key features. A comprehensive comparison indicates that XGBoost offers the best overall performance.

5.4. Ranking of Variable Importance

Although previous studies have primarily focused on the predictive performance of models, it is also crucial to understand the impact of influencing factors to validate the effectiveness of the models. Machine learning models outperform statistical analysis models due to their powerful feature learning capabilities [43,48,49]. However, their excellent feature learning abilities can lead to overfitting, complicating comprehensive and reliable collision cause analysis. Therefore, this study calculated the impact coefficients of each variable in the statistical analysis models and the importance of each predictor variable in the machine learning models. For comparison, the eight predictor variables were grouped into three categories: event-related (weather, accident pattern, collision vehicle type), time-related (time, holiday), and road condition-related (road alignment, vertical curve type, road surface condition). The variables were ranked in descending order of importance, with the top two most important predictors in each model highlighted in bold, and less important variables omitted (importance less than 0.1), as shown in

Table 11. Importance ranking of all models.

Model	Event-Related	Temporal	Road Condition-Related
Ordered Logit Model	Accident pattern	Time	Road alignment, Vertical curve type
Partial Proportional Odds Model	Collision vehicle type, Accident pattern, Weather		Road alignment
Multi-nominal Logit Model	Accident pattern, Collision vehicle type	Time	Vertical curve type, Road alignment
Decision Tree	Accident pattern		Road alignment, Vertical curve type
Random Forest	Accident pattern		Road alignment, Vertical curve type
Gradient Boosting	Accident pattern	Time	Vertical curve type, Road alignment
AdaBoost	Accident pattern, Collision vehicle type, Weather
Extra Trees	Accident pattern		Vertical curve type, Road alignment
XGBoost	Accident pattern, Collision vehicle type	Time	Vertical curve type, Road alignment

.

Overall, all models identified accident pattern as significantly affecting the severity of collisions. Most models determined road alignment and vertical curve type as important factors, consistent with previous studies. However, only the ordered logit and multinomial logit models identified time as important, possibly due to data not meeting the assumptions of these models, resulting in biased estimates and impaired interpretability. In contrast, the PPO model identified vehicle type as the most important event-level factor, which differs significantly from the conclusions of other models, likely due to different modeling mechanisms. Statistical models build a linear relationship between predictors and response. However, collision data are complex, making it difficult to distinguish between causality and correlation, complicating the application of statistical models in this context. Machine learning models, being non-linear, can capture complex relationships and interactions without requiring strict assumptions about the training data. Thus, for this study’s dataset, machine learning models were better suited for analyzing collision causes.

In most machine learning models, only three factors were identified as important. In models such as Decision Trees, Random Forests, AdaBoost, and Extra Trees, the calculated importance of accident patterns was excessively high. Consequently, the importance of other factors was downplayed, masking potential factors related to the dependent variable and hindering the further quantification of individual and interactive impacts of risk factors on accident severity. However, gradient boosting and XGBoost, as advanced gradient boosting algorithms, demonstrated significant advantages in explaining feature importance [50,51]. These models use an iterative optimization process to gradually refine the identification of each feature’s contribution to the predictive outcome. In each iteration, the model adjusts according to the previous round’s bias, continuously improving the assessment of feature importance and more accurately capturing the impact of each feature. Specifically, the XGBoost model introduces a regularization term, effectively suppressing overfitting, enhancing the precision of feature selection, and thereby improving the reliability and interpretability of feature importance. This understanding of feature importance provides a more precise and transparent perspective for analyzing the causes of traffic accidents, revealing the complex factors and interactions behind the accidents.

6. Contributing Factors Analysis

Lundberg and Lee proposed SHAP (SHapley Additive exPlanations), a game theory-based method to explain the contribution of each feature value [52]. SHAP significantly enhances the interpretability of the XGBoost model, transforming machine learning from a “black box” into an interpretable model. Therefore, an increasing number of studies are using SHAP to interpret the results of machine learning algorithms in pedestrian collision analysis [51,53]. This chapter utilizes the SHAP method to analyze, first, from a macro perspective, the contribution ranking of accident causes under different severity levels. Secondly, it selects the three most influential predictors and discusses the impact of their sub-variables on different severity levels of traffic accidents. This allows for more precise accident prevention.

6.1. SHAP Summary Plot Analysis

The SHAP bar plot illustrates the overall contribution of different features to predicting accident severity but does not distinguish the specific contribution of each feature to each severity level. To address this, a second type of SHAP summary plot is introduced. This plot separately displays the contribution of each predictor to the different levels of the response variable. By evaluating the marginal contribution when introduced into the model, it quantifies the impact of each feature on the prediction. The summary plot (see Figure 8) reveals the relative contribution of each feature to the prediction and clarifies the relationship between feature values and prediction outcomes, aiding the understanding of the model’s decision-making based on different categories. The horizontal axis represents the magnitude of SHAP values, while the color indicates the size of the feature values. Higher SHAP values indicate a greater impact on the prediction results.

In the analysis of minor accidents (see Figure 8a), the top four contributing factors are AP, VCT, TE, and RA. In the analysis of ordinary accidents (see Figure 8b), the top four contributing factors are AP, CVT, VCT, and RA. In the analysis of major accidents (see Figure 8c), the top four contributing factors are VCT, AP, CVT, and RA.

By comparing these, it can be observed that WR and RSC have relatively small impacts on traffic accidents. AP has the highest importance and significantly contributes to all three levels of accident severity. This is followed by road factors (both VCT and RA are road factors) and then by collision vehicle type (CVT) [6,14]. This result has also been supported in previous studies. Although VCT has a high importance, the different sub-variables do not show significant differences in their contributions to different accident severity levels. Therefore, a more detailed analysis will be conducted on AP, CVT, and RA.

6.2. Direct Effects of Main Causal Factors

In the previous section, this study identified accident pattern (AP), collision vehicle type (CVT), and road alignment (RA) as the main factors influencing the severity of accidents. Next, this study will explore the detailed relationships between these factors and accident severity by visualizing how AP, CVT, and RA are associated with the three levels of accident severity.

6.2.1. Direct Effects of AP

The accident pattern (AP) significantly influences accidents of varying severity levels. To explore the impact of AP on different severity levels, we analyzed the SHAP values associated with different accident patterns across varying levels of severity. The SHAP correlation plots are presented in Figure 9. In these plots, the horizontal axis represents the accident pattern categories (as indicated in the note), while the vertical axis represents the SHAP values. A positive SHAP value indicates a positive contribution, meaning that the particular accident pattern is likely to increase the probability of an accident occurring at that severity level. Conversely, a negative SHAP value indicates a negative contribution, suggesting that the accident pattern might decrease the likelihood of an accident occurring at that severity level.

From Figure 9, it is observed that different accident patterns exhibit significant variations in SHAP values for minor accidents. In minor accidents, the SHAP values for collisions with fixed objects (AP = 0) and rollovers (AP = 1) are approximately normally distributed, with the values concentrated around zero. This distribution is similar to that of side collisions (AP = 3) and scratches (AP = 8), indicating that these four accident patterns have a relatively small impact on the likelihood of minor accidents. Conversely, the SHAP values for vehicle falling (AP = 2), head-on collisions (AP = 5), collisions with pedestrians (AP = 6), and other collisions (AP = 7) generally trend negatively, suggesting a lower likelihood of minor accidents occurring under these accident patterns. In contrast, the SHAP values for rear-end collisions (AP = 4) trend positively overall, indicating a higher likelihood of minor accidents in rear-end collision scenarios.

For general accidents, the SHAP distributions for rollovers (AP = 1), side collisions (AP = 3), collisions with pedestrians (AP = 6), and scratches (AP = 8) do not show any clear trends. However, the SHAP values for collisions with fixed objects (AP = 0), vehicle falling (AP = 2), rear-end collisions (AP = 4), and head-on collisions (AP = 5) are predominantly negative, suggesting a lower likelihood of general accidents under these patterns. The SHAP values for other collisions (AP = 7) are notably positive, indicating that this accident pattern is more likely to result in general accidents compared to others.

In severe accidents, the differences in SHAP values across accident patterns are even more pronounced. However, the SHAP values for rollovers (AP = 1) and scratches (AP = 8) do not show clear trends. Although some SHAP values for collisions with fixed objects (AP = 0) are negative, around -1, the overall distribution remains near zero, indicating no clear tendency. On the other hand, the SHAP values for side collisions (AP = 3), rear-end collisions (AP = 4), and other collisions (AP = 7) are distinctly negative, suggesting that these patterns suppress the occurrence of severe accidents. The SHAP values for vehicle falling (AP = 2), head-on collisions (AP = 5), and collisions with pedestrians (AP = 6) are generally positive, with particularly high SHAP values for head-on collisions (AP = 5) and vehicle falling (AP = 2), indicating a significant positive contribution to the occurrence of severe accidents.

In summary, this study found that collisions with fixed objects and other types of collisions are less likely to result in minor or major accidents. Collisions with fixed objects typically occur at low speeds (such as during turns) and, while they may cause some injury to the driver, they are unlikely to lead to major accidents. “Other collisions” mainly involve vehicles colliding with special objects such as livestock or electric bikes. The severity of these accidents is generally not too high (as drivers’ attention is usually highly focused in complex traffic environments, effectively reducing the severity of accidents) or too low (as electric bike riders and other non-motorized vehicle drivers lack protection and may be injured in a collision). Therefore, in these two types of accident pattern, the probability of minor and major accidents is relatively low, consistent with the findings of Behnood and Al-Bdairi [54]. However, vehicle falling, head-on collisions, and collisions with pedestrians significantly increase the likelihood of severe accidents, with vehicle falling and head-on collisions associated with greater accident severity, aligning with the results of Zhu and Srinivasan, as well as Wen et al. [6,55]. The positive contribution of pedestrian collisions to severe accidents is relatively small, which can be explained by the fact that such collisions often occur in villages or residential areas, where drivers may be more vigilant, leading to more opportunities to decelerate or avoid pedestrians, thus reducing the impact energy. Rear-end collisions and side collisions are associated with a reduced likelihood of severe accidents. Unlike previous research, such as the 2017 report by the National Highway Traffic Safety Administration (NHTSA) which indicated that over 50% of traffic fatalities in mountainous areas of Wyoming were related to rollovers, this study found that the SHAP values for rollovers were close to zero across minor, general, and severe accidents, indicating no clear tendency towards severity. Similarly, the distribution of SHAP values for scratches was highly concentrated around zero, suggesting a minimal contribution to changes in accident severity.

6.2.2. Direct Effects of CVT

By analyzing the SHAP values associated with different collision vehicle types (CVT) across varying levels of accident severity, we can gain insights into how these vehicle types influence the severity of accidents. Figure 10 presents the SHAP correlation plots, which illustrate the SHAP values of different CVT types in minor, general, and major accidents.

In minor accidents, the SHAP values for vehicle-pedestrian collisions (CVT = 0) are mostly positive, indicating a strong positive impact on minor accidents, meaning that such collisions are more likely to result in minor accidents. Conversely, the SHAP values for single-vehicle accidents (CVT = 1) are widely distributed, with many values close to zero and some below −1, suggesting a lower likelihood of resulting in minor accidents. For multiple-vehicle accidents (CVT = 2), the SHAP values are generally low, showing a weaker association with minor accidents.

Regarding general accidents, the SHAP values for vehicle–pedestrian collisions (CVT = 0) and single-vehicle accidents (CVT = 1) are more dispersed and predominantly negative, indicating a lower probability of leading to general accidents. On the other hand, multiple-vehicle accidents (CVT = 2) have mostly positive SHAP values, suggesting a strong positive correlation with general accidents.

In major accidents, the SHAP values for different CVT types exhibit clear differences. Vehicle–pedestrian collisions (CVT = 0) and single-vehicle accidents (CVT = 1) show SHAP values mainly concentrated between 0 and 0.5, indicating an increased likelihood of resulting in major accidents. In contrast, the SHAP values for multiple-vehicle accidents (CVT = 2) are almost all negative, suggesting a lower probability of leading to major accidents.

The comparison of the impact of different collision vehicle types on accident severity indicates that the effect of vehicle–pedestrian collisions on accident severity is quite dispersed, making it difficult to establish a clear trend. In single-vehicle collisions, the likelihood of minor and general accidents is low, but the probability of severe accidents increases significantly. In contrast, the SHAP values for multi-vehicle collisions are concentrated between 0 and −1, suggesting that this collision pattern reduces the likelihood of severe accidents. This finding aligns with the results of studies by Wang et al. and Wen and Xue [5,19]. However, it contradicts the findings of Chen and Chen [22], who observed that multi-vehicle accidents on Colorado’s mountainous roads tend to result in more severe accidents compared to single-vehicle accidents, with substantial support from other studies [56,57]. Consequently, single-vehicle and multi-vehicle collisions may not be the definitive factors determining accident severity. Existing research indicates that the influence of single-vehicle and multi-vehicle collisions on accident severity is shaped by a combination of factors, including road conditions, driver behavior, and weather conditions [25,58].

6.2.3. Direct Effects of RA

On mountainous roads, complex road alignments are one of the primary factors contributing to traffic accidents. To further investigate the impact of different road alignments (RA) on various levels of accident severity, Figure 11 presents the SHAP dependence plots for RA across different accident severities.

For minor accidents, the SHAP values for horizontal curve sections (RA = 0) are relatively dispersed but predominantly positive, with some high positive values, indicating a strong correlation between these sections and the occurrence of minor accidents. The SHAP values for longitudinal slope sections (RA = 1) are also dispersed, while the SHAP values for straight road sections (RA = 2) are concentrated within the range of −0.5 to 0.5, with more negative values, suggesting that minor accidents are less likely to occur on these road types. Conversely, the SHAP values for combined curved and sloping sections (RA = 3) are more dispersed and predominantly positive, indicating a strong correlation between these sections and the occurrence of minor accidents.

For general accidents, the SHAP values for horizontal curve sections (RA = 0), longitudinal slope sections (RA = 1), and combined curved and sloping sections (RA = 3) are relatively dispersed. Among these, the SHAP values for longitudinal slope sections (RA = 1) and combined curved and sloping sections (RA = 3) exhibit more negative values, suggesting that general accidents are less likely to occur on these road types. The SHAP values for straight road sections (RA = 2) are highly concentrated around 0, indicating a minimal impact on general accidents.

In the case of major accidents, the SHAP values for different road alignments show significant differences. Horizontal curve sections (RA = 0) and combined curved and sloping sections (RA = 3) exhibit notable negative contributions, indicating that major accidents are less likely to occur on these road types. The SHAP values for horizontal curve sections (RA = 0) are particularly low compared to those for combined curved and sloping sections, suggesting that the probability of major accidents is lowest on horizontal curve sections. Additionally, the SHAP values for straight road sections (RA = 2) are highly concentrated around 0, indicating a minimal impact on major accidents. Although the SHAP values for longitudinal slope sections (RA = 1) are mostly between 0 and −1, some extreme positive values exist, indicating that major accidents are most likely to occur on these sections.

In summary, straight road sections contribute minimally to all levels of traffic accident, whereas longitudinal slope sections are more likely to lead to major accidents, consistent with the findings of Huang et al. [22]. Horizontal curve sections and combined curved and sloping sections have a suppressive effect on major accidents. However, this study found that, contrary to previous research indicating that a lower radius of horizontal curves increases the likelihood of major accidents, horizontal curve sections actually have the strongest suppressive effect on major accidents, though they may also lead to a higher occurrence of minor accidents [59]. The reason may be that the radius of horizontal curves studied in this research is smaller than in previous studies. Such sharp turns require drivers to significantly reduce speed and increase their attention, thereby reducing the likelihood of major accidents. However, sharp turns can also lead to more frequent braking and steering maneuvers, making it difficult for vehicles to control steering angles effectively. This may result in side collisions with other vehicles, rear-end collisions, or collisions with fixed objects. As analyzed in Section 6.2.1, these accident patterns are more likely to cause minor accidents, increasing the probability of minor accidents on these road sections.

7. Conclusions

This study provided a comprehensive review of nine methods widely used for causal analysis of traffic accidents in mountainous areas. These methods were applied to a traffic accident dataset from Yunnan Province to identify key risk factors affecting accident severity, with the aim of constructing a safe and sustainable transportation environment for local residents. Three statistical analysis methods (the Ordinary Least Squares Regression (OLM), the Poisson Proportional Odds Model (PPOM), and the Multinomial Logistic Model (MLM)) and six machine learning methods (Decision Trees, Random Forests (RF), Gradient Boosting (GB), AdaBoost, Extra-Trees, and XGBoost) were selected. Utilizing data from a dual-lane mountainous highway in Yunnan Province, the study assessed the performance of these methods in predicting accident severity and explaining influencing factors. The study began with a brief overview of the nine methods and the dataset, using SMOTE to address data imbalance issues. The analysis of nine models’ predictive factors, and the exploration of differences between the two main categories of method, revealed notable distinctions in prediction performance and importance analysis. Based on these findings, the following conclusions were drawn:

• Among the statistical models, the Partial Proportional Odds Model performed better than other statistical analysis models [37,38], while XGBoost outperformed other machine learning models;
• Machine learning models were found to be generally superior to statistical analysis models in terms of accuracy. After considering model performance and the rationality of analysis results, XGBoost emerged as the optimal model;
• The analysis revealed that accident patterns have the most significant impact, followed by road factors (such as vertical curve type and road alignment) and collision vehicle types. Environmental factors like weather and road conditions had the least impact on accidents. This conclusion is almost consistent with the findings of Li et al. regarding the causes of traffic accidents on mountain roads in Jiangxi Province [4];
• Consistent with previous research, this study found that head-on collisions [6,55], vehicle falls, and collisions with pedestrians increase the likelihood of major accidents. Similarly, major accidents are also more likely to occur on longitudinal slope sections. Furthermore, single-vehicle and multi-vehicle collisions are not the sole determinants of accident severity. The severity of these accident types often interacts with various factors such as road conditions, driver behavior, and weather conditions, collectively influencing the overall severity of accidents;
• In contrast to previous research, this study found that the likelihood of major accidents decreases while the likelihood of minor accidents increases on road sections with lower radii of horizontal curves and on combined curved and sloping sections. This may be because, under such extreme road conditions, drivers are more cautious and attentive, which reduces the severity of accidents.

However, since the study utilized data from only one province, the conclusions may lack comprehensiveness and generalizability. Future research should expand the scope by collecting data from a broader range of mountainous areas to obtain more universally applicable findings. These analyses will aid traffic management authorities in mountainous regions to establish more detailed regulations and contribute to the sustainable development of local communities.