category: literaturenote citekey: kimspatiotemporalurbantrafficsafety2025 title: Spatiotemporal urban traffic safety analytical framework by integrating nonparametric approaches authors: "Kim, Youngwoong; Lee, Dongwoo; Derrible, Sybil" year: 2025 date: 2025-00-00 2025 doi: 10.1016/j.aap.2025.108088 publication: "Accident Analysis & Prevention" url: "https://doi.org/10.1016/j.aap.2025.108088" zotero_key: 2ZU3A27V zotero_storage: C4KQFIIS collections: transpordi_planeerimine folder: 001_artiklid firstAuthor: "Kim, Youngwoong"

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Accident Analysis and Prevention

journal homepage: www.elsevier.com/locate/aap

Spatiotemporal urban traffic safety analytical framework by integrating nonparametric approaches

^a Department of Smart Cities, University of Seoul, Seoul 02504, Republic of Korea
^b Department of Civil and Materials Engineering, University of Illinois at Chicago, USA

ARTICLE INFO

Keywords: Unobserved Heterogeneity Spatiotemporal Correlation Nonparametric modeling Urban Informatics Traffic Accident Gaussian Process

ABSTRACT

Since more than 75% of the population lives in cities, it is crucial to create a safe transportation environment for all urban residents. In this context, significant efforts are required to mitigate potential accident risks and make cities more inclusive. To gain insights into an inclusive traffic safety environment and develop a system that provides useful traffic safety information accessible to all stakeholders, from end-users to decision-makers, this article aims to develop a novel nonparametric modeling framework, the Mixed-Effect Tree Ensemble with a Gaussian Process (ME-GP), for city-wide traffic safety analysis. In this study, we use police-reported accident data from Seoul (South Korea). The framework leverages the advantages of integrating nonparametric modeling approaches to predict accident risks at the road-segment level while accounting for spatiotemporal heterogeneity and unobserved data complexities. The Gaussian process, in particular, enables us to capture nonlinearities and discontinuities when estimating random parameters. Due to the nature of the police-reported accident data, Treeensemble is integrated with the Gaussian process. Compared to other nonparametric models, including integrated modeling approaches, ME-GP demonstrated a 15% improvement in predictive accuracy and lower variance in out-of-sample predictions, highlighting its robustness and reliability. The result revealed that demographics, traffic conditions, and road structure are the most determinant factors in accident risks. As expected, the relationship between determinant factors and accident risks is nonlinear and spatiotemporally heterogeneous. Elderly accidents were found to have a maximum accident risk of 20% higher than that of youth. In contrast, children who are also physically vulnerable showed a lower accident risk, which is partly because of school zones that effectively protect children. The findings from the framework can provide useful insights into establishing safe and inclusive urban networks.

1. Introduction

Traffic accidents are significant social costs (e.g., property damage and human casualties) responsible for about 1.3 million fatalities annually, with young people aged 5 to 29 being the primary victims (WHO, 2023). In 2020, 40 % of all road fatalities in European countries (i.e., EU27) occurred on urban roads (GHSA, 2023). Since more than 75 % of the population lives in cities, investigating traffic accidents and associated behaviors is important for establishing strategies for traffic safety (Lie et al., 2024). In this context, a comprehensive city-wide traffic safety assessment tool that predicts the level of accident risk at road segments holds much potential for providing practical insights into traffic safety assessment and further management.

Predicting accident risks and relevant factors affecting accidents in

urban areas is challenging. Accident events and their severities, in particular, involve inherent uncertainties, including aleatoric and epistemic. Due to the interrelated nature of accidents (e.g., unobserved intercorrelation between human and spatiotemporal factors), aleatoric uncertainties are inevitable. Furthermore, the limited number of vectorized datasets for road networks and built environments can increase epistemic uncertainties. These two uncertainties must be alleviated somehow by making efforts to collect datasets and model heterogeneities. Although traditional modeling approaches (e.g., parametric models) can address these uncertainties with a robust theoretical background, parametric approaches with strong assumptions may still suffer from recognizing complex patterns among predictors (Hou et al., 2022). The limitation of traditional approaches becomes exacerbated due to the discrete nature of accident data (i.e., manually reported at the

E-mail address: eastrain@uos.ac.kr (D. Lee).

^* Corresponding author.

scene) with high cardinality. Thus, it is important to have modeling approaches that can incorporate random variability into predictable patterns.

In this context, many efforts have been conducted to better understand and predict traffic accidents by collecting data and developing more flexible modeling approaches. In terms of data collection effects, South Korea has established integrated traffic accident data and analytical platforms (a.k.a. Traffic Accident Analysis Systems, TAAS) that are mainly constructed by police-reported data at the scene, including a wide range of information—e.g., human, structural, and spatiotemporal factors affecting traffic accidents. In particular, TAAS provides a multi-layered GIS-based database to end-user services by merging the police-reported accident datasets with the existing traffic safety infrastructures and policies. Analytics in traffic accidents data platform (e.g., TAAS) aimed to provide direction for enhancing traffic safety by understanding factors affecting high-risk roads. Nevertheless, the existing traffic accidents data platform may be limited to modeling the datasets with high cardinality and accounting for potential heterogeneity.

Previous studies have substantially investigated various technical challenges in modeling traffic accidents and behaviors—e.g., spatiotemporal correlation, heterogeneity, fixed parameters, and issues of over- and under-dispersion (Lord & Mannering, 2010). To tackle these detrimental issues, advanced statistical modeling approaches (e.g., random parameters models adding mixing distributions) have been widely adopted to overcome these technical challenges (F. L. Mannering et al., 2016; Washington et al., 2020). Nonetheless, advanced statistical models are mostly based on parametric modeling, and in the context of traffic accident modeling—where a complex mixture of continuous and discrete variables exist with strong interdependencies—it may be impractical for analysts to estimate all parameters accurately.

Taking advantage of repetitive optimization, nonparametric algorithms such as Machine Learning (ML), free from predetermined assumptions about statistical parameters, are used in traffic accident modeling. Rule-based models, for instance, outperform in modeling datasets with high cardinality (Lee et al., 2018; F. L. Mannering et al., 2016), and ensemble models further overcome the prediction instability inherent in single decision tree models. However, the family of automated machine-oriented models can struggle to reflect spatiotemporal correlation (F. Mannering et al., 2020), and methodologically incorporating unobserved heterogeneity in the data is challenging (F. Manner ing et al., 2020). As highlighted by Mannering et al., (2016), ignoring unobserved heterogeneity in traffic accident modeling may lead to biased results, showing limitations in the independent use of highly automated models for accident prediction.

To alleviate these algorithmic dilemmas, integrated modeling approaches by adding advanced statistical theories (e.g., random parameters) to automated machine-oriented models have been recently adopted. This article develops a mixed effect tree ensemble with a Gaussian process (ME-GP) toward a comprehensive city-wide traffic safety assessment tool by predicting the level of accident risk at the level for the road segment. Specifically, ME-GP incorporates nonparametric random parameters models with higher flexibility to an ensemble wellsuited for predicting the discrete nature of police-reported accident data. At the time of writing this article, there was no existing literature combining the Gaussian process with an ensemble to predict traffic accident risks and associated behaviors in city-wide traffic safety analytics. To predict the level of risks by road segments, the generalized accident risk index is introduced to comprehensively account for the accident risks (e.g., frequencies and severities).

To quantify accident factors and provide practical policy implications, most previous studies have focused on describing the average behavior of the estimated ML models based on visualization by using the model-agnostic methods (e.g., the Shapley value). Although describing the average behaviors of ML models is particularly useful for understanding the overall mechanisms in the datasets and associated models, it has some limitations in providing in-depth interpretation and applicable to the practical policy implications. Our study, therefore, conducted an additional scalable interpretation of how much impact each factor has on accident risk based on Shapley values considering spatiotemporal correlation and unobserved heterogeneity. Thus, the additional scalable interpretation can fill technical knowledge gaps in conducting model-agnostic interpretation. Lastly, nonparametric random parameter approximation for large-scale spatiotemporal datasets can fill the technical knowledge gaps by enhancing the adaptability of the advanced methodologies to the existing applications.

The spatiotemporal urban traffic safety analytical framework developed as following procedures. First, we explore how the unobserved heterogeneity of traffic accidents is modeled in existing studies by using an independent and integrated approach. Second, we describe data preprocessing and descriptive statistics from the spatiotemporal perspectives. Third, we discuss how Mixed effect Tree-ensemble (ME-TE) and ME-GP are modeled for the TAAS data. A single ML and other mixture modeling approaches were compared to the ME-GP to validate the robustness and predictive performances. Lastly, we perform a postinterpretation analysis of potential accident factors considering spatiotemporal correlation and unobserved heterogeneity using the modified Shapley Value.

2. Literature review

In the realm of traffic safety analysis, there is a large body of literature supporting the importance of the nonparametric model. The family of ML, including DL, has been extensively used to overcome the limitations of parametric models (e.g., predetermined assumptions) thanks to their machine-based repetitive computational power. ML approaches have proven relatively high predictive performances in analyzing a wide variety of modeling tasks compared to traditional parametric approaches. This is partly because ML can be specified by fewer predetermined assumptions than parametric models, while it is easy to handle complex and high-dimensional data (Hastie et al., 2009). By combining many local estimators, in particular, the Addictive Regression Tree model (Ding et al., 2018) and Ensemble model (Abdel-Aty et al., 2024; Keramati et al., 2020; Li et al., 2020; Osman et al., 2019) have been adopted in modeling traffic accidents in various aspects, while having relative competitive for datasets with high-dimensionality and cardinality (Hastie et al., 2009). Recently, DL algorithms have also gained attention in accident prediction. Neural Networks have been used for vehicle trajectory tracking to model lane-changing trajectory planning (J. Wu et al., 2023), while models incorporating Generative Adversarial Networks (GAN) and Convolutional Neural Networks (CNN) have shown high performance in real-time highway accident prediction (Cai et al., 2020). Nonetheless, the modeling approach adopting either a single ML or DL generally suffers from alleviating detrimental issues in modeling, such as unobserved heterogeneity or spatiotemporal correlation of accidents. Moreover, the lack of interpretability can lead to failure in incorporating the causality of accident factors (F. Mannering et al., 2020).

Some previous studies have adopted integrated ensemble and statistical models to maximize the inherent ability of rule-based methods to handle mixed- or hierarchical-type data sets (Hastie et al., 2009).

Negative-Binomial Bayesian Addictive Regression Trees (NB-BART) (Krueger et al., 2020) and Geographical Weighted Random Forests (GW-RF) (Gu et al., 2023; Wang et al., 2024; D. Wu et al., 2024) have modeled the spatial correlation of accidents. Thanks to the tree structure, NB-BART & GW-RF have performed factor analysis considering spatial correlation using Feature Importance & Local Feature Importance, alleviating most of the limitations of traditional ML (e.g., model interpretation) or statistical models (e.g., parametric or predetermined assumptions) in traffic accident prediction models. NB-BART can also quantify uncertainties in prediction by adopting nonparametric tree structures while alleviating uncertainty issues about spatial correlation. In terms of modeling applications, however, subjective prior distribution assumptions are required in NB-BART, and these assumptions can be computationally expensive for large datasets. GW-RF applies the same bandwidth for each region to consider heterogeneous within-region characteristics, but it has limitations in addressing but it has limitations in addressing robustness of prediction due to deterministic method. Algorithms combining random parameter modeling and ML for accident prediction have also emerged. Mixture modeling approaches (e.g., ME-TE), for instance, integrates random parameters with ensemble modeling possessing a highly interpretable nature (e.g., rule-based) while maximizing the advantages of both approaches (Hajjem et al., 2011, 2014). Although ME-TE shows high predictive power on highcardinality and multi-level data, it generally adopts parametric specifications for random parameters. Therefore, convergence in distributions may face challenges with various skewness and kurtosis and may lead to biased estimates due to limitations in predetermined assumptions for parameters. Furthermore, the random parameters in the ME-TE assume independence at the individual accident or group level; therefore, spatial correlation among accidents in densely populated areas may be ignored, leading to biased estimates (Wang et al., 2024; Xu & Huang, 2015). As seen in the literature, many types of modeling approaches are available, especially from the field of econometrics and ML, including DL. Both modeling approaches have their own advantages and technical trade-offs—e.g., modeling specification, interpretability, and predictive performances (Lee et al., 2018). In this light, the primary purpose of this study is to provide practical insights into traffic safety assessment and further management by taking advantages of both modeling approaches.

To tackle some limitations in parametric estimation, the Gaussian Process is a nonparametric and flexible way to enable modeling unobserved heterogeneity by adopting random parameters approaches. The Gaussian Process, in particular, allows for obtaining continuous, or smooth, prediction for spatial data while being able to capture nonlinearities and discontinuities (Sigrist, 2023) and has other benefits in quantifying uncertainties (e.g., the robustness of prediction). Hence, the Gaussian process can have great potential to account for heterogeneity in mean and variances, especially for spatial analysis. Despite its computational cost, the Gaussian process has been struggling with approximating high-dimensional datasets. To tackle this computation issue, Vecchia approximation can be adopted for the large-scale spatial and Gaussian process models where computational efficiency is critical. Consequently, the real-world application of traffic safety analytics platform such as TAAS is largely depending on computational efficiency and scalability. As seen in the literature, many types of modeling approaches are available, especially from the field of econometrics and ML, including DL. Both modeling approaches have their own advantages and technical trade-offs—e.g., modeling specification, interpretability, and predictive performances (Lee et al., 2018). In this light, the primary purpose of this study is to provide practical insights into traffic safety assessment and further management by taking advantages of both modeling approaches, represented in Fig. 1.

3. Data processing

3.1. Accident data

In this study, we use accident data from TAAS, specifically focusing on Seoul Metropolitan City, ranging from 2012 to 2019. The data were collected from police accident reports conducted at the scene. TAAS encompasses various variables related to certain accidents, including:

i. Accident details: fatalities, severe injuries, minor injuries
ii. Personal information: gender and age of both perpetrators and victims, human behavior at the time of the accident, and details of any violations of traffic regulations
iii. Road structure information: presence of intersections, road linear characteristics, existence of median barriers, tunnels, and overall road layout
iv. Spatiotemporal information: year, month, day, time, and geographical coordinates of accident occurrence

The dataset exclusively records accidents involving personal injuries. The classification of personal injuries is as follows as Table 1.

The road network data for Seoul (a.k.a. the Intelligent Transportation System Network) was adopted (See Fig. 2) to aggregate the location of accident records into associated road segments. To merge the accident dataset into the associated road segment, Referring to the nodelink data integration guidelines provided by the Korea Road Traffic Authority, the closest segment within a 30-meter radius of the accident occurrence point was designated as the accident segment. Accident data points without any associated segments within this radius were considered anomalies—such as cases where the accident location was mistakenly recorded. To minimize biased estimation, these anomalous data points were removed from the analysis.

3.2. Data preprocessing & descriptive analysis

Police-reported data at the scene rely on the subjective judgment of officers, making it difficult to verify reliability (Ulak & Ozguven, 2024). Nevertheless, building a data-driven decision-making framework requires a reliable dataset and meticulous data preprocessing. Initially, it was observed that data entry rules varied by year. For example, from 2012 to 2016, driver behavior types were recorded as "left or right turn," whereas from 2017 to 2019, they were separately recorded as "left turn" and "right turn." To enhance data reliability and reduce model complexity, we standardized the data entry methods across all years. In addition, the TAAS variables were largely composed of high-cardinality categorical variables, which increases model complexity and may lead to the curse of dimensionality; thus, refinement was necessary. Categorical variables with fewer than 10 unique values were removed. Specifically, variables related to traffic violations, which had significantly higher cardinality (e.g., blood alcohol concentration, driver violation details), were refined based on the Korean Road Traffic Act. All categorical variables that underwent refinement were encoded as dummy variables. Dummy encoding of high-cardinality categorical variables can lead to multicollinearity issues. To verify this, we conducted a VIF test, which revealed that the neglecting safety duty and driver age variables had VIF values of 24.40 and 11.59, respectively, indicating potential multicollinearity issues. However, both variables were retained as they are key factors explaining perpetrator-related characteristics linked to accidents. To alleviate unobserved yearspecific heterogeneities for each segment, the year variable was encoded as a dummy variable to reduce omitted variable bias.

After preprocessing and data integration, the structure of the final dataset represents a multi-level accident event for each segment from 2012 to 2019. The final dataset contains 200,457 accidents count: 1,706 fatalities, 69,486 serious injuries, 205,674 slight injuries, and 25,137 very slight injuries. Detailed descriptive statistics of accidents are shown in Appendix.

3.3. Generalized Indexing for traffic accident severities

The primary purpose of this article is to develop a comprehensive city-wide traffic safety assessment tool by predicting the level of accident risk at road segments. In addition, identifying factors that affect risk and accidents per road entry can provide practical insights into traffic safety assessment and further management. Although a single metric (i. e., the total number of accidents per roadway segment) can represent the risks of accidents at roadway segments, accident frequencies without considering severity (e.g., injury type) underestimate the effect of a particular factor that can be varied by severity.

Fig. 1. Analytical flow of study.

Table 1 Accident Severity description in TAAS.

Level of Accident Severity	Description
Fatal	refers to cases where death occurs within 30 days of a traffic accident.
Serious	refers to injuries requiring treatment for more than 3 weeks due to a traffic accident.
Slight	refers to injuries requiring treatment for 5 days or more but less than 3 weeks due to a traffic accident.
Very slight	refers to injuries requiring treatment for less than 5 days due to a traffic accident.

Using an independent metric of accidents (e.g., the number of casualties) can lead to biased estimation for the level of traffic accident risks, particularly for road segments where most accidents either result in fatalities or occur on highways. Pedestrian accidents, for instance, have a significantly higher number of severe injuries compared to vehicle-to-vehicle accidents (see Appendix). Similarly, as shown in Fig. 3, while the number of casualties decreases with increasing age of victims, the number of serious and fatal injuries increases, and independent metrics may overlook the accident risk for elders. Therefore, assessing accident risk using independent metrics may underestimate the risk pedestrians face. Hence, to comprehensively account for the accident risks faced by all users in urban networks, it is necessary to develop a generalized accident risk index.

Fig. 2. Road network by types: Case of Seoul, Republic of Korea.

Fig. 3. Casualties, Fatal and Serious injuries along the victim age.

In previous studies, severity, generally analyzed through the family of logit models, provides intuitive insights into factors contributing to fatal accidents (Lord & Mannering, 2010). Nonetheless, to conduct a comprehensive traffic safety assessment, EPDO is adopted to consider the correlations of accident severity and frequency. EPDO assigns disproportionately higher weights to fatal accidents than serious or slight injuries. Not having appropriate weights from spatial proximity in urban areas can cause biased estimation. This study calculated the generalized accident risk index (GARI) to better capture the given road environments in Korea. Accident severity is weighted by 4:2:1—i.e., fatal, serious, and slight injuries, respectively. To make a direct comparison among road segments, the weighted accident frequencies are normalized to minimize biased safety assessment by road type. Accidents occurring on highways, which generally have longer individual segment lengths, may be underestimated. Therefore, a weight proportional to the average length ratio between highways and general roads was applied to accidents occurring on highways.

The normalized index is transformed to logarithm values to alleviate potential detrimental issues—e.g., heteroskedasticity issue (see Fig. 4). The equation for GARI is as follows:

$$GARI = log\left(\frac{4F + 2S + SL + VS}{L}\right) \tag{1}$$

where F, S, SL, and VS represent the number of fatalities, serious, and very slight injuries, respectively. Also, L denoted the length of the road segment.

3.4. Spatiotemporal descriptive analysis of GARI

As highlighted by Lord & Mannering (2010) and (Mannering et al., 2016), long-term and city wide accident data can exhibit spatiotemporal correlation and unobserved heterogeneity. As shown in Fig. 5, the TAAS data also reveal different accident patterns over time for each segment. In some segments, accident risk is higher during the daytime, while in others, it is higher at night. In certain segments, no accidents were observed at night throughout the data collection period. Similarly, some roads experienced accidents continuously throughout the years, while others had only a single accident in the entire data collection period. Thus, different spatiotemporal correlations exist for each segment, which must be accounted for in the modeling process.

The unobserved heterogeneity in each segment may be similar based on spatial proximity (Lord & Mannering, 2010). When modeling spatial heterogeneity using a Gaussian process, it is important to determine how spatial heterogeneity is manifested to set the covariance function parameters appropriately. To investigate the patterns of spatial heterogeneity, we used Local Moran's I. In Fig. 6, hot spot clusters (High-High, HH) were densely concentrated in the southern part of Seoul, while cold spot clusters (Low-Low, LL) were concentrated in the northeast part of Seoul. The concentration of HH in Gangnam, the central urban area of Seoul, and LL in the northern regions suggests a gradual change in spatial heterogeneity by region. This pattern may result from the relatively lower exposure to accidents in northern Seoul, attributable to lower traffic volumes and population compared to southern Seoul, excluding the central business district. Areas exhibiting sharp spatial changes or discontinuities, such as HL (High-Low) and LH (Low-High), were also widely distributed across various regions of Seoul. The presence of widely distributed HL-LH indicates that sharp changes occur within the overall gradual variation in spatial heterogeneity. Hence, to model the traffic accident risk of segments in Seoul, we require a flexible covariance function to account for the widely distributed HH-LL and HL-LH patterns. To achieve flexible spatiotemporal heterogeneity modeling, we employed the mat´ern covariance function (Rasmussen & Williams, 2006), which allows for controlling the variability of the covariance function. Detailed modeling using the mat´ern function is discussed in the methodology section.

3.5. Dataset Splitting for model validation

To develop a robust model, three different types of validation processes, including hold-out, cross-validation, and out-of-sample prediction, are conducted to increase the predictive performances and the applicability of models. Specifically, the data from 2012 to 2016 were split into a 7:3 ratio for hold-out validation, respectively. To ensure the accuracy and stability of the model, the data from 2017 to 2019 were reserved as an external validation set. In particular, out-of-sample issues are required to be validated somehow to enhance the applicability of the estimated model (Sifringer et al., 2020). Road segments, which are never seen in both model estimation and validation processes, were used to evaluate the model's performance additionally. In order to have a comparative base, this study use ME-TE (Sigrist, 2022), XGBoost (Chen & Guestrin, 2016), and Linear Mixed Model (LMM). Description of variable are shown in Table 2 and detailed statistic are show in Appendix.

4. Methodology

4.1. Integrated ensemble and random parameter modeling framework

This article developed the integrated modeling framework combining ML and random parameter approaches accounting for heterogeneity in means and variances. This integration is developed to

Fig. 4. Distribution of GARI.

Fig. 5. Temporal heterogeneity of GARI by Road Segments (a) Time, (b) Month, (c) Year.

Fig. 6. Spatial heterogeneity of GARI by traffic accident: (a) High-High, (b) Low-Low (c) High-Low, (d) Low-High.

leverage both ensemble and robust theoretical background to alleviate detrimental effects. ME-TE and ME-GP to consider the heterogeneity of each segment in traffic accidents. ME-TE and ME-GP model framework follows mixed effect modeling framework of (Laird & Ware, 1982; Pinheiro & Bates, 2009) as follows:

$$y = F(X) + Zb(s) + \varepsilon \tag{2}$$

$$b N(0,\Sigma), \varepsilon N(0,\sigma^2 I_n)$$ (3)

where y is the dependent variable, F(X) is a fixed ensemble function,

Table 2 Description of Variable.

Category	Acronym of variable	Description
Random	Link id	Unique ID of the individual segment
parameter	X & Y	Central coordinates of the segment
variable	Time	Time of the accident occurrence
Fixed	Year	Year of the accident occurrence
variable	Season	Season of the accident occurrence
	Holiday	Presence of holidays at the time of the accident occurrence
	Lanes	Number of lanes on the segment where the accident occurred
	Intersection	Intersection type of the segment where the accident occurred
	Road type	Road type of the segment where the accident occurred (e.g., bridge, tunnel, underpass)
	Road slope	Gradient type of the segment where the accident occurred (e.g., uphill, downhill)
	Central	Presence of median barriers on the segment
	separation	where the accident occurred
	facility
	Bed count	Number of university hospital beds in the
		district of accident occurrence
	Driver age1	Age of the perpetrator
	Driver age2	Age of the victim
	Sex1	Sex of the perpetrator
	Sex2	Sex of the victim
	Drinking1	Degree of alcohol consumption by the perpetrator at the time of the accident occurrence
	Violation1	Type of traffic law violation by the perpetrator at the time of the accident
	Behavior1	occurrence Behavior type of the perpetrator at the time of the accident occurrence (e.g., making a right
	Behavior2	turn, making a U-turn…) Behavior type of the victim at the time of the accident occurrence (e.g., making a left turn, stationary, walking…)

Z is a random parameter matrix, and b is a random parameter with a covariance matrix, which can be estimated by grouped random parameter, full-Bayesian, or Gaussian Process (Sigrist, 2022). The marginal distribution of y in Equation (4) and the negative log-likelihood of this model in Equation (5) is as follows:

$$y N(F(X), \Psi), \Psi = Z\Sigma Z^T + \sigma^2 I_n$$ (4)

$$L(y, F, \theta) = \frac{1}{2}(y - F)^{T}\Psi^{-1}(y - F) + \frac{1}{2}logdet(\Psi) + \frac{n}{2}log(2\pi)$$ (5)

where Ψ is an expected variance of predictor variable and it can be different for ME-TE and ME-GP. L(y, F, θ) denotes a loss function corresponding to the negative loglikelihood, where F = F(X) and θ ∈ Θ ∈ ^R*^q*is all variance and covariance parameter, i.e., *σ*2 and ∑.

4.2. ME-TE Inference for unobserved heterogeneity

To clearly understand the advantages of the Gaussian process over the group effect in accident analysis, it is necessary to examine how the heterogeneity of individual segments through the group effect is reflected within ME-TE. Accidents occurring within individual segments may be correlated with one another, and accidents occurring between segments may be heterogeneous. To control for unobserved heterogeneity in accidents over time, we apply different random slopes for each segment over time. In this context, ME-TE can be defined as shown in Equation (6). In this model, bi is independent and identically distributed (a.k.a. IID) grouped random parameter of each segment, which accounts for correlation between accidents in each segment and bj refers to random slope shifts over time.

$$y = F(X_i) + Zb_i \bullet b_j + \varepsilon_i b_i^{iid} N(0, \sigma_1^2), b_j^{iid} N(0, \sigma1^2), \varepsilon N(0, \sigma\varepsilon^2)$$ (6)

$$Cov(b) = \sigma_1^2 I_n$$ (7)

4.3. ME-GP Inference for spatiotemporal correlation and unobserved heterogeneity

Group effect modeling can reflect the heterogeneity of individual segments. Nonetheless, modeling the spatial correlation between segments is challenging. To tackle this challenge, a Gaussian Process with mat´ern covariance function can be utilized to estimate random parameters based on the central coordinates (m,n) of segments (Equations (9) & (10)). In this context, to model spatiotemporal correlation, the bij of ME-GP does not follow the IID assumption, unlike the bi and bj in ME-TE. With the parameter v, controlling smoothness in a Gaussian process, the mat´ern covariance function considers the dynamic spatiotemporal heterogeneity of GARI. If the v is 0.5, the mat´ern covariance function is an exponential function, while 2.5 denotes dynamic change of the covariance function. In this study, modeling the spatial correlation between roads, various unobserved factors such as structural factors, human factors, and traffic factors may cause different types of accidents between highways and local roads. As shown in Fig. 2, Seoul has highways and freeways passing through the city center, and if we consider the spatial correlation between adjacent streets and highways, biased estimates may occur. Therefore, assuming independence based on road hierarchy and modeling the spatial correlation between segments within the hierarchy as random parameters are necessary. ME-GP framework corresponds to Equation (8) and (9).

$$y = F(Xi) + Zb{ijk} + \varepsilon_i \tag{8}$$

$$b f(0, K(m, n)), m, n \in \mathbb{R}^d, \varepsilon N(0, \sigma_{\varepsilon}^2)$$ (9)

where k refers to street, main road, country road, and highway, respectively. Gaussian process b is an isotropic autocorrelated mat´ern covariance function decaying ρ with distance of each segment coordinates. The basic model of Gaussian process b corresponds to Equation (10).

$$K(m,n) = \frac{2^{1-\nu}}{\Gamma(\nu)} \left( \frac{\sqrt{2\nu} |m-n|}{l} \right)^{\nu} K_{\nu} \left( \frac{\sqrt{2\nu} |m-n|}{l} \right)$$ (10)

In this model, ‖m − *n*‖ is a Euclidean distance of segment, l is a length scale and v is a smoothness of kernel function and Kv is a modifed Bessel function. As shown in Figs. 5 and 6, the spatiotemporal heterogeneity of GARI changes continuously while also exhibiting sections of abrupt change. If v is defined as 0.5, K(m, n) becomes especially simple, similar to an exponential function, capturing rapidly changing heterogeneity. On the other hand, when v is set to 2.5, it assumes very smooth spatial continuity. To account for both HH-LL and HL-LH spots, we assumed v to be 1.5. Furthermore, to simultaneously consider spatiotemporal correlation, we expand Equation (10) with temporal parameter t, explaining spatiotemporal distance of data point suggested by Sigrist (2022) as shown below.

$$d = \sqrt{\frac{(t-t')^2}{l_t^2} + \frac{(m-m')^2 + (n-n')^2}{l_s^2}}$$ (11)

ls is spatial smoothness and lt is a temporal smoothness. Hence, d is a distance of two data points, (t, m, n) and (t ʹ , m^ʹ *, n*ʹ ). Finally, spatiotemporal mat´ern function is defined as follows.

$$k{v}(t,m,n,t',m',n') = \frac{2^{1-v}}{\Gamma(v)} \left(\sqrt{2} d\right)^{v} K{v}(\sqrt{2}d)$$ (12)

4.4. Vecchia approximation for large dataset

Gaussian process models face significant computational challenges due to the need to invert large covariance matrices. This makes them impractical for large datasets. Vecchia's approximation, by conditioning only on a subset of nearest neighbors instead of the full dataset, drastically reduces this computational burden. By limiting the dependency structure, it approximates the likelihood while maintaining accuracy, particularly in high-dimensional spaces where nearest neighbors can provide sufficient information(Katzfuss et al., 2018; Sigrist, 2022; Vec chia, 1988). In our model, the likelihood of ME-GP is approximated as Equation (13)

$$p(y|F,\theta) = \prod_{i=1}^{n} p(y_i|(y1, \dots, y{i-1}), F, \theta) \approx \prod_{i=1}^{n} p(yi|(y{N(i)}), F, \theta)$$ (13)

p(y|F, θ) is likelihood and N denotes corresponding subsets of indices, which means nearest neighbor count of (t, m, n).

4.5. Combining boosting with random parameter model

To combine boosting with random parameter models, a joint minimizer from Equation (5) is required to

$$(\widehat{F}(\bullet),\widehat{\theta}) = \operatorname{argmin} R(F(\bullet),\theta)$$ (14)

$$R(F(\bullet),\theta):(F(\bullet),\theta))\to L(y,F,\theta)|_{F=F(X)}$$ (15)

where L(y, F, θ) is a loss function corresponding to the negative loglikelihood in Equation (5). This article adopts a regression tree as a basis and minimizes the expected loss function. Since minimizing the loss function cannot be done analytically, we use functional gradient descent for approximation, as shown in Equation (13).

$$Fm(\bullet) = F{m-1}(\bullet) + f_m(\bullet), \ f_m(\bullet) \in \mathcal{S}(m=1, \dots, M)$$ (16)

4.6. Quantifying ML variable Coefficient using Shapely value

Shapley addictive Explanation (Lundberg & Lee, 2017) can explain feature importance and feature interaction leading to interpreting spatiotemporal correlation or unobserved heterogeneity relationships (Chang et al., 2022; Yuan et al., 2022) of ML. In the ML regression model, Shapley values are calculated as follows:

$$\phi{i} = \sum{S \subseteq F(i)} \frac{|S|!(|F| - |S| - 1)!}{|F|!} \left[ f{S \cup {i}} \left( \mathbf{x}{S \cup {i}} \right) - f{S}(\mathbf{x}{S}) \right]$$ (17)

5. Model results

5.1. Model validation

To evaluate model prediction performance, Root Mean Squared Error (RMSE), Mean Absolute Percentage Error (MAPE), and R-squared (R2) metrics were adopted to compare predictive performance. Model validation results are shown in Table 3 and Fig. 7 and 8. When it comes to hold-out validation, XGBoost, which does not incorporate random parameters or spatiotemporal correlation terms, exhibited low predictive performance, R2 0.561. In comparison, ME-TE and ME-GP show significantly high predictive power with R2 0.50 and 0.715. All models show lower prediction performance in external validation compared to hold-out validation; however, ME-GP, shows a lower decrease in prediction performance compared to others. In contrast to the other validations, ME-TE and LMM show much lower predictive power compared to XGBoost in out-of-sample validation. ME-GP reveals higher predictive accuracy compared to XGBoost, although the performance drop from external validation to out-of-sample validation was more pronounced for ME-GP than for XGBoost. The sharp decline in performance for ME-

Table 3 Model Validation Results.

	Model	MAPE	RMSE	R squared
Accident Predict	XGBoost	0.282	0.736	0.561
Train: Test (7:3)	LMM	0.233	0.720	0.581
	ME-TE	0.221	0.657	0.650
	ME-GP	0.213	0.593	0.715
Accident Predict	XGBoost	0.335	0.798	0.477
External validation	LMM	0.254	0.814	0.456
	ME-TE	0.244	0.697	0.602
	ME-GP	0.230	0.624	0.680
Segment risk prediction in external	XGBoost	0.247	3.407	0.860
validation	LMM	0.218	2.928	0.896
	ME-TE	0.177	2.281	0.937
	ME-GP	0.151	1.932	0.955
Out-of-sample accident prediction	XGBoost	0.353	1.098	0.430
	LMM	0.484	1.855	− 0.630
	ME-TE	0.409	1.470	− 0.023
	ME-GP	0.303	1.057	0.471
Out-of-sample Segment prediction	XGBoost	0.331	1.203	0.513
	LMM	0.466	2.029	− 0.379
	ME-TE	0.386	1.618	0.123
	ME-GP	0.284	1.164	0.546

TE in out-of-sample prediction will be addressed in the next section of this study.

To build a safer traffic environment within cities, it is essential to predict high-risk segments. To achieve this, we aggregate the predicted GARI for individual accidents per segment and compare it to the actual summed GARI for each segment. Using external validation and out-ofsample prediction results, the predicted high-risk road segments were evaluated. In external validation, ME-GP R2 values of 0.955. Thus, in terms of predicting and managing real-world high-risk segments, ME-GP was found to be an effective model.

5.2. Interpretation of random parameter

5.2.1. Estimated random parameter analysis

Two different validation data sets, including hold-out and external validation, estimate random parameters for the different road segments (see details in Figs. 9 and 10). Although both ME-TE and ME-GP were implemented under identical conditions, only the ME-GP that estimates random parameters using the Gaussian process successfully approximated the random parameter distribution, while the others failed. Specifically, ME-TE and LMM yielded significantly biased estimates compared to the estimation based on the Gaussian Process (i.e., ME-GP). As depicted in Figs. 9 and 10, numerous points were identified in the distribution of random parameters Zb for ME-TE, where the convergence of random parameters failed (where b is 0). This is partly due to the fact that ME-GP is taking advantage of nonparametric estimation with less predetermined assumptions than ME-TE (Eager & Roy, 2017; F. L. Mannering et al., 2016).

5.2.2. Quantifying robustness of prediction

To quantify the robustness of the prediction, we further analyzed the variance of the prediction. Fig. 11 shows the variance values of predictions by accident location and time of occurrence. Compared to ME-TE, ME-GP demonstrated lower prediction variance values across most segments, indicating more robust prediction performance. It is important to note that, although rare, the instability of ME-GP prediction was found in some segments. Regarding the increased uncertainty in ME-GP's predictions, we hypothesized that this could be due to a lack of samples sufficient to estimate random parameter covariance according to spatiotemporal correlation. To verify this, we analyzed the spatiotemporal accident count density using DB-SCAN and compared the variance across clusters. The result is summarized in Table 4. The result revealed that while the average variance across all clusters was 0.3, the

Fig. 7. External validation between actual and predicted values for (a) Accident and (b) Segment.

Fig. 8. Out-of-sample validation between actual and predicted values for (a) Accident and (b) Segment.

average variance in outlier clusters, which had low spatiotemporal density and were not clustered, was found to be 1.40. This reveals that ME-GP may have limitations in predicting data with low spatiotemporal density.

5.3. Interpretation of fixed variable

5.3.1. Determinant variable affecting the severity of accident risk

To identify the variables that primarily influence traffic accident risk, we examined the relative importance of variables using Shapley Addictive Explanation (SHAP) to globally interpret average behavioral characteristics as depicted in Fig. 12. To quantitatively assess how much each fixed variable contributes to the accident risk, we converted the SHAP values of fixed variables into percentages relative to the average prediction (SHAP base value). In Fig. 12, the point where accident risk (%) equals 0 represents the average accident risk, and points to the left or right indicate how much each fixed variable increases or decreases accident risk relative to the average. The variables with the greatest

impact on accident risk were found to be demographic variables (e.g., age, human behavior), traffic and structural variables (e.g., central separation facility), and holidays. Elderly accidents were found to have a maximum accident risk 20 % higher than that of youth. It is evident that physically vulnerable individuals, such as the elderly, are more likely to suffer severe consequences in the event of an accident. Despite this, children who are also physically vulnerable showed a lower accident risk. This suggests that children in Seoul are protected by various safety measures, such as school zones, whereas the elderly remain more exposed to traffic accident risks. Various factors related to driver behavior were also found to increase accident risk. In particular, traffic violations like drunk driving and running red lights were shown to increase accident risk by approximately 5–10 %. During lane changes or while making left or right turns, the risk of accidents was found to decrease, possibly because drivers tend to be more cautious during these maneuvers. However, if driver behavior or structural factors influencing turns are controlled, different results might emerge. Areas without central separation facilities showed up to a 5 % lower accident risk,

Fig. 9. Random parameter distribution of hold-out validation (Left panel: ME-TE and right panel: ME-GP).

Fig. 10. Random parameter distribution of external validation (Left panel: ME-TE and right panel: ME-GP).

whereas areas with central barriers had approximately a 1 % higher accident risk. This contrasts with existing studies suggesting that central barriers reduce accident risk (Donnell & Mason, 2006; Hunter et al., 2001), indicating that poorly designed central barriers may sometimes increase risk. For instance, Zou & Tarko (2016) suggested that wide roads without central barriers have a higher likelihood of rollover accidents for vehicles veering off the road. However, as accident types were not controlled in our analysis, controlling for specific accident types such as rear-end or head-on collisions may yield different results.

5.3.2. Analysis of nonlinear Association of accident risk factor

Despite controlling for spatiotemporal heterogeneity using a Gaussian process, various factors, including human-related ones, can simultaneously influence accident occurrence. As indicated by the feature importance analysis, human factors emerged as a significant contributor to increased accident risk, a finding consistent with previous studies that highlight human factors as a primary cause of unobserved heterogeneity. Therefore, to quantitatively analyze the marginal effects between variables and accident risk while also accounting for heterogeneity due to human factors, we conducted a partial dependence

analysis based on the age of traffic accident perpetrators and victims.

Fig. 13 illustrates the accident risk associated with major variables according to the age of the perpetrator driver. The changes in accident risk by perpetrator age show no significant variation between the ages of 20 and 60, but a decrease is observed from 60 to 80, followed by an increase after 80. This suggests that, from a city-wide perspective, the age of the perpetrator does not significantly impact accident risk. However, different outcomes may arise when age-related factors interact with external factors such as road and weather conditions. Notably, significant differences in structural factors (e.g., tunnels and underground passes) on the roads between young and elderly drivers are observed. In tunnels and underground passages, the accident risk for young drivers 20 s primarily is approximately 6 %, while for elderly drivers, it varies from about 10 %. Similarly, on downhill roads, the accident risk for drivers from the 20 s to 80 s is 0.8 % to 1 %, whereas for drivers aged 80 and above, it increases by approximately 2 %. Previous studies (Hakamies-Blomqvist, 1993; Langford & Koppel, 2006; McGwin & Brown, 1999; Rahman et al., 2021; Rolison et al., 2018) suggest that elderly drivers may experience reduced physical abilities compared to younger drivers, leading to decreased reaction times and increased

Fig. 11. Comparison of the variance of prediction for (a) ME-GP and (b) ME-TE.

Table 4 ME-GP prediction variance of DB-SCAN cluster.

	Outlier cluster	Other clusters
Average predicted variance	1.459	0.313

collision risk, especially in specialized environments such as intersections and turns. Therefore, considering the unique conditions of tunnels and downhill roads, the accident risk for the elderly may be higher. Conversely, during snowy conditions, young drivers in their 20 s and 30 s exhibit higher accident risk compared to drivers aged above 30 s. This suggests that inexperienced drivers with limited coping abilities in complex driving situations may experience significantly increased accident risk on winter roads where complicated driving situations may occur. Previous studies have also indicated that novice drivers experience difficulties in complex driving situations (Crundall, 2016; McGwin & Brown, 1999; Silva et al., 2023).

As indicated by the feature importance analysis, the relationship between victim age and accident risk was found to be linear except for the 0–10 age range. This suggests that traffic safety environments for the elderly in Seoul may be relatively inadequate. Accordingly, we analyzed nonlinear relationships focusing on elderly pedestrian accidents, as shown in Fig. 14. The results revealed that, for most age groups, accident risk while walking on the road was 1.0–2.0 % lower than the average. However, the risk for the elderly was similar to the average. Pedestrians crossing near crosswalks showed that those aged 0–64 had a 0.4 % lower accident risk compared to the average, whereas the elderly had up to 0.4 % higher accident risk compared to the average. Similar to the elderly, children, who also have physical vulnerabilities, did not show a particularly high accident risk in pedestrian accidents. This is likely due to the effectiveness of safety measures such as school zones in Seoul. Conversely, it indicates that elderly pedestrians are more exposed to traffic accident risks. Additionally, while most age groups showed that men had a higher average accident risk compared to women, elderly

Fig. 12. Relative feature importance of ME-GP.

Fig. 13. Nonlinear relationship of GARI with: (a) perpetrator age, (b) downhill slope, (c) tunnel & underpass, and (d) snowy weather, interacting with perpetrator age groups.

Fig. 14. Nonlinear relationship of GARI with: (a) victim age, (b) near crosswalk, (c)walk on the road, and (d) walk on the road side, interacting with victim age groups.

individuals aged 66 and over exhibited higher accident risks for women compared to men. Specifically, elderly women were found to have an accident risk approximately 0.5 % higher than the average.

5.4. Road safety Service design

This study presents a prediction of high-risk roads in Seoul and an analysis of key risk factors by road segment and time of day based on the local SHAP value of ME-GP (Fig. 15). A data-driven traffic safety framework can provide useful information to road users and road safety managers. The high-risk road analysis used the ME-GP segment risk prediction results from the external validation, as presented in Table 5, and divided them into four levels using Natural Breaks. The specific standards are shown in Table 5.

The prediction results indicated that high-risk roads are primarily located near urban highways along the Han River, which connect different regions of Seoul. The urban highways along the Han River are major arterial roads that connect the east and west of Seoul and are characterized by heavy traffic congestion.

To simultaneously inform about hazardous roads and detect risk factors for each segment, we aggregate the Local SHAP value of accidents for each segment per time. Then, we analyzed the factors that contributed most to accident risk by segment and time of day (Fig. 16).

The analysis revealed that multi-leg and roundabout intersections were the most frequently identified accident risk factors, followed by holidays, signal violations, and drunk driving. While the local SHAP value analysis results may exhibit some variability due to the limitations of SHAP in causal interpretation, the framework proposed in this study is expected to assist decision-makers in identifying and addressing critical road safety risk factors more effectively.

Table 5 Description of Segment Safety Level.

Safe level	Description	Standard
Level 1	Safe	Below the 39.23 % of predicted risk
Level 2	Caution	Within the top 39.23 % of predicted risk
Level 3	Danger	Within the top 11.64 % of predicted risk
Level 4	Very Danger	Within the top 1.52 % of predicted risk

6. Conclusions

This article developed the integrated modeling framework, ME-GP, that can not only alleviate unobserved heterogeneity and spatial correlation resulted policy-reported accident data but also enhance scalability for high-dimensional and − cardinality data sets in traffic accidents. ME-GP can address the acknowledged technical challenges in predicting traffic accidents and severities: 1) unobserved heterogeneity and spatial correlation, 2) limitations of parameters, and 3) constraints in inferring causality of accident factors in machine-oriented modeling.

ME-GP, which estimates random parameters nonparametrically, demonstrated higher predictive performance compared to LMM and ME-TE with random parameters assumed to be linear. Specifically, in modeling random parameters for out-of-sample predictions, while ME-TE failed due to nonconvergence limits, ME-GP showed no signs of nonconvergence and exhibited a difference in predictive performance. Additionally, ME-GP showed more robustness in terms of predictions than ME-TE.

To quantify accident factors and provide practical policy implications, we incorporated scalable interpretation into the model-agnostic approach, taking into account spatiotemporal correlations and unobserved heterogeneity. We analyzed the relationship between accident risk and variables while considering the heterogeneity of individuals, specifically focusing on the ages of both perpetrators and victims. Elderly drivers exhibited higher accident risk in specific road structures

Fig. 15. Prediction of segment safe level in Seoul.

Fig. 16. Determinant Factors on Accident Risks by Spatial (Road Segment) and Temporal (Time) in Seoul.

compared to younger drivers, whereas younger drivers showed increased accident risk in situations involving inexperience, such as driving on icy roads. Furthermore, while Seoul's pedestrian environment was found to be generally safe for younger individuals, it posed higher risks for the elderly.

Furthermore, this study demonstrates the potential to develop a framework that can create a safer road environment within the city and provide useful information to decision-makers. By using ME-GP, the prediction of risk for each segment and the identification of the key factors contributing to higher risk can serve as valuable inputs in developing a system to support decision-making for traffic safety management.

This study has addressed some limitations of existing algorithms, but several challenges remain. Firstly, in predicting accident risk per kilometer, there is a possibility of overestimation or underestimation of highway accident risk compared to the actual risk due to the calculation of average weights assigned to accidents on highways with generally longer segment lengths. Secondly, although ME-GP showed significantly higher predictive power in out-of-sample predictions compared to other algorithms, it did not completely overcome the limitations of the mixed effect model framework, resulting in inconsistent predictive performance between out-of-sample and inner-sample data. While combining full Bayesian methods with boosting may yield consistent predictive performance, this was not feasible in our study due to the lack of prior assumptions about accidents and the substantial computational costs involved. While some causality can be inferred, proving substantive causality would require complete independence between variables.

Therefore, to assess realistic accident risk in future research, it is suggested that these challenges be overcome through the development of new metrics or the refinement of weighting methods for traffic accident risk. The latter could be achieved with advancements in computing technology or the development of more efficient computational methodologies for ensembles and Bayesian approaches.

CRediT authorship contribution statement

Youngwoong Kim: Writing – original draft, Visualization, Validation, Software, Methodology, Investigation, Formal analysis, Data curation. Dongwoo Lee: Writing – review & editing, Writing – original draft, Validation, Supervision, Resources, Project administration, Methodology, Investigation, Funding acquisition, Formal analysis, Data curation, Conceptualization. Sybil Derrible: Writing – review & editing, Validation, Conceptualization.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by the 2024 Research Fund of the University of Seoul for Dongwoo Lee, 202405291007.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi. org/10.1016/j.aap.2025.108088.

Data availability

Data will be made available on request.

References

Abdel-Aty, M., Ugan, J., Islam, Z., 2024. Exploring the influence of drivers' visual surroundings on speeding behavior. Accident Analysis & Prevention 198, 107479. https://doi.org/10.1016/j.aap.2024.107479.

Cai, Q., Abdel-Aty, M., Yuan, J., Lee, J., Wu, Y., 2020. Real-time crash prediction on expressways using deep generative models. Transportation Research Part c: Emerging Technologies 117, 102697. https://doi.org/10.1016/j.trc.2020.102697.
Chang, I., Park, H., Hong, E., Lee, J., Kwon, N., 2022. Predicting effects of built environment on fatal pedestrian accidents at location-specific level: Application of XGBoost and SHAP. Accident Analysis & Prevention 166, 106545. https://doi.org/ 10.1016/j.aap.2021.106545.
Chen, T., Guestrin, C., 2016. XGBoost: A Scalable Tree Boosting System. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, pp. 785–794. https://doi.org/10.1145/2939672.2939785.
Crundall, D., 2016. Hazard prediction discriminates between novice and experienced drivers. Accident Analysis & Prevention 86, 47–58. https://doi.org/10.1016/j. aap.2015.10.006.
Ding, C., Chen, P., Jiao, J., 2018. Non-linear effects of the built environment on automobile-involved pedestrian crash frequency: A machine learning approach. Accident Analysis & Prevention 112, 116–126. https://doi.org/10.1016/j. aap.2017.12.026.
Donnell, E.T., Mason, J.M., 2006. Methodology to Develop Median Barrier Warrant Criteria. Journal of Transportation Engineering 132 (4), 269–281. https://doi.org/ 10.1061/(ASCE)0733-947X(2006)132:4(269).
Eager, C., & Roy, J. (2017, January 5). Mixed Effects Models are Sometimes Terrible. arXiv. Org. https://arxiv.org/abs/1701.04858v1.
GHSA. (2023). Pedestrian Traffic Fatalities by State. https://www.ghsa.org/resources/ Pedestrians24.
Gu, Y., Liu, D., Arvin, R., Khattak, A.J., Han, L.D., 2023. Predicting intersection crash frequency using connected vehicle data: A framework for geographical random forest. Accident Analysis & Prevention 179, 106880. https://doi.org/10.1016/j. aap.2022.106880.
Hajjem, A., Bellavance, F., Larocque, D., 2011. Mixed effects regression trees for clustered data. Statistics & Probability Letters 81 (4), 451–459. https://doi.org/ 10.1016/j.spl.2010.12.003.
Hajjem, A., Bellavance, F., Larocque, D., 2014. Mixed-effects random forest for clustered data. Journal of Statistical Computation and Simulation 84 (6), 1313–1328. https:// doi.org/10.1080/00949655.2012.741599.
Hakamies-Blomqvist, L.E., 1993. Fatal accidents of older drivers. Accident Analysis & Prevention 25 (1), 19–27. https://doi.org/10.1016/0001-4575(93)90093-C.
Hastie, T., Tibshirani, R., Friedman, J., 2009. The Elements of Statistical Learning. Springer.https://doi.org/10.1007/978-0-387-84858-7.
Hou, Q., Huo, X., Leng, J., Mannering, F., 2022. A note on out-of-sample prediction, marginal effects computations, and temporal testing with random parameters crashinjury severity models. Analytic Methods in Accident Research 33, 100191. https:// doi.org/10.1016/j.amar.2021.100191.
Hunter, W.W., Richard Stewart, J., Eccles, K.A., Huang, H.F., Council, F.M., Harkey, D.L., 2001. Three-Strand Cable Median Barrier in North Carolina: In-Service Evaluation. Transportation Research Record 1743 (1), 97–103. https://doi.org/10.3141/1743-13.
Katzfuss, M., Guinness, J., Gong, W., & Zilber, D. (2018). Vecchia approximations of Gaussian-process predictions. arXiv.Org. https://doi.org/10.1007/s13253-020- 00401-7.
Keramati, A., Lu, P., Iranitalab, A., Pan, D., Huang, Y., 2020. A crash severity analysis at highway-rail grade crossings: The random survival forest method. Accident Analysis & Prevention 144, 105683. https://doi.org/10.1016/j.aap.2020.105683.
Krueger, R., Bansal, P., Buddhavarapu, P., 2020. A new spatial count data model with Bayesian additive regression trees for accident hot spot identification. Accident
Analysis & Prevention 144, 105623.https://doi.org/10.1016/j.aap.2020.105623. Laird, N.M., Ware, J.H., 1982. Random-Effects Models for Longitudinal Data. Biometrics
38 (4), 963–974. https://doi.org/10.2307/2529876. Langford, J.W., Koppel, S.N., 2006. Epidemiology of older driver crashes—Identifying older driver risk factors and exposure patterns. Transportation Research Part f: Traffic
Psychology and Behaviour 9, 309–321.https://doi.org/10.1016/j.trf.2006.03.005. Lee, D., Derrible, S., Pereira, F.C., 2018. Comparison of Four Types of Artificial Neural Network and a Multinomial Logit Model for Travel Mode Choice Modeling. Transportation Research Record 2672 (49), 101–112. https://doi.org/10.1177/ 0361198118796971.
Li, L., Prato, C.G., Wang, Y., 2020. Ranking contributors to traffic crashes on mountainous freeways from an incomplete dataset: A sequential approach of multivariate imputation by chained equations and random forest classifier. Accident Analysis & Prevention 146, 105744.https://doi.org/10.1016/j.aap.2020.105744.
Lie, A., Tingvall, C., Michael, J.P., Fell, J.C., Bella Dinh-Zarr, T., 2024. Vision Zero and Impaired Driving: Near and Longer-Term Opportunities for Preventing Death and Injuries. Accident; Analysis and Prevention 194, 107344. https://doi.org/10.1016/j. aap.2023.107344.
Lord, D., Mannering, F., 2010. The statistical analysis of crash-frequency data: A review and assessment of methodological alternatives. Transportation Research Part a: Policy and Practice 44 (5), 291–305.https://doi.org/10.1016/j.tra.2010.02.001.
S. Lundberg S.-I. Lee A Unified Approach to Interpreting Model Predictions 2017 arXiv. Org.
Mannering, F., Bhat, C.R., Shankar, V., Abdel-Aty, M., 2020. Big data, traditional data and the tradeoffs between prediction and causality in highway-safety analysis. Analytic Methods in Accident Research 25, 100113. https://doi.org/10.1016/j. amar.2020.100113.
Mannering, F.L., Shankar, V., Bhat, C.R., 2016. Unobserved heterogeneity and the statistical analysis of highway accident data. Analytic Methods in Accident Research 11, 1–16. https://doi.org/10.1016/j.amar.2016.04.001.
McGwin, J., Gerald, & Brown, D. B., 1999. Characteristics of traffic crashes among young, middle-aged, and older drivers. Accident Analysis & Prevention 31 (3), 181–198. https://doi.org/10.1016/S0001-4575(98)00061-X.
Osman, O.A., Hajij, M., Karbalaieali, S., Ishak, S., 2019. A hierarchical machine learning classification approach for secondary task identification from observed driving behavior data. Accident Analysis & Prevention 123, 274–281. https://doi.org/ 10.1016/j.aap.2018.12.005.
Pinheiro, J.C., Bates, D., 2009. Mixed-Effects Models in S and S-PLUS. Springer Science & Business Media.
Rahman, M.A., Hossain, M.M., Mitran, E., Sun, X., 2021. Understanding the contributing factors to young driver crashes: A comparison of crash profiles of three age groups. Transportation Engineering 5, 100076. https://doi.org/10.1016/j.treng.2021.100076.
Rasmussen, C.E., Williams, C.K.I., 2006. Gaussian processes for machine learning. MIT
Rolison, J.J., Regev, S., Moutari, S., Feeney, A., 2018. What are the factors that contribute to road accidents? An assessment of law enforcement views, ordinary drivers' opinions, and road accident records. Accident Analysis & Prevention 115, 11–24. https://doi.org/10.1016/j.aap.2018.02.025.
Sifringer, B., Lurkin, V., Alahi, A., 2020. Enhancing discrete choice models with representation learning. Transportation Research Part b: Methodological 140, 236–261. https://doi.org/10.1016/j.trb.2020.08.006.
F. Sigrist Gaussian process boosting | The Journal of Machine Learning Research 2022 https://dl.acm.org/doi/abs/10.5555/3586589.3586821.
Sigrist, F. (2023). Latent Gaussian Model Boosting. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(2), 1894–1905. IEEE Transactions on Pattern Analysis and Machine Intelligence. https://doi.org/10.1109/TPAMI.2022.3168152.
Silva, V.C., Dias, A.S., Greve, J.M.D., Davis, C.L., de Soares, A.L., S., Brech, G. C., Ayama, S., Jacob-Filho, W., Busse, A. L., de Biase, M. E. M., Canonica, A. C., & Alonso, A. C., 2023. Crash Risk Predictors in Older Drivers: A Cross-Sectional Study Based on a Driving Simulator and Machine Learning Algorithms. International Journal of Environmental Research and Public Health 20 (5), 5. https://doi.org/10.3390/ ijerph20054212.
Ulak, M.B., Ozguven, E.E., 2024. Identifying the latent relationships between factors associated with traffic crashes through graphical models. Accident Analysis & Prevention 197, 107470. https://doi.org/10.1016/j.aap.2024.107470.
Vecchia, A.V., 1988. Estimation and Model Identification for Continuous Spatial Processes. Journal of the Royal Statistical Society. Series B (methodological) 50 (2),
Wang, S., Gao, K., Zhang, L., Yu, B., Easa, S.M., 2024. Geographically weighted machine learning for modeling spatial heterogeneity in traffic crash frequency and determinants in US. Accident Analysis & Prevention 199, 107528. https://doi.org/ 10.1016/j.aap.2024.107528.
S. Washington M.G. Karlaftis F. Mannering P. Anastasopoulos Statistical and Econometric Methods for Transportation Data Analysis (3rd ed.). 2020 Chapman and Hall/CRC 10.1201/9780429244018.
Who Global status report on road safety 2023 2023.
Wu, D., Zhang, Y., Xiang, Q., 2024. Geographically weighted random forests for macrolevel crash frequency prediction. Accident Analysis & Prevention 194, 107370. https://doi.org/10.1016/j.aap.2023.107370.
Wu, J., Chen, X., Bie, Y., Zhou, W., 2023. A co-evolutionary lane-changing trajectory planning method for automated vehicles based on the instantaneous risk identification. Accident Analysis & Prevention 180, 106907. https://doi.org/10.1016/ j.aap.2022.106907.
Xu, P., Huang, H., 2015. Modeling crash spatial heterogeneity: Random parameter versus geographically weighting. Accident Analysis & Prevention 75, 16–25. https://doi.org/ 10.1016/j.aap.2014.10.020.
Yuan, C., Li, Y., Huang, H., Wang, S., Sun, Z., Wang, H., 2022. Application of explainable machine learning for real-time safety analysis toward a connected vehicle environment. Accident Analysis & Prevention 171, 106681. https://doi.org/10.1016/ j.aap.2022.106681.
Zou, Y., Tarko, A.P., 2016. An insight into the performance of road barriers − redistribution of barrier-relevant crashes. Accident Analysis & Prevention 96, 152–161. https://doi.org/10.1016/j.aap.2016.07.022.

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