Multilevel Analysis of Road Accident Frequency: The Impact of the Road Category

Each year, road accidents result in high economic and social costs for nations, families, and individuals [1]. Experts in road safety have recently made determining the causes of road accidents a priority to reduce accident risk. Depending on the purpose of the study, models for forecasting accident frequency may incorporate numerous variables. According to numerous sources, various causes contribute to road accidents [2-5]. Guerrero-Barbosa et al. [6, 7] studied the influence of factors related to roadway geometry, traffic volumes, and speeds on accident frequency on an urban road network and people responses to speed limits. Marcianò and Vitetta [8] examined the effect of changing traffic parameters on pedestrian accidents. Joly et al. [9] investigated the influence of geographical and socio-ecological variations on pedestrian and cyclist accidents in different zones.

The accuracy of accident prediction models is based on extracting patterns from similar or historical accident data. In the past, the concept of prototypical accident scenario has been used [10]. In this method an in-depth investigation is made in order to extract a chain of facts and causal relationships from a series of accidents data and diagrams [11] in different stages. The modern science applies more accurate statistical models for studying accident-related parameters. The parameters may include environmental or traffic elements. These elements may include abnormal events. For example, the period of Covid-19 cited a significant effect not only on transportation sectors but on economy and life of all countries [12, 13].

The existing studies have also examined the precision of accident prediction models. Hauer et al. [14] studied the practical applications of the Empirical Bayesian method. In his methodology the expected number of accidents is calculated by combining the accident records of the entity and the accident frequency expected at similar entities by a weight factor. The author claimed that the precision of road accidents' estimation can be enhanced when the accident record is sparse and the regression to mean bias is eliminated. The benefit of the Empirical Bayesian method has also improved by the studies [15, 16]. In their paper they have examined the performance of different accident prediction models developed from network segmentation methods on Hungarian expressways.

Road safety analysis may include data on different levels of aggregation [17, 18]. Russo and Vitetta [18] defined two structural levels of road safety data, aggregated and disaggregated data. The aggregated level is focusing almost on spatial data of a large geographical areas (urban area, central business district, etc.) and apply a macroscopic analysis for predicting accident occurrence. In contrast, the disaggregated level concerns small infrastructural elements (road segment, junction, parking area, etc.) and uses a set of micro-level variables (incident, driver, etc.) to estimate accident severity or frequency. Generally, existing research has examined traffic safety independently at either the micro or macro level.

At the microlevel, road accident analysis included detailed factors related to one or a small group of accidents, such as, geometric road features [19, 20], traffic characteristics [21], or weather and environmental conditions [22, 23]. Most of these studies have been performed for small spots or road segments. In contrast, the macro-level applied factors related to a large group of accidents at an area or regional level, such as road category [24], urban planning including population and building density [25], or vehicle mile-travel [26]. However, the selection of a suitable analysis level depends on the purpose of the study and the type of available data.

On the other hand, accident prediction models in every literature were limited to a specific road category or intersection. Castro et al. [27] applied a latent variable generalized ordered response framework for modeling accident count at urban intersections. The results revealed some critical unobserved components influencing accident propensity at intersections, including roadway configuration, approach roadway functional type, and total daily entering traffic volume. Persaud and Mucsi [28] used the hourly traffic volumes in a regression model for estimating accident potential on two-lane rural roads. Persaud and Dzbik [29] developed a generalized linear model to study the change in accident frequency and severity on the freeway. Most of these studies were limited and dedicated to a specific road type or intersection. Differences in the characteristics of different roads make it difficult to construct a uniform model for all road categories. Ghadi and Török [30] compared the performance of some black spot identification methods between highway and secondary roads. They discovered that the performance of the applied approaches could be significantly affected by the broad category and the speed factor. Gururaj et al. [31] used un-supervised machine learning algorithms for predicting the injury severity of traffic accidents. However, failing to account for the hierarchical structure of accident data might lead to underestimating accident prediction model parameters.

Multilevel models are specifically geared to analyze data with a hierarchical or cluster structure [32]. The multilevel analysis includes modeling the relationship between different groups of accidents by identifying a hierarchical system of data that takes advantage of the clustered dataset. This means that the model's outcome is affected by a nested relationship between individual accidents' lower-level characteristics (level one) and higher-level group characteristics (level two). Lenguerrand et al. [33] investigated the advantages of applying a multilevel logistic model to analyze the hierarchical structure of accident data for vehicle occupants compared to a traditional generalized estimating equation and logistic models. They found that the multilevel analysis provides a more efficient model than the traditional models. Haghighi et al. [20] explored the nested relationship between individual crash characteristics and environmental and roadway features. They applied a multilevel ordinal logistic regression to analyze the hierarchical structure of accident data and its impact on accident severity outcome. Few literatures investigated the influence of multilevel analysis on accident counts. Cai et al. [34] developed a Bayesian integrated spatial model to analyze accident frequency at the macro-and micro-levels between district and road entities (i.e., segments and intersections) simultaneously. The results indicated that the model could simultaneously identify both micro-and macro-level factors contributing to the accident occurrence and with higher performance.

A road accident is generally an unforeseen occurrence that might occur on different roadways under different conditions. A given road segment's environmental and geometrical parameters significantly influence the density of accidents per segment length. Typically, these accident risk data of individual road segments are grouped within groupings (e.g., roadways with different categories). Due to the hierarchical nature of these data structures, similarities in accident risk across road segments (i.e., individuals) of consecutive highways (i.e., groups) may exist. They must be accounted for in the analysis. The multilevel analysis presents an opportunity to study the hierarchical nature of road accident properties, attempting to understand the risk of individual road segments within a group context. For example, on the one hand, small roadway segments may vary in some parameters, such as traffic characteristics (i.e., traffic volume, speed limit, truck volume) and geometric features (i.e., roadside hazard, median type, curves, surface condition). From another hand, accident frequency can be counted from group characteristics that might be aggregated from lower-level characteristics, such as category or level of service, including road design standard, average speed limit, and the average annual daily traffic (AADT).

No study has, to our knowledge, examined the variation of road accident risks for different road categories using a single micro-and macro-level model. This study believed every road could be subdivided into smaller portions with distinct environmental and geometric design characteristics. The nested link between roadways of various categories and their short segments is utilized to develop a multilevel model capable of predicting accident counts at a road segment for every road category in the case study.

Appropriate accident prediction models are regarded as fundamental ways of analyzing road safety. Accident frequency analysis is applicable at both the micro and macro levels. Differently, the characteristics of several road types can considerably add to the safety risk of each road segment. In other words, accident frequency may fluctuate not only across road types but also between road segments.

The frequency of accidents per road section is a count including both zeros and positive numbers. If accident counts are uncommon, they may adhere to a Poisson distribution. A property of the Poisson distribution is that the mean and variance must be equal. More often they not, the observed accident variance exceeds the mean. The exclusion of crucial explanatory variables or dependent observations is the known cause. Using a negative binomial regression, the problem of overdispersion can be overcome [36].

The hidden effects of the hierarchical relationship must be investigated to analyze the accident frequency and reveal the correlation between explanatory variables at both micro and macro levels. Accident frequency can be analyzed at different information levels (see Figure 1), including regional-level characteristics (i.e., population, residents), road level characteristics (i.e., category, level of service, average speed limit), or minor road segment level characteristics (i.e., AADT, speed limit, roadside hazard, curvature). For instance, the correlation may exist among road segments in which accidents occurred on the same road due to possible unobserved characteristics. Similarly, roads in the same district are more likely to share similar characteristics than roads in other districts. Considering the multilevel correlation between variables may increase the accuracy and help produce a more general model. The multilevel analysis includes modeling the relationship between different groups of accidents by identifying a hierarchical system of data that takes advantage of the clustered dataset. This means that the outcome of the model is affected by a nested relationship between the lower-level characteristics (level-one) of individual road segments and higher-level group characteristics (level-two) related to the road characteristics (which will be considered in this study), as presented in Figure 1.

This research examines accident frequency by discovering the hidden influences of a hierarchical relationship between explanatory factors in the methods section. To achieve this, a two-level technique was utilized to analyze the nested relationship between the number of roadways belonging to five distinct groups and the accident frequency per road segment. The description of the two-level model is provided below.

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Figure 1. Multilevel hierarchical structure of road accident data

3.1 Level-one modelling

The level-one model treats all road segments similarly, assuming the accident risk does not change on different roads. The general single-level model tries to link the expected accident's outcome to the predicted accidents through the log-odd link function, which can be written as follows [37].

$\eta_{i j}=\log \left(\lambda_{i j}\right)=\beta_{0 j}+\sum_{q=1}^Q \beta_{q j} X_q$               (1)

where, $\eta_{i j}$ is equal to the natural logarithm of the expected accident count ($\lambda_{i j}$) per segment $i$ at road $j$. $\beta_0$ is the intercept, and $X_q$ is the slope for a predictor $q$. $\beta_q$ is the fixed effect coefficient.

The odds ratio can result from exponentiation with the log-odd coefficients (exp.($\eta_{i j}$)) when the odds ratio is less than one, the probability of the outcome decreases while it increases for a higher odds ratio above one.

3.2 Level-two modeling (developing multilevel model)

Multilevel model is distinguished from the single-level model by nesting of individual observations within higher-level groups. The multilevel model treats individual road segments as parts of groups. Each group is corresponding to a specific road with distinguished characteristics (i.e., road category). Because individual segments of the same road are likely to share similar characteristics, they are more likely to respond in the same way compared with individuals of other roads, which in turn violating the assumptions of a single model.

Unlike the fixed-effect of slopes and intercept of the single-level model, the variation of the multilevel model is random. The variation of level-one intercept values (β_0j) between groups j (i.e., roads) indicates the importance of group-level characteristics on the outcome. The level-one intercept values represent a group mean when all explanatory variables are zero or at their average base [38]. The general form of the level-two model is presented in the following equation [37].

$\beta_{0 j}=\gamma_{00}+\left(\sum_j \gamma_{0 j} W_j\right)+u_{0 j}$               (2)

At the level-two, more level-one intercepts (β_0j) can be modeled as a function of level-two random effect variance (u_0j) with a fixed level-two intercept (γ₀₀). In some cases, the random change in slope coefficient (γ_0j) between groups can be considered as a level-two parameter (W_j) of the model. However, a general multilevel model can be formed by combining both levels (Eqns. (1)+(2)) in a single formula (Eq. (3)) [37].

$\eta_{i j}=\gamma_{00}+\left(\sum_i \gamma_{i 0} X_i\right)+\left(\sum_j \gamma_{0 j} X_j\right)+u_{0 j}$               (3)

where, X_i and X_j are fixed-effect predictors of accident frequency at level-one and level-two, respectively. γ_i0 is a coefficient of X_i and γ_0j is a coefficient of X_j.

The estimation of the level-two variance (u_0j) can judge whether groups are significantly different from each other. For multilevel model outcome, there is no separate variance (error) term at level-one, because individuals of a single group are assumed to be similar in many variables, and the variation only exists between level-two groups.