Several studies in the last decade have emphasized the association of higher speed limits with the most severe outcomes occurrence (Behnood & Mannering, 2017; Chen & Shen, 2016; Dash et al., 2022; S. Islam & Hossain, 2015; S. Liu et al., 2021; Zhu, 2021).

The crash severity is significantly influenced by roadway factors, including the area in which the crash occurs, road and pavement characteristics, the number of lanes, and the presence of road signage (Anysz et al., 2021; Das et al., 2023; Dash et al., 2022; Katanalp & Eren, 2020; Prati et al., 2017; Sener et al., 2019; Zhu, 2021). This reinforces the importance that roadway plays in determining cyclist safety.

Environmental factors are also important as the analysis indicates that the most severe cyclist crashes are more likely to occur during the summer season, at night, or in low-illumination conditions (Chen & Shen, 2016; Das et al., 2023; Dash et al., 2022; S. Islam & Hossain, 2015; Salon & Mcintyre, 2018; Sun et al., 2022b).

Similarly, individual cyclist characteristics including age, gender, and race have been identified as factors associated to an increase in crash severity (Bahrololoom et al., 2020; Balakrishnan et al., 2019; Behnood & Mannering, 2017; Chen & Shen, 2016; Joo et al., 2017; J. Liu et al., 2020; Macioszek & Granà, 2022; Prati et al., 2017; Sun et al., 2022a; Zhu, 2021). Among cyclists behaviours, alcohol consumption, riding on the wrong side of the road, and helmet and reflective clothing usage significantly influence the crash severity (S. Islam & Hossain, 2015; S. Liu et al., 2021; Wahi et al., 2018).

In motor-vehicle crashes involving cyclists, various factors associated both with the driver as well as the vehicle affect the injury severity. Prior studies identified a significant influence of drivers gender, age, alcohol consumption, distraction, and driving on the wrong side of the road on the cyclist crash outcome (Balakrishnan et al., 2019; Das et al., 2023; Liu and Fan, 2021; Rahimi et al., 2020).

Moreover, the involvement of heavy vehicles and the extent of damage sustained by the vehicles contribute to the likelihood of severe injuries in cyclist crashes. Recognizing this dual aspect highlights the need to consider not only factors specific to cyclists but also the vehicles characteristics (Joo et al., 2017; Katanalp & Eren, 2020).

Several studies focused on crashes occurring at intersections, revealing noteworthy insights. Akgun et al. (2018) found that a higher speed limit reduces safety for cyclists at roundabouts, with the probability of a serious casualty increasing for each additional lane on approach and with a higher entry path radius. Shen et al. (2020) extended this exploration to various intersection types, including roundabouts, crossroads, and T-junctions, highlighting differences in factors influencing cycling safety across these intersections. Another perspective was offered by Wahi et al. (2018) who identified factors contributing to bike-motor vehicle crash severity under different traffic control measures at intersections. Their findings indicated increased injuries for cyclists aged 40-49 and 60+ without helmets, particularly at regulated intersections. Especially, faulty cyclists experienced more severe injuries at stop signs, with speed emerging as an important risk factor specifically at these intersections. Bahrololoom et al. (2020) focused on bike-car crashes at intersections, showing that pre-collision car kinetic energy and post-collision bike kinetic energy affect injury severity. The study further highlighted that older cyclists are more susceptible to severe crashes, while the use of helmets serves as a mitigating factor in injury severity.

The literature analysis indicates different methodology families employed in previous studies (Table 1). Among them, econometric models have a solid foundation for crash analysis. They can be classified into ordinal and non-ordinal methods. The ordinal models, such as Ordered Logit (S. Liu et al., 2021), Ordered Mixed Logit (Balakrishnan et al., 2019; Chen & Shen, 2016), Ordered Probit (Joo et al., 2017; S. Liu et al., 2021), Geographically Weighted Ordinal Logit (J. Liu et al., 2020) and Generalized Ordered Logit (Chen & Shen, 2016; Shen et al., 2020) have been used to analyse the crash severity in a graduated manner, considering increasing levels of injuries.

On the other hand, non-ordinal models included the Generalized Additive Model (Chen and Shen., 2016), the generalized linear model (Xing et al., 2020), the Logit Model (Akgun et al., 2018; Dash et al., 2022; Macioszek & Granà, 2022; Salon & Mcintyre, 2018; Sener et al., 2019), the Mixed Logit (Bahrololoom et al., 2020; Behnood & Mannering, 2017; Das et al., 2023; S. Islam & Hossain, 2015; Sun et al., 2022b, 2022a; Wahi et al., 2018), the Partial Proportional Odds Logit (S. Liu et al., 2021; Shen et al., 2020), and the Latent Class Analysis (Sun et al., 2022a).

Furthermore, the literature analysis indicates a growing use of machine learning techniques such as Association Rules (Anysz et al., 2021), Decision Trees (Dash et al., 2022; Joo et al., 2017; Katanalp & Eren, 2020; Prati et al., 2017; Rahimi et al., 2020; Xing et al., 2020), DT-Based Converted Fuzzy Logic (Katanalp & Eren, 2020), Random Forest (Dash et al., 2022; Rahimi et al., 2020), Gradient Boosting (Zhu, 2021) and Bayesian Network (Prati et al., 2017; Sun et al., 2022b).

The machine learning methods are characterised by their ability to handle complex and nonlinear relationships in data without specific assumptions about data distribution. Thus, in presence of large and complex datasets, machine learning technique may be preferred to econometric models, needing short data preparation time, and providing enough accuracy (F. Mannering et al., 2020; Montella et al., 2021; Moral-Garcia et al., 2019; Rella Riccardi, Galante, et al., 2022; Zhu, 2021).

Thus, while econometric models provide a solid analytical framework, machine learning methods offer the more flexibility to address complex relationships and dataset.

In this paper, both econometric methods, such as the Mixed Logit Model (MLM), and machine learning tools, specifically the Classification Tree (CT), were employed to identify the factors influencing the cyclist crash severity.

Among econometric models, the MLM was chosen because it accounts for unobserved heterogeneity among observations, providing a full understanding of variability in the data. This is particularly useful in the context of cyclist crashes, where individual characteristics may affect outcomes (Rella Riccardi, Mauriello, Sarkar, et al., 2022; Scarano et al., 2022b). Moreover, our study introduces an innovative approach that combines both traditional econometric methods and machine learning techniques. While traditional econometric models provide a solid foundation in statistics and econometrics field, our research makes a step forward by also using advanced machine learning tools such as the CT. This integration represents a conventional practice that overtakes the singular method limitations.

Finally, our study is in line with the contemporary trend in the literature, showing a growing trust on machine learning techniques. The inclusion of decision trees as data mining tools, as showed in a recent analysis carried out by Scarano et al. (2023), represents a progress in our research. Indeed, CT emerge as a practical technique able to effectively manage discrete variables or variables with a high number of categories. This approach not only demonstrates ability in handling outliers but also eliminates the need for a priori assumptions regarding variable distributions, overcoming the regression model limitations (Prati et al., 2017).

Classification trees represent a methodology aimed at obtaining a hierarchical segmentation of the cyclist crashes by iteratively partitioning the dataset into subgroups that are homogeneous in terms of cyclist crash severity. This process shows the variables that have the stronger influence on the outcome.

The tree is a directed graph that starts from a root node. Then, this root node is progressively split into leaf nodes by using an explanatory variable named “splitter”. Although all independent variables are considered potential candidates for splits at each internal node, the predictor that makes the best partition is selected.

We implemented the Classification and Regression Trees (CART) algorithm introduced by Breiman et al. (1984). The evaluation of impurity at each node was performed using the Gini reduction criterion. A higher Gini index value indicates increased homogeneity in the node resulting from the split. The Gini reduction criterion is calculated as follows:

(1) i Y ( t ) = 1 − ∑ j = 1 J p ( j | t ) 2

where p(j|t) represents the proportion of observations in node (t) belonging to the j_th class of the response variable. A node is pure when contains all observations belonging to a single severity class, resulting in an impurity value of zero.

The total impurity of the tree (T) is calculated as follows:

(2) i Y ( T ) = ∑ t ∈ T ~ i Y ( t ) p ( t )

where iY(t) represents the impurity of the node t, p(t)=N(t)N is the node’s weight (N(t) is the count of observations in node (t), N is the overall count of observations), and T~ denotes the all the terminal nodes in the tree. The terminal nodes exhibit lower impurity levels in contrast to the root node. The overall impurity of the tree decreases through the identification, at each tree node, of the optimal partitioning of observations into distinct severity classes, ensuring external heterogeneity and internal homogeneity.

The CART algorithm comprises the following steps:

The algorithm is applied to each node until the tree construction stops. Before choosing the most appropriate stopping criterion for the tree, a literature review was carried out (Table 2).

Based on the information presented in Table 2, it was decided to adopt stopping techniques according to two criteria: (1) when the decrease in Gini index fell below a minimum threshold set at 0.0001; and (2) when the tree reached a maximum depth of 4 levels.

For each node, the assigned severity class depends on the PCR highest value. This PCR compares the percentage of observations for each severity class in the terminal node with those in the root node (Rella Riccardi, Galante, et al., 2022):

(3) P C R ( j | t ) = p ( j | t ) p ( j | t r o o t )

where p(j|t) denotes the crashes in node t belonging to severity class j, troot is the tree root node.

For each node, the class j∗ with the highest PCR value determines the class of that node, selected as follows:

(4) j ∗ | t : max j P C R ( j | t )

The terminal nodes allow us to identify relationships between variables that affect the severity of cyclist crashes. The classification trees were carried out using the SPSS software.

The MLM represents a generalized version of multinomial logistic regression (Rella Riccardi, Mauriello, Scarano, et al., 2022). Unlike the standard logit model, the MLM allows coefficients of the variables β_j to vary across observations or groups of observations. Thus, the β_j coefficients can be decomposed into their means (b) and standard deviations β~j (F. L. Mannering et al., 2016):

(5) β j = b + β ~ j

In the contest in which the MLM is applied to predict crash injury severity, the propensity of crash i (where i = 1,…, 72,363) towards the severity category j (where j varies from 1 to 3: 1 = slight injury, 2 = serious injury, 3 = fatal) is expressed through the injury-severity function S_ij, which is determined by the sum of V_ij (the systematic component) and ε_ij (the unobservable stochastic error):

(6) S i j = V i j + ε i j = β j X i j + ε i j

where Xij is a column vector of characteristics (explanatory variables) that influence the cyclist injury severity level j, βj is a column vector of the parameters to be estimated for the crash severity category j, and εij is the error term assumed to be independently and identically distributed (McFadden & Train, 2000; Washington et al., 2020).

The mixed logit probability represents a weighted average of the standard logit probabilities at different values of parameter β. Thus, the mixed logit probability is the integral of standard logit probabilities over a density of parameters β, defines as follows (Alogaili & Mannering, 2020; Train, 2009):

(7) P i j = ∫ e β j X i j ∑ J e β j X i j f ( β | σ ) d β

where: f(β|σ) is the continuous density function adopted by vector βj, σ is a vector of parameters that specify the density function (mean and variance), and all other terms are as previously defined (Anastasopoulos & Mannering, 2011). Note that in the simplified case where f(β|σ) = 1, the model reduces to the standard logit (Washington et al., 2020)

A normal distribution is chosen for f(β|σ) due to its proven suitability over other distributions studies (Azimi and Asgari, 2023; M. Islam et al., 2022; Uddin & Huynh, 2020).

To determine which variables should be treated as random parameters, we employed a forward stepwise selection procedure based on the improvement of model fit, as measured by the Akaike Information Criterion (AIC) which balances model complexity and goodness of fit (Burnham & Anderson, 2004). Specifically, we initially estimated a base model with only fixed effects and sequentially introduced random effects for different variables, retaining only those that improved model performance in terms of AIC values. Furthermore, since categorical variables were transformed into dummy variables, only specific categories were tested as random rather than the entire variable.

The β_j coefficients explain the effect of the independent variables. For a proper interpretation of the model results, it is important to assess the magnitude of the impact of the independent variables on the dependent variable. In evaluating the explanatory variable influence on the crash severity, various methodological approaches are available, including odds ratio, marginal effect, or elasticity (Lord et al., 2021). Among these, Odds Ratio (OR) stands out as the most practical choice (Norton & Dowd, 2018). The OR is the exponentiation of β_j (exp(β_j)), showing the proportional increase (OR > 1) or decrease (OR < 1) in the likelihood of the outcome when the corresponding indicator variable is set to 1 (Lord et al., 2021). Thus, the OR provides a complete understanding of the impact of each variable on the outcome, representing a vigorous and convenient tool for analysing the complexities of factors influencing the cyclist crash severity.

The MLM was executed in the R-CRAN software environment by using the “mlogit” package.

As part of the preliminary analysis, a chi-square test was conducted to identify any significant relationships between our categorical variables. Using a significance level of 10%, the test results show there is not any statistically significant relationship between the variables.

In the cyclist crash severity analysis, the model performance assessment is important to guarantee a complete understanding of the factors associated with cyclist crash severity.

For the MLM, the McFadden’s Pseudo R² was employed:

(8) M c F a d d e n R 2 = 1 − L L f u l l L L 0

where: LL₀ is the loglikelihood of the null model and LL_full is the loglikelihood of the model including all the statistically significant variables.

The McFadden’s Pseudo R² metric works as a goodness of fit indicator in discrete choice models. Specifically, it shows how much variance the full model that incorporate independent variables explains in the data compared to what would be explained using the null model. The McFadden’s Pseudo R² variability range is between 0 and 1 with the higher values indicating better model performance. McFadden’s Pseudo R² greater than 0.20 indicates a very good fit (Andreß et al., 2013).

For both the MLM and the CT tool, our focus extends to the G mean and F measures as performance indicators. They are composite indicators that integrate more individual metrics into a unified performance measure (Guo et al., 2008).

The G-mean (Eq. 9) shows how well the model can correctly identify both positive and negative instances:

(9) G − m e a n = ( A c c − × A c c + ) 1 2

where:

Acc−=TNTN+FP is the true negative rate; TN is the number of true negatives; FP is the number of false positives;

Acc+=TPTP+FN is the true positive rate; TP is the number of true positives; FN is the number of false negatives.

The F-measure (Eq. 11) balances precision and recall, providing an assessment of the model performance in terms of true cases classification. Thus, a higher F-measure value reflects a better trade-off between precision and recall.

(10) F − m e a s u r e = ( 1 + β 2 ) × P r e c i s i o n × R e c a l l P r e c i s i o n + R e c a l l

where:

Precision=TPTP+FP is the accuracy of positive predictions among the instances predicted as positive;

Recall=Acc+=TPTP+FN is the model capacity to identify all actual positive instances;

β is a coefficient to adjust the relative importance of precision versus recall.

β was set 1 indicating an equal emphasis on both precision and recall (Bekkar et al., 2013).

The CT is composed by 13 terminal nodes (Figure 1). Among these terminal nodes, 7 are associated with fatal crashes, 4 with serious injuries, and the other 2 with slight injuries.

The CT starts from a first splits based on the speed limit. Furthermore, the following splits are based on nine specific variables, including the manoeuvre of the second vehicle, vehicle 2 type, driver age, junction type and details, the first road class, and the first point of impact of the second vehicle, the cyclist age, and whether the second vehicle hit an object in the carriageway.

The PCR was calculated for all terminal nodes to evaluate how well each node predicts a crash severity class (Table 3). The nodes 15, 17 and 21 demonstrates higher PCRs (10.62, 8.97, and 7.71, respectively), by highlighting their effectiveness in fatal crash prediction.

The Node 15 has a PCR of 10.62. It highlights a scenario that includes situations where the speed limit exceeds 50 mph, the second vehicle is overtaking or proceeding straight, the crash occurs outside an intersection or at crossroads, and the second vehicle’s first point of impact is the front of the bike. This combination of factors creates a dangerous situation that increase the fatal crash likelihood.

Node 17, which has a PCR of 8.97, starts from a split based on speed limit between 20 and 30 mph. At these speed limits, fatal crashes are associated with specific conditions such as the truck involvement, the driver of the second vehicle aged between 25 and 74 years, and the first road class equal to A or a motorway. These conditions together create a hazardous scenario where even moderate speeds can result in fatal cyclist crashes.

Node 21 has a PCR of 7.71 and represents another dangerous scenario including a speed limit split of 30 mph, the involvement of a car or a two-wheeler (e.g., bike or PTW) proceeding ahead or overtaking and colliding with a curb. Furthermore, the collision with the curb increases the proportion of fatal crashes from 0.003 (node 13) to 0.046 (node 21).

Regarding variable importance, the Figure 2 highlights variables with normalized importance above 20%. Six of these variables have normalized importance greater than 50%, indicating they are significant in classifying crash severity:

Results of the CT analysis were used as input for the MLM. Specifically, we identified the first two terminal nodes with the highest PCR for fatal crashes, such as the node 15 and the node 17, and traced their pathways back to the root node, showing the following interactions:

The performance metrics, expressed through F-measure and G-mean, provide an understanding of our model’s predictive capabilities (Table 4).

For fatal crashes, the G-mean index demonstrates a notably high value of 0.78, indicating the model’s ability to accurately identify both positive and negative instances and providing a balanced prediction. However, the F-measure, which balances precision and recall, yields a lower value of 0.06, suggesting a challenge in effectively managing this severity level.

In the case of serious injury crashes, there is a significant improvement in the F-measure, with a value of 0.20, highlighting a better balance between precision and recall. Conversely, the G-mean index for this category is lower, with a value of 0.38, indicating a diminished capacity of the model to recognize both positive and negative instances in a balanced manner.

The findings for both the fixed and random variables are presented in Table 5 where, for each significant variable (p-value <0.05), we reported the estimated value (β_j) and its OR.

To refine the regression analysis and explore potential interaction effects, we incorporated the interactions derived from the CT analysis as dummy variables: interaction 1-4, interaction 4-9, interaction 9-15, interaction 2-5, interaction 5-11, interaction 11-17.

In estimating fatal crashes, 21 explanatory variables and 45 indicator variables emerged as statistically significant in addiction to 6 interaction variables. Conversely, for estimating serious outcome, 17 explanatory variables, 30 indicator variables and 5 interaction variables demonstrated statistical significance.

For fixed parameters, for each severity category, positive β coefficients indicate an increase in odds and negative β coefficients indicate a decrease in odds, relative to the reference category.

Understanding the random variable outcomes is a bit more complicated. Examining the normal distribution of random parameters reveals that certain observations in one group are more likely to have a severity level, while others are less likely. In our model, cyclist age ≥75 (specific to the fatal crashes) is a random variable with a mean of 3.29 and a standard deviation of 0.66. According to the normal distribution, it can be inferred that 99.9% of the crashes involving an elderly cyclist had a higher probability of resulting in the fatal severity level. The remaining small percentage (< 0.1%) of the crashes were more likely to result in slight or serious injuries. Another significant random parameter is the indicator variable driver age = 55-64 (specific to the serious injury level), with a mean of -0.12 and a standard deviation of 0.51. The distribution for this variable indicates that 59.0% of the crashes where the cyclist collides with a driver aged between 55 and 65 years old had a higher probability of resulting in a serious injury level, while the remaining 41.0% of these crashes were more likely to result in one of the other severity levels (slight injury or fatal). Additionally, the indicator variable for cyclist gender = male has resulted a significant random parameters for both fatal and serious outcomes. As regards the fatal crashes, the mean and the standard deviation of the random parameter cyclist gender = male were 0.37 and -0.97, respectively. This indicates that 64.7% of the crashes involving a male cyclist had a higher probability of resulting in a fatal outcome, while 35.3% were more likely to result in a slight or serious injury. For serious outcomes, the mean and the standard deviation of the random parameter cyclist gender = male were -0.11 and 1.56, respectively. This indicates that 52.8% of the crashes with male cyclist were more likely to result in severe injuries, while the 47.2% were more likely to result in slight injuries or fatalities.

Among the fixed-effect parameters, high speed limit has a dramatic effect on crash severity. The OR of fatal crashes associated with speed limit equal to 40 mph (with a baseline of 30 mph) is 1.60 and increases to 2.96 for speed limit ≥ 50 mph. If a cyclist crash occurs in a rural area, the probability of both fatal (OR=1.78) and serious injury crashes (OR= 1.25) increases. Compared to the single carriageway the road type with the lower probability of fatal crash is the roundabout with an OR of 0.65. While dual carriageway and slip road have an OR respectively equal to 1.24 and 2.06. Darkness condition shows greater propensity towards most severe crashes having an OR equal to 1.66 for fatal crash and 1.13 for serious crash. The wet/frozen pavement is significant both for fatal crash with an OR of 1.50 and for serious crash with an OR of 1.09, whereas weekend increased the probability of both fatal and serious crashes, with an OR respectively equal to 1.53 and 1.16. Bike leaving the carriageway nearside, offside ore straight are strongly associated with crash severity showing an OR respectively of 3.17, 12.91 and 18.95 for fatal crash. Considering vehicle 2 engine capacity equal to 1501-2000 as baseline, vehicle 2 engine capacity >3000 is associated with higher probability of both fatal crashes exhibiting an OR of 2.24 and serious crash with an OR of 1.13. When the second vehicle skids or overturns, there is a significant increase in the likelihood of both fatal (OR = 2.79) and serious injury crashes (OR = 1.60). Regarding driver related factors, young drivers (≤17, 18-24 years old) increased probability of fatal crash. The most influential variable is the cyclist age. Compared to the young cyclist (25-34), the involvement of an elderly cyclist increases the probability of fatal crashes: 35-44 with an OR of 1.21, 45-54 with an OR of 1.37, 55-64 with an OR of 3.57, 65-74 with an OR of 7.26, and ≥75 (random variable) with an OR of 26.90.

The results of the MLM confirm also that all tested interaction terms are statistically significant, highlighting the risk effect associated with the combination of some factors on crash severity. The interaction between higher speed limits (≥40 mph) and the manoeuvre of the second vehicle (going ahead or overtaking) is associated with an increase in the probability of fatal crashes (interaction 1-4, OR = 1.48). However, this effect is not significant for serious crashes, suggesting that crashes occurring under these conditions are more likely to be fatal rather than serious. Similarly, the interaction between the second vehicle’s manoeuvre and the junction type (not at a junction, crossroads, or other junctions) exhibits a positive effect on both fatal (OR = 2.22) and serious crashes (OR = 1.23) (interaction 4-9). This finding indicates that crashes occurring outside intersections, or at crossroads, become more severe when the second vehicle is proceeding straight or overtaking.

Another significant interaction is observed between junction type and the first point of impact of the second vehicle (front) (interaction 9-15). This interaction increases the probability of fatal crashes (OR = 1.55). Speed limits of 20–30 mph combined with the involvement of a truck also show an effect on crash severity (interaction 2-5). While this interaction increases the likelihood of fatal crashes (OR = 1.37), it is negatively associated with serious crashes (OR = 0.66). This suggests that although lower-speed environments generally reduce crash severity, the presence of truck vehicles can still result in fatal consequences.

The most pronounced effect is observed for the interaction between the involvement of a truck the age of the second driver (25–74 years old) (interaction 5-11). This interaction significantly increases the likelihood of both fatal (OR = 6.04) and serious crashes (OR = 2.53).

Finally, the interaction between driver age and the type of road (A roads or motorways) is associated with an increase in fatal crash risk (OR = 1.49) and a slight increase in serious crashes (OR = 1.06) (interaction 11-17). This suggests that driving behaviour among older age groups, particularly in high-speed road environments, can influence crash severity outcomes.

Thus, the results indicate that specific combinations of factors, such as speed limits, vehicle type, driver age, and road design, can significantly increase crash severity risks.

The MLM shows a robust fit with a McFadden Pseudo R² of 0.21. F-measures is reasonable for serious injuries (0.29) but less satisfactory for fatal crashes (0.06). G-mean reveals differences in classification performance, with the model exhibiting higher effectiveness for fatal crashes (0.80) compared to serious injuries (0.51) (Table 6).

Antonella Scarano: Conceptualization, Formal analysis, Methodology, Software, Writing—original draft, Writing—review & editing. Maria Rella Riccardi: Conceptualization, Methodology, Writing—review & editing. Filomena Mauriello: Conceptualization, Methodology, Writing—review & editing. Carmelo D’Agostino: Conceptualization, Writing—review & editing. Alfonso Montella: Conceptualization, Methodology, Supervision, Writing—review & editing.

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.

The authors declare that no generative AI was used in this work.

Crash data used in this research were collected by the Department for Transport (GOV.UK) and were retrieved from the STATS19 dataset (https://www.gov.uk/transport-statistics-notes-and-guidance-road-accident-and-safety). Thus, this research was exempted from requiring an ethical approval.

One of the authors, Carmelo D’Agostino, is a member of the editorial board of the Traffic Safety Research journal. To minimize the risk for conflict of interest during the review process, an external guest editor was called to handle this paper.

Guest editor: Ragnhild Davidse, SWOV Institute for Road Safety Research, the Netherlands

Reviewer: Paul Schepers, Ministry of Infrastructure and Water Management, the Netherlands