Modelling the effects of stress on gap-acceptance decisions in a driving simulator experiment using physiological sensors

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1 Modelling the effects of stress on gap-acceptance decisions in a driving simulator experiment using physiological sensors Evangelos Paschalidis 1, Charisma F. Choudhury 2, Stephane Hess 3 1,2,3 Choice Modelling Centre, Institute for Transport Studies, University of Leeds, University Rd, Leeds LS2 9JT 1 tsep@leeds.ac.uk, 2 C.F.Choudhury@leeds.ac.uk, 3 s.hess@its.leeds.ac.uk Abstract Driving behaviour is an inherently complex process affected by various factors ranging from network topography, traffic conditions and vehicle features to driver characteristics like age, experience, aggressiveness and emotional state. The effect of emotional state and stress has received considerable attention in the context of crash analysis and safety research where driving behaviour has been found to be affected by drivers mental state/stress, cognitive workload and distraction. However, these studies are mostly based on questionnaire surveys and self-reports which can be prone to response bias and reporting/measurement errors. On a parallel stream of research, advances in sensor technologies have made it possible to observe drivers stress through human physiological responses, e.g. heart rate, electro-dermal activity etc. However, these studies have been primarily focused on detecting stress rather than quantifying or modelling its effects on driving decisions. The present paper combines these two approaches in a single framework and investigates the gap-acceptance behaviour of drivers during an intersection crossing task with data collected using a driving simulator. The participants were subjected to stress, induced by time pressure, and their stress levels were measured using physiological indicators namely, skin conductance and heart rate. In addition to statistical analyses, discrete choice models were developed to build mathematical relationships between the accept-reject choices and the driver demographics, traffic conditions and stress levels. The results of the models indicated significant impacts of stress levels leading to increased probabilities of accepting a gap. The improvement in model fit and safety implications derived from model estimates are also discussed. The insights from the results can be used for designing appropriate intervention strategies. Keywords: gap-acceptance, driving stress, driving simulator, heart rate, skin conductance 1. Introduction Road safety continues to be an important issue with road crashes among the leading causes of death - accounting for more than 1.2 million fatalities and 50 million injuries globally each year. Driving behaviour is a factor in over 90% of crashes, with speeding as one of the major contributors (World Health Organization, 2015). Driving behaviour models, which provide mathematical representations of drivers decisions involving acceleration-deceleration, lane-changing, overtaking, etc., are increasingly being used for evaluation and prediction of road safety parameters and formulating remedial measures. Reliable driving behaviour models are also critical for accurate prediction of congestion

2 levels in microscopic traffic simulation tools (Barceló, 2015) and analyses of emissions (Ahn et al., 2002). Driving decisions are affected by various factors, including network topography, traffic conditions, and driver characteristics - which include, among others, demographics, personality traits and emotional state. Existing driving behaviour models address many of these factors, either fully or partially, where the effects of surrounding traffic conditions have received considerable attention (Ossen & Hoogendoorn, 2005; Toledo, 2007; Choudhury, 2007; Marczak et al., 2013 to name a few). However, in most cases, the models do not adequately capture the sophistication of driver behaviour and the causal mechanism behind their observed decisions. In particular, research in other realms, in the context of crash analysis and safety research, has confirmed that driving behaviour is significantly affected by drivers mental state/mood (e.g. anger) (Garrity & Demick, 2001), cognitive workload (Hoogendoorn et al., 2010), distraction (Young et al., 2003) and fatigue (Thiffault & Bergeron, 2003). Previous literature on drivers stress, has mainly focused on the investigation of the relationship between stress and aberrant behaviour and its impact on safety (Ge et al., 2014; Westerman & Haigney, 2000; Hill & Boyle, 2007). However, these studies primarily examined the effects of stress based on self-reported surveys which can be prone to response bias and reporting/measurement errors. On a parallel stream of research, recent advances in sensor technologies have however made it possible to measure drivers stress levels through human physiological responses, e.g. changes in heart rate, electro-dermal activity etc. (Healey & Picard, 2005; Ahmed et al., 2015). However, these studies have been primarily focused on detecting stress rather than quantifying or modelling its effects on driving decisions in detail. This paper aims to fill in this research gap by developing gap acceptance models with explicit consideration of the effect of stress on driving behaviour. The gap-acceptance models developed in this research are based on an extensive experimental study in the University of Leeds Driving Simulator (UoLDS) where the drivers were intentionally subjected to stressful driving conditions caused by time pressure and surrounding traffic conditions. Their choices of accepted gaps were recorded alongside physiological measurements of stress indicators (skin conductance and heart rate), self-reported stress levels, traits (e.g. risk-taking propensity) and observed characteristics (age, gender, experience). A series of gap acceptance models was developed and augmented by continuous physiological measurements. The rest of the paper is organised as follows: next section presents a review of the literature. The section after that describes the methodological approach of the study. This is followed by the experimental setting and the data analyses. The estimation results are presented next followed by concluding remarks where insights from the models are discussed. 2. Literature review 2.1. Stress and driving context Driver stress has been defined as a situation that challenges drivers abilities, reduces their perceived control or threatens their mental/physical health (Gulian et al., 1989). Driver stress may arise as a consequence of several factors including the direct demands of the

3 driving task, the environmental conditions (e.g. fog occurrence), network characteristics (e.g. surface characteristics), junction frequency, speed and flow per lane and/or potential secondary tasks (e.g. use of navigation system, texting etc.) (Hill & Boyle, 2007). Moreover, time urgency and the level of congestion have been identified as two important factors influencing drivers stress (Hennessy & Wiesenthal, 1999). There is a substantial body of literature that investigates the effects of stress on driving behaviour. Drivers under stress may be overwhelmed by negative emotions and thus are more likely to get involved in hazardous situations (Ge et al., 2014). Self-reported stress has been linked to aberrant driving behaviour, namely errors and violations (Kontogiannis, 2006). These types of impaired behaviour are related to road crashed and incidents, therefore stress is considered as an issue related to traffic safety (Westerman & Haigney, 2000; Useche et al., 2015, Qu et al., 2014). Moreover, Ge et al. (2014) found that perceived stress is linked to aggressive and risky driving behaviour. Also, Clapp et al. (2011), grouped reactions under stressful situations in three main categories which are the extremely cautious driving behaviour, aberrant behaviour and aggressive (or hostile) behaviour. The aforementioned findings provide compelling evidence regarding the effects of stress on driving, however, they are based on self-reported survey results and therefore can be prone to response bias and reporting/measurement errors. An alternative, and potentially more reliable, approach to detect drivers level of stress and study its effects, is through its implications on human physiology. Recent advances in sensor technologies and affective computing have made it possible to measure drivers stress levels through physiological responses, e.g. changes in heart rate, skin conductance, blood volume pulse etc. There are several existing studies, related to driving stress, that use this type of data to detect stress (some examples Healey & Picard, 2005; Singh & Queyam, 2013; Rigas et al., 2012). However, the aforementioned studies mostly focused on detecting stress rather than investigating its effects on observed driving behaviour. Two of the most widespread physiological indicators - also used in the present study - are heart rate and skin conductance. Heart rate represents the observed heartbeats per minute. Lower heart rate is generally linked to a relaxed state while it increases under the presence of emotional stimuli or mental effort (Katsis et al., 2011). Skin conductance is related to the sweat gland activity and it is an indicator that increases or decreases proportionally to stress effort (Katsis et al., 2011). Skin conductance is composed of two different parts, namely the skin conductance level (SCL tonic part) and skin conductance response (SCR phasic part). While SCL is slow varying and related to individual characteristics, SCRs are expressed as a sudden and fast increase of skin conductance owing to the presence of a specific stimulus and thus have been linked to acute stress. Skin conductance responses are identified if the increase in skin conductance activity exceeds specific critical values. 2.2 Gap-acceptance models Driving behaviour models primarily include car-following, lane-change and gap-acceptance (Toledo, 2007). The latter of the aforementioned concepts focuses on two different aspects; the decision of drivers to change lane and the attempt of a turning or crossing manoeuvre at an intersection. In literature, several methodological approaches

4 have been developed in order predict the intersection crossing decisions of drivers. This type of gap acceptance behaviour is of prime importance when studying issues as network capacity, delays and rοad safety (Ashton, 1971; Fitzpatrick, 1991). The majority of these methodologies is based on the critical gap concept, which is defined as the minimum time gap in the priority stream which a driver moving on the minor road is willing to accept in order to cross through the conflict zone. According to Brilon et al., (1999), there are at least different methods related to gap-acceptance decisions. Some of the most cited are namely the Raff method (Raff & Hart, 1950), the Greenshields method (Greenshields et al., 1946), the lag method (see Brilon et al., 1999), the logit method (Maze, 1981) - which is a method based on traditional choice modelling techniques (see Ben-Akiva & Lerman, 1985) - the Ashworth s method (Ashworth, 1969), and the maximum likelihood method (Miller & Pretty, 1968). The main limitations regarding some of the existing methodologies, are two assumptions regarding driving behaviour namely, consistency and homogeneity (Bottom & Ashworth, 1978; Pollatschek et al., 2002). The first of these two assumptions indicates that each driver has a specific critical gap threshold and accepts all observed gaps with a value greater than this. This type of behaviour is characterised as consistent. The assumption of consistency denotes that gap-acceptance decisions are independent with respect to each available gap, thus it ignores the within-driver variability as each driver is expected to always behave in a specific way. The assumptions of gap-acceptance methodologies raise limitations in the representation of drivers behaviour since they both ignore their sophisticated decision-making process. For instance, critical gap varies among and within drivers, in different situations, and should be treated as a random variable (Guo et al., 2014). The drawbacks imposed by these assumptions have been discussed already in some studies and several methodologies have been developed to address them. Ashworth (1969) used statistical distributions to express critical gap while Pollatschek et al. (2002) developed a gap-acceptance approach to account for individual preferences and different groups of drivers (cautious or risk-takers). Moreover, in logit methodology, a behaviour cannot be considered as inconsistent if an explanatory variable is able to capture and explain it (Amin & Maurya, 2015). Despite the advances in gap-acceptance methodological approaches, not all variables related to driving behaviour have been investigated. Some of the aspects which are not yet addressed include drivers strategies when deciding to cross an intersection or not, the motivation behind an observed inconsistent behaviour and finally the effects of individual traits and characteristics (e.g. socio-demographics, personality, attitudes, state of mind, level of stress etc.). The aim of the present study is to provide an extended gap-acceptance framework, through the development of a model that accounts for variables related to driver s individual characteristics, with explicit consideration of drivers acute stress levels, and contribute to filling in this gap of driving behaviour modelling research. 3. Methodology 3.1 The gap acceptance model The gap-acceptance approach of the current paper was formulated as a binary choice model, where each gap was considered as a different accept/reject decision. This approach is a modification of the logit method mentioned in the previous section. The model

5 assumes that a driver will accept a specific gap if the utility for this decision is higher, compared to the utility of rejecting it. For model identification purposes (see e.g. Hensher et al., 2005), the utility of rejecting a gap is given a fixed value of zero and only the utility of gap-acceptance probability is estimated, with respect to that fixed value (e.g. a positive estimated utility would imply a higher probability of gap acceptance while a negative would indicate the opposite). The gap-acceptance behaviour is then defined as: GA nt = { 1 if U nt GA > 0 0 if U GA nt 0 where n and t indicate an individual driver and a specific available gap respectively. Also, GA U nt represents the utility of the driver to accept a gap. The utility of gap-acceptance is not observed therefore it is modelled as a random variable which is a function of explanatory variables, as shown in Equation 1: U GA nt = β nt X nt + γ n Z n + aν n + ε nt (1) where X nt is a vector of gap-specific variables and Z n are individual-specific variables (e.g. socio-demographics). Moreover, ν n represents a standard normal disturbance term which is used to capture the effect of unobserved variables and ε nt is the Gumbell distributed disturbance term used in choice models. Finally, β nt, γ n and a are vectors of parameters to be estimated. Following the aforementioned assumptions, the probability of gap-acceptance is defined as: P GA nt = e (U nt GA ) 1 + e (U nt GA ) (2) If the observed choice of a driver to accept a gap is set as Y nt =1, the conditional full probability of an observed drivers decision can be expressed, as shown in Equation 3: P nt = (P GA nt ν) Y nt(1 P GA nt ν) 1 Y nt (3) The conditional probability of a sequence of T observed decisions of the same driver takes the form indicated by Equation 4: T P n ν = (P nt ν) t=1 (4) As explained above, it is assumed that νn is standard normally distributed. Thus, the unconditional joint probability of the observations of a given driver is given by Εquation 5 as:

6 + P n = (P n ν)φ( ν)dν (5) where a φ(ν) is the probability density function of the individual specific disturbance term. Given that the integral in Equation 5 is indefinite, it was approximated through simulation using 1000 Halton draws Physiological data analysis The model described in the previous section, was augmented by continuous physiological measurements. These observations were used as direct explanatory variables, in order to investigate whether the gap-acceptance model would be more behaviourally representative, when drivers stress would be included. Two different responses were considered, namely, heart rate and skin conductance. The physiological variables were initially processed and transformed before their incorporation in the model. Instead of using the raw observations, the heart rate data was normalised at individual level, applying a z-score transformation ( x μ ), where x is a heart σ rate observation, μ is the heart rate mean value across the whole urban task and σ is its standard deviation (Picard et al., 2001; Maaoui & Pruski, 2010). The skin conductance observations were processed using using the Matlab package Ledalab (Karenbach, 2005). The responses were obtained applying trough-to-peak analysis and their amplitude was considered as explanatory variable in the models. The skin conductance analysis was based on event-related response activation; each gap was considered as a different stimulus. The initiation of each gap was used as a starting point and responses were detected 1-4s after that moment. Moreover, since all variables used in the models refer to the initial moment of a gap (as defined in the next section), and given that SCRs detection works forward, the SCRs activity during the previous gap was considered as an explanatory variable of a current one. An example of SCRs analysis is illustrated in Figure 1. Following literature indications (e.g. Sano et al., 2014), a critical value equal to 0.01μS was selected as a minimum critical SCRs. Moreover, each significant amplitude (above 0.01μS) was divided by the maximum observed SCR amplitude, during the simulator experiment, to minimise the effects of individual differences (Lykken, 1972). Figure 1: Example of SCRs extraction

7 4. Data collection 4.1 Driving simulator experiment The data used in this research was based on primary data collected as part of a comprehensive driving simulator study (Next Generation Driving Behaviour Models NG-DBM) for investigating the effect of stress in different driving decisions (e.g. acceleration-deceleration, overtaking, red light violation, gap acceptance, etc.). The experiments were conducted using the University of Leeds Driving Simulator (UoLDS). The UoLDS (Figure 2) is a high fidelity, dynamic simulator, with all driver controls available and fully operational, such as steering wheel and breaking pedal, while there is also a fully operational dashboard. The vehicle is placed in a 4m diameter spherical projection dome. The dome provides fully textured 3-D graphical scene with a horizontal field of view of 250 o and 45 o vertical. The raw data output consits of observations of 60Hz frequency. It may be noted that though driving simulator data has the risk to be prone to behavioural incongruence, it offers the flexibility to fully control the surrounding traffic and driving contexts (e.g. inducing time pressure and stressful scenarios) which are crucial for this particular study. Figure 2: The University of Leeds Driving Simulator [sources: University of Leeds, University of Leeds Driving Simulator] The full data collection process involved around 90 minutes of total driving in the simulator. Participants initially had a short briefing session about the simulator and its operation followed by a practice session of approximately 15 minutes duration to get familiarised with the simulated environment and vehicle dynamics (i.e. motion system). For safety reasons, participants were accompanied by a researcher, during the practice run, in the back seat. After the practice session, participants staretd the main driving sessions, composed by two different environments, an urban and a motorway, with a short break in between. At the end of each driving session, participants answered a brief questionnaire related to the events they encountered and their perceived stress levels. During the various driving scenarios, stress was induced through a series of tasks/events (e.g. unpredictable behaviour of neighbouring vehicles, amber dilemma, slow moving leader, gap-acceptance tasks etc.) and driving under time pressure. The majority of the scenarios was examined both without and under the presence of time pressure. Before each of the two main tasks, participants were instructed that they had to complete them within 35 minutes without however being accurately informed about the remaining time; they could only see a face image, placed on the dashboard (Figure 3). The green and amber states would indicate that the driver was still on time while the red was interpreted as being late to complete the task. Participants were informed that, during the whole driving task, a

8 sophisticated algorithm was running in the background evaluating variables as current speed, speed limit, distance to the end, an average estimated delay that will be caused by the events ahead etc. and printed, as an outcome, one of the three face images, which was related to their performance. However, the state of the time pressure faces was not related to their actual performance but was pre-decided in order to induce additional pressure in specific road segments. The choice of 3 different faces to indicate time pressure, was preferred to a conventional countdown timer since it would be easier to manipulate. In order to increase the likelihood that participants would consider time pressure indications, they were instructed that a penalty would be imposed in their monetary reward, for their particpation, in case they were late at the end of a scenario (red face). However, that was never the case since both main scenarios were programmed to end during and amber time pressure state. Figure 3: Time pressure indications Drivers physiological data, across the whole experiment, was collected using the Empatica E4 wristband which is a non-intrusive device that provides information about heart rate (HR), skin conductance (SC), blood volume pulse (BVP) and temperature (TEMP). Each of the physiological indicators was collected with a different frequency, depending on the attributes of the wristband. Skin conductance and temperature have 4Hz frequency, blood volume pulse 64Hz and hear rate 1Hz. Apart from the observed driving simulator and physiological data, participants also completed a series of surveys including sociodemographic characteristics, personality scales derived from the International Personality Item Pool (IPIP) (Goldberg, 1999), the multidimensional driving style inventory (MDSI) (Taubman-Ben-Ari, 2004) and some supplementary questions related to the driving scenarios. 4.2 The gap-acceptance task In the present study, the gap-acceptance task was shown twice, as a part of the urban driving scenario. Drivers faced the first gap-acceptance task without time pressure while there was time pressure (red face) during the second one. The scenario itself consisted of two groups of vehicles. At first, six blocking vehicles were shown to participants, moving at short headway distances. These vehicles were used to force drivers to stop before the main gap acceptance task. This first group of vehicles was followed by eleven vehicles that created 10 gaps. The gaps had an increasing trend, however, shorter gaps were also introduced in between, while they were identical for both intersections and across participants. For each gap-acceptance task, the drivers could choose to accept the available gap and cross or even reject them all. However, there was not a priori knowledge regarding the number of the oncoming vehicles or the waiting time required. It should be mentioned that for purposes of simplicity it was decided to constrain the gap-acceptance scenario by

9 developing a case where cars were shown only coming from the left side of the driver. Moreover, it is worth highlighting that although there might be learning or other effects (e.g. fatigue, impatience) in drivers behaviour, time pressure was always applied at the second intersection. The main reason for this design was related to drivers physiology, since it was attempted to minimise the risk of increasing their responses at the beginning of the driving task by inducing additional stressors (e.g. time pressure), that would potentially influence and prevent them from returning to the baseline levels. Also, it would be more realistic for the participants to receive a red face indication closer to the end of the driving task, rather than during the first part. A general outline of the gap-acceptance scenario setting is illustrated in Figure 4. Moreover, the presented gap sizes are presented in Table 1. The increasing trend of gaps was chosen in order to secure that drivers would not face a large gap in the beginning of the scenario and miss information related to their willingness to accept a shorter one. Figure 4: Illustration of the intersection Table 1: The available gaps and gaps sizes Gap ID Gap size (s) Explanatory analysis 5.1 Sample analysis The sample of the current analysis consisted of 41 participants (22 male, 19 female), staff members or students at the University of Leeds, that successfully completed the urban task. The mean age of participants was approximately 34 years, with 11 years standard deviation. Almost half of the participants stated that they were driving on a daily basis. The average driving experience of participants was almost 14 years. Regarding accident involvement, 6 particiants reported involvement in minor accidents while 4 reported engagement in serious accidents. It is worth mentioning that as a serious (or major) accident was defined an incident where at least one person required medical treatment and/or there was property damage above 500. Finally, 7 participants stated a ticket penalty for speeding behaviour. The descriptive statistics of the sample are also outlined in Table Gap-acceptance task analysis Before the development of the model, participants gap-acceptance behaviour was

10 examined with respect to the effects of time pressure. In Table 3 are presented the accepted gaps of each individual, for the two cases, and their respective size (a value 999 is given if no gap was accepted). A similar illustration is also provided in Figure 5. It should be mentioned that 12 out of 41 participants did not accept any of the presented to them gaps in both cases. On the other hand, six participants accepted a gap only under the time pressure conditions while they had not done it without time pressure. The remaining 23 participants accepted a gap at both intersections. The latter group of participants always accepted the same or a gap that was shown earlier, compared to the one accepted without the external stressor. To further investigate this outcome, a paired samples t-test was applied in order to compare the significance in the difference of the accepted gaps sizes at the two intersections. The results (Table 4) indicated that the mean size of the accepted gaps was statistically significant smaller at the second intersection. As mentioned in the data collection section, this decision might be triggered by learning effects however, between the two intersections, participants faced a series of additional tasks and they did at least 15min of driving. These extra tasks, could have a diminishing influence on the learning effects, increasing the likelihood observing drivers actions driven by time pressure. Table 2: Descriptive statistics of the sample Variable Intervals Frequency % mean std. dev. min max Gender Female Male Age Driving experience Frequency of driving Minor accident involvement Major accident involvement Ticket for speeding Everyday times/week Once/ week Less often No Yes No Yes No Yes Furthermore, with reference to Table 3, under the time pressure conditions, three of the participants accepted the first gap. These drivers, did not actually behave as expected during the task (stop at the intersection and wait for a gap, or not, to cross) but they drove through the streaming of oncoming vehicles without stopping. This behaviour, might seem unrealistic or irrational for the real-life driving context however, it might also consist and indication that external stressors could increase risk-taking (even such extreme behaviour would not be observed in real life). Moreover, it is worth mentioning that the 10 th gap was never accepted although it was the largest one in terms of headway size. This behaviour may indicate anticipation effects in gap-acceptance behaviour; drivers that waited until the last available gap preferred to wait additional time and cross when the intersection was clear rather than engaging in crossing under the presence of oncoming traffic. As mentioned above, almost 1/3 of participants showed this behaviour, without being influenced by time pressure in the second task.

11 Table 3: Accepted gap(s) of each participant at the two intersections ID First intersection (without time pressure) Second intersection (under time pressure) Gap ID Gap size (s) Gap ID Gap size (s) ID First intersection (without time pressure) Second intersection (under time pressure) Gap ID Gap size (s) Gap ID Gap size (s)

12 Gap size (s) Gap ID 12 Accepted gap Driver ID No time pressure Time pressure Size of accepted gap (s) Driver ID No time pressure Time pressure Figure 5: Accepted gaps and sizes without and under time pressure

13 First intersection (no time pressure) Second intersection (under time pressure) Descriptives Table 4: Results of the paired samples t-test Paired samples t-test 95% CI for Mean SD SE Mean Mean SE t df p Difference Difference Difference Lower Upper Gap-acceptance model 6.1 Parameter estimation results and interpretation A series of gap-acceptance models was estimated based on the methodology presented in section 3.1. The initial model included only traffic related variables, while more variables were gradually added. Those additional variables were grouped in socio-demographics, time pressure and stress variables. Each new model included all the previous variables plus new ones. The aim of this approach was to compare model fit and investigate whether the addition of specific variables could actually improve the model. The results of all four models are presented in Table 5. All parameter estimates are significant at 95% level ( t-ratio >1.96). Variable Table 5: Gap-acceptance models parameter estimates Traffic related variables only model Model 1 (Base) Socio-demographics included model (Model 2) Time pressure included model (Model 3) Physiological observations included model Model 4 (Final) estimate t-ratio estimate t-ratio estimate t-ratio estimate t-ratio Constant Gap size Last gap dummy Speed (first gap) Position α acc Age dummy Frequency of driving dummy Time pressure dummy Skin conductance response Heart rate LL LL R adjusted R observations The first model included as explanatory variables the gap size (in seconds), vehicle position during waiting time, vehicle speed when arriving at the intersection area, a dummy variable indicating whether there is another gap following, or not, and the standard normal

14 disturbance term (Model 1). As expected, gap size had a positive effect on gap acceptance behaviour; drivers sensitivity in accepting a gap increases with its size. Vehicle position is a variable that captures participant s position at the intersection area (starting from a value of zero) with an increasing trend as the vehicle moves forward. If a participant was outside of the intersection area during the task (was a case for some participants during the first shown gap), the variable could also take negative values. The inclusion of this variable attempted to capture drivers behaviour to better position themselves and increase the likelihood of accepting the next available gap. This variable was considered in the model since, during the data collection, it was observed that a proportion of drivers was slowly moving the car forward during the waiting time period. As expected, the effect of this variable was positively related to the gap-acceptance probability and drivers were more likely to accept a gap, the closer to the intersection the vehicle was. Another variable of this model is vehicle speed, which was considered only for the first gap of each intersection, and ignored for all the rest. It s a case specific variable used to capture the behaviour of the three participants that during the time pressure period did not stop at the junction, as expected, but slightly modified their speed and accepted the first gap. The model was initially estimated without trying to capture this abnormal behaviour, however, when vehicle speed was included, model fit was significantly improved and thus the variable was considered. Finally, the dummy variable of the next gap has a negative effect which implies that drivers gap-acceptance decisions are not shortsighted and focused on the current gap only but there are anticipation effects and drivers further consider the next available gaps before deciding whether to cross or not. This outcome was expected, considering the relative discussion presented in the explanatory analysis section. A summary of all dummy variables used in the various models and the respective coding is presented in Table 6. Table 6: Dummy variables coding Dummy variable Value 0 1 Last gap No Yes Age Below or 45 years old Above 45 years old Driving frequency Not everyday Everyday Time pressure conditions No Yes The first gap-acceptance model was further updated and variables related to participants sociodemographic characteristics were also included (Model 2). Among the several sociodemographic variables tested, those with a significant effect were age and driving frequency. Both were used as dummy variables, since they provided better model fit with this coding, rather than having a continuous or ordinal form. The age dummy had a negative effect on gap-acceptance probability, indicating that older drivers were less likely to accept an available gap compared to younger. Moreover, all others being equal, participants who stated driving everyday were more likely to accept a gap. The effect of both sociodemographic variables used in the model is further discussed in the last section, with respect to their potential safety implications. The third gap-acceptance model (Model 3) included all the variables of Model 2 and also accounted for the time pressure conditions induced at the second gap-acceptance task. The time pressure parameter had a positive effect indicating that drivers were more likely to

15 accept a gap under the presence of time pressure. Finally, the model was estimated including physiological variables related to heart rate and skin conductance responses. The extraction and transformation/normalization of the physiological responses is described in section 3.2. Both variables had a significant a positive effect. This outcome, together with the abovementioned effect of time pressure conditions, may indicate that drivers (gap-acceptance) behaviour is not only influenced by traffic conditions but also by external stressors (time pressure in this case) or acute stress levels. In the current case, drivers stress was reflected through physiological responses during gap-acceptance choices, where a raise in these indicators also implied increase in the probability of crossing. However, if crossing behaviour, as examined in the present study, is interpreted as an action that involves risk-taking propensity, then drivers physiological responses might also consist indicators of potential aberrant or risky behaviour that could lead to a crash. This conclusion however, needs to be further examined in additional and various driving contexts Model comparison As shown in Table 6, while the gap-acceptance model was enriched with new parameters, indices of model fit as final log-likelihood (LL) or R 2 and adjusted R 2 got improved. However, the undertaking of collecting and analysing driving simulator or physiological data can be demanding, time consuming and maybe more expensive, compared to collecting e.g. real traffic video data from intersections or similar approaches. This section investigates how the gap-acceptance model got benefited from the variables collected in the simulator environment and wouldn t be available through more conventional data collection methods. All models were compared with the likelihood ratio test (e.g. Ben-Akiva and Lerman, 1985). In brief, the test can be defined as: -2LL = -2(LL R - LL U ) where L R is the LL value of the restricted model (the one with less variables) and L U is the LL of the unrestricted model (the model that includes the extra variables). This difference is asymptotically χ 2 -distributed and is compared with a critical value which depends on the degrees of freedom (difference of parameters). If log-likelihood exceeds that threshold value then the null hypothesis that both models perform equally is rejected. Table 7: Likelihood ratio tests results Models -2LL Degrees of freedom (df) χ 2 (99%,df) Null hypothesis Model 1 vs Model Rejected Model 2 vs Model Rejected Model 3 vs Model Rejected The results of the various likelihood ratio tests are presented in Table 7. In all cases, the null hypothesis was rejected at 99% level which implies that the model based on traffic related

16 variables only does not equally perform with the rest models. Moreover, the gradual addition of parameters managed to significantly improve the model enhancing the assumption that driving is a complex task and several factors can influence individual performance. Moreover, Model 3 does not equally perform with Model 4, thus the contribution of physiological variables was significant, in terms of model fit and capturing observed behaviour. These outcomes consist an indication that driving behaviour models, in general, should also focus on drivers attributes apart from traffic conditions. In the present case, socio-demographics and physiological responses provided better model fit and at the same time useful insights regarding crossing behaviour. 6.3 Sensitivity analysis The current section investigates the effect of each variable on gap-acceptance probability, based on the estimated parameters. This approach aims to compare the differences in gap-acceptance probabilities derived between Model 4, that had the best fit, and Model 1 which is a model based only on variables related to traffic conditions. For the rest of the section, the former model will be referred as the proposed model while the later as the base model. To this end, a sample average value was assumed for each of the variables - apart from one at a time - which was varying within predefined bounds, specified by the observations. Based on these values, the probabilities of gap-acceptance were estimated for each model; these probabilities, represent a person that belongs to the sample average. The fixed values of the continuous variables used were: 4.295s for gap size, 0.96m/s for speed, m for position (median value), for the normalised heart rate and for the normalised skin conductance responses. For the dummy variables, sample average values were also used (varying between zero and one): 0.18 for age, 0.46 for driving frequency, 0.45 for time pressure and 0.05 for last gap. The effect of the random disturbance term was integrated out in a similar way described in section 3.1. The results of the sensitivity analysis, for the base and proposed model, are presented in Figures 6 and 7 and refer only to traffic related variables. The rest of the proposed model s variables were not compared to the base model, since they are not included in that one and thus the calculated probabilities would remain constant and a comparison would not provide useful outcomes. However, these variables were investigated with respect to their effect on the gap-acceptance probability of the proposed model only. Figure 6: Sensitivity plots of gap size and speed on gap-acceptance probability A general outcome from Figures 6 and 7 is that all traffic variables have similar patterns in both models, however, the values for the base model are always higher. The inclusion of additional variables in the proposed model, apart from improving model fit, may also resulted in smaller probabilities and potentially assisted in avoiding overpredicted values,

17 as observed in the base model. Regarding individual parameter effects (Figure 6), the calculated probabilities for speed are higher, compared to gap size but have a similar magnitude with position (Figure 7, left). For the case of speed, the curves indicate that for drivers with speed above 8m/s, the probability for accepting the first gap approaches to one. As already mentioned in Section 6.1, this variable was used to capture drivers behaviour that did not brake at the intersection. Figure 7: Sensitivity plots of vehicle s position and next gap occurrence on gap-acceptance probability In terms of position (Figure 7, left), the probabilities trends show that the closer to the intersection a driver is positioned, during waiting time, the higher the probability to accept the available gap. When position is close to the median value however, probability levels are quite low, while the slope gets steeper as position values approach the centre of intersection (which is approximately placed at 10-11m from the beginning of the intersection area). Finally, the negative effect of the last gap dummy variable (Figure 7, right), is also reflected in the probability patterns, where it is observed that when there is no other vehicle coming, after the available gap, the probability of accepting this gap is close to zero. It is worth mentioning that this outcome is based on the observations from the current simulator experiment. Although in real life that probability could be higher, and some drivers would accept the last gap, this finding still consists an indication regarding drivers decision-making process. Figure 8: Sensitivity plots of the dummy variables used in the proposed model on gap-acceptance probability

18 In Figure 8 is depicted the effect of each of the dummy variables used in the proposed model. As explained already, since these variables were not included in the base model, their effect on gap-acceptance probabilities was not investigated across models but only for the proposed one. The results indicate that the lowest probability occurs when a driver is above 45 years (holding all the rest variables constant). On the other hand, the highest probability is observed for daily frequency of driving. Moreover, it is worth mentioning that the probabilities for < 45 years and time pressure have approximately the same values. Figure 9: Sensitivity plot of heart rate and skin conductance on gap-acceptance probability The last variables included in the proposed model were those related to drivers physiology. The effect of both variables is shown in Figure 9, after applying some scale adjustment on the x-axis to account for the different values after their normalisation. The results show that both variables have a similar pattern on gap-acceptance probability, however, skin conductance is linked with higher values. This finding may indicate that within the context of the study, skin conductance is a stronger predictor for accepting a gap. 6.4 Substitution rates At the final part of the analysis, it was attempted a comparison across all the estimated models. The comparison was based on the marginal rates of substitutions (MRS), that also assists in avoiding issues of differences in scales across models. This approach investigates the required change in a specific variable, in order to counterbalance the change in another variable and keep the total utility constant (see e.g. Kløjgaard & Hess, 2014). The MRS be briefly summarised as the calculation of βi/βj ratio, where β represent the parameter estimates of variables i and j. In most studies, MRS has been used to calculate marginal willingness to pay, using the marginal utility of price in the denominator part. For each of the four models of the present analysis, the parameter of gap size was used as the denominator and the ratios were computed using each of the rest parameters as numerators. The results are illustrated in Figure 10 where the calculated values represent the relative effect of each parameter with respect to the gap size parameter of each model.

19 Figure 10: Marginal rates of substitution It should be mentioned that since the parameter of gap size is positive, the ratios with negative parameters, as numerator, are expected negative while positive ratios are expected when the opposite holds. Thus, when interpreting the MRS values, what is important is whether the absolute ratio value is higher than unity, rather than the sign of the ratio itself. For instance, MRS >1 shows that the change in utility, from a one-unit shift from the baseline of a given variable, is greater than the one occurs from an increase in gap size for 1s. The opposite applies for MRS <1. When applying the aforementioned in e.g. the last gap dummy ratio, the outcome would be that the effect of the current gap being also the last in the sequence of gaps, is almost 8 times (traffic variables model) as negatively as the increase of 1s in the gap size in the utility of gap acceptance. For the same model, an increase in speed for 1m/s is twice as positive as an increase of 1s in gap size, in the gap-acceptance utility. In the present analysis, all absolute ratio values are larger than unity. Moreover, focusing on the variables included in all four models, all values decrease as more variables are included. An exception to this pattern is the last model, where relative values increase again. A potential explanation for this finding is that when stress variables are included, they manage to better capture the effect of some variables. However, in all cases, ratios still remain smaller, compared to the first model. Moreover, position the positive relative effect of position is on average higher, compared to speed. Also, the highest positive value from this group of variables is noticed for the random disturbance term of the first model. It should be mentioned that this variable reflects the effect of a series of unobserved variables/characteristics and follows a normal distribution. The fact that the highest value is observed for the first model, may consist an indication that the variables included in this model are not sufficient to capture observed gap-acceptance behaviour, therefore, the disturbance term has a higher relative effect, to capture the influence of omitted variables. With reference to the socio-demographic variables, all relative effects are smaller when

20 time pressure and physiological variables are included in the model. This outcome consists an indication that when the latter variables are added, the effect of socio-demographics is more representative, since these models also have better fit, and in fact their impact is not as high as initially estimated in the socio-demographics model. Finally, as already mentioned in the sensitivity analysis section, the effect of skin conductance in gap-acceptance utility is higher compared to heart rate. 7. Discussion The objective of the present paper was to mathematically model of a gap-acceptance model for intersection crossing scenarios, with and without time-pressure induced stress and compare the results. The driving simulator was used as the testbed and the level of stress was approximated through heart rate and skin conductance. The initial exploratory analysis showed that gap-acceptance can change under a different context (e.g. drivers may be willing to accept shorter gaps under time pressure). Also, under the presence of time pressure, three of the participants showed aberrant and extremely risky behaviour and crossed the intersection without actually stopping. Although this type of behaviour is rather unlikely to be observed in real life, this outcome still indicates that external stressors can potentially increase risk-taking tendency that may lead to dangerous incidents, even crashes. At the next step of the analysis, the model results indicated that gap-acceptance behaviour is not only related to traffic characteristics e.g. gap size but drivers individual characteristics may also influence this type of behaviour. For example, all else being equal, the driving frequency was found to increase the probability of accepting gaps while age had a negative effect. If the increased likelihood of accepting a gap could be a potential risk-taking indication, the effects of socio-demographics may also have safety implications. For instance, previous research (e.g. Matthews et al., 1999) used driving frequency as a measure of driving exposure and positively related it to crashes and speed violations. In the present case, participants driving on a daily basis and thus with higher exposure - were more likely to accept a gap and therefore might be considered as more risk-takers. Moreover, numerous studies have investigated the effects of age on driving and risk-taking behaviour (e.g. Jonah, 1990; Krahé & Fenske, 2002; Rhodes & Pivik, 2011; Taubman & Yehel, 2012). The results of the gap-acceptance model(s) of this study support the existing literature findings, since elder drivers also had smaller probability to accept a gap and thus engage in riskier situations. The abovementioned findings not only suggest that drivers individual attributes influence their choices and should be considered in the development of driving behaviour models (since most of the existing approaches ignore or attempt to capture them using random disturbance terms) but also that gap-acceptance behaviour may be driven by risk perception of specific groups of drivers. The time pressure variable had an expected positive effect on gap-acceptance choices. Similar research (Rendon-Velez et al., 2016) has shown that time pressure is linked to higher speed and is also reflected in auxiliary measures of safety. These findings may potentially lay time pressure, in gap-acceptance behaviour, as a variable with safety implications, in a similar way to drivers socio-demographics. Finally, in terms of stress