Driver behavior analysis on a curve through immersive simulation and a segmented regression model

<jats:p>Considering all the elements related to the occurrence of accidents, an important aspect is to identify the drivers most prone to accidents. This study aims to evaluate the behavior of drivers concerning gender and age. For this, a stretch of highway with a dangerous curve was modeled in a simulator using an immersive virtual environment and 59 people experienced the simulation. The car speed was registered along the route and from a segmented regression model, the behavior for both groups was evaluated regarding average speed. The results showed that older drivers (26 to 35 years old) of the female gender slowed the car before the other profile groups. Also, younger drivers (18 to 25 years old) took longer to slow down and had more accidents in the simulations. These results show that there are differences in driver’s behavior concerning gender and age.</jats:p>

section_content: According to statistics from the World Health Organization -WHO (2018), traffic accidents are responsible for more than 1. 35 million deaths every year. The causes of accidents are wide, so extensive research is needed to know and analyze all possible factors (Savolainen et al., 2011). In this context, broader research is needed to understand traffic safety, which is a result of an interaction between design factors, technology, the environment, and driver behavior (Perrels et al., 2015). 

Some studies showed that age and gender have a major impact on how drivers behave under certain conditions (Clarke et al., 2006; Rhodes and Pivik, 2011; Dafrallah et al., 2020). According to the WHO (2018), most of the accident victims are less than 29 years old. A survey carried by Rhodes and Pivik (2011) found that young age people and male drivers appear to be more reckless when compared to older people and women drivers. In addition, the authors also found that men have a lower perception of danger in risk situations than women. In another work, Clarke et al. (2006) analyzed a database of over 3000 accidents assessing the in5luence of gender and lack of experience on driving behavior. The authors considered a group between 17 and 25 years old and found that men under 20, driving on dimly lit road curves, are more likely to be involved in accidents, with the main causes of accidents been speeding and recklessness. The works of Roman et al. (2015) and McCartt et al. (2009) also showed similar results to the works of Clarke et al. (2006) and Rhodes and Pivik (2011). 

However, a research method that encompasses all variables of human behavior is difficult to achieve (Mannering, Shankar and Bhat, 2016). On the highways, the physical and mental abilities, the risk perception in certain situations, and reaction times vary greatly for each individual (Mannering, Shankar and Bhat, 2016). For that reason, it is important to understand the factors that can in5luence driving behavior. Several studies have shown correlations between accidents and characteristics of gender and age of drivers. These studies are mostly based on databases that store the history of traffic accidents, nevertheless, practical research related to driver's behaviors should be extended to precede accidents occurrence (Matar and Al-Mutairi, 2020). However, studies carried on existing highways are not safe for participants because is not possible to control all variables (environmental and behavioral). Therefore, this scenario increases the importance of driving simulators in this kind of study and the advantages of carrying experiments in a safe and controlled environment using virtual reality (VR) simulators (Taheri et al., 2017). 

The VR simulators can be described as simulation environments that use realistic 3D scenarios where the user interacts through driving controls (steering wheels and pedals) and has immersive visual response using VR headsets that track the users head position (Dickey, 2005; Bella, 2008; Ihemedu-Steinke et al., 2017). This tool became important due to its ability to give prior handling experience and feeling of a real scenario to its users (Tori, Kirner and Siscoutto, 2006; Lee et al., 2007). In terms of complexity, the driving simulators can be divided into basic, intermediate, and high-5idelity levels, depending on the realism and the application of the simulation (Lucas et al., 2013). Over time, many studies have been conducted to validate virtual reality and driving simulators in the 5ield of traffic, showing excellent results (Meuleners and Fraser, 2015; Taheri et al., 2017). Some of its application analyzes the distractions caused to drivers using cell phones while driving and evaluate the use of the tool with more than one driver, for example (Oeltze and Schießl, 2015; Farah et al., 2016; Morley, Lawrence and Smith, 2016; Vieira and Larocca, 2017). 

In recent studies, driving simulators have been used to compare driver behavior in accidents analysis. The comparison of age and gender in VR simulators has great advantages and shows that driving experience changes traf5ic speed (Branzi, Domenichini and La Torre, 2017). This study is similar to the work of Chaudry (2020) which aimed to evaluate human behavior but focused on driving the perception and experience of each of the only 15 participants. In the work of Goedicke et al. (2018), a virtual reality environment was created positioning the participants in a real car while the simulation was conducted, however, the overall study was limited both in its analysis and statistical power. Another related work of Peng et al. (2018) has the same statistical drawbacks. This research evaluated driving perception and driving experience but used small sample sizes and had very limited analyzes, lacking, consequently, statistical power (Goedicke et al., 2018; Peng et al., 2018; Chaudry, 2020). 

Given this context, this paper is based on the supposition that the virtual environment can reproduce a risky road stretch to evaluate the behavior of drivers regarding speed changes considering their gender and age. To overcome the small sample sizes and limited analyses that have been performed in general in the literature, we computed the minimum sample size as well as carried out an analysis using a segmented regression model to detect changes in speed along a road stretch recreated in a VR simulation environment.
section_name: INTRODUCTION

section_content: In this study a curved road stretch located at kilometer 47 in the RS-122 road in the city of Farroupilha, in the state of Rio Grande do Sul, Brazil, was modeled in an immersive virtual environment (Figure 1 ). In Figure 1, the points A, B, C, D, E, and F correspond to traf5ic signs for the 50 km/h speed limit and the sharp bend ahead. The stretch between the points G and H is where the sharp bend is. At the same point G, there is a radar speed trap of 50 km/h. This area was used due to the high occurrence of accidents, mostly because of the existence of the sharp curve with no visibility to the other side in5licting a high possibility of frontal crashes if the driver crosses the lane. According to the road authority databases, the ERS-122 road is one of the state's roads with the most accidents and casualties in the Rio Grande do Sul state (Comando Rodoviário da Brigada Militar -CRBM, 2021). For this area only, 246 fatal accidents have been registered in the last 11 years (2010 -2020). The peak of accidents occurred between 2010 until 2015. In 2016, a radar speed trap was installed, reducing the occurrence of accidents, however, the number of accidents is still high. 

This RS-122 stretch is known as the death's curve due to the high rates of accidents. This 180° curve has a length of 203 meters, and a radius of 100 meters (0. 06 miles), in 1225 meters (0. 76 miles). This road stretch has three lanes, with two in one direction, and one in the other direction (lane used in the simulation). Each lane has 3. 6 meters of width and a road shoulder in both directions of 1. 5 meters. 

The stretch was reconstructed on Bentley's OpenRoads ConceptStation® and OpenRoads Designer® platforms (Bentley | OpenRoads -Transportation, Civil Analiys, Design Software, 2021), which allow for detailed geometric reconstructions and integration of georeferenced satellite data. All vertical speed limit and sharp bend warning signs were identi5ied and modeled in the Autodesk Maya® software (Autodesk | Education Community, 2021), widely used in the computational area for modeling, simulation, 3D rendering, and animation. The simulation environment was recreated on the Unity 3D® game engine (Unity Real-Time Development Platform | 3D, 2D VR & AR Engine, 2021), importing the modeled 3D objects, physics, virtual cameras, and controls to create an immersive realistic environment. The vegetation, important for the perception of speed, was placed along the geometric tracing to follow the approximate densities found in the real environment, both in positioning and in shape. The 5inal scenario with vegetation and traf5ic signs is shown in Figure 2B. Invisible markers (colliders) were placed in the modeled road to collect speed information equidistant to 10 meters along the 1225 meters of the virtual road section. The speed information collected in each collider combined with the positions of the traf5ic signs allowed us to track and study the speed changes according to the behavior of the participant in the simulation. The tests were performed using a steering wheel connected to a computer mounted in a cockpit to provide immersive driving within the simulation. This was complemented by a Head Mounted Display (HMD) -Oculus Rift® (Oculus | VR Headsets, Games & Equipment, 2021) that provided to the user 360° visualization of the virtual car and the road, shown in Figure 2A. This setup allows physical interaction and immersion (look and feel) to make the user completely involved in the simulated environment (Munafo, Diedrick and Stoffregen, 2017). The simulation data were collected individually for each participant. Before each simulation, the phases of the present study were explained. First, the speed limits and car functioning were presented to the user. Into the simulation, each participant traveled a stretch to get used to the virtual environment and feel of the controls before entering the curved stretch. Students from the engineering department of our university participated voluntarily. To pro5ile the participants, a questionnaire was applied asking age, gender, driving experience, and how many times they drive per week.
section_name: MATERIAL AND METHODS

section_content: Considering the speed of our main quantitative variable, to estimate the minimum sample size for the detection of statistically signi5icant speed changes (if existent), it is necessary to know the standard variation (SD) of the speed that is performed in the real road stretch. Since this information is not available, we can use the six-sigma rule (Range = Maximum -Minimum = 6SD). Considering the experience of people that are used to drive on this road and a pilot sample in the simulator, the minimum, and maximum speed were estimated to be about 25km/h and 80km/h, respectively. Therefore, the standard deviation would be smaller than 10km/h. Knowing that the bigger the SD, the bigger the sample size, we considered an even larger SD of the speed in the curve, 15 km/h. Thus, for a con5idence level of 95% and an error margin of 4km/h, the computed minimum sample size was 55 participants. Thus, our sample was of 59 volunteer participants, who attended the inclusion criteria: age between 18 and 35 years old and own a driver's license. We tried to keep the approximate proportions of the sample according to the gender of the users of the road, for instance, more men than women. According to data from the National Traf5ic Department (Departamento Nacional de Trânsito -DENATRAN, 2021), 65% of drivers in Brazil are men. However, considering the experiment was carried out in a university, accessing older volunteers was dif5icult. 

Most of the participants had 18 to 25 years old, totaling 67. 8%. The rest of the participants with age between 26 and 35 years old accounted for 32. 2%. Regarding gender, 61. 8% were men and 38. 2% were women. Considering the time spent on driving, 47. 5% drive more than 5ive times per week, 22% drive one time per week or less, 15. 25% drive between one and three times per week, and an equal amount drive four to 5ive times per week. Analyzing the driver's experience, 47. 5% have driver's license for 5ive years or less, 42. 4% have driver's license between 5ive and ten years, and 10. 2% have driver's license over ten years. This pro5ile information was obtained by a questionnaire, that was given to the participants inquiring about their age, gender and driving experience, and how many times they drive weekly. 

To analyze the data collected, a Gaussian segmented linear regression was built as an extension of the linear model proposed by Quandt (1958) to estimate the difference in the average speed, the change in the slope (acceleration) for each gender and age as well as the difference in the slope between the pro5iles. It was considered that the change of speed does not necessarily happen in the exact position of the signalization, the change points can be considered in the proximity, depending on the data itself. Thus, the speed can be modeled at each position point t (spaced every 10 meters) as: is the difference in speed trend from men in relation to the women group in the i-th stretch; is a binary variable representing the gender (Woman = 0, Men = 1) or age group (18-25 = 0, 26-35 = 1), is the Gaussian error. This segmented model including gender or age variables considers the change point 5ixed prior to estimation. When necessary to estimate breakpoints, other regression models were built considering the breakpoints as parameters (Muggeo, 2003). The 95% con5idence intervals were also built to check if the moment of deceleration was different between the investigated groups (Muggeo, 2017). 

Because of the dependence in the data, the model was built considering the same principles of time series modeling where the dependence is also natural. After the model estimation, the assumptions of the model were checked. All analyses were implemented in the R language.
section_name: Sta s cal Analysis

section_content: In this section, the results are evaluated by gender and age. First, the speed pro5iles are evaluated only by gender. Then, the pro5iles are separated by gender and age group (18 -25 years old and 26 -35 years old), and, 5inally, the pro5iles are separated only by age. Then, the results of the accidents are presented separated by age, gender, and driver's experience. 

Analyzing the behavior of all drivers only by gender (Figure 3 ), it is observed that the trends in speed vary after each change point but not much difference is seen regarding gender. All trend changes (βW) were statistically signi5icant (p-value < 0. 05) except for the stretch between 180 and 230m (Table 1 ). No signi5icant difference was detected in the male trend (βM) or in the average level (βM0) (p-value > 0. 05). On the other hand, in all simulated stretch, on average, the drivers had a slowdown and an acceleration at the same points (Figure 3 ). It was also noted a lower speed when the participants entered the curve in comparison to the rest of the stretch, but still higher than the road speed limit (50 km/h), which may have been caused by a lack of real punishment for speeding.
section_name: RESULTS

section_content: In the following graphs (Figure 3, Figure 4, Figure 5, and Figure 6 ) A, B, C, D, E, and F correspond to traf5ic warning signals. The stretch between G and H is where the sharp curve is (yellow vertical lines). In G, there is a radar speed trap (50 km/h). The blue vertical lines indicate the position of the speed change points included in the segmented model. The speed limit of 50 km/h is represented by the horizontal black line. In Figure 3, the average speed (points) by gender on each observed position is shown. 2 show the behavior of the drivers with age between 18 and 25 years old, which includes 40 participants, 24 men, and 16 women. 

Analyzing Figure 4 and Table 2, it is observed that the group of young drivers participating in the study had a similar change in speed when approaching the curve. Both genders slowed after going through points C and G. However, men decelerated more than women after point G (curve -position 470) with statistically signi5icant slope difference of -1. 398 km/h each 10 meters (signi5icance level = 0. 05; p-value = 0. 002). This represents a faster change of speed by young male drivers. After the change point in position 210, it is observed that men tended to slow down more than women reaching about 55 km/h (change point in position 290 -about 80 meters later). The reductions from position 210 to 290 were on average 7. 7 km/h and 12. 2 km/h for women and men, respectively. After point G, this fact was more evident where the reduction for men was double (12. 6 km/h) of the women (6. 3 km/h). While women presented an average speed of 70 km/h at position 530, men were about 60 km/h. 

Figure 5 shows the behavior of the drivers age between 26 and 35 years old, which includes 19 participants, 12 men, and 7 women. For this age group, in general, differently from the young drivers, men tend to drive at a higher velocity than women. In point 290, the average speed was 53 km/h for women and 66 km/h for men. In the curve (point 530), the women reduced the speed to the average of 58. 7 km/h while the men's average speed at this point was 73 km/h. It is also noted that women tended to start the deceleration before men. As the change points in this model were included considering the woman group (Figure 5A ), two new models were built to estimate each change point separately according to gender focusing only on the curve stretch. From the estimated change points as well as their con5idence interval (CI) in Figure 5B, it is possible to con5irm what was supposed Figure 5A (focus only on the analyzed interval before the curve at point 530) -women started to slow down 30 meters before men. Besides, along the curve stretch, the speed changed more drastically for the female group. The men kept the average speed changing more smoothly. From Table 3 we can see that the speed slope was 2. 193 and 2. 424 larger for men than women (p-value < 0. 05) after the positions 240 and 440. In addition, the average speed in the two age groups can be compared, as shown in Figure 6. From Figure 6A and Table 4, it can be observed that the older group tended to drive faster and slow down earlier in the curve. Thus, we built a model to estimate the change point as well as its con5idence interval in the stretch 360-530m. From Figure 6B we can con5irm what was supposed in Figure 6A (focus only on the analyzed interval before the curve at point 530), -the older group slowed down 20 meters before in the curve. 

Despite the lower speed of the young drivers, this group had more accidents in the simulation (six of the seven accidents -85. 70%). Furthermore, analyzing the number of accidents in relation to the driver gender, it is noted that 5ive of the seven (71. 43%) were suffered by men and two by women.
section_name: Figure 3. Speed variation by gender

section_content: Comparing the difference in the behavior of each driver pro5ile, younger drivers take longer to start breaking, about 20 meters (Figure 6 ). In addition, it is possible to observe that drivers between 18 and 25 years old with up to 5ive years of experience had more accidents in the simulations. This factor is associated with the reckless behavior and high con5idence of these drivers, also identi5ied in the research of Rhodes and Pivik (2011). In a similar work of Branzi, Domenichini and La Torre (2017), gender and age were evaluated both in VR in an urban road. 

The results found corroborated ours, showing that the driving experience in5luenced the overall speed and behavior of the participants. In Figure 6B, older drivers had a high speed in all simulations, but it is noted that the younger drivers acted belatedly. This fact may be linked to the lack of experience that is an important factor in the occurrence of accidents. A similar conclusion was identi5ied by Clarke et al. (2006) and McCartt et al. (2009). 

When analyzing all participants, without differentiation by age, just by gender, it is noted that, in general, there is no relevant difference in the speed and behavior between the two groups (Figure 3 ). However, separating the groups by age, different behavior can be observed. In younger drivers (as mentioned earlier, the pro5ile more prone to more aggressive and careless behavior), it is noted that women are more prone to drive faster along the stretch than men in this age group (Figure 4 ). Despite this higher speed (which can be considered more dangerous), men drove more irregularly (also considered dangerous). However, women showed a change in behavior after 26 years old. From Figure 5, it is noted that men in this group drive faster than women. When analyzing behavior before the curve (Figure 5B ), which was measured by speed variation, it was observed that women from 26 to 35 years old decelerate before men. These behavior changes of women after 26 years old may indicate a cautious behavior or natural worrying that usually comes with time and experience. In men, this change was not observed in older drivers. In addition, women had fewer accidents than men in the simulations. This behavior change was also identi5ied in the research of Roman et al. (2015), who speci5ies that the male gender and younger age have the most dangerous behavior, and by Clarke et al. (2006), who observed that young men driving on curves located on poorly-lit rural roads are more prone to accidents. The results are also con5irmed from real data. On the route studied, most accidents were suffered by men. 

An important detail perceived through the simulations is that the drivers traveled the route without taking much care about the speed limit and speed radars. For this, it can be observed that in all speed pro5iles (Figure 3, Figure 4, Figure 5 and Figure 6 ), the drivers' speed was higher than the speed limit. This behavior is imprecise and may be related to the lack of real punishment or real danger for drivers in the event of accidents because it is a virtual reality (VR). In addition, the simulated environment did not present continuous traf5ic and overcoming (other cars on the route were not considered in the study), relying only on the change of speed when approaching and leaving the curve.
section_name: DISCUSSIONS

section_content: Accident analysis is an important matter when proposing policies for road safety. However, experiments on real roads are dangerous. The use of VR driving simulators can bring great possibilities for studies that aim to replicate real environments. Thus, we built a VR simulation environment replicating a high-risky road stretch and carried out an experiment to analyze the speed-changing behavior of drivers regarding their gender and age. Furthermore, we intended to overcome the small sample sizes and limited analyses that have been performed in general in the literature. With segmented regression analysis, it was possible to evaluate the speed changes considering the gender and age factors in the models. 

As a result, we found that younger drivers are more prone to accidents which relate to the data that was found by others research. In a general analysis, male and young drivers showed more aggressive and careless behavior. These results show that there are differences in driver´s behavior concerning gender and age. 

Considering that this research was developed in an engineering department of a university, one inherent limitation regards the inclusion of age groups older than 35 years. Future research could include older participants. However, our data of driver's gender 5it well with the demographic data and the proportion of licensed drivers registered in the transit government department in Brazil. Also, future work can consider simulated traf5ic to analyze other causes of accidents like frontal collisions as well as perform comparisons between scenarios with and without signaling.
section_name: CONCLUSION

section_name: ACKNOWLEDGEMENTS

section_content: This research was partially funded by the Coordenação de Aperfeiçoamento de Pessoal de Nıvel Superior -Brasil (CAPES) -Finance Code 001 (sponsorship to the third author), by National Council for Scienti5ic and Technological Development (CNPq), and by PETROBRAS and ANP ( 4600556376 -sponsorship to the second author). Thanks to Gabriel Fernando Ritter and Roberto Korte Mentz for the technical support in the experimental development.
section_name: ACKNOWLEDGEMENTS