# Pedestrian Behavior in Static and Dynamic Virtual Road Crossing Experiments
## 2 Materials and Methods
### Analysis
#### 3.2.2 Crossing Start Time  
An LMM of the crossing start time with random effects was included for the participants, and fixed effects for the initial speed, speed pattern, and experimental approach were fitted. A visual inspection of the residual plot indicated no deviations from skewness or homoscedasticity. [PERSON]'s tests exhibited significant effects of vehicle initial speed, F(1, 2167.54) = 9.73, \(p<0.01\), speed pattern, F(2, 2168.20) = 187.69, \(p<0.01\), experimental approach, F(1, 66.85) = 6.71, \(p=0.01\), and interaction between speed pattern and initial speed, F(1, 2165.70) = 3.42, \(p=0.03\). None of the interactions of the experimental approach with the other variables were significant.  
The model was refitted, discarding the experimental approach's interaction with the other variables, and contrasts were used to compare the different initial speeds, the speed patterns, the interaction between both, and the experimental approaches. Although the results of [PERSON]'s tests have revealed that initial speed explains the participants' crossing start time, contrasts showed that the crossing start time was not significantly different when comparing the initial speed of 30 km/h to the 20 km/h, b = 0.21, t(2172.19) = 1.08, \(p=0.28\).  
Regarding the speed patterns, differences were found between constant and slowing down patterns, b = 0.43, t(2172.08) = 6.12, \(p<0.01\), and between constant and stopping, b = 1.32, t(2173.78) = 18.84, \(p<0.01\), indicating a significant increase in crossing start time from constant to slowing down and also from constant to stopping. A third contrast was used to compare the experimental approach, showing that participants were significantly  
Figure 12: Percentage of crossings and mean standard error as a function of the experimental approach, per initial speed and speed pattern.  
quicker to decide in the static experiment than those who performed the dynamic experiment, b = \(-\)0.64, t(55.45) = \(-\)2.40, \(p\) = 0.02. The last contrast done to assess the differences between the initial speeds of 20 km/h and 30 km/h within the speed pattern revealed no significant differences in crossing start time caused by the interactions between all the levels of initial speed and speed pattern variables.  
Figure 13 shows that the crossing start time distribution is very similar between the different initial speeds, except for the point corresponding to the dynamic approach's constant speed pattern. An apparent increase in the time participants spent from the constant speed pattern to the slowing down, and the stopping, is also shown. Considering the results of the analysis of the percentage of crossing and the response time, it is observed that, such as in the static experiment, in the dynamic experiment, the participants felt they had more time to cross the road safely when the vehicle speed varied, having waited until the vehicle slowed down and crossed.  
However, the most notorious difference seen in Figure 13, also evidenced by Figure 8, is between the experimental approaches. In the dynamic approach, participants spent, on average, about 0.8 s more to make their crossing decision than those who performed the static experiment. This difference was already expected. In the static experiment, the participants were placed at the same point on the curb during the entire experiment, from the start till the end of each stimulus. In contrast, in the dynamic experiment, the participants had to walk 3 m after the stimulus had started until they reached the curb and crossed.