# Pedestrian Behavior in Static and Dynamic Virtual Road Crossing Experiments
## 2 Materials and Methods
### Analysis  
The study analyzed how various variables influenced participants' decision-making regarding crossing, focusing on the percentage of crossings, crossing start time, and time-to-passage (TTP)--the time until the vehicle reaches the observer's position. The percentage of crossings for each participant was calculated by assuming that: (i) in the static approach, a decision to cross was considered to have occurred in the trials in which the computer mouse was clicked before the vehicle had stopped or passed by the participants' position; and, (ii) in dynamic approach, a decision to cross was considered to have happened in the trials in which the participants crossed the half-length of the semi-virtual crosswalk before the vehicle stopped or passed in front of them. Since the participant's task was to cross the virtual road effectively, counting the number of crashes in the dynamic approach (contrary to the static approach) was possible. The crossing start time, corresponding to the time from the beginning of the stimulus presentation until the moment when the participant clicked the mouse or took the first step on the crosswalk, was also registered. A three-way repeated measures ANOVA was used to assess the influence of the experimental approach, vehicle initial speed, vehicle speed pattern, and vehicle initial distance on the percentage of crossings. Additionally, mixed-effects regression models were employed to evaluate the crossing start time and TTP, with random effects included for the participant and fixed effects defined for the abovementioned variables. The adoption of LMMs was justified by the presence of missing values in the data, matching to trials in which participants did not cross. A similar analysis was conducted in previous research [41]. Statistical analysis of pedestrian behavior in observational or experimental studies presents challenges due to its inherent complexity. LMMs offer a comprehensive and flexible approach, making them particularly effective for longitudinal or complex shared data. They are adept at addressing issues such as missing and skewed data, allowing researchers to identify meaningful relationships within the data. When applied to the analysis of pedestrian behavior, LMMs provide sophisticated statistical tools that offer insights into the complex interactions between pedestrians and their  
Figure 4: Participant performing the experiment: (**a**) dynamic; (**b**) static [41]. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Experimental** \\ **Approach** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **V\({}_{\text{i}}\) (km/h)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **D\({}_{\text{i-mov}}\) (m)** \\ \end{tabular} } & \multicolumn{3}{c}{**Crossing Start Time**} & \multicolumn{3}{c}{**TTP**} \\ \cline{3-8}  & & & **Mean (s)** & **SD (s)** & **SE (s)** & **Mean (s)** & **SD (s)** & **SE (s)** \\ \hline Static & 20 & 25 & 1.07 & 0.45 & 0.05 & 3.62 & 0.41 & 0.05 \\  & & 30 & 1.18 & 0.58 & 0.05 & 4.53 & 0.52 & 0.05 \\  & & 35 & 1.31 & 0.82 & 0.07 & 5.22 & 0.75 & 0.06 \\  & & 25 & 0.69 & 0.19 & 0.05 & 2.41 & 0.23 & 0.06 \\  & & 30 & 0.87 & 0.49 & 0.10 & 2.91 & 0.43 & 0.09 \\  & & 35 & 1.05 & 0.50 & 0.08 & 3.32 & 0.43 & 0.07 \\ \hline Dynamic & 20 & 25 & 2.74 & 0.35 & 0.06 & 2.08 & 0.34 & 0.06 \\  & & 30 & 2.83 & 0.37 & 0.03 & 3.16 & 0.37 & 0.03 \\  & & 35 & 2.93 & 0.46 & 0.03 & 3.81 & 0.39 & 0.03 \\  & & 25 & - & - & - & - & - \\  & & 30 & 2.28 & 0.15 & 0.08 & 1.68 & 0.21 & 0.10 \\  & & 35 & 2.41 & 0.30 & 0.08 & 2.14 & 0.25 & 0.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Descriptive statistics of crossing start time and TTP for each trial regarding the constant speed pattern.