## 3 Results
### Indirect Effects from Mediators  
The barrier-sidewalk ratio itself did not exhibit a statistically significant direct effect on perceived risk; however, it may still influence participants' judgments indirectly, particularly when obstructions are present. Therefore, a third analysis was conducted to examine the potential mediating effects of the barrier-sidewalk ratio, focusing exclusively on images that contained obstructions (i.e., those in groups O1_B0 and O1_B1). Additionally, to \begin{table}
\begin{tabular}{c c c} \hline  & **Model 1** & **Model 2** \\ \hline Independent Variable & Obstruction-sidewalk ratio & Barrier-sidewalk ratio \\ \hline Intercept & 2.20 (0.10) & 2.99 (0.16) \\ Coefficient & 3.24 (0.31) & \(-\)0.48 (0.28) \\ R\({}^{2}\) & 0.66 & 0.05 \\ Adjusted R\({}^{2}\) & 0.65 & 0.03 \\ F-statistics & 112.4 & 2.93 \\ \(p\)-value & \textless{}0.001 & 0.092 \\ N & 61 & 61 \\ \hline \end{tabular}
\end{table} 
Table 5: Results of ordinary least squares regression models. Figure 6: Scatter plots of pixel-based ratios and mean perceived risk. account for the visual characteristics observed in several outlier images--those perceived as dangerous despite exhibiting a low level of sidewalk encroachment--two more variables were introduced as potential mediators: the type of obstruction (1 = materials, 2 = heavy equipment) and the presence of construction workers (0 = No, 1 = Yes). In a mediation framework, the path from the independent variable (X) to the mediator (M) is denoted by \(a\), and the path from the mediator (M) to the dependent variable (Y), controlling for X, is denoted by \(b\)[43]. The indirect effect is typically computed as \(a\times b\), while the direct effect (\(c\)) is the path from X to Y when M is included in the model. However, when the distribution of M is asymmetric, the estimated indirect effect may differ from the product of separately estimated a and b, because the bootstrap captures sampling variability across repeated resamples [44]. Figure 7 illustrates the conceptual mediation model tested in this third analysis. As shown in the diagram, the obstruction-sidewalk ratio (X) may exert an indirect influence on the perceived risk (Y) through one of three potential mediators (M): (1) the barrier-sidewalk ratio, (2) the type of obstruction (materials vs. heavy equipment), or (3) the presence of construction workers. Overall, the direct effect of the obstruction-sidewalk ratio on perceived risk ranged from 0.202 to 0.211. This indicates that, holding other factors constant, a one-unit (%) increase in the obstruction-sidewalk ratio is associated with an approximate 0.2 unit increase in the perceived risk. In practical terms, this finding reaffirms that increasing the area of obstruction leads to a higher perceived risk. For the two potential mediators--obstruction type and the presence of construction workers--both path coefficients (\(a\) and \(b\)) were positive. Notably, \(b\) for the obstruction type was extremely large (143.12), and \(b\) for the presence of construction workers was also sizable (88.8). These large \(b\) values suggest that when the obstruction is heavy equipment rather than materials, or when construction workers are present rather than absent, even relatively small changes in the obstruction-sidewalk ratio can result in substantial increases in the perceived risk. In contrast, when considering the barrier-sidewalk ratio as a mediator, both \(a\) and \(b\) were negative. This implies that as the obstruction-sidewalk ratio increases,  
Figure 7: Conceptual mediation models (*** \(p<0.001\), *** \(p<0.01\)). the barrier-sidewalk ratio tends to decrease, and a lower barrier-sidewalk ratio is then associated with a higher perceived risk. Table 6 presents the results of the mediation analysis using a rank-based, non-parametric, bootstrap procedure (5000 resamples) [36].