# Effects of Distracted Pedestrian Behavior on Transportation Safety: Causes and Contributing Factors
## 3 Results
### Binary Logistic Regression  
Binary logistic regression was used to predict pedestrian distraction because the dataset mostly consisted of categorical variables. The alpha value or level of significance was set to 5% for the analysis using SPSS. The performance of both models (DIST_A and DIST_B) was evaluated using the following:  
* Cox and Snell R\({}^{2}\) and Nagelkerke R\({}^{2}\)
* Hosmer\(-\)Lemeshow test
* Omnibus chi-square test  
Table 6 presents the model summary for the Cox and Snell R\({}^{2}\) and Nagelkerke R\({}^{2}\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Perception of Safety** & **Frequency** & **Percentage (N\%)** \\ \hline Presence of Crosswalks & 152 & 59.6 \\ Visibility of Traffic Signals/Signs & 41 & 16.1 \\ High/low Traffic Volumes and Speed & 36 & 14.1 \\ Presence of Crossing Signals & 11 & 4.3 \\ Number of Lanes & 10 & 3.9 \\ Enforcement of Traffic Rules & 5 & 2.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Respondent’s perception of safety. Figure 2: Surveyor observational data. The value of Cox and Snell R2 for Dist_A is 0.551, and that for Dist_B is 0.449. Hence, the model can explain about 55.1% of the variability for Model 1 (pedestrian showing one type of distraction) and 44.9% of the variability for Model 2 (pedestrian showing two or more types of distraction), with a higher value of R\({}^{2}\) indicating a better fit of the model for that data. The results from Nagelkerke R\({}^{2}\) suggest that the model can explain approximately 80.3% of the variability for Model 1 and 64.1% of the variability for Model 2, indicating that the models used in the study displayed a good fit for the data. The model results were also assessed using the Hosmer-Lemeshow test (for the goodness of fit of data). A large chi-squared value with a small \(p\)-value indicates that the model has a poor fit, and a small chi-squared value with a \(p\)-value greater than the alpha value indicates that the model has a good fit. Table 7 presents the output of the Hosmer-Lemeshow test. The Hosmer-Lemeshow test results were significant (for alpha = 0.05) for Model 1 and not significant for Model 2. Hence, the null for Model 1 is rejected, and the null hypothesis for Model 2 is rejected. Failure to reject the null hypothesis for Model 2 suggests that there is no significant difference between the observed and expected outcomes of the model and that the model fits well with the data. However, the data did not fit well for Model 1, as the results indicate that there is a significant difference between the observed and expected outcomes. Omnibus chi-square tests were used to evaluate the overall significance of a logistic regression model, and the results are presented in Table 8.  
The Omnibus chi-square test was found to be significant for both Model 1 and Model 2. Hence, the variables had a significant relationship with the outcome variable. The first regression model was developed with pedestrians who demonstrated only one type of distracted behavior during the observational study. The dependent variable is DIST_A, i.e., the pedestrian was either using their mobile phones, being engaged in a conversation, or using earphones/headphones. The output of each independent variable against the dependent variable for the first model has been presented in Appendix B. The results for Model 1 are presented in Table 9. \begin{table}
\begin{tabular}{c c c c} \hline
**Step** & \(-\)**2 Log Likelihood** & **Cox and Snell R2** & **Nagelkerke R2** \\ \hline
1 (Dist\_A) & 86.269 & 0.551 & 0.803 \\
1 (Dist\_B) & 146.721 & 0.449 & 0.641 \\ \hline \end{tabular}
\end{table} 
Table 6: Respondents’ perception of safety. \begin{table}
\begin{tabular}{c c c c} \hline
**Step** & **Chi-Square** & **df** & **Sig.** \\ \hline
1 (Dist\_A) & 86.538 & 8 & \textless{}0.001 \\
1 (Dist\_B) & 8.110 & 8 & 0.423 \\ \hline \end{tabular}
\end{table} 
Table 7: Results of Hosmer\(-\)Lemeshow test.