# Effects of Distracted Pedestrian Behavior on Transportation Safety: Causes and Contributing Factors
## 2 Materials and Methods
### Analysis of Data  
Two types of analyses were conducted using data collected from in-person surveys, observational studies, and video data tally. The datasets collected from the surveys and observational studies were analyzed using binomial logistic regression, and the data collected from video data were analyzed using Heuristic Bins. For binomial logistic regression, models were developed for two cases in the study. In the first case, pedestrians demonstrated one type of distracted behavior during the observational study: either using their mobile phones, being engaged in a conversation, or using earphones/headphones while crossing the street. In the second case, pedestrians demonstrated two or more types of distracted behavior during the observational study: either using their mobile phones and being engaged in a conversation with someone, or using earphones/headphones and their mobile phones or being engaged in a conversation with someone and using earphones/headphones or using their mobile phones and being engaged in a conversation with someone and using their earphones/headphones. The dependent variable was the level of distraction of the pedestrian. The independent variables included factors that might lower the alertness of pedestrians while crossing the street, including the usage of mobile phones, earphones, and talking to someone. The list of independent variables includes the following:  
1. Race (Five categories)
2. Gender (Two categories)
3. Intersection Number (Ten different intersections)
4. Age
5. Employment Status (Yes/No)
6. Purpose of the Trip (Nine categories)
7. Frequency of Intersection Use (Four categories)
8. Near Misses at the Intersection (Yes/No)
9. Usage of Electronic Devices (Yes/No)
10. Usage of Noise Cancellation Earphones (Yes/No)
11. Billboards and Advertisements Awareness (Yes/No)
12. Perception of Safety
13. Major Sources of Distraction
14. Awareness of Safety Campaigns
15. Time of Day
16. Weather Condition17. Walking Alone or in Group
18. Pedestrian Behavior  
The general form of the regression model is  
\[\text{logit}\left(\text{P}\right)=\ln\left(\frac{\text{P}}{1-\text{P}}\right)= \beta 0+\sum\beta\text{i}\text{ Xi} \tag{1}\]  
where,  
P is Probability of occurrence of an event  
Logit(P) is the log odds of Probability  
\(\beta_{0}\) is the intercept  
\(\beta_{\text{i}}\) are the coefficients of each independent variable Xi  
Considering all the predictor variables and the predicted variable, the regression equation can be given as  
\[\text{Dist}_{-}\left(\text{A}/\text{B}\right)=\ln\left(\frac{\text{Dist}}{1- \text{Dist}}\right)=\beta 0+\sum\beta\text{i}\text{ Xi}+\ldots+\beta_{\text{n}}X_{\text{n}} \tag{2}\]  
where,  
\(\beta_{0}\) is the intercept  
\(\beta_{\text{i}}\) are the coefficients of each independent variable \(X_{\text{i}}\)  
Model evaluation was performed using the Omnibus chi-square test and the Hosmer\(-\)Lemeshow Test. For Heuristic Bins, the continuous variables from the video are categorized into a number of discrete bins or subspaces. Each subspace can represent a unique combination of states of variables, where both states are true. Hence, each subspace can be examined independently to calculate an approximation of the correlation coefficient for the intersection, and further analysis can be conducted on the state variables within each subspace. Tests for covariance are used to determine how much two variables within the bins change when the states of the variables change. That is represented as:  
\[\text{Approximate Covariance}\left(\text{Cov}_{1,2}\right)=\frac{\sum(\text{x} -\mu 1)(\text{x}-\mu 2)}{\text{n}} \tag{3}\]  
where,  
x is the variable when both state 1 and state 2 are true  
\(\mu 1\) is the mean of x when state 1 is true  
\(\mu 2\) is the mean of x when state 2 is true  
\(\mu 1\) is the sample size  
\[\text{Covariance error can be estimated by error}_{\text{cov}}=\frac{\text{cov}1,2 \,*\,\mu 2-\mu 2}{\mu 1,2} \tag{4}\]  
Video data collected from all 10 intersections were used for the analysis.