The majority of statistical data analysis is carried out by using SPSS tools. To determine the variables that influence the speed of pedestrian crossings, parametric procedures like t-tests and ANOVA tables are prepared.
4.1 Model development
The process of creating a model is iterative, before a model that confirms to the requirements is created. Several models are developed and tested and the best one is selected. In the context of this study, all pedestrian crossings have been modeled using the method of multiple linear regression analysis. The model was developed using SPSS tools.
To calculate the pedestrian crossing speed (Walking) the mathematical formulas are used.
\(Pcs=\frac{Distance \left(m\right)}{Avage time\left(Sec\right)}\) Eq. 1
Where\(Avage time=\frac{Time \left(\text{s}\text{e}\text{c}\right)}{N}\)
And
Pcs = Pedestrian crossing speed, N = Number of samples and Distance (m) is the width of the road at the point of crossing the respective intersection.
4.2 Multiple Regression Model
Multiple Regression models were developed from the collected data by considering dependent and independent variables. Two models were developed by considering Pedestrian crossing speed and Pedestrian Gap acceptance as dependent variables and traffic volume with composition, pedestrian volume, headway, existing road width at the point of crossing the intersection as independent variables.
Model 1:
Pedestrian crossing Speed = 3.396 + 0.002TV − 0.263PV + 0.027HW + 0.074RW Eq. 2
Where: TV = Traffic volume, PV = Pedestrian volume, HW = Headway, and RW = Road width.
Table 4
Anova Table for Pedestrian Crossing Speed
Coefficientsa |
Parameters | Unstandardized Coefficients | Standardized Coefficients | t | Sig. |
B | Std. Error | Beta |
1 | (Constant) | 3.396 | .375 | | 9.064 | .000 |
Traffic Volume | .002 | .002 | .035 | .966 | .341 |
Pedestrian volume | − .263 | .012 | − .807 | -21.576 | .000 |
Headway | .027 | .055 | .017 | .482 | .633 |
Road width | .074 | .003 | .772 | 21.227 | .000 |
R2 | 0.958 |
Adjusted R2 | 0.953 |
a. Dependent Variable: Pedestrian Crossing speed |
As displayed in Table 4, the first two explanatory variables' P values for the constant estimator are less than the level of significance. With R2 adjusted = 0.953, all predictor factors strongly predicted the pedestrian crossing speed. This can be translated to mean that traffic volume, pedestrian volume, headway, and road width are accountable for around 95.3% of the variation in pedestrian crossing speed. The R2 value for the MLR model's fitness using the training data set is 0.958, while the adjusted R2 value of 0.953. Therefore the values of correlated are strong relationships.
Model 2:
Pedestrian Gap acceptance = 6.5–0.014 TV + 6.71 HW + 3.28 Rweq 3
Table 5
Anova Table for Pedestrian Gap Acceptance
Coefficientsa |
Parameters | Unstandardized Coefficients | Standardized Coefficients | t | Sig. |
B | Std. Error | Beta |
1 | (Constant) | 0.650 | 2.045 | | .318 | .752 |
Traffic Volume | .027 | .012 | .124 | 2.301 | .027 |
Headway | − .371 | .324 | − .064 | -1.145 | .260 |
Road width | − .030 | .220 | − .026 | − .137 | .892 |
R2 | 0.896 |
Adjusted R2 | 0.888 |
As displayed in Table 5.The first two explanatory variables' P values for the constant estimator are greater than the level of significance. With R2 adjusted = 0.888, all predictor variables strongly predicted pedestrian gap acceptance. This shows that the Traffic volume, headway, and road width explain about 88.8% of the variation in pedestrian gap acceptance. The R2 value and Adjusted R2 values for the MLR model's fitness with the training data set are found as 0.888 and 0.896, respectively. Therefore the independent variables are strongly correlated with dependent variable.
4.3 Model Validation
Model validation is a step that comes after model training and involves comparing the trained model with a test set of data. The two models developed are validated in the present study by plotting and comparing the predicted and observed values as indicated in the figure
The above Fig. 8 indicates that the observed and predicted values of the Speed are identical, which indicates that the above model 1 is validated.
Figure 9 indicates the model validation for Model 2. Independent variables include Traffic speed, waiting time, Pedestrian gender, Headway, and Road width.
4.4 Gap Acceptance and Headway
In order to understand the relationship between the headway and gap acceptance, analysis is carried out using Pedestrian Gap Acceptance model. Figure 9 indicates the variation of Gap acceptance for different headways and for a given road width. The traffic volume is considered between 500 to 4000 pcu/hr, the headways are considered from 2 to 10 m, for a constant road width of 12m.
Figure 10 clearly shows that for a given road width and given headway, as the traffic volume is increasing, the gap acceptance decreases. Similarly, for a given road width and traffic volume, as the headways are increasing, the gap acceptance increases. This is because of that higher volumes on the road creates lesser headway and hence that situation is subjected to more rejections. Similarly, lower traffic volumes creates larger headways and hence that situation is more favor for accepting the gaps.