## 4 Test Site Results: Statistical Analysis
### Results Analysis  
Given the model results, the coefficients obtained may be interpreted to analyze the variables' impact on the average retroreflectivity. It is worth mentioning that in the time variable, the category \(X_{t,1}=(0,20]\) is the reference category. Therefore, the effects of the other time variables are interpreted in comparison to \(X_{t,1}\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Variable** & **Parameter** & **Estimate** & **Standard Error** & _p-Value_ \\ \hline Intercept & \(\theta_{0}\) & \(-7.330\) & \(0.362\) & \(<0.001\) \\ \(X_{t,2}\): (20, 40] & \(\theta_{1,2}\) & \(-5.850\) & \(0.640\) & \(<0.001\) \\ \(X_{t,3}\): (40,60] & \(\theta_{1,3}\) & \(-8.822\) & \(0.587\) & \(<0.001\) \\ \(X_{t,4}\): (60,80] & \(\theta_{1,4}\) & \(-8.281\) & \(0.720\) & \(<0.001\) \\ \(X_{t,5}\): (80,100] & \(\theta_{1,5}\) & \(-10.195\) & \(0.612\) & \(<0.001\) \\ \(X_{t,6}\): (100,200] & \(\theta_{1,6}\) & \(-11.199\) & \(0.421\) & \(<0.001\) \\ Main effects & \(X_{t,7}\): (200,300] & \(\theta_{1,7}\) & \(-11.308\) & \(0.590\) & \(<0.001\) \\ \(X_{t,8}\): (300,800] & \(\theta_{1,8}\) & \(-88.414\) & \(0.627\) & \(<0.001\) \\ \(V.sol\) & \(\theta_{2}\) & \(-0.003\) & \(0.005\) & \(0.404\) \\ \(\mathrm{bls}_{0}\) & \(\theta_{3}\) & \(0.011\) & \(0.005\) & \(<0.001\) \\ \(C_{\mathrm{U}}\) & \(\theta_{4}\) & \(6.652\) & \(0.113\) & \(<0.001\) \\ \(C_{\mathrm{C}}\) & \(\theta_{5}\) & \(9.055\) & \(0.150\) & \(<0.001\) \\ \(SPHT_{20}\) & \(\theta_{6}\) & \(0.186\) & \(0.054\) & \(<0.001\) \\ \hline \hline \end{tabular}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{2}{c}{\(V.sol\times X_{t,2}\): (20, 40] } & \(\theta_{7,2}\) & \(0.090\) & \(0.010\) & \(<0.001\) \\ \(V.sol\times X_{t,3}\): (40,60] & \(\theta_{7,3}\) & \(0.133\) & \(0.009\) & \(<0.001\) \\ \(V.sol\times X_{t,4}\): (60,80] & \(\theta_{7,4}\) & \(0.118\) & \(0.011\) & \(<0.001\) \\ \(V.sol\times X_{t,5}\): (80,100] & \(\theta_{7,5}\) & \(0.148\) & \(0.010\) & \(<0.001\) \\ \(V.sol\times X_{t,6}\): (100,200] & \(\theta_{7,6}\) & \(0.159\) & \(0.007\) & \(<0.001\) \\ \(V.sol\times X_{t,7}\): (200,300] & \(\theta_{7,7}\) & \(0.156\) & \(0.010\) & \(<0.001\) \\ \(V.sol\times X_{t,8}\): (300,800] & \(\theta_{7,8}\) & \(0.120\) & \(0.010\) & \(<0.001\) \\ \(C_{\mathrm{U}}\times C_{\mathrm{C}}\) & \(\theta_{8}\) & \(-4.841\) & \(0.078\) & \(<0.001\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The model’s estimated parameters. Figure 8: Model’s diagnostic plots: (**a**) Residuals \(\times\) Fitted Values; (**b**) Residuals \(\times\) Index; (**c**) Residuals distribution; (**d**) Normal Q-Q plot. Regarding the covariates without interactions, it is noteworthy that the parameter estimates for the \(\text{X}_{\text{blg}_{0}}\) and \(\text{X}_{\text{spht}_{20}}\) variables are positive, indicating that an increase in their values is associated with an increase in the mean retroreflectivity. Enhancing the roundness of glass beads (\(\text{X}_{\text{blg}0}\)) by 0.1 results in an average increase of 11.59% in retroreflectivity because \(\exp(\theta_{3}\times\text{X}_{\text{blg}_{0}})-1=\exp(0.011\times 0.1\times 1 00)-1=0.1159\). Analogously, the impact of glass beads' sphericity on the pavement markings may be calculated as \(\exp\left(\theta_{6}\times\text{X}_{\text{spht}_{20}}\right)-1=\exp(0.186\times 1 )-1=0.205\), i.e., pavement markings with glass beads with a sphericity higher than 0.59 present retroreflectivity, on average, 20.5% higher when compared to pavement markings with glass beads with sphericity lower than 0.59. These parameters characterize the glass beads' shape, and the results confirm the importance of shape to retroreflectivity [8]. To analyze the impact of \(\text{C}_{\text{U}}\) and \(\text{C}_{\text{C}}\) on retroreflectivity, it is necessary to consider the interaction between these variables. The size and gradation of glass beads also impact the retroreflectivity.