## 4 Test Site Results: Statistical Analysis  
The data collected at experimental test sites 1, 2, and 3 yielded over 19,000 retroreflectivity values, encompassing the characteristics of paints, glass beads, and the test site itself. Relying solely on graphical analysis for evaluating pavement markings' performance would introduce bias into the qualitative analysis results. To ensure a robust results analysis and to quantify the impact of each variable on retroreflectivity values and pavement markings' performance, statistical analysis was conducted. In this section, the Generalized Additive Models for Location, Scale, and Shape (GAMLSSs) are implemented due to their flexibility in addressing a wide range of distributions and incorporating random effects to account for data correlation [37; 38]. The GAMLSSs can be understood as an extension of the Generalized Linear Models (GLMs). The model was adjusted and its parameters were estimated using the _gamlss_ library of the software R version 4.2.2 [39]. In the descriptive analysis, it was observed that the distribution of retroreflectivity is positively skewed. Therefore, a Weibull distribution was considered in this study to be suitable for modeling the positive random variable (retroreflectivity) representing values until the end of service. It is worth noting that the normal distribution did not fit the data well, as expected based on the data distribution. Let y\({}^{\prime}\)jik be a vector representing the retroreflectivity observed for i paint characteristics during a j time period of days after painting at the k test site. Conditional on the random effects u, assume that the elements of y are independent and follow a Weibull distribution. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Glass Bead**} & \multicolumn{8}{c}{**Parameters**} \\ \cline{2-11}  & **D\({}_{\text{10}}\)*** & **D\({}_{\text{30}}\)*** & **D\({}_{\text{60}}\)*** & **C\({}_{\text{U}}\)** & **C\({}_{\text{C}}\)** & **bl\({}_{\text{20}}\)** & **bl\({}_{\text{50}}\)** & **bl\({}_{\text{80}}\)** & **SPHT\({}_{\text{20}}\)** & **SPHT\({}_{\text{50}}\)** & **SPHT\({}_{\text{80}}\)** \\ \hline \(\alpha\)-7030 Br & 0.368 & 0.489 & 0.625 & 1.698 & 1.040 & 0.62 & 0.84 & 0.93 & 0.53 & 0.75 & 0.82 \\ \(\alpha\)-100 Br & 0.335 & 0.450 & 0.557 & 1.663 & 1.085 & 0.61 & 0.82 & 0.92 & 0.51 & 0.74 & 0.81 \\ \(\beta\)-7030 Br & 0.348 & 0.457 & 0.577 & 1.658 & 1.040 & 0.60 & 0.84 & 0.94 & 0.59 & 0.76 & 0.83 \\ \(\beta\)-100 Br & 0.323 & 0.415 & 0.520 & 1.610 & 1.025 & 0.57 & 0.81 & 0.93 & 0.56 & 0.75 & 0.82 \\ \(\omega\)-7030 Br & 0.305 & 0.430 & 0.553 & 1.813 & 1.096 & 0.67 & 0.91 & 0.98 & 0.62 & 0.74 & 0.78 \\ \(\omega\)-100 Br & 0.270 & 0.494 & 0.518 & 1.919 & 1.745 & 0.67 & 0.91 & 0.98 & 0.62 & 0.74 & 0.78 \\ \(\delta\)-7030T & 0.447 & 0.620 & 0.810 & 1.812 & 1.062 & 0.81 & 0.93 & 0.97 & 0.71 & 0.77 & 0.82 \\ \(\delta\)-5050T & 0.485 & 0.698 & 0.886 & 1.827 & 1.134 & 0.83 & 0.93 & 0.97 & 0.71 & 0.77 & 0.82 \\ \(\delta\)-3070T & 0.568 & 0.805 & 0.928 & 1.634 & 1.229 & 0.85 & 0.93 & 0.97 & 0.71 & 0.77 & 0.82 \\ \(\varepsilon\)-7030 Br & 0.348 & 0.457 & 0.577 & 1.658 & 1.040 & 0.60 & 0.84 & 0.94 & 0.59 & 0.76 & 0.83 \\ \hline \hline \end{tabular}  
* Diameter in mm.  
\end{table} 
Table 3: Characterization parameters for the glass beads’ compositions. Thus, the Weibull regression model considered is described by Equation (3):  
\[ \begin{split}\text{$\mathrm{Y_{ij}}$}|\text{$\mathrm{u}$}\,\sim \text{$\mathrm{Weibull}$}(.)\\ \text{$\mathrm{ln}$}\Big{(}\mu_{\text{ijk}}\Big{)}=(\theta_{0}+ \text{$\mathrm{u}_{k}$})+\sum\limits_{j=1}^{8}\theta_{1,j}\text{$\mathrm{X_{ij} }$}+\theta_{2}\text{$\mathrm{X_{v.sol}}$}+\theta_{3}\text{$\mathrm{X_{bj50}}$}+ \theta_{4}\text{$\mathrm{X_{CU}}$}+\theta_{5}\text{$\mathrm{X_{CC}}$}+\theta_{6 }\text{$\mathrm{X_{spht_{20}}}$}\\ +\sum\limits_{j=1}^{8}\theta_{7,j}\text{$\mathrm{X_{tj\times v.sol} }$}+\theta_{8}\text{$\mathrm{X_{CU\times CC}}$},\end{split}