## 4 Test Site Results: Statistical Analysis
 \tag{3}\]  
where \(\mu_{\text{ijk}}\) is the mean of the response variable related to the explanatory variables through the logarithm link function. The explanatory variables considered in this study are paints' volume solids (\(\text{$\mathrm{X_{v.sol}}$}\)), glass beads' coefficient of uniformity (\(\text{$\mathrm{X_{CU}}$}\)), coefficient of curvature (\(\text{$\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{ \mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{  \mathrm{         }}}}}}}}}}}}}}}\)) and shape characteristics (\(\text{$\mathrm{X_{spht_{20}}}$}\) and \(\text{$\mathrm{X_{b_{100}}}$}\)), and the dichotomous time variables \(\text{$\mathrm{X_{t,1}}$}=(0,20]$}\), \(\text{$\mathrm{X_{t,2}}$}=(20,40]$}\), \(\text{$\mathrm{X_{t,3}}$}=(40,60]$}\), \(\text{$\mathrm{X_{t,4}}$}=(60,80]$\mathrm{X_{CU}}$0\mathrm{X_{t,5}}$\mathrm{X_{CU}}$1}\), \(\text{$\mathrm{X_{CU}}$2}=(100,200]$\mathrm{X_{CU}}$3\mathrm{X_{t,7}}$\mathrm{X_{CU}}$4}\), and \(\text{$\mathrm{X_{CU}}$5}=(300,800)\), which represent the time periods (days elapsed since the test site construction) during which retroreflectivity was observed. Note that parentheses brackets indicate an open interval, not including a start point, while a closed interval includes the end point and is denoted with the square brackets, as a mathematical notation. Thus, if \(\text{$\mathrm{X_{CU}}$6}=1\), the retroreflectivity was measured in the first 20 days of application of the pavement marking; the other time variables assume a value of zero in this case. Categorizing the time variable helps to evaluate changes in the degradation rate of pavement markings over time, which is not linear. It is important to highlight that the variable time accounts for the effect of traffic and weather on the pavement marking degradation. The continuous variables \(\text{$\mathrm{X_{CU}}$7},\text{$\mathrm{X_{CU}}$8},\text{$\mathrm{X_{CU}}$9}\), and \(\text{$\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{ \mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{  \mathrm{         }}}}}}}}}}}}}}}\)) and shape characteristics (\(\text{$0}\) represent the values of these properties obtained from the characterization tests. On the other hand, the variable \(\text{$\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{ \mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{  \mathrm{         }}}}}}}}}}}}}}}\)) and shape characteristics (\(\text{$1}\) is dichotomous and assumes a value of one when the SPHT\({}_{20}\) of the paint is higher than 0.59, or zero otherwise. Finally, the \(\text{$\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{ \mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{  \mathrm{         }}}}}}}}}}}}}}}\)) and shape characteristics (\(\text{$2}=(\theta_{0},\ldots,\theta_{8})\) vector represents the fixed parameters to be estimated using maximum likelihood [37; 38], and the random intercept \(\text{$\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{ \mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{\mathrm{  \mathrm{         }}}}}}}}}}}}}}}\)) and shape characteristics (\(\text{$3}\text{withk}=1,2,3\) was considered to deal with the variability of the measurement at a distinct test site. During the model selection process, other variables, such as paint consistency and density, were considered. However, these variables were insignificant to the model (\(p\)-value \(>0.05\)). Therefore, only variables contributing to the model significance were included in Equation (3). In addition, interactions between explanatory variables were also considered. Interactions evaluate whether the association between the target variable and the independent variable varies based on the value of another independent variable.