## 4 Results and Discussion  
### The Relationship between Retroreflectivity and Other Factors  
The results from linear regression models, two logarithmic models (Model 1 and Model 2), and backward selection on Model 1 for the VTI and NMF data are shown in  
Figure 5: Statistical analysis design to determine those factors/predictors that significantly affect retroreflectivity and also predict retroreflectivity. Tables 3 and 4, respectively. Model 1 is a logarithmic regression model that uses all factors in the data as predictors without considering interaction between any two predictors. Model 2 is a logarithmic regression model that investigates the effects of interaction between age and three other predictors (direction, colors, and classes). As color and classes are categorical factors, the blue color was used as a reference factor for colors and Class 1 was used as a reference factor for classes in the regression models (Model 2). In this study, GPS position is used to locate the region where the signs are mounted and included as predictors in the models to find the relationship between the location of the traffic sign and its deterioration. Model 2 for the VTI data shows that the interaction between age and the other three predictors (direction, white color, and classes) was significant, but the estimate of the interaction effect with age was very small and had no visible impact on the prediction models (almost identical R\({}^{2}\) values for Model 1 and Model 2). Model 2 for the NMF data shows that age has no significant interaction with colors or classes. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Factors**} & \multirow{2}{*}{\begin{tabular}{c} **Linear** \\ **Regression** \\ \end{tabular} } & \multicolumn{2}{c}{\
\begin{tabular}{c} **Logarithmic** \\ **Regression** \\ \end{tabular} } & \multicolumn{2}{c}{
\begin{tabular}{c} **Logarithmic** \\ **Regression Model 2** \\ \end{tabular} } & \multicolumn{2}{c}{**Backward Selection 3**} \\ \hline X & \(-615.12\) & *** & \(-1.73\) & *** & \(-1.85\) & *** & \(-1.74\) & *** \\ \hline Y & \(1086.71\) & *** & \(8.84\) & *** & \(8.85\) & *** & \(8.84\) & *** \\ \hline Green color & \(-88.19\) & *** & \(-0.72\) & *** & \(-0.53\) & & \(-0.71\) & *** \\ \hline Red color & \(-18.65\) & & \(-0.46\) & ** & \(-0.41\) & & \(-0.46\) & ** \\ \hline White color & \(86.66\) & *** & \(0.05\) & & \(0.58\) & ** & \(0.05\) & \\ \hline Yellow color & \(-32.12\) & * & \(-0.97\) & *** & \(-1.11\) & *** & \(-0.98\) & *** \\ \hline (Direction/360) & \(-10.05\) & & \(-0.25\) & * & \(0.10\) & & \(-0.25\) & * \\ \hline GPS latitude & \(8.44\) & ** & \(0.12\) & *** & \(0.11\) & *** & \(0.12\) & *** \\ \hline GPS longitude & \(-2.54\) & & \(0.01\) & & \(0.03\) & & - & \\ \hline Age & \(-3.34\) & *** & \(-0.05\) & *** & \(-0.07\) & *** & \(-0.05\) & *** \\ \hline Class 2 & \(42.77\) & ** & \(1.39\) & *** & \(-0.24\) & & \(1.39\) & *** \\ \hline Class 3 & \(254.47\) & *** & \(1.90\) & *** & \(1.16\) & *** & \(1.90\) & *** \\ \hline I (Direction/360): Age & & & & \(-0.02\) & * & & \\ \hline Green color: Age & & & & \(-0.02\) & & & \\ \hline Red color: Age & & & & \(-0.00\) & & & \\ \hline White color: Age & & & & \(-0.04\) & *** & & \\ \hline Yellow color: Age & & & & \(0.01\) & & & \\ \hline Class 2: Age & & & & \(0.09\) & *** & & \\ \hline Class 3: Age & & & & \(0.06\) & *** & & \\ \hline R\({}^{2}\) & \(0.53\) & \(0.57\) & \(0.58\) & & \(0.57\) & \\ \hline \hline \end{tabular}  
*, *** indicates significance at the 5%, 1%, and 0.1% level, respectively; \({}^{1}\) No interaction between predictors included; \({}^{2}\) Interaction between age and three predictors (direction, color, and class) is included; \({}^{3}\) Logarithmic regression considering no interaction between predictors.  
\end{table} 
Table 3: The relationship between retroreflectivity and other factors in the VTI data.