## 4 Results and Discussion
### The Relationship between Retroreflectivity and Other Factors
Because of the small or marginal effect of interaction between age and other predictors, the models used in the additional analysis do not consider interaction between any factors in the data. As depicted in Tables 3 and 4 for Model 1, the age of the road traffic sign was significant in both the VTI and NMF data. In addition, the X coordinate of the CIE color space and the class of road traffic signs were also significant in both datasets. The backward stepwise selection begins with the full least squares model containing all predictors and then iteratively removes the least useful predictor, one at a time [22]. The reduced model that best explains the VTI and NMF data is shown in Tables 3 and 4, respectively. It is worth mentioning that logarithmic models were used for backward stepwise selection because they satisfied all the model diagnostics reasonably well and gave higher R\({}^{2}\) values compared to the linear models (no transformation of the response factor). GPS longitude was insignificant in the backward stepwise models for the VTI data, while the Y coordinate of the CIE color space and \(\beta\) were insignificant in the model for the NMF data. An important finding is that the effect of GPS position on retroreflectivity is significant for the latitude but not longitude (shown in Table 3). It is clear from the results that road signs mounted in the southern regions of Sweden fade faster compared with those in the northern parts. There are many reasons why road signs fade faster in the southern regions. The high intensity of traffic and high humidity in the south may be the main factors that distinguish it from the north. The population size in the north is considerably smaller than that in the southern and central regions, while the summer period lasts longer in the south. In addition, Sweden's four largest lakes lie within the southern regions and they may increase the humidity in these regions. \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}{**Logarithmic**} & \multicolumn{2}{c}{**Logarithmic**} & \multicolumn{2}{c}{**Backward**} \\  & & & & & & & & **Selection** \\ \hline X & 34.19 & 1.45 & * & 1.68 & ** & 1.47 & ** \\ \hline Y & \(-\)231.24 & & \(-\)0.58 & & \(-\)0.72 & & \(-\) \\ \hline \(\beta\) & \(-\)559.15 & *** & \(-\)0.30 & & \(-\)0.30 & & - & \\ \hline Green color & 106.85 & * & 0.75 & *** & 0.82 & *** & 0.57 & *** \\ \hline Red color & 81.51 & & 0.32 & & 0.15 & & 0.18 & \\ \hline White color & 548.87 & *** & 2.34 & *** & 2.27 & *** & 2.09 & *** \\ \hline Yellow color & 417.25 & *** & 1.79 & *** & 1.69 & *** & 1.51 & *** \\ \hline Age & \(-\)4.36 & * & \(-\)0.04 & *** & \(-\)0.04 & ** & \(-\)0.04 & *** \\ \hline Class 2 & 36.00 & *** & 0.88 & *** & 0.91 & *** & 0.89 & *** \\ \hline Class 3 & 165.05 & *** & 1.88 & *** & 1.89 & *** & 1.89 & *** \\ \hline Green color: Age & & & & & \(-\)0.01 & & \\ \hline Red color: Age & & & & & 0.02 & & \\ \hline White color: Age & & & & & 0.01 & & \\ \hline Yellow color: Age & & & & & 0.02 & & \\ \hline Class2: Age & & & & \(-\)0.01 & & & \\ \hline Class3: Age & & & & \(-\)0.00 & & & \\ \hline R\({}^{2}\) & 0.74 & 0.95 & 0.95 & 0.95 & 0.95 & \\ \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 two predictors (color and class) is included; \({}^{3}\) Logarithmic regression considering no interaction between predictors.  
\end{table} 
Table 4: The relationship between retroreflectivity and other factors in the NMF data. A logarithmic regression model (Model 1) was further conducted in Section 4.2, with the R\({}^{2}\) values of 0.57 and 0.95 for the VTI and NMF data, respectively (see Tables 3 and 4), being higher than the R\({}^{2}\) for a linear regression model (0.53 and 0.75).