## 4 Panel Data Analysis-Based Surface Texture Prediction Model
### Influence of Panel Data Time Scale on Surface Texture Prediction Model
To characterize the individual differences between road sections, the random error component (\(u_{i}\)) of the surface texture prediction model using one year, two years, three years, and four years SMTD panel data are calculated (shown in Figure 6). The smaller the random error component, the smaller the individual difference between different road sections. The random error components of different sections of the same pavement structure are different, which is mainly caused by the differences in materials, construction, and \begin{table}
\begin{tabular}{c c} \hline \hline
**Time Scale** & **Prediction Formulas** \\ \hline One year SMTD data & SMTD\({}_{i}=4.3015-0.0925\log(\text{CSAL}_{i})+0.0038\text{MAT}_{i}-0.004\text{MAH}_{i}\) \\  & \(+0.0005\text{MAR}_{i}-4.763\text{CNA}_{i}+0.9222\text{EAC}_{i}-2.3979\text{FAF} _{i}+u_{i}\) \\ Two years SMTD data & SMTD\({}_{i}=4.3838-0.0981\log(\text{CSAL}_{i})+0.0023\text{MAT}_{i}-0.003\text{MAH}_{i}\) \\  & \(+0.000\text{AMAR}_{i}-4.4661\text{CA}_{i}+1.0495\text{FAC}_{i}-2.5784\text{FAF} _{i}+u_{i}\) \\ Three years SMTD data & SMTD\({}_{i}=3.8721-0.0588\log(\text{CSAL}_{i})+0.0008\text{MAT}_{i}-0.0021\text{MAH}_{i}\) \\  & \(-0.000\text{MAR}_{i}-4.6375\text{CNA}_{i}+4.1011\text{TAF}_{i}-2.6364\text{FAF} _{i}+u_{i}\) \\ Four years SMTD data & SMTD\({}_{i}=3.7616-0.0451\log(\text{CSAL}_{i})+0.0002\text{MAT}_{i}-0.0014\text{MAH}_{i}\) \\  & \(-0.0001\text{MAR}_{i}-4.9650\text{CNA}_{i}+9.0860\text{FAC}_{i}-2.6250\text{FAF} _{i}+u_{i}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Prediction formulas of random-effects model using different time scales of SMTD data. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**One Year SMTD**} & \multicolumn{2}{c}{**Two Years SMTD**} & \multicolumn{2}{c}{**Three Years SMTD**} & \multicolumn{2}{c}{**Four Years SMTD**} \\ \cline{3-8}
**Variables** & \multicolumn{2}{c}{**Data**} & \multicolumn{2}{c}{**Data**} & \multicolumn{2}{c}{**Data**} & \multicolumn{2}{c}{**Data**} & \multicolumn{2}{c}{**Data**} \\ \cline{2-8}  & \(p\) **Value** & **Level** & \(p\) **Value** & **Level** & \(p\) **Value** & **Level** & \(p\) **Value** & **Level** \\ \hline CSAL & 0.000 & *** & 0.000 & *** & 0.000 & *** & 0.000 & *** \\ MAT & 0.000 & *** & 0.000 & *** & 0.014 & *** & 0.470 & -- \\ MAH & 0.000 & *** & 0.000 & *** & 0.000 & *** & 0.000 & *** \\ MR & 0.233 & ** & 0.168 & ** & 0.022 & ** & 0.000 & *** \\ CA & 0.000 & *** & 0.000 & *** & 0.000 & *** & 0.000 & *** \\ FAC & 0.019 & ** & 0.004 & *** & 0.003 & *** & 0.003 & *** \\ FAF & 0.000 & *** & 0.000 & *** & 0.000 & *** & 0.000 & *** \\ Intercept & 0.000 & *** & 0.000 & *** & 0.000 & *** & 0.000 & *** \\ \hline \hline \end{tabular} Note: The smaller the \(p\) value, the more significant the influence of this factor on the surface texture. ** corresponds to \(p\) value ranging from 0.01 to 0.05; *** corresponds to \(p\) value less than 0.01.  
\end{table} 
Table 9: Comparison of the variable significance level of the random-effects model based on different time scales of SMTD data. measurement. It can be seen from Figure 6 that for the same asphalt pavement structure, the differences between the obtained random error components of panel data analysis models based on different time scales of SMTD data are relatively small, indicating that the time scale of the input panel data has insignificant influence on the random error component of the panel data analysis-based prediction model. The absolute value of the random error component is less than 0.1 mm (except for SRT-11), which is one order of magnitude smaller than the predicted SMTD value. The maximum deviation of the random error component for SRT-11 is 0.14 mm in absolute value. Thus, the individual difference is little affected by the test cycle, and even the model based on the first year data can already reflect the individual difference in surface texture between different road sections.