## 4 Panel Data Analysis-Based Surface Texture Prediction Model
### Development of Panel Data Analysis-Based Surface Texture Prediction Model  
The SMTD data collected from 19 test structures in RIOHTrack between December 2016 to December 2020 are taken as the panel data for analysis. Considering that most environmental factors change periodically, at least one-year panel data should be used as the input of the prediction model. Importantly, the time scale of the input data needs to be determined according to the regression results of the panel data analysis-based prediction model, which will be discussed in detail later. As an analytical example, the surface texture prediction model is developed and evaluated using the first 3 years SMTD panel data (from year 2017 to 2019), and the obtained prediction formulas are presented in Table 5.  
Table 6 shows the regression results of a panel data analysis-based surface texture prediction model using the first 3 years SMTD panel data. The significance level of each influencing factor, depending on the calculated \(p\) value, can be determined from the regression results. The smaller the \(p\) value, the more significant the influence of this factor on the surface texture. For the mixed-effects and random-effects models, all these selected influencing factors have a significant impact on the surface texture. For the fixed-effects model, only 4 influencing factors (the cumulative axle loads, monthly average temperature, monthly average humidity, and monthly rainfall) have a significant impact on the surface texture. The regression R\({}^{2}\) value of the three models are 0.732, 0.822, and 0.398, respectively. However, it cannot be concluded that the larger the R\({}^{2}\) value of regression, the more applicable the model is [28]. Normally, the developed panel data analysis-based models should be examined by F test, LM test, and Hausman test to determine whether these models are qualified. Then we can choose the most applicable model.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Asphalt Mixture** & **SAC13-65\%** & **SAC13-70\%** & **SMA13-75\%** & **PAC13-80\%** \\ \hline CA & 0.136923 & 0.128655 & 0.087533 & 0.075702 \\ FAC & 0.452107 & 0.543860 & 0.616667 & 0.453782 \\ FAF & 0.694915 & 0.701613 & 0.837838 & 0.629630 \\ \hline \end{tabular}
\end{table}
Table 4: Bailey method-based CA, FAC, and FAF ratios calculated for the four types of mixtures.  
\begin{table}
\begin{tabular}{c c} \hline
**Model Type** & **Prediction Formulas** \\ \hline Mixed-effects model & \(\text{SMTD}_{i}=3.8711-0.0588\log(\text{CSAL}_{i})+0.0008\text{MAT}_{it}-0.002 \text{IAM}_{it}\) \\  & \(-0.0007\text{MAR}_{it}-4.6333\text{CA}_{it}+1.0121\text{FAC}_{it}-2.6346\text{ FAF}_{it}\) \\ Fixed-effects model & \(\text{SMTD}_{i}=14.0860-0.059\log(\text{CSAL}_{it})+0.0008\text{MAT}_{it}-0.0002 \text{IAM}_{it}\) \\  & \(-0.0000\text{MAR}_{it}-4.03\text{SCAL}_{it}-1.0925\text{FAC}_{it}-2.324\text{ AFAF}_{it}+u_{i}\) \\ Random-effects model & \(\text{SMTD}_{i}=3.8721-0.0588\log(\text{CSAL}_{it})+0.0008\text{MAT}_{it}-0.002 \text{IAM}_{it}\) \\  & \(-0.0007\text{MAR}_{it}-4.6375\text{CA}_{it}+1.0111\text{FAC}_{it}-2.6346\text{ AFAF}_{it}+u_{i}\) \\ \hline \end{tabular}
\end{table}
Table 5: Prediction formulas of surface texture model using the first 3 years SMTD panel data.