## 4 Panel Data Analysis-Based Surface Texture Prediction Model
### Examination of Panel Data Analysis-Based Surface Texture Prediction Model  
In order to select the most suitable panel data analysis-based model, a series of tests need to be conducted on the model. The flow chart of examining the panel data analysis model is shown in Figure 5. The first step is to judge whether there is individual heterogeneity in the surface texture data set collected from multiple sections of same type of pavement structure. If there is, the panel data analysis model is initially considered to be a random-effects form. Then, the LM test is carried out. If the LM test condition is accepted, the analysis model is recognized as the mixed-effects model. If the LM test condition is rejected, the Hausman test is performed. If there is no individual heterogeneity in the data set from different sections, the panel data analysis model is initially considered to be a fixed-effects form, then the F test is implemented. If the F test condition is accepted, the analysis model is recognized as the mixed-effects model. If the F test condition is rejected, the Hausman test is conducted. The Hausman test is an effective tool to distinguish the fixed-effects model and the random-effects model. If the Hausman test condition is accepted, the analysis model is a random-effects model. Otherwise, it is a fixed-effects model. Table 7 shows the results of the panel data analysis model examination. The \(p\) value is the probability that the null hypothesis is true, that is, the smaller the \(p\) value is, the smaller the probability of the null hypothesis is; the greater the \(p\) value is, the greater the probability of the null hypothesis is. It is seen that the \(p\) value obtained by LM Test and F test is 0, indicating that these two test conditions are both rejected. The \(p\) value obtained by Hausman test is 1, that is, the Hausman test condition is accepted. Therefore, the random-effects model is the most suitable model to predict the asphalt pavement surface texture of RIOHITrack (see Figure 5). Ref. [28] developed a panel data-based skid resistance model using skid number (SN). This model is also a random-effects model and it achieves good results; the regression between the predicted and the measured SN results was fitted with the R\({}^{2}\) coefficient of 0.74. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{**Factors**} & \multicolumn{1}{c}{**CSAL**} & \multicolumn{1}{c}{**MAT**} & \multicolumn{1}{c}{**MAH**} & \multicolumn{1}{c}{**MR**} & \multicolumn{1}{c}{**CA**} & \multicolumn{1}{c}{**FAC**} & \multicolumn{1}{c}{**FAF**} & \multicolumn{1}{c}{**Intercept**} & \multicolumn{1}{c}{**R\({}^{2}\)**} \\ \hline Mixed-effects model & \(p\) value & 0.000 & 0.043 & 0.000 & 0.06 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 & 0.000 \\  & significance level & ** & ** & ** & ** & ** & ** & ** & ** & ** \\ \hline Fixed-effects model & \(p\) value & 0.000 & 0.016 & 0.000 & 0.022 & 0.538 & 0.868 & 0.972 & 0.814 & 0.82 \\  & significance level & ** & ** & ** & ** & ** & ** & & & \\ \hline Random-effects model & \(p\) value & 0.000 & 0.014 & 0.000 & 0.023 & 0.000 & 0.003 & 0.000 & 0.000 & 0.39 \\ \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 0.05 to 0.1; ** corresponds to \(p\) value ranging from 0.01 to 0.05; *** corresponds to \(p\) value less than 0.01.  
\end{table} 
Table 6: Regression results of panel data analysis-based surface texture prediction model using the first 3 years SMTD panel data. Figure 5: The flow chart of the panel data analysis model examination. The prediction formula of the asphalt pavement surface texture based on the 3 years SMTD panel data is shown in Equation (12).