# Data-Driven Prediction of Binder Rheological Performance in RAP/RAS-Containing Asphalt Mixtures
## 3 Results and Discussion
### Statistical Evaluation of Model Predictions  
In a comparative statistical analysis of linear and RF nonlinear models for the four rheological parameters, it was found that, in terms of goodness of fit and accuracy of prediction, the RF models can be considered superior to the linear models, as shown in Table 2. The RF models displayed much higher R\({}^{2}\) values (0.84 and 0.75) than (0.66 and 0.67) and much lower RMSE values (8.60 and 1038.87) than the RMSE values of (27.69 and 1644.82) for rutting and fatigue cracking, respectively, indicating that the RF models provide better predictions. The residual analysis of the models further supported the RF  
Figure 20: Measured versus predicted thermal cracking parameters based on an RF model.  
models, as the RF nonlinear models produced a lower STD of residuals, evidenced by the lower bias and more consistent results than the other models. For thermal cracking, both models proved to be good prediction models, as the RF nonlinear model provided a slight improvement in terms of the residual spread (STD of residuals of 1.13 versus 1.58). In terms of block cracking, the RF model had a statistically superior metric with an R value of 1.00; this model overfitted the data with poor generalization, with a higher RMSE and STD of residuals. Therefore, RF nonlinear models provide better predictive capability in most scenarios; however, caution should be exercised with overfitting when models are applied to datasets that can be very variable, as block cracking can compound a great deal of variability. Apart from model-based limitations, challenges arise from the variability of RAP/RAS and their binders. The extracted binders used in this study represent a limited range of RAP/RAS binder replacement levels (0-35%). Therefore, the applicability of the developed models with RAP/RAS binder replacement levels outside this range may be limited unless recalibrated with additional data. Hence, this study emphasized that measures of accuracy should be paired with residual analysis to provide a comprehensive view of both strength and reliability in modeling rheological behaviors.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{\begin{tabular}{c} **Rheological** \\ **Parameter** \\ \end{tabular} } & \multirow{2}{*}{**Model**} & \multicolumn{4}{c}{**Goodness of Fit**} & \multicolumn{4}{c}{**Accuracy of Prediction**} \\ \cline{3-8}  & & & **R\({}^{2}\)** & **R** & **Se/Sy** & \begin{tabular}{c} **Mean of** \\ **Residuals** \\ \end{tabular} & \begin{tabular}{c} **STD of** \\ **Residuals** \\ \end{tabular} & **RMSE** \\ \hline \multirow{2}{*}{\begin{tabular}{c} **Rutting** \\ \end{tabular} } & Linear & 0.66 & 0.81 & 0.58 & 6.58 & 26.90 & 27.69 \\ \cline{2-8}  & RF Nonlinear & 0.84 & 0.94 & 0.40 & 3.08 & 8.03 & 8.60 \\ \hline \multirow{2}{*}{\begin{tabular}{c} **Fatigue** \\ **Cracking** \\ \end{tabular} } & Linear & 0.67 & 0.82 & 0.57 & 381.89 & 1599.87 & 1644.82 \\ \cline{2-8}  & RF Nonlinear & 0.75 & 0.86 & 0.50 & 449.27 & 936.70 & 1038.87 \\ \hline \multirow{2}{*}{\
\begin{tabular}{c} **Block** \\ **Cracking** \\ \end{tabular} } & Linear & 0.84 & 0.92 & 0.40 & 241.41 & 1542.36 & 1561.14 \\ \cline{2-8}  & RF Nonlinear & 0.81 & 1.00 & 0.44 & \(-\)882.72 & 2014.34 & 2199.26 \\ \hline \multirow{2}{*}{
\begin{tabular}{c} **Thermal** \\ **Cracking** \\ \end{tabular} } & Linear & 0.89 & 0.94 & 0.34 & 0.04 & 1.58 & 1.58 \\ \cline{2-8}  & RF Nonlinear & 0.87 & 0.95 & 0.36 & \(-\)0.53 & 1.13 & 1.25 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Statistical analyses of rheological prediction models.  
Figure 21: Feature importance in the thermal cracking parameter RF model.