## 5 Model Results
### Variable Importance Analysis  
A primary strength of the MARS model is its capability to discern if a particular input factor is vital for predicting output values or if it merely offers a slight enhancement to the model's precision. The varImp function in the caret package [64] produces a matrix that displays the relative importance of features within the model, utilizing two distinct methods to assess feature significance:  
* The raw residual sum-of-squares (RSS) method proceeds in two phases. Initially, it assesses the RSS decrease for each subset, contrasting it with the preceding subset's value. Subsequently, for every relevant feature, it accumulates these reductions across all subsets that incorporate that feature. Finally, the overall sum of these reductions is analyzed. Features leading to substantial RSS declines hold greater importance. * The generalized cross-validation (GCV) method operates analogously to the RSS method, but it employs GCV in place of RSS. GCV assesses feature performance in subsets, pinpointing the most pivotal subset (with smaller GCV values being preferable). Figure 8: Comparative performance of MARS vs. MEP models: (**a**) RMSE; (**b**) R\({}^{2}\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Compaction Parameters** & **Performance Measures** & **Overall** \\ \hline \(w_{opt}\) & MAE (\%) & 1.3 \\  & RMSE (\%) & 1.68 \\  & R\({}^{2}\) & 0.921 \\ \(\rho_{\text{dmax}}\) & MAE (Mg/m\({}^{3}\)) & 0.054 \\  & RMSE (Mg/m\({}^{3}\)) & 0.073 \\  & R\({}^{2}\) & 0.867 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Performance metrics of the MEP models for training, testing, and overall datasets. Figure 9 displays the outcomes of the contributions and the selections made by different independent variables on the prediction performance of \(w_{opt}\) and \(\rho_{\text{dmax}}\). Figure 9 displays the impact of various independent variables on the \(\rho_{\text{dmax}}\) MARS model. The figure is sorted based on the decreasing influence of these variables. The top two influential factors are PL (%) and \(\text{C}_{\text{F}}\) (%), with RSS values of 100 and 55.01, and GCV values of 100 and 75, respectively. These statistics suggest that PL (%) holds the most significant influence on the \(\rho_{\text{dmax}}\) MARS model, followed closely by \(\text{C}_{\text{F}}\) (%). Other factors listed in decreasing order of influence are E (kJ/m\({}^{3}\)), LL (%), and \(\text{C}_{\text{S}}\) (%). Figure 9 showcases the influence of different independent variables on the \(w_{opt}\) MARS model. The two most impactful factors in this table are \(\text{C}_{\text{F}}\) (%) and PL (%). \(\text{C}_{\text{F}}\) (%) takes the lead with RSS and GCV values of 100, indicating its paramount significance in the model. PL (%) follows next with RSS at 63.49 and GCV at 85.71. These results allow us to state that \(\text{C}_{\text{F}}\) (%) has the most considerable influence on the \(w_{opt}\) MARS model, but PL (%) also retains significant sway. Other listed factors, in order of influence, include E (kJ/m\({}^{3}\)), LL (%), and \(\text{C}_{\text{S}}\) (%). To more deeply assess the reliability of the MARS models, a parametric analysis can be undertaken. This type of analysis examines the alignment of the model's predictions with existing geotechnical knowledge, experimental data, and anticipated outcomes. This study scrutinized how the predicted soil parameters from the suggested models responded to hypothetical data, spanning the lower and upper bounds of the data used in model training. This approach entailed modifying a single input variable while maintaining others at their average. Synthetic data for this individual parameter were produced via raising it step by step. These inputs were then used in the prediction equation to determine soil parameters. This method was iteratively applied for different variables to gauge the model's reaction to each input change.