## 3 Results and Discussion
### Effect of the Stabilization Process  
Brandies before and after both stabilization processes are highlighted in the scores plot of Figure 1B. The most distinct ester profile was observed for the brandies submitted to room temperature stabilization, as is shown by a clear separation in component 2 of the PCA (Figures 1B and 2B). However, due to the large differences observed between brandies, predominantly related to the ageing and the paired structure of the data [21] with repeated measurements of the same samples (before stabilization, after cold stabilization, and after room temperature stabilization), differences related to stabilization were not clearly highlighted, especially for the samples stabilized at cold temperature. Therefore, a multilevel decomposition was applied, to focus on the effect of the treatment, and a partial least squares discriminant analysis (ML-PLS-DA) was performed for the three  
Figure 1: Principal component analysis (PCA) carried out on the brandy samples. Scores plot for the first two principal component highlighting brandies according to the ageing factor (**A**), and before and after cold stabilization and filtration treatment (**B**). NonStab: non-stabilized brandy; ColdT: brandy stabilized at cold temperature; RoomT: brandy stabilized at room temperature. Figure 2: Loadings bar plot on component 1 (**A**) and component 2 (**B**) of the principal component analysis carried out on the brandy samples. classes: brandies before stabilization, after cold stabilization and filtration, and after room temperature stabilization and filtration (Figure 3). The model was optimized and validated following a double cross-validation scheme. The sub-models were predominantly optimized into two components, revealing the low complexity of the model (also shown during the PCA assessment) and reducing the risk of overfitting (Figure 3B). The ML-PLS-DA displayed a good performance, with a BER of 0.09 \(\pm\) 0.05 (Table 1). Brandies stabilized at room temperature were correctly assigned in all the cases, supporting a more distinct ester profile, while the error of the model was due to incorrect assignment between brandies without stabilization and after cold stabilization. Therefore, this error suggested a lower impact on the ester profile when cold stabilization was applied. Then, the model was successfully validated using a permutation test. The null distributions calculated from the class label permutation are shown in Figure 4 for the three diagnostics statistics: BER, AUROC and NMC, which displayed an expected Gaussian shape (Figure 4). The average performance of the model fell in the tail of the null distribution for the three diagnostics, obtaining a \(p\)-value of the model below 0.05 in all the cases (Table 1). All these results supported the robustness of the ML-PLS-DA, being the most model suitable for analyzing and interpreting the dataset. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Mean BER**} & \multirow{2}{*}{**Class**} & **Mean Class** & **Predicted as** & **Predicted as** & **Predicted as** & \(p\)**-Value** \\  & & **Error** & **NonStab** & **ColdT** & **RoomT** & **(Model)** \\ \hline \multirow{3}{*}{0.09 \(\pm\) 0.05} & NonStab & 0.15 \(\pm\) 0.11 & 765 & 135 & 0 & BER, AUROC, \\  & ColdT & 0.14 \(\pm\) 0.10 & 122 & 778 & 0 & NMC: 0.001 \\ \cline{1-1}  & RoomT & 0.00 \(\pm\) 0.00 & 0 & 0 & 900 & NMC: 0.001 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Multilevel partial least squares discriminant analysis (ML-PLS-DA) performance (from a double cross-validation scheme). Figure 3: Graphical outputs of the multilevel partial least squares discriminant analysis (ML-PLS-DA) carried out to discriminate between the brandy samples before and after cold stabilization and filtration. (**A**) Scores plot for component 1 (X-variate 1) and component 2 (X-variate 2), and (**B**) histogram of the number of components optimized for the sub-models during the double-cross validation.