## 3 Results and Discussion
### Prediction Models
#### 3.4.1 Prediction Model for Chemical Analysis  
Among the PLSR models obtained with NIR spectra, no outliers were identified for DM, CP, and starch, while the other parameters had outlier values ranging from 2 to 5 in the calibration set. The outliers in the validation set did not exceed three units for all the models analysed, with EE, CF, and starch having no outliers identified. In the same tables (Table 5), the latent variables of the calibration model are reported, ranging from a minimum of 4 to a maximum of 7. The optimal number of LVs was selected based on the explained variance plateau criterion, ensuring that additional LVs were included only when they significantly improved model performance. Furthermore, to prevent overfitting, we set a maximum limit of seven LVs. Considering the chemical composition, good calibration models (R\({}^{2}\)c > 0.90) were obtained for DM, CP, EE, aNDF, and starch. However, the R\({}^{2}\) for each parameter in calibration, cross-validation, and prediction did not fall below 0.8. In the five-fold cross-validation, the R\({}^{2}\) value decreased, as expected, for all the chemical components considered, achieving an R\({}^{2}\)cv > 0.90 only for DM, CP, and starch. For all parameters evaluated, the SECV was slightly higher than the SEC, but it did not exceed 10 percentage points (p.p.). When comparing SECV with SEP, the increase ranged from a minimum of 0.15 p.p. to a maximum of 1.77 p.p. for CF. To assess model performance based on the RPDcv value (Table 6), following the guidelines provided by [39; 40] and as outlined in Table 2, no parameters had an RPDcv lower than 2, thereby excluding any models classified as poor and not recommended for use. The RPDcv values exceeded the threshold of 2.5 for almost all parameters, with DM surpassing the threshold of 4. Notably, all parameters had an REcv greater than 10. The external validation, using the validation set, is considered essential for evaluating the applicability of the model to independent datasets. For this prediction analysis, the R\({}^{2}\) of the considered chemical parameters ranged from 0.81 to 0.89, demonstrating \"fair\" performance [39]. In the prediction phase, due to the increase in SEP compared to SECV, the RPDp values were lower. However, DM maintained a value above 4, despite being slightly lower than in cross-validation. The remaining parameters ranged from a minimum of 2.7 to a maximum \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & & & \multicolumn{4}{c}{**Calibration Set**} & \multicolumn{4}{c}{**Independent Set for Validation**} \\ \hline
**\%** & **LV** & **OUT** & **R\({}^{2}\)c** & **SEC** & **R\({}^{2}\)cv** & **SECV** & **OUT** & **R\({}^{2}\)p** & **SEP** \\ \hline DM * & 7 & 0 & 0.93 & 1.22 & 0.92 & 1.32 & 1 & 0.89 & 1.41 \\ Ash & 5 & 5 & 0.87 & 0.25 & 0.86 & 0.26 & 1 & 0.85 & 0.29 \\ CP & 4 & 0 & 0.91 & 0.45 & 0.90 & 0.47 & 2 & 0.88 & 0.58 \\ EE & 6 & 2 & 0.90 & 0.12 & 0.89 & 0.13 & 0 & 0.87 & 0.15 \\ CF & 7 & 4 & 0.87 & 1.55 & 0.85 & 1.68 & 0 & 0.84 & 1.77 \\ aNDF & 7 & 5 & 0.90 & 1.41 & 0.88 & 1.55 & 1 & 0.81 & 1.71 \\ ADF & 6 & 4 & 0.88 & 1.07 & 0.87 & 1.12 & 1 & 0.85 & 1.36 \\ ADL & 5 & 2 & 0.83 & 0.39 & 0.82 & 0.42 & 3 & 0.81 & 0.43 \\ Starch & 7 & 0 & 0.92 & 0.74 & 0.91 & 0.79 & 0 & 0.88 & 0.82 \\ \hline \end{tabular}
\end{table} 
Table 5: Calibration, cross-validation (cv), and prediction (p) statistics for the chemical composition (% of DM) of Total Mixed Ratios (TMRs) from both the calibration and validation set. of 3.22. In prediction, DM, CP, aNDF, and starch maintained performances classified as good, while the remaining parameters were rated as fair. No chemical parameter showed a predictive model classified as poor. For all tested models, the RER remained consistently above 10, ranging from 13.89 for ADF to 19.54 for CP in cross-validation and from 12.18 for CF to 16.42 for CP in prediction.