# Multiblock Analysis Applied to TD-NMR of Butters and Related Products
## 3 Results and Discussion
### Multi Block Calibrations  
Table 2 shows that better results are achieved using T\({}_{\rm 1L}\) and T\({}_{\rm 1S}\) simultaneously. All standard errors are less than 1%. The best results are obtained using the SO-PLS model at 6 \({}^{\circ}\)C, which presents a SEP of 0.68% and a bias almost null. This result is very satisfactory compared to those reported in the literature using the T2 signal for the fat content estimation: 3.1% in [28], from 2.7% to 4.4% in [13], from 0.45% to 0.84% in [9] and 1.2% in [8]. The repeatability error is 0.32%, which is almost two times lower than the repeatability error achieved using the standard Soxhlet method in [29]. The SO-CovSel model \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline  & T \(\,\)C\(\mathbf{\theta}\) & \(\mathbf{\mu}\)\(\mathbf{\lambda}\)\(\mathbf{T}_{\rm 1L}\)\(\mathbf{T}_{\rm 1S}\) & \(\mathbf{RMSECV}\) (\(\mathbf{\psi}\)) & \(\mathbf{R}_{\rm 2}^{2}\) & \(\mathbf{RMSECV}\) (\(\mathbf{\psi}\)) & \(\mathbf{R}_{\rm 2V}^{2}\) & \(\mathbf{RMSEP}\) (\%) & \(\mathbf{SEP}\)(\%) & \(\mathbf{Bias}\) (\%) & \(\mathbf{\sigma}_{\rm MP}\) (\%) \\ \hline \multirow{4}{*}{**T\({}_{\rm 1L}\)**} & PLS & 6 & 1.05 & 0.98 & 1.33 & 0.97 & 1.15 & 1.14 & \(-\)0.18 & 0.55 \\  & 15 & 7 & 1.12 & 0.98 & 1.32 & 0.97 & 1.29 & 1.24 & \(-\)0.36 & 0.61 \\ \cline{2-11}  & CovSel & 6 & 7 & 1.00 & 0.98 & 1.33 & 0.97 & 1.22 & 1.20 & \(-\)0.21 & 0.63 \\  & 15 & 8 & 1.11 & 0.98 & 1.32 & 0.97 & 1.33 & 1.28 & \(-\)0.37 & 0.73 \\ \hline \multirow{4}{*}{**T\({}_{\rm 1S}\)**} & PLS & 6 & 2 & 4.60 & 0.61 & 5.01 & 0.54 & 4.61 & 4.50 & 1.01 & 0.60 \\  & 15 & 2 & 3.91 & 0.71 & 4.31 & 0.66 & 5.20 & 5.20 & 0.22 & 0.67 \\ \cline{2-11}  & CovSel & 6 & 2 & 4.64 & 0.60 & 5.03 & 0.53 & 4.60 & 4.53 & 0.83 & 0.61 \\  & 15 & 2 & 3.93 & 0.71 & 4.30 & 0.66 & 5.27 & 5.27 & 0.17 & 0.69 \\ \hline \multirow{2}{*}{SO–PLS} & 6 & 61 & 0.77 & 1.00 & 0.96 & 0.99 & 0.68 & 0.68 & \(-\)0.04 & 0.32 \\  & 15 & 72 & 0.81 & 0.99 & 1.11 & 0.99 & 1.00 & 0.95 & \(-\)0.32 & 0.47 \\ \hline \multirow{2}{*}{SO–CovSel} & 6 & 71 & 0.79 & 0.99 & 1.05 & 0.99 & 0.77 & 0.77 & \(-\)0.08 & 0.41 \\  & 15 & 81 & 0.89 & 0.99 & 1.16 & 0.99 & 0.92 & 0.89 & \(-\)0.23 & 0.45 \\ \hline \end{tabular}
\end{table} 
Table 2: Figures of merit of the models at the two different temperatures. \(R_{\rm 2}^{2}\) are the square correlation coefficients between actual and predicted values, \(\sigma_{\rm MP}\) is the standard deviation of repeatability calculated on the triplicates. #LV is the number of variables used in the models. at 6 \({}^{\circ}\)C also gave good results. The SO-PLS model at 15 \({}^{\circ}\)C is much worse than at 6 \({}^{\circ}\)C, with a SEP of 0.95%, a bias of \(-\)0.32% and a repeatability error of 0.47%. The SO-CovSel at 15 \({}^{\circ}\)C performs slightly better, with a SEP of 0.89%, a bias of \(-\)0.23% and a repeatability error of 0.45%. It is remarkable to mention that calibration models using T\({}_{\rm{IT}}\) (T\({}_{\rm{IT}}\) = T\({}_{\rm{IL}}\) + T\({}_{\rm{IS}}\)) were carried out and gave errors of about 4% (data not shown). Therefore, the use of SO-PLS and SO-CovSel combining the two signals, T\({}_{\rm{IL}}\) and T\({}_{\rm{IS}}\), in a fusion process presents a good alternative to quantify fat content in butter-related products. Figure 3 shows the values of _Fw_ predicted by the different multiblock models as a function of the _Fw_ values measured by the reference method. Figure 3a shows the great results of SO-PLS at 6 \({}^{\circ}\)C. It can be seen that each of the three replicates is well predicted. Only one replicate of the margarine class is significantly underestimated. In Figure 3b it can be observed that the predictions of SO-CovSel at 6 \({}^{\circ}\)C present approximately the same behavior. In addition to the margarine sample, already poorly predicted by SO-PLS, a group of three replicates of a concentrated fat was underestimated. In Figure 3c the effect of dispersion's increase in the SO-PLS predictions, mainly for concentrated fat, is observed.