3.2.1. Model Results

The CV and validation results of the five models developed for each category of FAs in the first step are shown in Table 5.



LV: latent variables, CV: cross-validation, SNV: standard normal variate, MSC: multiplicative scatter correction, RMSE: root mean square error, SFAs: saturated fatty acids, MUFAs: monounsaturated fatty acids, PUFAs: polyunsaturated fatty acids, ω-3: omega-3 fatty acids, ω-6: omega-6 fatty acids.

In Table 5, all the models developed for the validation of SFAs, MUFAs, PUFAs, ω-3 and ω-6 achieved good results, with R2val values of 0.98, 0.97, 0.96, 0.99 and 0.95; small errors of 0.68, 1.27, 0.85, 0.60 and 0.90; and a low bias value of −0.40, 0.25, −0.49, −0.26, −0.34, respectively.

On the other hand, the results of the five models developed in the second step (CV and external validation) are shown in Table 6.

**Table 6.** Principal statistics calculated for the five models developed in the second step.


LV: latent variables, CV: cross-validation, SNV: standard normal variate, MSC: multiplicative scatter correction,RMSE: root mean square error, SFAs: saturated fatty acids, MUFAs: monounsaturated fatty acids, PUFAs:polyunsaturated fatty acids, ω-3: omega-3 fatty acids, ω-6: omega-6 fatty acids.

In this case (Table 6), models for SFAs, MUFAs, PUFAs and ω-3 achieved good results in the external validation set regarding R<sup>2</sup> (0.98, 0.97, 0.97 and 0.99), RMSEP (0.94%, 1.71%, 1.11% and 0.98%) and bias ( −0.78%, −0.12%, −0.80% and −0.67%), respectively.

Although the ω-6 model achieved good results in terms of R2, the RMSEP and the bias in the validation showed high values: 2.09% and −1.76%, respectively. This is very common in quantitative NIRS and may be due to block effects occurring between measuring conditions [37]. In this case, there are two possible reasons for these effects. (i) The measurement conditions: all the measurements were performed in a laboratory under controlled temperature; therefore, the authors believe they might have a small effect. (ii) The possibly different origins of the oils, including different fish species and different processing industries. Seawater fish, the most consumed type of fish, is naturally low in ω-6 FAs, with most PUFAs resulting from the presence of ω-3 FAs [38,39]. However, as stated in Section 3.1.1, some of the fish oil samples had a higher content of ω-6 FAs. This finding could result from: (i) the presence of vegetable oils mixed with the fish oil, which is plausible if some of the samples came from the canning industry or (ii) the presence of samples from industries where the raw material is freshwater fish. However, the model can be corrected using techniques such as bias and slope correction (BSC) [40]. Applying this

technique to the external test set (Figure 1), the following results are obtained: R<sup>2</sup> = 0.95; RMSEP = 1.09%; bias = −0.05%.

**Figure 1.** Results of the external validation of the PLSR for prediction of ω-6 before (**a**) and after (**b**) bias and slope correction.

These results are in accordance with those of other studies found in the literature that studied the fish oil profile of different matrices. In dietary supplements, Hespanhol et al. [26] and Bekhit et al. [22] obtained similar R<sup>2</sup> values (0.97 and 0.98, respectively) for ω-3 prediction, although their models were less complex, with one and two latent variables (LVs), respectively. The differences in complexity may be due to the fact that in the present study, the fish oil was analyzed directly from by-products with no previous processing (cleaning, refining, etc.), as it was made with dietary supplements. The results from the MUFAs, ω-3 and ω-6 models are similar to those obtained by Karunathilaka et al. [14] in dietary supplements, with RMSEP values of 1.03, 1.42 and 0.93, respectively. In other matrices, such as the model system created by Afseth et al. (using 70 different mixtures of protein, water and oil blends) [41], the error obtained for SFAs, MUFAs and PUFAs was similar to our results, with RMSEP values of 1.20, 0.80 and 0.60, respectively.

The good results achieved by the SFAs, MUFAs, PUFAs and ω-3 models in external validation and in the ω-6 models after the BSC sugges<sup>t</sup> that the models can predict new samples from different fish oil industries. Furthermore, the ω-6 model could be improved with the addition of new samples of different origins, which would correct the bias and slope deviation.

### 3.2.2. Spectral Information of the Models

Raw spectra of the oil mixtures used during the experiment are shown in Figure 2.

Although information is usually hidden in the NIR spectrum, characteristic absorption bands from oil samples are observed in the raw spectra (Figure 2) at 900, 1020, 1200 and 1400 nm. The first two weak peaks observed are around 900 and 1020 nm. The former corresponds to the C-H stretching third overtone of CH3, whereas the latter is a combination of the C-H stretching first overtone and the C-H deformation second overtone, again from CH3 [11]. The first strong peak at 1200 nm is due to the second overtone of the stretching mode of C-H bonds in various chemical groups [42,43]. The second strong peak, localized between 1300 and 1500 nm, is caused by the combination of the stretching and deformation first overtone of C-H in CH, CH2 and CH3 [11].

**Figure 2.** Raw spectra of the oil mixtures used during the experiment.

The loadings corresponding to the first and second latent variables (LV1 and LV2) of the five models developed in the second step, which contain information about all the data used in the experiments, are shown in Figure 3. LV1 retains the greatest amount of variance in most of the models, except for the SFAs model, wherein LV2 retains the most information. The large peaks in the loadings of the models resemble the main peaks of the raw spectra.

NIR absorption peaks related to the FAs information are associated with the vibrations of C-H and CH2 [44]. Although they are usually above 1700 nm in the spectra, where two important regions are located at 1720 and 2143 nm [45], the presence of other bands related to C-H overtones at shorter wavelengths makes possible the measurement of oils with devices whose spectral range covers only wavelengths lower than 1700 nm, as demonstrated by Basri et al. [46].

As can be seen in Figure 3a–e, LV1 and LV2 of all the models show important peaks in the region between 1050 and 1300 nm. This region corresponds to the second overtone of C-H stretching, and it is one of the most important regions to determine FAs with this technology [42–44].

LV1 of PUFAs, ω-3 and ω-6 (Figure 3c–e) and LV2 in all the models (Figure 3a–e) show peaks in the region between 1300 and 1500 nm (Figure 3a,c–e). This absorption region is caused by the combination of the stretching and deformation of the first overtone of C-H in CH, CH2 and CH3 [11].

The increase found in the region between 1600 and 1670 nm can be seen in LV1 of PUFAs, ω-3 and ω-6 (Figure 3c–e) and in LV2 of MUFAs, PUFAs, ω-3 and ω-6 (Figure 3b–e). According to Hourant et al. [47], the wavelengths between 1600 and 1780 nm are related to the first overtone of the C-H group in -CH3, and the peak that is starting to grow may correspond with the first part of that region. On the contrary, LV1 of SFAs and MUFAs (Figure 3a,b) and LV2 of SFAs (Figure 3a) present a peak with a maximum around 1600 nm. This region of the spectra is related to the C-H first overtone of = CH2, which acquires its maximum at 1620 nm [48].

**Figure 3.** LV1 and LV2 of the second-step models. (**<sup>a</sup>**,**b**) SFAs, (**<sup>c</sup>**,**d**) MUFAs, (**<sup>e</sup>**,**f**) PUFAs, (**g**,**h**) ω-3, (**i**,**j**) ω-6.

The similarity in shape between PUFAs and ω-3 loadings suggests that they are closely related (Figure 3c,d). ω-6 loadings also present peaks at similar wavelengths (Figure 3e) as PUFAs and ω-3 loadings. This result was expected because fish PUFAs are mostly composed of ω-3 and ω-6 FAs [49], as can be seen in Table 3.
