Composition assessment of sous vide beef meat by near-infrared spectroscopy based on compact spectrophotometers, multivariate regression, and jack-knife variable selection

Composition assessment of sous vide beef meat by near-infrared spectroscopy based on compact spectrophotometers, multivariate regression, and jack-knife variable selection | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Composition assessment of sous vide beef meat by near-infrared spectroscopy based on compact spectrophotometers, multivariate regression, and jack-knife variable selection Débora Rezende FERREIRA, Edimar Aparecida Filomeno FONTES, Celio PASQUINI, and 4 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7776526/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 10 You are reading this latest preprint version Abstract ‘Sous vide’ is a cooking process that uses long time and low temperatures, affecting the quality and composition of the product. This study aimed to develop and validate prediction models for the proximate composition of sous vide beef tenderloin using near-infrared reflectance spectroscopy (NIRS) and to compare the performance of two portable NIR spectrometers. Original spectra were pretreated using the Standard Normal Variate (SNV) method, followed by the 1st derivative. Models using partial least squares regression (PLS) were constructed with all spectral variables, and after the jack-knife algorithm performed wavelength selection. The centesimal composition of the ground samples was accurately determined by the models, except for the carbohydrate content. The prediction errors resulting from external validation (RMSEP) for the InnoSpectra and NeoSpectra evaluated compact instruments were, respectively, 0.92% and 0.65% for moisture, 0.72% and 0.93% for fat, 0.93% and 0.60% for protein, and 0.12% and 0.03% for ash. Conversely, poor results were obtained for samples where readings were taken from whole roasters with or without packaging. A new method for assessing the quality and usefulness of multivariate models was proposed based on RMSEP and comparing the distributions of the reference and validation data. The NIRS-based method is fast, requires simple sample preparation, does not require the use of chemicals, and employs low-cost instruments. sous vide meat near-infrared spectroscopy chemometrics variable selection quality characteristics Figures Figure 1 Figure 2 Figure 3 1. Introduction 'Sous vide' is a French technique, meaning 'under vacuum' (Baldwin, 2012 ), characterized by cooking vacuum-sealed food for long periods at low temperatures (Kathuria et al., 2022 ). Food is cooked in thermostable packaging, followed by cooling and storage at low temperatures (Yang et al., 2020 ). This technique has been used for various raw materials, such as fruits, vegetables, seafood, and meats (Kathuria et al., 2022 ). Several studies demonstrate the advantages of applying the 'sous vide' technique for meats and meat products, including reduced cooking loss and improved nutrient retention. (Baldwin,2012; Joung et al. 2018; Zhu et al. 2018; Ismail et al. 2019; Bıyıklı et al. 2020; Lee et al. 2021). These advantages are reflected in the proximate composition of the processed product (Roldan et al., 2014 ). The chemical composition of 'sous vide' beef tenderloins is predominantly composed of water, protein, lipids, and ash (NEPA, 2011 ). Understanding the product's composition is crucial for meeting the requirements of official inspection and regulatory bodies (USDA, 2025;BRASIL, 2018), as well as ensuring the contracted quality standard demanded by customers (Weeranantanaphan et al., 2011 ). According to the Food and Drug Administration (FDA), which sets the rules for nutritional labeling in the United States, detailed in the Code of Federal Regulations (CFR), the content of naturally occurring nutrients in food must be at least 80% of the declared value on the label (USDA, 2025). A similar percentage variation is established by Brazilian legislation, through Collegiate Board Resolution (RDC) N° 429 of the National Health Surveillance Agency, which allows, for inspection purposes, up to 20% above the declared value on the label for various components, including fat and carbohydrate, and the same percentage below for protein and minerals (BRASIL, 2020). Considering legal tolerance, the food industry typically creates nutritional tables during the development of a new product and often does not account for possible variations in processed raw materials, especially those of animal origin. Conversely, consumers are increasingly concerned about food composition, and nutritional labeling is a key source of information that influences their purchasing decisions (Duarte et al., 2021 ). Thus, accurate information is essential for consumers to make informed purchasing decisions (Weeranantanaphan et al., 2011 ). North American legislation mandates that the proximate composition of a product be determined using official AOAC analytical methods or other reliable and appropriate methods (USDA, 2025). Although RDC N° 429 (BRASIL, 2020). permits the use of direct and indirect calculations based on the constituents used in product formulation to determine its proximate composition, the most precise methodology for this determination is laboratory analysis. However, given the existing legal requirements that allow for a 20% variation from the declared value and the cost of establishing and maintaining an in-house laboratory, many industries opt to outsource their physical-chemical analyses. These analyses are often performed only during the development of a new product or when facing an official audit. Another challenge in using laboratory analysis to determine the proximate composition of food is the requirement for exclusive use of official reference methods. Most of these methods are not suitable for meeting the demands of production in a global market, as they require complex sample preparation, long processing times, and are expensive and polluting (Prieto et al., 2017a ). Consequently, the results are time-consuming, rendering official methods inadequate for industrial use because they do not provide the rapid and reproducible results necessary to continuously and representatively certify product quality (Cozzolino et al., 2011 ). Therefore, to meet practical industrial demands, instrumental methods must be objective, fast, economical, and precise. Near-infrared (NIR) spectroscopy possesses these characteristics and has proven highly suitable for food products (Aleixandre-Tudó et al., 2020 ). This technique emerges as an alternative to traditional analytical methods for determining various properties or constituents of agricultural matrices (Williams & Sobering, 1993 ). NIRS is a widely recognized technique, based on the interaction of electromagnetic radiation in the wavelength range of 750 to 2500 nm with the vibrational bonds of the molecular species constituting various types of samples (Pasquini, 2018 ). NIR radiation interacts with matter in various ways, with the absorption of radiation by the sample's constituents being the most relevant source of information for analytical applications. This is because the interaction of NIR radiation with the substances present in the sample stimulates vibrational energy transitions in the chemical bonds between atoms, generating absorption spectra that provide qualitative and quantitative analytical information associated with various sample properties (Pasquini, 2003 ). Near-infrared spectroscopy offers advantages such as speed, minimal or no sample preparation, ease of use (Cozzolino et al., 2011 ), ecological friendliness, the ability to quantify various components from measurements taken in a few seconds, and applicability to molecules containing CH, NH, SH, or OH bonds (Qu et al., 2015 ). Disadvantages include the difficulty in assigning chemical groups, as information is often obscured in complex spectra characterized by weak signals (Olinger & Griffiths, 1988 ), broad bands, and severe overlaps (Porep et al., 2015 ). Other sources of variability, such as instrumental noise, scattering, environmental effects, and sample heterogeneity, also contribute to the complexity of a NIR spectrum (Dos Santos et al., 2017 ). To remove uninformative sources of variability and enhance spectral characteristics, NIR spectral data undergo some form of pre-treatment before being used for qualitative or quantitative purposes. The primary source of this type of variability in solid samples originates from the scattering of radiation by pulverized solid samples (Pasquini, 2018 ). Analytical information from pre-treated NIR spectra is extracted using chemometric tools for the appropriate multivariate analysis of the data, enabling both qualitative and quantitative purposes. Chemometrics has enabled significant advances in applying spectroscopic techniques to food and other commodity analysis (Cozzolino et al., 2011 ). Principal Component Analysis (PCA) and Partial Least Squares (PLS) regression are commonly used multivariate analytical techniques for exploratory analysis and regression of multivariate data. Considering regression models, after the calibration process is complete, the precision and robustness of the model must be tested with an independent sample set (validation set) (Ziegel, 2004 ). The predictive capacity of multivariate models is typically evaluated by calculating the error associated with their estimates. The determination of the Root Mean Square Error of Prediction (RMSEP) and/or the Standard Error of Prediction (SEP) is an indicator of prediction accuracy and is the most common way to assess the quality of regression models (Bro et al., 2005 ). Continuous advancements in chemometric methods, technology, and instrumentation have enabled NIR spectroscopy to achieve increasingly robust models for identification and quantification. NIR spectrometers basically include a light source, a wavelength selector, a sample detector, an optical detector, and a data processing/analysis system (Pasquini, 2018 ; Prieto et al., 2017a ).The development of compact spectrophotometers operating in the near-infrared region has made it possible to monitor, characterize, and identify products, as well as reduce the time and cost of analyses in the pharmaceutical and food industries, for example (Savoia et al., 2020 ). The advancement of the NIR technique has expanded its versatility, enabling the replacement of some slow, expensive, and labor-intensive instrumental analysis methods with vibrational spectrophotometric methods. This technique can perform real-time analyses at the production site with a similar level of precision and accuracy (Dos Santos et al., 2017 ). This versatility was reaffirmed by Patel et al. ( 2021 ) when they highlighted portable NIR instruments as a fast and practical option in meat processing plants for collecting spectra and developing prediction models, and by Porep et al. ( 2015 ), who stated that it is a suitable technique for implementation as an analytical tool in industrial processing. Therefore, the objective of this study was to compare the performance of two low-cost portable NIR spectrometers for the construction and validation of regression models aimed at determining the proximate composition of 'sous vide' beef tenderloins during their industrial processing, on an individualized basis, with an evaluation of the possibility of printing the nutritional table, displaying its composition in a more representative way. 2. Material and methods 2.1 Preparation of packaged beef tenderloins Chilled beef tenderloin cuts (temperature between 0 and 4°C, pH between 5.7 and 5.8), sourced from a licensed slaughterhouse inspected by the Brazilian Federal Inspection Service (SIF), were transported in refrigerated trucks and kept in a cold chamber at 4°C until sample preparation. In a tumbler, ice water (0 and 4°C), modified cassava starch, maltodextrin, salt, and black pepper were added to form a brine (temperature between 0 and 4°C). The beef tenderloin cuts were added to the tumbler after the ingredients were homogenized and were tumbled for 40 minutes to incorporate the brine. Subsequently, the cuts were stored in a cold chamber at 4°C until they reached a temperature between 10 and 12°C. They were then rolled, wrapped in PVC plastic film, and frozen in cold chambers at -12°C. After the cuts reached temperatures between − 2 and − 5°C, the plastic film was removed, and transverse cuts (diameters between 57 and 60 mm and thickness between 38 and 40 mm) were made manually. These were individually weighed on a digital scale, yielding a mass of (125 ± 5) g, which allowed for approximately thirteen rounds / slices to be obtained from each piece, known as tenderloin. The tenderloin was seared on a hot plate (approximately 215°C) to achieve a golden-brown surface color. The product reached an approximate surface temperature of 40°C and was then stored in a cold chamber at 4°C before being packaged. Once chilled (between 4 and 10°C), they were placed in thermoformed polystyrene trays and vacuum-sealed (Multivac). The product was then subjected to cooking at 58°C for 32 minutes, cooled to 4°C, and frozen in a nitrogen tunnel at -18°C. A set of 132 samples of 'sous vide' beef tenderloins was used for the construction and validation of the regression models. The sample set had its composition identified and quantified by reference methods, representing the samples industrially processed between August 2023 and May 2024. The chilled beef tenderloin was sampled according to their production by the industry, with 4 samples being collected per production batch. These different times made it possible to cover greater variability in the composition of the raw material in order to build a more accurate predictive model. 2.2. Description of the portable NIR spectrophotometers Two spectrophotometers were used throughout this study: the InnoSpectra (Texas Instruments Inc.) and the NeoSpectra (Si-Ware, Egypt). These instruments are portable and compact, capable of monitoring the near-infrared spectral ranges of 921–1683nm and 1350–2550 nm, respectively, with a nominal resolution of 10 nm. The NeoSpectra consists of an illumination unit containing three tungsten filament sources and an optical coupling system, designed for reflection measurements. The instrument is based on a complete Michelson interferometer implemented on a MEMS chip. The manufacturer reports a signal-to-noise ratio (SNR) of 2,000 at a wavelength of 2350 nm with a 2 s integration time. In turn, the manufacturer of the InnoSpectra reports an SNR of 6000:1 and a scan time of 0.3 seconds, with Grade-MEMS technology. The instruments were connected to the USB port of a notebook (Dell Technologies, 16 GB DDR4, 512 GB SSD) and powered on for 30 minutes to allow for stabilization before the measurements began. The radiation source was activated only during the acquisition of the spectra (Fig. 1 ). 2.3. Protocol for obtaining sample spectra The acquisition of representative NIR spectra of the samples was performed in three ways: on the whole tenderloin covered by its packaging; on the whole tenderloin covered by a glass Petri dish (diameter of 7.2 cm and height of 1.3 cm); and with the ground tenderloin placed in the glass Petri dish, filling its entire extension up to its maximum height. For the measurements of the whole product, its original packaging was opened, and its surface was gently blotted with a paper towel to standardize the surface moisture. The part of the packaging without graphic printing was placed over the product, and the equipment was positioned to obtain the spectra. A Spectralon® reference tile (corresponding to 100% reflection of NIR radiation) covered by the product packaging or by the glass of the Petri dish was used for spectral reference measurements necessary for calculating the reflectance spectra. The reference was measured before each sample was taken. The readings on the whole tenderloin, covered by a glass Petri dish, were performed in the same manner as the measurements of the product in its packaging, with the only difference being the replacement of the plastic packaging with the glass Petri dish. For the ground product, a domestic food processor (Walita Philips, 600W) was used, where the product, cut into approximately 1cm slices, was minced for 3 minutes at speed 2 of the equipment. The resulting ground meat mass was spread evenly on a 7.2 cm diameter glass Petri dish, avoiding the presence of air bubbles, to produce a layer with a thickness of 1.3 cm. With the dish covered, it was turned upside down and the spectrophotometer was placed on the original bottom of the dish to perform the readings. The Spectralon (reference corresponding to 100% reflection of NIR radiation) covered by the lid of the Petri dish was used for spectral reference measurements, which are necessary for calculating the reflectance spectra. The samples in all their forms were measured in quintuplicate, obtaining a representative average spectrum with an improved signal-to-noise ratio. Figure 2 shows, for a ground sample, the position of the reading points. The spectra of the samples were obtained at ambient temperature (25 ± 1°C) over a period of thirteen days at the GAES Chemistry Laboratory (Group for Analysis and Education for Sustainability) at the Federal University of Viçosa. Three samples were measured five times according to the procedure described above to estimate the repeatability of the validated NIR models showing the best performance. 2.4. Proximate composition The determination of total water (ISO 1442: 2023 (E), 2023 ), fixed mineral residue (ash) (ISO 936: 1998 (E), 1998 ), total fats (NMKL 181, 2005 ), and nitrogen content (ISO 1871: 2009 (E), 2009 ) were performed according to official methods for the analysis of products of animal origin. The obtained nitrogen value was multiplied by 6.25 to determine the protein content (Brasil, 2022 ). Carbohydrate content was calculated by difference from the proximate composition. 2.5 Multivariate analysis and construction of regression models The obtained spectral datasets were processed using the chemometric software Unscrambler 10.5. Preliminary regression models based on Partial Least Squares (PLS) Regression were constructed with all samples in the set and for each of the studied properties, aiming to estimate the levels of protein, water, fat, ash, and carbohydrates present in the samples. With preliminary models constructed, the Kennard-Stone algorithm (Kennard & Stone, 1969 ) was used to select the calibration set (typically comprising 90 samples) and the validation set (comprising 42 samples). This procedure guarantees the selection of a uniform and representative subset (of calibration) of the samples. The spectra were pre-treated using Standard Normal Variate (SNV) followed by the 1st derivative calculated using the Savitzky-Golay algorithm, employing 11 points in the smoothing window and a 2nd -degree polynomial fit, to minimize the effect of radiation scattering, highlighting the relevant information. Models were constructed using the entire useful spectral range of the spectrophotometers and using only the variables selected by the jack-knife algorithm available in the Unscrambler 10.5 software. The objective of the variable selection performed by this algorithm is to use in the regression process only the variables that produce, in a first analysis, stable regression coefficients identified during the cross-validation (employing 20 subsets of samples randomly selected) process that accompanies the construction of the regression models (Esbensen & Swarbrick, 2018 ). 3. Results and discussion 3.1. Spectral data The original average spectra obtained from the five readings of the intact tenderloins, using both spectrophotometers, with and without packaging, and for the ground samples, are shown in Fig. 3 (A and C). For analysis by conventional methods, the product must be grounded and homogenized. This implies that in developing the regression models, the NIR spectra of the intact product (with and without packaging) must be compared with the results of analyses performed using traditional methods on the ground product. It should be anticipated that the spectra of the intact samples, despite efforts to minimize the effect of the packaging and the glass Petri dish, better reflect their surface composition than their average composition as determined by the reference methods. The intact product undergoes a searing step, which results in a darkening of its surface, primarily due to the Maillard reaction. Thus, the spectra obtained under these conditions are not representative of the sample as a whole (bulk). The obtained spectra were transformed to minimize the effects of radiation scattering by applying the standard normal variate (SNV) followed by a 1st derivative calculated using the Savitzky-Golay algorithm with 11 points in the smoothing window and a 2nd degree polynomial fit. Figure 3 shows the spectra before (A and C) and after the pre-treatments (B and D) for the ground "sous vide" tenderloin samples. 3.2 Sample quality characteristics. The results of the proximate composition analysis of the 'sous vide' beef tenderloins obtained by the reference method (Table 1 ) are close to those listed in the Brazilian Food Composition Table (NEPA, 2011 ) for raw beef tenderloin, which averages 71.9% water, 21.6% protein, and 5.6% fat. A study by Hocquette et al. ( 2018 ) mentions that beef contains 21% to 31% protein, which indicates that the values found in the present study fall within these ranges. Table 1 Mean values (± standard deviation) and results for moisture, ash, protein, fat, and carbohydrate content of the 132 ground 'sous vide' beef tenderloin samples obtained by reference methods statistcs water content (%) ash (%) protein (%) fat (%) carbohydrates (%) mean ± std deviation 68.96 ± 1.76 1.77 ± 0.19 24.14 ± 1.44 3.99 ± 1.78 1.14 ± 1.14 max 72.70 2.68 28.31 11.29 5.74 min 63.29 1.47 20.78 0.45 0.01 range 9.41 1.20 7.53 10.84 5.73 variance 3.10 0.04 2.08 3.18 1.31 Mitsumoto et al. ( 1991 ) Compared the quality of beef cuts using near-infrared (NIR) spectroscopy with reflectance, transmittance, and a fiber optic probe. The mean values found by the authors for protein, water, and fat were similar to those of the 'sous vide' beef tenderloin, at 18.8%, 69.7%, and 8.8%, respectively. The most significant inverse correlations are observed between the protein and carbohydrates content (r = -0.5403) and fat and water (r = -0.7556) (Table 2 ), with the latter exhibiting the highest correlation coefficient among the property values determined by the reference methods. Table 2 Correlation analysis between the water, ash, protein, fat, and carbohydrate content of 'sous vide' beef tenderloins using values determined by reference methods statistcs water content (%) ash (%) protein (%) fat (%) carbohydrate (%) water content (%) 1 0.3122 -0.2801 − 0.7556 − 0.0611 ash (%) 0.3122 1 0.4413 − 0.2597 0.3103 protein (%) − 0.2801 − 0.4413 1 − 0.1369 − 0.5403 fat (%) − 0.7556 − 0.2597 − 0.1369 1 − 0.1790 carbohydrates (%) − 0.0611 0.3103 − 0.5403 − 0.1790 1 3.3 Elaboration, optimization, and validation of regression models. Preliminary PLS regression models were developed using the complete pre-treated spectra obtained from the two instruments for each of the three sample measurement forms. The models constructed with the spectral data set from the intact samples, both with and without packaging for both instruments, did not yield satisfactory results. Coefficients of determination (R²) below 0.300 and high root mean square error of cross-validation (RMSECV) values indicate that the representativeness of the spectra, obtained predominantly from the surface of the intact samples, is insufficient to establish a correlation between the spectral data and their properties, which are inferred from portions of the ground and homogenized samples processed by conventional methods. Conversely, the results for the preliminary models built with the spectra from the ground and homogenized samples for both instruments show satisfactory R² and RMSECV values for all modeled parameters, except for carbohydrate content. Therefore, the results presented below pertain only to the models constructed with spectra from the ground samples. The preliminary models were refined by eliminating anomalous samples (outliers) from the data sets, using leverage, the spectral residuals of the samples, and the X-Y relation of anomalous samples (X-Y relation outliers)(Esbensen & Swarbrick, 2018 ). Subsequently, the remaining samples were divided using the Kennard-Stone algorithm (Kennard & Stone, 1969 ) to produce a calibration set containing 90 samples and an external validation set constituted of the remaining samples. Tables 3 and 4 present the preliminary calibration and validation results for the PLS models developed to determine the protein, fat, water, ash, and carbohydrate content using all spectral variables from the full spectral range accessible by both instruments. The same tables also display the results obtained using only the variables selected by the jack-knife algorithm in Unscrambler 10.5 software, which was used for chemometric data treatment. This algorithm analyzes the behavior of the regression coefficients for all variables used in the PLS model construction in relation to their stability during the cross-validation process. In this study, segmented cross-validation was employed with 20 groups, each containing 4 to 5 randomly selected samples. The behavior of the 20 sets of regression coefficients was statistically evaluated, and spectral variables associated with highly unstable regression coefficients were eliminated. The selected variables for each modeled property and for each of the two instruments are shown in Tables S1 and S2 in the supplementary material. New models were constructed using the selected variables, and the results are presented in Tables 3 and 4 . As observed in Tables 3 and 4 , the models built with the selected variables perform better than those using all variables. The RMSECV values for the models with selected variables are invariably better than those obtained with all variables. A notable point is the reduction in the number of PLS factors required by the models with selected variables, as seen in all models except for the water content model from the InnoSpectra data, which increased from 4 to 6, and the ash content model from the NeoSpectra data, which remained at 3. These results indicate that models based on selected variables are generally simpler, more robust, and utilize the most relevant spectral information for each modeled parameter. The results for the models constructed with or without variable selection for determining carbohydrate content showed unsatisfactory performance. This result is likely due to the low carbohydrate content and its non-homogeneous distribution on the sample surface. Furthermore, its content is determined with lower precision and accuracy, as it is calculated indirectly by subtracting the sum of the other constituents. The ash content of the samples refers to inorganic constituents present in the meat that should not exhibit spectral characteristics in the near-infrared (NIR) region. However, models for determining ash content exhibit acceptable performance. This performance likely results from the indirect association of other organic sample constituents with this property. However, due to the characteristics of this property, the results should be considered with caution and must be submitted to further evaluation. The repeatability of the predicted results determined by the validated models employing jack-knife selection of variables was evaluated by the mean estimated standard deviation of the results obtained by 3 samples measured in quintuplicate as, 0.46, 0.43%; 0.52, 0.45%; 0.39, 0.35% and 0.05, 0.02% for protein, water, fat and ash contents and models obtained using the NeoSpectra and InnoSpectra, respectively. The repeatability of the results obtained by the NIR method is very good, shows values lower than the RMSEP of the validated models, and is, in general, somewhat better for the InnoSpectra instrument. Figures S1 -S4 in the supplementary material present the cross-validation results for each instrument during model construction for water, fat, ash, and protein content, using all spectral variables, selected variables, and the validation of models with variable selection. The models built with the selected variables were successfully validated, yielding promising root mean square errors of prediction (RMSEP) for determining the main quality characteristics of the "sous vide" samples, as shown in Tables 3 and 4 . Table 3 Results of the full spectrum models, with Jack-Knife variable selection, and validated (InnoSpectra) with external samples, developed for the components of the ground 'sous vide' beef tenderloin model full spectrum selected variables JK validation (with variable selection) Nc F R² RMSECV (%) BIAS(%) Nc F R² RMSECV (%) BIAS (%) Nv F R² RMSEP (%) BIAS(%) Protein 90 8 0.559 0.94 0 90 6 0.598 0.88 0.01 39 6 0.330 0.93 -0.15 Water content 90 4 0.706 0.94 0 90 6 0.856 0.67 0 42 6 0.517 0.92 0.09 Fat 90 3 0.785 0.84 0 90 2 0.795 0.82 0 42 2 0.710 0.72 0.05 Ash 90 10 0.428 0.13 0 90 4 0.589 0.11 0 38 4 0.453 0.12 0 Carboydrates 132 1 NA 1.2 0 132 1 0.002 1.15 0 * Nc = number of samples / Nv = number of validation samples / F = number of factors / R² = coefficient of determination / RMSECV = cross-validation error / BIAS = systematic deviation / RMSEP = prediction error from external validation. Table 4 Results of the full spectrum models, with Jack-Knife variable selection, and validated (NeoSpectra ) with external samples, developed for the components of the ground 'sous vide' beef tenderloin model full spectrum selected variables JK validation (with variable selection) Nc F R² RMSECV (%) BIAS (%) Nc F R² RMSECV (%) BIAS (%) Nv F R² RMSEP (%) BIAS(%) Protein 90 4 0.440 1.11 0.01 90 3 0.610 0.93 0 39 3 0.259 0.96 -0.42 Water content 90 5 0.865 0.65 0 90 4 0.879 0.61 0.01 40 4 0.784 0.69 -0.19 Fat 90 3 0.884 0.59 0 90 2 0.895 0.56 0 42 2 0.668 0.76 0.11 Ash 90 3 0.402 0.14 0 90 3 0.450 0.14 0 42 3 0.305 0.13 -0.02 Carboydrates 132 1 NA 1.11 0 144 1 0.006 1.14 0 * Nc = number of calibration samples / Nv = number of validation samples / F = number of factors / R² = coefficient of determination / RMSECV = cross-validation error / BIAS = systematic deviation / RMSEP = prediction error from external validation. 3.4. Considerations on the evaluation of model quality Several criteria for classifying the quality of multivariate models are described in the literature. The Standard Practices for Infrared Multivariate Quantitative Analysis (ASTM) has issued two guides recommending best practices for quantitative and qualitative multivariate analysis based on NIRS (ASTM E1655-05, 2012 ; ASTM E1790-04, 2016). For multivariate regression, these ASTM guides do not recommend the coefficient of determination (R²) as a model quality criterion, as it is heavily dependent on the data distribution. That is, R² depends on the variance of the concentration or reference values. Despite this, it is very common to find it expressed in NIR spectroscopy literature as a measure of the quality of multivariate models. Many of these present comparison plots between the values predicted by an NIR model and the reference values, where most values are, for example, close to the upper limit, while a few are near the lower limit, indicating an asymmetric distribution. In such cases, R² can approach 1, being considered excellent. However, if the few lower values are removed, R² would assume much smaller values (Pasquini, 2018 ). The R² values obtained in the validation of the models built in this work ranged from 0.258 to 0.784 for the protein and water content models, respectively, using data from NeoSpectra, and from 0.330 to 0.710 for the protein and fat content models, respectively, using InnoSpectra. It is noted that the protein content values are distributed in a narrow range in the calibration set and an even narrower range in the validation set. Considering the standard deviation of the reference method for this parameter, it is evident that the R² value could not reach much higher values. However, the RMSEP of the models shows values of 0.93% and 0.96% for protein content obtained with models from the NeoSpectra and InnoSpectra data, respectively, despite R² values that are much lower than 1. These error values are acceptable for expressing product quality within Brazilian labeling standards. The agricultural field, including food science, frequently uses the ratio of performance to deviation (RPD) as a quality criterion for a model (Prieto et al., 2017b ; Leone et al., 2012). Its calculation considers the ratio between the model's validation error (RMSEP) and the standard deviation of the reference values. However, this quality criterion is susceptible to the presence of outliers in the validation set, which can significantly affect the calculation of the standard deviation of the reference data. Thus, this criterion is also subject to data distribution. The RPD-based criterion advocates values greater than 2 for models of satisfactory quality (Prieto et al., 2017b ; Leone et al., 2012). To minimize the effect of outliers on the calculation of a criterion similar to RPD, the ratio of performance to interquartile (RPIQ, the ratio between performance and interquartile) was proposed (Bellon-Maurel et al., 2010 ; Olivieri, 2018). This parameter is less susceptible to data distribution, as the presence of outliers has a lesser influence on it. However, the literature does not mention a consensus critical value by which models could be considered of adequate quality. Thus, RPIQ is more useful for comparing the performance of different models than for quantifying their absolute quality. Based on the foregoing considerations, it is suggested that the RMSEP value, analyzed according to the accuracy required to attest product quality, be preferentially used as a quality criterion that is less dependent on the reference data distribution and more suitable for real-world situations where this distribution does not always favor the calculation of R² or RPD. Thus, for example, if this work were repeated using the InnoSpectra equipment, the average agreement between the reference method and the model should be 0.92% for moisture, 0.72% for fat, 0.93% for protein, and 0.12% for ash (Table 3 ), which are adequate values to express the product's quality. On the other hand, to verify if the predicted values from the models maintain the original distribution of the reference data, we propose observing the variation in the maximum, minimum, median, and quartiles 1 and 3 between the results from the reference methods and those from the model validation. The criterion for verifying the distribution of results considers the distributions of the reference and validation results to be indistinct if the differences between the values are less than the model's RMSEP, considering that RMSEP values can be accepted to estimate quality parameters with the necessary accuracy. Tables 5 and 6 show the results of the evaluation of the differences between the quartiles for each of the models and for the InnoSpectra and NeoSpectra equipment, respectively. Adopting this criterion, it is observed that for the InnoSpectra instrument, there is a distortion of the distribution for high predicted values of protein content. For fat content, the validation results using this equipment show a significant distortion in the distribution of predicted values relative to the reference values, with most of the differences being greater than the model's RMSEP. Regarding the NeoSpectra instrument, the analysis of the distribution behavior of the reference results compared to the validation results shows minor differences for the models built for protein and fat determination, allowing for the attestation of the quality of all models built for the four quality parameters. In other words, with this equipment, acceptable prediction errors are obtained to attest to the product's quality, and simultaneously, the validation results of the models maintain their original distribution. The quality analysis of the models proposed in this work is not based on a single parameter, such as R², RPD, or RPIQ, to determine the model's quality. It employs the results concerning the accuracy of the models (RMSEP) and, if these are satisfactory for the problem at hand, analyzes the non-parametric distribution of the results obtained by the reference method compared to those obtained by the model. The procedure is effective as it considers aspects inherent to the accuracy requirements of the model (RMSEP) while maintaining attention to the distribution of the validation results. Table 5 Difference related to the distribution of results obtained by reference methods and by the validation of optimized models built with spectral data from the InnoSpectra equipment for ground samples reference/validation values model validation results with JK variable selection difference water content (%) ash (%) protein (%) fat (%) water content (%) ash (%) protein (%) fat (%) Δwater content (%) Δash (%) Δprotein (%) Δfat (%) max 72.2 2.2 27.6 6.6 71.6 2.1 25.9 7.8 0.6 0.1 1.7 -1.2 min 66.4 1.5 21.8 0.5 66.3 1.5 22.5 1.5 0.1 0.0 -0.7 -1.0 median 69.3 1.7 24.0 3.3 69.7 1.7 24.0 3.5 -0.4 0.0 0.0 -0.1 Q1 68.9 1.6 23.5 2.5 68.6 1.7 23.5 2.8 0.3 -0.1 0.0 -0.3 Q3 70.2 1.8 24.8 4.5 70.5 1.8 24.7 4.2 -0.3 0.0 0.1 0.3 RMSEP 0.92 0.12 0.93 0.72 RPD 1.44 1.42 1.23 1.88 RPIQ 1.41 1.60 1.39 2.70 Table 6 Difference related to the distribution of results obtained by reference methods and by the validation of optimized models built with spectral data from the NeoSpectra equipment for ground samples reference/validation values validation results of models with JK variable selection difference water content (%) ash (%) protein (%) fat (%) water content (%) ash (%) protein (%) fat (%) Δwater content (%) Δash (%) Δprotein (%) Δfat (%) max 71.6 2.2 26,9 6.8 71.5 2.0 25.7 6.4 0.1 0.2 1.2 0.3 min 65.2 1.5 22.0 0.5 65.6 1.6 22.9 1.5 -0.4 -0.1 -0.9 -1.0 median 69.4 1.7 24.5 3.3 69.3 1.8 24.2 3.1 0.1 -0.1 0.3 0.2 Q1 68.8 1.6 23.5 2.3 68.4 1.7 23.5 2.6 0.4 -0.1 0.0 -0.3 Q3 70.4 1.8 25.1 4.3 69.9 1.8 24.4 4.3 0.5 0.0 0.7 0.0 RMSEP 0.69 0.13 0.96 0.76 RPD 2.17 0.80 1.16 1.75 RPIQ 2.31 1.54 1.60 2.63 3.5. Comparison of the performance of the InnoSpectra and NeoSpectra equipment Table 7 allows for a comparison of the external validation results for the models built with variables selected by the jack-knife algorithm for both instruments used in this work. Considering only the validation error values (RMSEP), both instruments demonstrated similar and adequate performance in determining the four quality parameters of "sous vide" meat, to express them on the product label. The NeoSpectra shows more accurate results for the model built to determine the water content. This is associated with the spectral information obtained by this instrument, which monitors a broader spectral range, which the InnoSpectra does not access (Wilson et al., 2015 ). Table 7 Results of external validation of the models based on the selection of variables by jack-knife for the InnoSpectra and NeoSpectra equipment validation InnoSpectra validation NeoSpectra Nv F R² RMSEP (%) Bias(%) RPD RPIQ Nv F R 2 RMSEP (%) Bias(%) RPD RPIQ protein 39 6 0.330 0.93 -0.15 1.23 1.39 39 3 0.258 0.96 -0.42 1.16 1.60 water content 40 6 0.517 0.92 0.09 1.44 2.31 42 4 0.784 0.69 -0.19 2.17 2.31 fat 42 2 0.710 0.72 0.05 1.75 2.70 42 2 0.668 0.76 0.11 1.75 2.63 ash 42 4 0.453 0.12 0.00 1.42 1.60 38 3 0.305 0.13 -0.02 0.80 1.54 Nv: number of validation samples; F: number of factors The performances of portable visible NIR (Vis-NIRS), NIRS, and a Micro-NIRS instrument were evaluated by Patel et al. ( 2021 ) by constructing and evaluating prediction models for beef characteristics from spectra obtained directly from its surface. As in the present study, the authors concluded that the prediction performances of the three instruments were similar, although the Micro-NIRS performed better for some characteristics. If RPD or RPIQ values were adopted as the quality criterion for the models, it would indicate that only the models built for determining water and fat content obtained by the InnoSpectra could be accepted based on RPIQ values greater than 2. Likewise, for the NeoSpectra, only these two models would have their quality attested by the RPIQ values, with the water content model also being acceptable based on its RPD. However, adopting the criterion established in this work, which considers the accuracy (RMSEP) sufficient for the intended purpose of the models and the maintenance of the distribution of the predicted values when compared to the distribution of the reference results, only the model for fat and the protein model, considering high contents, obtained with the InnoSpectra would require caution for routine use. The models obtained by the NeoSpectra are deemed adequate according to this quality criterion. Both instruments can operate completely autonomously, utilizing batteries, and allow for the remote transmission of the obtained spectra. However, the cost of the InnoSpectra is about 5 times lower than the cost of the NeoSpectra. 3.6. Comparison with similar results found in literature In assessing the intramuscular fat and protein content of lyophilized ground beef using near-infrared spectroscopy, Bailes et al. ( 2022 ) obtained validation error (RMSEP) values of 0.16% and 0.50% respectively, showing that prediction models can be used with precision for the evaluated product/characteristics. A good correlation was also found between the data obtained by the reference method and NIR for water content. Water has a high absorption in the near-infrared spectral region, which is why NIR spectroscopy is widely used to measure water content (Weeranantanaphan et al., 2011 ). When comparing the prediction error results from the external validation of the beef characteristics measured by Patel et al. ( 2021 ) is observed that the results obtained for the 'sous vide' beef tenderloin were slightly better for water and lipids. For water, the validation error for the tenderloin varied between 0.69% − 0.92% and for the beef between 0.96% − 1.25%, depending on the instrument used. Lipids varied between 0.72% – 0.76% for the tenderloin and 0.80% − 1.06% for beef. For protein, a slightly better validation error was obtained for the beef, ranging from 0.51% to 0.62%, and for the tenderloin, from 0.93% to 0.96%. The validation error results for ash were very similar between the studies, varying between 0.12% – 0.13% for the tenderloin and 0.06% for beef, independent of the instrument used. Dixit et al. ( 2017 ) explored the potential of near-infrared (NIRS) spectroscopy to predict the fat and water content of ground beef samples in both on-line and at-line modes. Although the performance of the PLSR models was measured by R² and RPD, the authors presented a table with SEP values, being 6.84 for fat and 4.72 for water for the at-line mode, and, 5.95 for fat and 4.33 para água para o modo on-line. These values were reported without units hidden a more accurate comparison with the results of this work. Considering the results provided by Dixit et al. ( 2017 ) express absolute values, the validation results obtained in this work are considerably better with being of 0.92% e 0.69% for water content, and 0.72% e 0.76% for fat employing the InnoSpectra e NeoSpectra, respectively. The results for the bias were also presented by those authors. For fat content are reported bias of 3.89 (at line) and 6.95 (on line). For water content − 1.24 (at line) and − 4.01. Both are higher than observed in the present work (Tables 3 and 4 ). Although there is an intrinsic correlation between water and fat contents, as shown in Table 2 , the regression coefficients of the models differ significantly, as illustrated in Figures S5 (A and B) in the supplementary material. This means that the spectra provide distinct information used to estimate water and fat content. If the regression coefficients were equal, only inverted since the observed correlation is negative, it would not be viable to state that the NIR accessed information individually associated with the water and fat present in the sample. The only work found in the literature using NIR spectroscopy on ‘sous vide’ meat products (Perez-Palacios et al., 2019 ) reports the determination of characteristics related to the texture of pork loin cooked ‘sous vide’ at different cooking times. Among the parameters, the total water content was determined, but only the R² and the scaled mean absolute error (MASE) were presented as quality criteria for the obtained model, which were 0.83 and 0.054%, respectively. The authors classify models based on their correlation coefficients, distinguishing between those with high correlation coefficients (R² >0.75), acceptable correlations (R² = 0.5–0.75), and low correlations (R² = 0.25–0.5). Using this metric, the model obtained for humidity in this work using the NeoSpectra spectrometer also had a high correlation coefficient (R² = 0.784), and the InnoSpectra resulted in an acceptable correlation model (R² = 0.517). The authors also evaluated the influence of sample presentation (ground and in 1cm wide pieces), finding no influence on the absorbance values obtained by NIR, suggesting that similar results could be obtained if the sample spectra had been obtained from the product before seared. 4. Conclusion Near-infrared spectroscopy associated with multivariate calibration methods using PLS enabled the development of a rapid method for determining the water, protein, fat, and ash content of pre-processed 'sous vide' beef tenderloins. The results indicate that the models developed using variable selection via the jack-knife algorithm provide reliable results, demonstrating the potential for implementing NIR technology for process control and monitoring, for research in the field, and for meeting the requirements of regulatory agencies. The results obtained by the two instruments were similar, except for the determination of water content, as the NeoSpectra instrument covers a spectral region where water absorbs with greater intensity. A new approach to certifying the quality and utility of the validated NIR models is proposed, based on the analysis of the adequacy of the errors (RMSEP) and the preservation of the data distribution, as assessed by the differences between the parameters of maximum, minimum, median, first quartile (Q1), and third quartile (Q3) between the reference results and the prediction results of the validation samples. This study represents a significant contribution to the field of meat product processing, as studies involving 'sous vide' technology and NIR spectroscopy are scarce. The results demonstrate that the developed PLS-NIR multivariate calibration models enable the implementation of printing nutritional tables on the packaging of 'sous vide' beef tenderloins with greater frequency, on a per-production-lot basis, thereby generating more accurate and reliable information. Objective quality measurements of the products will also enable industrial managers to achieve higher levels of quality for their products. A complementary future study is suggested to evaluate non-pre-processed (seared) products, that is, without the interference caused by surface alterations, as it is believed that good results could be obtained for the intact product without packaging, enabling the implementation of non-destructive in-line inspection. Declarations Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments: IF Sudeste MG for the financial support; Brasil Gourmet Indústria e Comércio de Alimentos S/A; LADINA (Laboratory of Analysis, Development and Innovation of Foods) of the Federal University of Viçosa. This work was supported by the Instituto Nacional de Ciências e Tecnologias Analíticas Avançadas (INCTAA)/Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) [grant number 465768/2014-8], INCTAA/Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) [grant number 2014/50951-4]. MCH and CP are grateful to CNPq for the research fellowships [grants number 305649/2021-3 and 305406/2024-8, respectively]. LPF and KAMLC thank CAPES-PROCAD for the scholar fellowships [grant number 88887.808376/2023-00 and 88887.838359/2023-00, respectively]. This work was carried out with the support of the Coordination for the Improvement of Higher Education Personnel – Brazil (CAPES) – Financing Code 001; the National Council for Scientific and Technological Development – CNPq. CRediT authorship contribution statement D.R. Ferreira: Investigation, Methodology, Data curation, Writing - Original Draft, Writing - Review & Editing . E.A.F. Fontes: Resources, Writing - Original Draft, Writing - Review & Editing, Supervision, Project administration, Funding acquisition. C. Pasquini : Conceptualization, Formal analysis, Writing - Original Draft, Writing - Review & Editing, Funding acquisition. M. C. Hespanhol : Conceptualization, Formal analysis, Resources, Writing - Original Draft, Writing - Review & Editing. S.S. Pereira : Investigation, Methodology, Data curation. L. P. Foli : Investigation, Methodology, Data curation. K. A. M. L. Cruz : Investigation, Methodology, Data curation. 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18:36:12","extension":"html","order_by":13,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":172355,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-7776526/v1/91770657a48120ead9dc8843.html"},{"id":94595587,"identity":"d9ba5f04-f8ef-498f-923d-1dd92f95fd3c","added_by":"auto","created_at":"2025-10-28 18:35:10","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":227677,"visible":true,"origin":"","legend":"\u003cp\u003eInstruments set-up used to obtain the spectra of sous vide samples: a) NeoSpectra; b) InnoSpectra\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7776526/v1/908035547fea7f8c2bfe3ef2.png"},{"id":94595882,"identity":"63d6391f-9d5f-4eb2-948b-c687c637f4c9","added_by":"auto","created_at":"2025-10-28 18:36:35","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":25631,"visible":true,"origin":"","legend":"\u003cp\u003eSelected locations on the ground meat sample placed in a Petri dish for spectra acquisition. Center (1), top corner (2), bottom corner (3), left corner (4), and right corner (5)\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7776526/v1/9bf7a13e1ade60fe856073aa.png"},{"id":94595774,"identity":"3b0f072f-b0f8-4f63-a981-3958143c5fc1","added_by":"auto","created_at":"2025-10-28 18:36:12","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":147369,"visible":true,"origin":"","legend":"\u003cp\u003e(A) and (B) show the raw and pre-treated average spectra from the 132 samples obtained using the Nano_NIR spectrophotometer; (C) and (D) show the raw and pre-treated average spectra obtained by the NeoSpectra spectrophotometer\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7776526/v1/92c4da1b26bc9639e8dc7349.png"},{"id":94598509,"identity":"98275971-d9a6-4555-9847-14ae4eefa162","added_by":"auto","created_at":"2025-10-28 18:54:04","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1765784,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7776526/v1/c73d4556-6255-495b-afd9-855cdc2610e8.pdf"},{"id":94595770,"identity":"d6a50961-c780-4f3e-a4d8-a1c5c4f319ce","added_by":"auto","created_at":"2025-10-28 18:36:10","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":321385,"visible":true,"origin":"","legend":"","description":"","filename":"SUPPLEMENTARYMATERIALWITHAuthorIdentifiers.docx","url":"https://assets-eu.researchsquare.com/files/rs-7776526/v1/be24f0b9fb9b079f0ca54252.docx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Composition assessment of sous vide beef meat by near-infrared spectroscopy based on compact spectrophotometers, multivariate regression, and jack-knife variable selection","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003e'Sous vide' is a French technique, meaning 'under vacuum' (Baldwin, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2012\u003c/span\u003e), characterized by cooking vacuum-sealed food for long periods at low temperatures (Kathuria et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Food is cooked in thermostable packaging, followed by cooling and storage at low temperatures (Yang et al., \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). This technique has been used for various raw materials, such as fruits, vegetables, seafood, and meats (Kathuria et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2022\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eSeveral studies demonstrate the advantages of applying the 'sous vide' technique for meats and meat products, including reduced cooking loss and improved nutrient retention. (Baldwin,2012; Joung et al. 2018; Zhu et al. 2018; Ismail et al. 2019; Bıyıklı et al. 2020; Lee et al. 2021). These advantages are reflected in the proximate composition of the processed product (Roldan et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2014\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThe chemical composition of 'sous vide' beef tenderloins is predominantly composed of water, protein, lipids, and ash (NEPA, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). Understanding the product's composition is crucial for meeting the requirements of official inspection and regulatory bodies (USDA, 2025;BRASIL, 2018), as well as ensuring the contracted quality standard demanded by customers (Weeranantanaphan et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2011\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eAccording to the Food and Drug Administration (FDA), which sets the rules for nutritional labeling in the United States, detailed in the Code of Federal Regulations (CFR), the content of naturally occurring nutrients in food must be at least 80% of the declared value on the label (USDA, 2025). A similar percentage variation is established by Brazilian legislation, through Collegiate Board Resolution (RDC) N\u0026deg; 429 of the National Health Surveillance Agency, which allows, for inspection purposes, up to 20% above the declared value on the label for various components, including fat and carbohydrate, and the same percentage below for protein and minerals (BRASIL, 2020). Considering legal tolerance, the food industry typically creates nutritional tables during the development of a new product and often does not account for possible variations in processed raw materials, especially those of animal origin.\u003c/p\u003e\u003cp\u003eConversely, consumers are increasingly concerned about food composition, and nutritional labeling is a key source of information that influences their purchasing decisions (Duarte et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Thus, accurate information is essential for consumers to make informed purchasing decisions (Weeranantanaphan et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2011\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eNorth American legislation mandates that the proximate composition of a product be determined using official AOAC analytical methods or other reliable and appropriate methods (USDA, 2025). Although RDC N\u0026deg; 429 (BRASIL, 2020). permits the use of direct and indirect calculations based on the constituents used in product formulation to determine its proximate composition, the most precise methodology for this determination is laboratory analysis. However, given the existing legal requirements that allow for a 20% variation from the declared value and the cost of establishing and maintaining an in-house laboratory, many industries opt to outsource their physical-chemical analyses. These analyses are often performed only during the development of a new product or when facing an official audit.\u003c/p\u003e\u003cp\u003eAnother challenge in using laboratory analysis to determine the proximate composition of food is the requirement for exclusive use of official reference methods. Most of these methods are not suitable for meeting the demands of production in a global market, as they require complex sample preparation, long processing times, and are expensive and polluting (Prieto et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2017a\u003c/span\u003e). Consequently, the results are time-consuming, rendering official methods inadequate for industrial use because they do not provide the rapid and reproducible results necessary to continuously and representatively certify product quality (Cozzolino et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2011\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eTherefore, to meet practical industrial demands, instrumental methods must be objective, fast, economical, and precise. Near-infrared (NIR) spectroscopy possesses these characteristics and has proven highly suitable for food products (Aleixandre-Tud\u0026oacute; et al., \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). This technique emerges as an alternative to traditional analytical methods for determining various properties or constituents of agricultural matrices (Williams \u0026amp; Sobering, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e1993\u003c/span\u003e). NIRS is a widely recognized technique, based on the interaction of electromagnetic radiation in the wavelength range of 750 to 2500 nm with the vibrational bonds of the molecular species constituting various types of samples (Pasquini, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eNIR radiation interacts with matter in various ways, with the absorption of radiation by the sample's constituents being the most relevant source of information for analytical applications. This is because the interaction of NIR radiation with the substances present in the sample stimulates vibrational energy transitions in the chemical bonds between atoms, generating absorption spectra that provide qualitative and quantitative analytical information associated with various sample properties (Pasquini, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2003\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eNear-infrared spectroscopy offers advantages such as speed, minimal or no sample preparation, ease of use (Cozzolino et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2011\u003c/span\u003e), ecological friendliness, the ability to quantify various components from measurements taken in a few seconds, and applicability to molecules containing CH, NH, SH, or OH bonds (Qu et al., \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Disadvantages include the difficulty in assigning chemical groups, as information is often obscured in complex spectra characterized by weak signals (Olinger \u0026amp; Griffiths, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e1988\u003c/span\u003e), broad bands, and severe overlaps (Porep et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Other sources of variability, such as instrumental noise, scattering, environmental effects, and sample heterogeneity, also contribute to the complexity of a NIR spectrum (Dos Santos et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2017\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eTo remove uninformative sources of variability and enhance spectral characteristics, NIR spectral data undergo some form of pre-treatment before being used for qualitative or quantitative purposes. The primary source of this type of variability in solid samples originates from the scattering of radiation by pulverized solid samples (Pasquini, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eAnalytical information from pre-treated NIR spectra is extracted using chemometric tools for the appropriate multivariate analysis of the data, enabling both qualitative and quantitative purposes. Chemometrics has enabled significant advances in applying spectroscopic techniques to food and other commodity analysis (Cozzolino et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). Principal Component Analysis (PCA) and Partial Least Squares (PLS) regression are commonly used multivariate analytical techniques for exploratory analysis and regression of multivariate data.\u003c/p\u003e\u003cp\u003eConsidering regression models, after the calibration process is complete, the precision and robustness of the model must be tested with an independent sample set (validation set) (Ziegel, \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2004\u003c/span\u003e). The predictive capacity of multivariate models is typically evaluated by calculating the error associated with their estimates. The determination of the Root Mean Square Error of Prediction (RMSEP) and/or the Standard Error of Prediction (SEP) is an indicator of prediction accuracy and is the most common way to assess the quality of regression models (Bro et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2005\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eContinuous advancements in chemometric methods, technology, and instrumentation have enabled NIR spectroscopy to achieve increasingly robust models for identification and quantification. NIR spectrometers basically include a light source, a wavelength selector, a sample detector, an optical detector, and a data processing/analysis system (Pasquini, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Prieto et al., \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2017a\u003c/span\u003e).The development of compact spectrophotometers operating in the near-infrared region has made it possible to monitor, characterize, and identify products, as well as reduce the time and cost of analyses in the pharmaceutical and food industries, for example (Savoia et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eThe advancement of the NIR technique has expanded its versatility, enabling the replacement of some slow, expensive, and labor-intensive instrumental analysis methods with vibrational spectrophotometric methods. This technique can perform real-time analyses at the production site with a similar level of precision and accuracy (Dos Santos et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). This versatility was reaffirmed by Patel et al. (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) when they highlighted portable NIR instruments as a fast and practical option in meat processing plants for collecting spectra and developing prediction models, and by Porep et al. (\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2015\u003c/span\u003e), who stated that it is a suitable technique for implementation as an analytical tool in industrial processing.\u003c/p\u003e\u003cp\u003eTherefore, the objective of this study was to compare the performance of two low-cost portable NIR spectrometers for the construction and validation of regression models aimed at determining the proximate composition of 'sous vide' beef tenderloins during their industrial processing, on an individualized basis, with an evaluation of the possibility of printing the nutritional table, displaying its composition in a more representative way.\u003c/p\u003e"},{"header":"2. Material and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e\u003ch2\u003e2.1 Preparation of packaged beef tenderloins\u003c/h2\u003e\u003cp\u003eChilled beef tenderloin cuts (temperature between 0 and 4\u0026deg;C, pH between 5.7 and 5.8), sourced from a licensed slaughterhouse inspected by the Brazilian Federal Inspection Service (SIF), were transported in refrigerated trucks and kept in a cold chamber at 4\u0026deg;C until sample preparation.\u003c/p\u003e\u003cp\u003eIn a tumbler, ice water (0 and 4\u0026deg;C), modified cassava starch, maltodextrin, salt, and black pepper were added to form a brine (temperature between 0 and 4\u0026deg;C). The beef tenderloin cuts were added to the tumbler after the ingredients were homogenized and were tumbled for 40 minutes to incorporate the brine. Subsequently, the cuts were stored in a cold chamber at 4\u0026deg;C until they reached a temperature between 10 and 12\u0026deg;C. They were then rolled, wrapped in PVC plastic film, and frozen in cold chambers at -12\u0026deg;C. After the cuts reached temperatures between \u0026minus;\u0026thinsp;2 and \u0026minus;\u0026thinsp;5\u0026deg;C, the plastic film was removed, and transverse cuts (diameters between 57 and 60 mm and thickness between 38 and 40 mm) were made manually. These were individually weighed on a digital scale, yielding a mass of (125\u0026thinsp;\u0026plusmn;\u0026thinsp;5) g, which allowed for approximately thirteen rounds / slices to be obtained from each piece, known as tenderloin.\u003c/p\u003e\u003cp\u003eThe tenderloin was seared on a hot plate (approximately 215\u0026deg;C) to achieve a golden-brown surface color. The product reached an approximate surface temperature of 40\u0026deg;C and was then stored in a cold chamber at 4\u0026deg;C before being packaged. Once chilled (between 4 and 10\u0026deg;C), they were placed in thermoformed polystyrene trays and vacuum-sealed (Multivac).\u003c/p\u003e\u003cp\u003eThe product was then subjected to cooking at 58\u0026deg;C for 32 minutes, cooled to 4\u0026deg;C, and frozen in a nitrogen tunnel at -18\u0026deg;C.\u003c/p\u003e\u003cp\u003eA set of 132 samples of 'sous vide' beef tenderloins was used for the construction and validation of the regression models. The sample set had its composition identified and quantified by reference methods, representing the samples industrially processed between August 2023 and May 2024. The chilled beef tenderloin was sampled according to their production by the industry, with 4 samples being collected per production batch. These different times made it possible to cover greater variability in the composition of the raw material in order to build a more accurate predictive model.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e\u003ch2\u003e2.2. Description of the portable NIR spectrophotometers\u003c/h2\u003e\u003cp\u003eTwo spectrophotometers were used throughout this study: the InnoSpectra (Texas Instruments Inc.) and the NeoSpectra (Si-Ware, Egypt). These instruments are portable and compact, capable of monitoring the near-infrared spectral ranges of 921\u0026ndash;1683nm and 1350\u0026ndash;2550 nm, respectively, with a nominal resolution of 10 nm.\u003c/p\u003e\u003cp\u003eThe NeoSpectra consists of an illumination unit containing three tungsten filament sources and an optical coupling system, designed for reflection measurements. The instrument is based on a complete Michelson interferometer implemented on a MEMS chip. The manufacturer reports a signal-to-noise ratio (SNR) of 2,000 at a wavelength of 2350 nm with a 2 s integration time. In turn, the manufacturer of the InnoSpectra reports an SNR of 6000:1 and a scan time of 0.3 seconds, with Grade-MEMS technology.\u003c/p\u003e\u003cp\u003eThe instruments were connected to the USB port of a notebook (Dell Technologies, 16 GB DDR4, 512 GB SSD) and powered on for 30 minutes to allow for stabilization before the measurements began. The radiation source was activated only during the acquisition of the spectra (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec5\" class=\"Section2\"\u003e\u003ch2\u003e2.3. Protocol for obtaining sample spectra\u003c/h2\u003e\u003cp\u003eThe acquisition of representative NIR spectra of the samples was performed in three ways: on the whole tenderloin covered by its packaging; on the whole tenderloin covered by a glass Petri dish (diameter of 7.2 cm and height of 1.3 cm); and with the ground tenderloin placed in the glass Petri dish, filling its entire extension up to its maximum height.\u003c/p\u003e\u003cp\u003eFor the measurements of the whole product, its original packaging was opened, and its surface was gently blotted with a paper towel to standardize the surface moisture. The part of the packaging without graphic printing was placed over the product, and the equipment was positioned to obtain the spectra. A Spectralon\u0026reg; reference tile (corresponding to 100% reflection of NIR radiation) covered by the product packaging or by the glass of the Petri dish was used for spectral reference measurements necessary for calculating the reflectance spectra. The reference was measured before each sample was taken.\u003c/p\u003e\u003cp\u003eThe readings on the whole tenderloin, covered by a glass Petri dish, were performed in the same manner as the measurements of the product in its packaging, with the only difference being the replacement of the plastic packaging with the glass Petri dish.\u003c/p\u003e\u003cp\u003eFor the ground product, a domestic food processor (Walita Philips, 600W) was used, where the product, cut into approximately 1cm slices, was minced for 3 minutes at speed 2 of the equipment. The resulting ground meat mass was spread evenly on a 7.2 cm diameter glass Petri dish, avoiding the presence of air bubbles, to produce a layer with a thickness of 1.3 cm. With the dish covered, it was turned upside down and the spectrophotometer was placed on the original bottom of the dish to perform the readings. The Spectralon (reference corresponding to 100% reflection of NIR radiation) covered by the lid of the Petri dish was used for spectral reference measurements, which are necessary for calculating the reflectance spectra.\u003c/p\u003e\u003cp\u003eThe samples in all their forms were measured in quintuplicate, obtaining a representative average spectrum with an improved signal-to-noise ratio. Figure\u0026nbsp;2 shows, for a ground sample, the position of the reading points.\u003c/p\u003e\u003cp\u003eThe spectra of the samples were obtained at ambient temperature (25\u0026thinsp;\u0026plusmn;\u0026thinsp;1\u0026deg;C) over a period of thirteen days at the GAES Chemistry Laboratory (Group for Analysis and Education for Sustainability) at the Federal University of Vi\u0026ccedil;osa. Three samples were measured five times according to the procedure described above to estimate the repeatability of the validated NIR models showing the best performance.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec6\" class=\"Section2\"\u003e\u003ch2\u003e2.4. Proximate composition\u003c/h2\u003e\u003cp\u003eThe determination of total water (ISO 1442:\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2023\u003c/span\u003e (E), \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), fixed mineral residue (ash) (ISO 936:\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e1998\u003c/span\u003e (E), \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e1998\u003c/span\u003e), total fats (NMKL 181, \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2005\u003c/span\u003e), and nitrogen content (ISO 1871:\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2009\u003c/span\u003e (E), \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2009\u003c/span\u003e) were performed according to official methods for the analysis of products of animal origin. The obtained nitrogen value was multiplied by 6.25 to determine the protein content (Brasil, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Carbohydrate content was calculated by difference from the proximate composition.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e\u003ch2\u003e2.5 Multivariate analysis and construction of regression models\u003c/h2\u003e\u003cp\u003eThe obtained spectral datasets were processed using the chemometric software Unscrambler 10.5. Preliminary regression models based on Partial Least Squares (PLS) Regression were constructed with all samples in the set and for each of the studied properties, aiming to estimate the levels of protein, water, fat, ash, and carbohydrates present in the samples.\u003c/p\u003e\u003cp\u003eWith preliminary models constructed, the Kennard-Stone algorithm (Kennard \u0026amp; Stone, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e1969\u003c/span\u003e) was used to select the calibration set (typically comprising 90 samples) and the validation set (comprising 42 samples). This procedure guarantees the selection of a uniform and representative subset (of calibration) of the samples.\u003c/p\u003e\u003cp\u003eThe spectra were pre-treated using Standard Normal Variate (SNV) followed by the 1st derivative calculated using the Savitzky-Golay algorithm, employing 11 points in the smoothing window and a 2nd -degree polynomial fit, to minimize the effect of radiation scattering, highlighting the relevant information. Models were constructed using the entire useful spectral range of the spectrophotometers and using only the variables selected by the jack-knife algorithm available in the Unscrambler 10.5 software. The objective of the variable selection performed by this algorithm is to use in the regression process only the variables that produce, in a first analysis, stable regression coefficients identified during the cross-validation (employing 20 subsets of samples randomly selected) process that accompanies the construction of the regression models (Esbensen \u0026amp; Swarbrick, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e\u003c/div\u003e"},{"header":"3. Results and discussion","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e\u003ch2\u003e3.1. Spectral data\u003c/h2\u003e\u003cp\u003eThe original average spectra obtained from the five readings of the intact tenderloins, using both spectrophotometers, with and without packaging, and for the ground samples, are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003e (A and C).\u003c/p\u003e\u003cp\u003eFor analysis by conventional methods, the product must be grounded and homogenized. This implies that in developing the regression models, the NIR spectra of the intact product (with and without packaging) must be compared with the results of analyses performed using traditional methods on the ground product. It should be anticipated that the spectra of the intact samples, despite efforts to minimize the effect of the packaging and the glass Petri dish, better reflect their surface composition than their average composition as determined by the reference methods. The intact product undergoes a searing step, which results in a darkening of its surface, primarily due to the Maillard reaction. Thus, the spectra obtained under these conditions are not representative of the sample as a whole (bulk).\u003c/p\u003e\u003cp\u003eThe obtained spectra were transformed to minimize the effects of radiation scattering by applying the standard normal variate (SNV) followed by a 1st derivative calculated using the Savitzky-Golay algorithm with 11 points in the smoothing window and a 2nd degree polynomial fit. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the spectra before (A and C) and after the pre-treatments (B and D) for the ground \"sous vide\" tenderloin samples.\u003c/p\u003e\u003cp\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec10\" class=\"Section2\"\u003e\u003ch2\u003e3.2 Sample quality characteristics.\u003c/h2\u003e\u003cp\u003eThe results of the proximate composition analysis of the 'sous vide' beef tenderloins obtained by the reference method (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e) are close to those listed in the Brazilian Food Composition Table (NEPA, \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2011\u003c/span\u003e) for raw beef tenderloin, which averages 71.9% water, 21.6% protein, and 5.6% fat. A study by Hocquette et al. (\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2018\u003c/span\u003e) mentions that beef contains 21% to 31% protein, which indicates that the values found in the present study fall within these ranges.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eMean values (\u0026plusmn;\u0026thinsp;standard deviation) and results for moisture, ash, protein, fat, and carbohydrate content of the 132 ground 'sous vide' beef tenderloin samples obtained by reference methods\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"8\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003estatistcs\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c3\" namest=\"c2\"\u003e\u003cp\u003ewater content (%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e\u003cp\u003eash (%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eprotein (%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003efat (%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c8\"\u003e\u003cp\u003ecarbohydrates (%)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e\u003cp\u003emean\u0026thinsp;\u0026plusmn;\u0026thinsp;std deviation\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e68.96\u0026thinsp;\u0026plusmn;\u0026thinsp;1.76\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.77\u0026thinsp;\u0026plusmn;\u0026thinsp;0.19\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u003cp\u003e24.14\u0026thinsp;\u0026plusmn;\u0026thinsp;1.44\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e3.99\u0026thinsp;\u0026plusmn;\u0026thinsp;1.78\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1.14\u0026thinsp;\u0026plusmn;\u0026thinsp;1.14\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e\u003cp\u003emax\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e72.70\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e2.68\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u003cp\u003e28.31\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e11.29\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e5.74\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e\u003cp\u003emin\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e63.29\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.47\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u003cp\u003e20.78\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.45\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.01\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e\u003cp\u003erange\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e9.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1.20\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u003cp\u003e7.53\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e10.84\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e5.73\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c2\" namest=\"c1\"\u003e\u003cp\u003evariance\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3.10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.04\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c6\" namest=\"c5\"\u003e\u003cp\u003e2.08\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e3.18\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1.31\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eMitsumoto et al. (\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e1991\u003c/span\u003e) Compared the quality of beef cuts using near-infrared (NIR) spectroscopy with reflectance, transmittance, and a fiber optic probe. The mean values found by the authors for protein, water, and fat were similar to those of the 'sous vide' beef tenderloin, at 18.8%, 69.7%, and 8.8%, respectively.\u003c/p\u003e\u003cp\u003eThe most significant inverse correlations are observed between the protein and carbohydrates content (r = -0.5403) and fat and water (r = -0.7556) (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), with the latter exhibiting the highest correlation coefficient among the property values determined by the reference methods.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eCorrelation analysis between the water, ash, protein, fat, and carbohydrate content of 'sous vide' beef tenderloins using values determined by reference methods\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003estatistcs\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003ewater content (%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eash (%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eprotein (%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003efat (%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003ecarbohydrate (%)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ewater content (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.3122\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e-0.2801\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.7556\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.0611\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eash (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.3122\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.4413\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.2597\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.3103\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eprotein (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.2801\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.4413\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.1369\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.5403\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003efat (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.7556\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.2597\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.1369\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.1790\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ecarbohydrates (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.0611\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.3103\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.5403\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u0026minus;\u0026thinsp;0.1790\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec11\" class=\"Section2\"\u003e\u003ch2\u003e3.3 Elaboration, optimization, and validation of regression models.\u003c/h2\u003e\u003cp\u003ePreliminary PLS regression models were developed using the complete pre-treated spectra obtained from the two instruments for each of the three sample measurement forms. The models constructed with the spectral data set from the intact samples, both with and without packaging for both instruments, did not yield satisfactory results. Coefficients of determination (R\u0026sup2;) below 0.300 and high root mean square error of cross-validation (RMSECV) values indicate that the representativeness of the spectra, obtained predominantly from the surface of the intact samples, is insufficient to establish a correlation between the spectral data and their properties, which are inferred from portions of the ground and homogenized samples processed by conventional methods.\u003c/p\u003e\u003cp\u003eConversely, the results for the preliminary models built with the spectra from the ground and homogenized samples for both instruments show satisfactory R\u0026sup2; and RMSECV values for all modeled parameters, except for carbohydrate content. Therefore, the results presented below pertain only to the models constructed with spectra from the ground samples.\u003c/p\u003e\u003cp\u003eThe preliminary models were refined by eliminating anomalous samples (outliers) from the data sets, using leverage, the spectral residuals of the samples, and the X-Y relation of anomalous samples (X-Y relation outliers)(Esbensen \u0026amp; Swarbrick, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Subsequently, the remaining samples were divided using the Kennard-Stone algorithm (Kennard \u0026amp; Stone, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e1969\u003c/span\u003e) to produce a calibration set containing 90 samples and an external validation set constituted of the remaining samples.\u003c/p\u003e\u003cp\u003eTables\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e present the preliminary calibration and validation results for the PLS models developed to determine the protein, fat, water, ash, and carbohydrate content using all spectral variables from the full spectral range accessible by both instruments. The same tables also display the results obtained using only the variables selected by the jack-knife algorithm in Unscrambler 10.5 software, which was used for chemometric data treatment. This algorithm analyzes the behavior of the regression coefficients for all variables used in the PLS model construction in relation to their stability during the cross-validation process. In this study, segmented cross-validation was employed with 20 groups, each containing 4 to 5 randomly selected samples. The behavior of the 20 sets of regression coefficients was statistically evaluated, and spectral variables associated with highly unstable regression coefficients were eliminated. The selected variables for each modeled property and for each of the two instruments are shown in Tables S1 and S2 in the supplementary material. New models were constructed using the selected variables, and the results are presented in Tables\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\u003cp\u003eAs observed in Tables\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, the models built with the selected variables perform better than those using all variables. The RMSECV values for the models with selected variables are invariably better than those obtained with all variables. A notable point is the reduction in the number of PLS factors required by the models with selected variables, as seen in all models except for the water content model from the InnoSpectra data, which increased from 4 to 6, and the ash content model from the NeoSpectra data, which remained at 3. These results indicate that models based on selected variables are generally simpler, more robust, and utilize the most relevant spectral information for each modeled parameter.\u003c/p\u003e\u003cp\u003eThe results for the models constructed with or without variable selection for determining carbohydrate content showed unsatisfactory performance. This result is likely due to the low carbohydrate content and its non-homogeneous distribution on the sample surface. Furthermore, its content is determined with lower precision and accuracy, as it is calculated indirectly by subtracting the sum of the other constituents.\u003c/p\u003e\u003cp\u003eThe ash content of the samples refers to inorganic constituents present in the meat that should not exhibit spectral characteristics in the near-infrared (NIR) region. However, models for determining ash content exhibit acceptable performance. This performance likely results from the indirect association of other organic sample constituents with this property. However, due to the characteristics of this property, the results should be considered with caution and must be submitted to further evaluation.\u003c/p\u003e\u003cp\u003eThe repeatability of the predicted results determined by the validated models employing jack-knife selection of variables was evaluated by the mean estimated standard deviation of the results obtained by 3 samples measured in quintuplicate as, 0.46, 0.43%; 0.52, 0.45%; 0.39, 0.35% and 0.05, 0.02% for protein, water, fat and ash contents and models obtained using the NeoSpectra and InnoSpectra, respectively. The repeatability of the results obtained by the NIR method is very good, shows values lower than the RMSEP of the validated models, and is, in general, somewhat better for the InnoSpectra instrument.\u003c/p\u003e\u003cp\u003eFigures \u003cspan refid=\"MOESM1\" class=\"InternalRef\"\u003eS1\u003c/span\u003e-S4 in the supplementary material present the cross-validation results for each instrument during model construction for water, fat, ash, and protein content, using all spectral variables, selected variables, and the validation of models with variable selection.\u003c/p\u003e\u003cp\u003eThe models built with the selected variables were successfully validated, yielding promising root mean square errors of prediction (RMSEP) for determining the main quality characteristics of the \"sous vide\" samples, as shown in Tables\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eResults of the full spectrum models, with Jack-Knife variable selection, and validated (InnoSpectra) with external samples, developed for the components of the ground 'sous vide' beef tenderloin\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"16\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c14\" colnum=\"14\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c15\" colnum=\"15\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c16\" colnum=\"16\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003emodel\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e\u003cp\u003efull spectrum\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"5\" nameend=\"c11\" namest=\"c7\"\u003e\u003cp\u003eselected variables JK\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"5\" nameend=\"c16\" namest=\"c12\"\u003e\u003cp\u003evalidation (with variable selection)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNc\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eF\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eR\u0026sup2;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eRMSECV (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eBIAS(%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eNc\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003eF\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003eR\u0026sup2;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003eRMSECV (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003eBIAS\u003c/p\u003e\u003cp\u003e(%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003eNv\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003eF\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003eR\u0026sup2;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u003cp\u003eRMSEP (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c16\"\u003e\u003cp\u003eBIAS(%)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eProtein\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.559\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.598\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e0.88\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e0.01\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e39\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e0.330\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u003cp\u003e0.93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c16\"\u003e\u003cp\u003e-0.15\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eWater content\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.706\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.94\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.856\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e0.67\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e42\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e0.517\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u003cp\u003e0.92\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c16\"\u003e\u003cp\u003e0.09\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eFat\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.785\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.84\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.795\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e0.82\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e42\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e0.710\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u003cp\u003e0.72\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c16\"\u003e\u003cp\u003e0.05\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAsh\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.428\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.589\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e0.11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e38\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e0.453\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u003cp\u003e0.12\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c16\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCarboydrates\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e132\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eNA\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e132\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.002\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c16\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e* Nc\u0026thinsp;=\u0026thinsp;number of samples / Nv\u0026thinsp;=\u0026thinsp;number of validation samples / F\u0026thinsp;=\u0026thinsp;number of factors / R\u0026sup2; = coefficient of determination / RMSECV\u0026thinsp;=\u0026thinsp;cross-validation error / BIAS\u0026thinsp;=\u0026thinsp;systematic deviation / RMSEP\u0026thinsp;=\u0026thinsp;prediction error from external validation.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eResults of the full spectrum models, with Jack-Knife variable selection, and validated (NeoSpectra ) with external samples, developed for the components of the ground 'sous vide' beef tenderloin\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"16\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c14\" colnum=\"14\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c15\" colnum=\"15\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c16\" colnum=\"16\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003emodel\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e\u003cp\u003efull spectrum\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"5\" nameend=\"c11\" namest=\"c7\"\u003e\u003cp\u003eselected variables JK\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"5\" nameend=\"c16\" namest=\"c12\"\u003e\u003cp\u003evalidation (with variable selection)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNc\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eF\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eR\u0026sup2;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003eRMSECV (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003eBIAS (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003eNc\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003eF\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003eR\u0026sup2;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003eRMSECV (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003eBIAS\u003c/p\u003e\u003cp\u003e(%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003eNv\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003eF\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003eR\u0026sup2;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u003cp\u003eRMSEP (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c16\"\u003e\u003cp\u003eBIAS(%)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eProtein\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.440\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.01\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.610\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e0.93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e39\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e0.259\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u003cp\u003e0.96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c16\"\u003e\u003cp\u003e-0.42\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eWater content\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.865\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.65\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.879\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e0.61\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e0.01\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e40\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e0.784\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u003cp\u003e0.69\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c16\"\u003e\u003cp\u003e-0.19\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eFat\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.884\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.59\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.895\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e0.56\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e42\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e0.668\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u003cp\u003e0.76\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c16\"\u003e\u003cp\u003e0.11\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAsh\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.402\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e90\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.450\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e0.14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e42\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e0.305\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u003cp\u003e0.13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c16\"\u003e\u003cp\u003e-0.02\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCarboydrates\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e132\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eNA\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e1.11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e144\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.006\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c16\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e* Nc\u0026thinsp;=\u0026thinsp;number of calibration samples / Nv\u0026thinsp;=\u0026thinsp;number of validation samples / F\u0026thinsp;=\u0026thinsp;number of factors / R\u0026sup2; = coefficient of determination / RMSECV\u0026thinsp;=\u0026thinsp;cross-validation error / BIAS\u0026thinsp;=\u0026thinsp;systematic deviation / RMSEP\u0026thinsp;=\u0026thinsp;prediction error from external validation.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec12\" class=\"Section2\"\u003e\u003ch2\u003e3.4. Considerations on the evaluation of model quality\u003c/h2\u003e\u003cp\u003eSeveral criteria for classifying the quality of multivariate models are described in the literature. The Standard Practices for Infrared Multivariate Quantitative Analysis (ASTM) has issued two guides recommending best practices for quantitative and qualitative multivariate analysis based on NIRS (ASTM E1655-05, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; ASTM E1790-04, 2016).\u003c/p\u003e\u003cp\u003eFor multivariate regression, these ASTM guides do not recommend the coefficient of determination (R\u0026sup2;) as a model quality criterion, as it is heavily dependent on the data distribution. That is, R\u0026sup2; depends on the variance of the concentration or reference values. Despite this, it is very common to find it expressed in NIR spectroscopy literature as a measure of the quality of multivariate models. Many of these present comparison plots between the values predicted by an NIR model and the reference values, where most values are, for example, close to the upper limit, while a few are near the lower limit, indicating an asymmetric distribution. In such cases, R\u0026sup2; can approach 1, being considered excellent. However, if the few lower values are removed, R\u0026sup2; would assume much smaller values (Pasquini, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). The R\u0026sup2; values obtained in the validation of the models built in this work ranged from 0.258 to 0.784 for the protein and water content models, respectively, using data from NeoSpectra, and from 0.330 to 0.710 for the protein and fat content models, respectively, using InnoSpectra. It is noted that the protein content values are distributed in a narrow range in the calibration set and an even narrower range in the validation set. Considering the standard deviation of the reference method for this parameter, it is evident that the R\u0026sup2; value could not reach much higher values. However, the RMSEP of the models shows values of 0.93% and 0.96% for protein content obtained with models from the NeoSpectra and InnoSpectra data, respectively, despite R\u0026sup2; values that are much lower than 1. These error values are acceptable for expressing product quality within Brazilian labeling standards.\u003c/p\u003e\u003cp\u003eThe agricultural field, including food science, frequently uses the ratio of performance to deviation (RPD) as a quality criterion for a model (Prieto et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2017b\u003c/span\u003e; Leone et al., 2012). Its calculation considers the ratio between the model's validation error (RMSEP) and the standard deviation of the reference values. However, this quality criterion is susceptible to the presence of outliers in the validation set, which can significantly affect the calculation of the standard deviation of the reference data. Thus, this criterion is also subject to data distribution. The RPD-based criterion advocates values greater than 2 for models of satisfactory quality (Prieto et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2017b\u003c/span\u003e; Leone et al., 2012).\u003c/p\u003e\u003cp\u003eTo minimize the effect of outliers on the calculation of a criterion similar to RPD, the ratio of performance to interquartile (RPIQ, the ratio between performance and interquartile) was proposed (Bellon-Maurel et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2010\u003c/span\u003e; Olivieri, 2018). This parameter is less susceptible to data distribution, as the presence of outliers has a lesser influence on it. However, the literature does not mention a consensus critical value by which models could be considered of adequate quality. Thus, RPIQ is more useful for comparing the performance of different models than for quantifying their absolute quality.\u003c/p\u003e\u003cp\u003eBased on the foregoing considerations, it is suggested that the RMSEP value, analyzed according to the accuracy required to attest product quality, be preferentially used as a quality criterion that is less dependent on the reference data distribution and more suitable for real-world situations where this distribution does not always favor the calculation of R\u0026sup2; or RPD. Thus, for example, if this work were repeated using the InnoSpectra equipment, the average agreement between the reference method and the model should be 0.92% for moisture, 0.72% for fat, 0.93% for protein, and 0.12% for ash (Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e), which are adequate values to express the product's quality.\u003c/p\u003e\u003cp\u003eOn the other hand, to verify if the predicted values from the models maintain the original distribution of the reference data, we propose observing the variation in the maximum, minimum, median, and quartiles 1 and 3 between the results from the reference methods and those from the model validation. The criterion for verifying the distribution of results considers the distributions of the reference and validation results to be indistinct if the differences between the values are less than the model's RMSEP, considering that RMSEP values can be accepted to estimate quality parameters with the necessary accuracy. Tables\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and \u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e show the results of the evaluation of the differences between the quartiles for each of the models and for the InnoSpectra and NeoSpectra equipment, respectively.\u003c/p\u003e\u003cp\u003eAdopting this criterion, it is observed that for the InnoSpectra instrument, there is a distortion of the distribution for high predicted values of protein content. For fat content, the validation results using this equipment show a significant distortion in the distribution of predicted values relative to the reference values, with most of the differences being greater than the model's RMSEP.\u003c/p\u003e\u003cp\u003eRegarding the NeoSpectra instrument, the analysis of the distribution behavior of the reference results compared to the validation results shows minor differences for the models built for protein and fat determination, allowing for the attestation of the quality of all models built for the four quality parameters. In other words, with this equipment, acceptable prediction errors are obtained to attest to the product's quality, and simultaneously, the validation results of the models maintain their original distribution.\u003c/p\u003e\u003cp\u003eThe quality analysis of the models proposed in this work is not based on a single parameter, such as R\u0026sup2;, RPD, or RPIQ, to determine the model's quality. It employs the results concerning the accuracy of the models (RMSEP) and, if these are satisfactory for the problem at hand, analyzes the non-parametric distribution of the results obtained by the reference method compared to those obtained by the model. The procedure is effective as it considers aspects inherent to the accuracy requirements of the model (RMSEP) while maintaining attention to the distribution of the validation results.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eDifference related to the distribution of results obtained by reference methods and by the validation of optimized models built with spectral data from the \u003cb\u003eInnoSpectra\u003c/b\u003e equipment for ground samples\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"14\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c14\" colnum=\"14\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e\u003cp\u003ereference/validation values\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"4\" nameend=\"c10\" namest=\"c7\"\u003e\u003cp\u003emodel validation results with JK variable selection\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"4\" nameend=\"c14\" namest=\"c11\"\u003e\u003cp\u003edifference\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003ewater content (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eash (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e\u003cp\u003eprotein (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003efat (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003ewater content (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003eash (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003eprotein (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003efat (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003eΔwater content (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003eΔash (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003eΔprotein (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003eΔfat (%)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003emax\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e72.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003e2.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e27.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e6.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e71.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e2.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e25.9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e7.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e0.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e0.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e1.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e-1.2\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003emin\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e66.4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003e1.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e21.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e66.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e22.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e0.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e0.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e-0.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e-1.0\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003emedian\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e69.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003e1.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e24.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e3.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e69.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e24.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e3.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e-0.4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e0.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e0.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e-0.1\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eQ1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e68.9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003e1.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e23.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e2.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e68.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e23.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e2.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e0.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e-0.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e0.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e-0.3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eQ3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e70.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003e1.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e24.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e4.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e70.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e24.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e4.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e-0.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e0.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e0.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e0.3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRMSEP\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.92\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.12\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e0.72\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRPD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.44\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1.42\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e1.23\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.88\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRPIQ\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.41\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1.60\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e1.39\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e2.70\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eDifference related to the distribution of results obtained by reference methods and by the validation of optimized models built with spectral data from the \u003cb\u003eNeoSpectra\u003c/b\u003e equipment for ground samples\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"14\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c14\" colnum=\"14\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colspan=\"5\" nameend=\"c6\" namest=\"c2\"\u003e\u003cp\u003ereference/validation values\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"4\" nameend=\"c10\" namest=\"c7\"\u003e\u003cp\u003evalidation results of models with JK variable selection\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"4\" nameend=\"c14\" namest=\"c11\"\u003e\u003cp\u003edifference\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003ewater content (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003eash\u003c/p\u003e\u003cp\u003e(%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c5\" namest=\"c4\"\u003e\u003cp\u003eprotein\u003c/p\u003e\u003cp\u003e(%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003efat (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003ewater content (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003eash\u003c/p\u003e\u003cp\u003e(%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003eprotein\u003c/p\u003e\u003cp\u003e(%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003efat (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003eΔwater content (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003eΔash (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003eΔprotein (%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003eΔfat (%)\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003emax\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e71.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003e2.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e26,9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e6.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e71.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e2.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e25.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e6.4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e0.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e0.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e1.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e0.3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003emin\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e65.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003e1.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e22.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e65.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e22.9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e-0.4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e-0.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e-0.9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e-1.0\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003emedian\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e69.4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003e1.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e24.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e3.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e69.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e24.2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e3.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e0.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e-0.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e0.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e0.2\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eQ1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e68.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003e1.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e23.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e2.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e68.4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e23.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e2.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e0.4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e-0.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e0.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e-0.3\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eQ3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e70.4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u003cp\u003e1.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e25.1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e4.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e69.9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e24.4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e4.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e0.5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e0.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e0.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e0.0\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRMSEP\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e0.69\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e0.96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e0.76\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRPD\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e2.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e0.80\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e1.16\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e1.75\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eRPIQ\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colspan=\"2\" nameend=\"c4\" namest=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e2.31\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1.54\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u003cp\u003e1.60\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e2.63\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u0026nbsp;\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e\u003ch2\u003e3.5. Comparison of the performance of the InnoSpectra and NeoSpectra equipment\u003c/h2\u003e\u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e allows for a comparison of the external validation results for the models built with variables selected by the jack-knife algorithm for both instruments used in this work. Considering only the validation error values (RMSEP), both instruments demonstrated similar and adequate performance in determining the four quality parameters of \"sous vide\" meat, to express them on the product label. The NeoSpectra shows more accurate results for the model built to determine the water content. This is associated with the spectral information obtained by this instrument, which monitors a broader spectral range, which the InnoSpectra does not access (Wilson et al., \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2015\u003c/span\u003e).\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eResults of external validation of the models based on the selection of variables by jack-knife for the InnoSpectra and NeoSpectra equipment\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"16\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c11\" colnum=\"11\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c12\" colnum=\"12\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c13\" colnum=\"13\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c14\" colnum=\"14\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c15\" colnum=\"15\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c16\" colnum=\"16\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colspan=\"6\" nameend=\"c7\" namest=\"c2\"\u003e\u003cp\u003evalidation InnoSpectra\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colspan=\"2\" nameend=\"c9\" namest=\"c8\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colspan=\"7\" nameend=\"c16\" namest=\"c10\"\u003e\u003cp\u003evalidation NeoSpectra\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eNv\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eF\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eR\u0026sup2;\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eRMSEP (%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eBias(%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c7\"\u003e\u003cp\u003eRPD\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c8\"\u003e\u003cp\u003eRPIQ\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/th\u003e\u003cth align=\"left\" colname=\"c10\"\u003e\u003cp\u003eNv\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c11\"\u003e\u003cp\u003eF\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c12\"\u003e\u003cp\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c13\"\u003e\u003cp\u003eRMSEP (%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c14\"\u003e\u003cp\u003eBias(%)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c15\"\u003e\u003cp\u003eRPD\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c16\"\u003e\u003cp\u003eRPIQ\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eprotein\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e39\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.330\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.93\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e-0.15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.23\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1.39\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e39\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e0.258\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e0.96\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e-0.42\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u003cp\u003e1.16\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c16\"\u003e\u003cp\u003e1.60\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ewater content\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e40\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.517\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.92\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.09\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.44\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e2.31\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e42\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e0.784\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e0.69\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e-0.19\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u003cp\u003e2.17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c16\"\u003e\u003cp\u003e2.31\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003efat\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e42\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.710\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.72\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.05\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.75\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e2.70\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e42\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e0.668\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e0.76\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e0.11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u003cp\u003e1.75\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c16\"\u003e\u003cp\u003e2.63\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eash\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e42\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.453\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.12\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.00\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c7\"\u003e\u003cp\u003e1.42\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c8\"\u003e\u003cp\u003e1.60\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c9\"\u003e\u0026nbsp;\u003c/td\u003e\u003ctd align=\"left\" colname=\"c10\"\u003e\u003cp\u003e38\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c11\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c12\"\u003e\u003cp\u003e0.305\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c13\"\u003e\u003cp\u003e0.13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c14\"\u003e\u003cp\u003e-0.02\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c15\"\u003e\u003cp\u003e0.80\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c16\"\u003e\u003cp\u003e1.54\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003ctfoot\u003e\u003ctr\u003e\u003ctd colspan=\"16\"\u003eNv: number of validation samples; F: number of factors\u003c/td\u003e\u003c/tr\u003e\u003c/tfoot\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe performances of portable visible NIR (Vis-NIRS), NIRS, and a Micro-NIRS instrument were evaluated by Patel et al. (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) by constructing and evaluating prediction models for beef characteristics from spectra obtained directly from its surface. As in the present study, the authors concluded that the prediction performances of the three instruments were similar, although the Micro-NIRS performed better for some characteristics.\u003c/p\u003e\u003cp\u003eIf RPD or RPIQ values were adopted as the quality criterion for the models, it would indicate that only the models built for determining water and fat content obtained by the InnoSpectra could be accepted based on RPIQ values greater than 2. Likewise, for the NeoSpectra, only these two models would have their quality attested by the RPIQ values, with the water content model also being acceptable based on its RPD. However, adopting the criterion established in this work, which considers the accuracy (RMSEP) sufficient for the intended purpose of the models and the maintenance of the distribution of the predicted values when compared to the distribution of the reference results, only the model for fat and the protein model, considering high contents, obtained with the InnoSpectra would require caution for routine use. The models obtained by the NeoSpectra are deemed adequate according to this quality criterion.\u003c/p\u003e\u003cp\u003eBoth instruments can operate completely autonomously, utilizing batteries, and allow for the remote transmission of the obtained spectra. However, the cost of the InnoSpectra is about 5 times lower than the cost of the NeoSpectra.\u003c/p\u003e\u003c/div\u003e\u003cdiv id=\"Sec14\" class=\"Section2\"\u003e\u003ch2\u003e3.6. Comparison with similar results found in literature\u003c/h2\u003e\u003cp\u003eIn assessing the intramuscular fat and protein content of lyophilized ground beef using near-infrared spectroscopy, Bailes et al. (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) obtained validation error (RMSEP) values of 0.16% and 0.50% respectively, showing that prediction models can be used with precision for the evaluated product/characteristics. A good correlation was also found between the data obtained by the reference method and NIR for water content. Water has a high absorption in the near-infrared spectral region, which is why NIR spectroscopy is widely used to measure water content (Weeranantanaphan et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2011\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eWhen comparing the prediction error results from the external validation of the beef characteristics measured by Patel et al. (\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) is observed that the results obtained for the 'sous vide' beef tenderloin were slightly better for water and lipids. For water, the validation error for the tenderloin varied between 0.69% \u0026minus;\u0026thinsp;0.92% and for the beef between 0.96% \u0026minus;\u0026thinsp;1.25%, depending on the instrument used. Lipids varied between 0.72% \u0026ndash; 0.76% for the tenderloin and 0.80% \u0026minus;\u0026thinsp;1.06% for beef. For protein, a slightly better validation error was obtained for the beef, ranging from 0.51% to 0.62%, and for the tenderloin, from 0.93% to 0.96%. The validation error results for ash were very similar between the studies, varying between 0.12% \u0026ndash; 0.13% for the tenderloin and 0.06% for beef, independent of the instrument used.\u003c/p\u003e\u003cp\u003eDixit et al. (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) explored the potential of near-infrared (NIRS) spectroscopy to predict the fat and water content of ground beef samples in both on-line and at-line modes. Although the performance of the PLSR models was measured by R\u0026sup2; and RPD, the authors presented a table with SEP values, being 6.84 for fat and 4.72 for water for the at-line mode, and, 5.95 for fat and 4.33 para \u0026aacute;gua para o modo on-line. These values were reported without units hidden a more accurate comparison with the results of this work.\u003c/p\u003e\u003cp\u003eConsidering the results provided by Dixit et al. (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2017\u003c/span\u003e) express absolute values, the validation results obtained in this work are considerably better with being of 0.92% e 0.69% for water content, and 0.72% e 0.76% for fat employing the InnoSpectra e NeoSpectra, respectively. The results for the bias were also presented by those authors. For fat content are reported bias of 3.89 (at line) and 6.95 (on line). For water content \u0026minus;\u0026thinsp;1.24 (at line) and \u0026minus;\u0026thinsp;4.01. Both are higher than observed in the present work (Tables\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e and \u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eAlthough there is an intrinsic correlation between water and fat contents, as shown in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, the regression coefficients of the models differ significantly, as illustrated in Figures S5 (A and B) in the supplementary material. This means that the spectra provide distinct information used to estimate water and fat content. If the regression coefficients were equal, only inverted since the observed correlation is negative, it would not be viable to state that the NIR accessed information individually associated with the water and fat present in the sample.\u003c/p\u003e\u003cp\u003eThe only work found in the literature using NIR spectroscopy on \u0026lsquo;sous vide\u0026rsquo; meat products (Perez-Palacios et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) reports the determination of characteristics related to the texture of pork loin cooked \u0026lsquo;sous vide\u0026rsquo; at different cooking times. Among the parameters, the total water content was determined, but only the R\u0026sup2; and the scaled mean absolute error (MASE) were presented as quality criteria for the obtained model, which were 0.83 and 0.054%, respectively. The authors classify models based on their correlation coefficients, distinguishing between those with high correlation coefficients (R\u0026sup2; \u0026gt;0.75), acceptable correlations (R\u0026sup2; = 0.5\u0026ndash;0.75), and low correlations (R\u0026sup2; = 0.25\u0026ndash;0.5). Using this metric, the model obtained for humidity in this work using the NeoSpectra spectrometer also had a high correlation coefficient (R\u0026sup2; = 0.784), and the InnoSpectra resulted in an acceptable correlation model (R\u0026sup2; = 0.517). The authors also evaluated the influence of sample presentation (ground and in 1cm wide pieces), finding no influence on the absorbance values obtained by NIR, suggesting that similar results could be obtained if the sample spectra had been obtained from the product before seared.\u003c/p\u003e\u003c/div\u003e"},{"header":"4. Conclusion","content":"\u003cp\u003eNear-infrared spectroscopy associated with multivariate calibration methods using PLS enabled the development of a rapid method for determining the water, protein, fat, and ash content of pre-processed 'sous vide' beef tenderloins. The results indicate that the models developed using variable selection via the jack-knife algorithm provide reliable results, demonstrating the potential for implementing NIR technology for process control and monitoring, for research in the field, and for meeting the requirements of regulatory agencies. The results obtained by the two instruments were similar, except for the determination of water content, as the NeoSpectra instrument covers a spectral region where water absorbs with greater intensity.\u003c/p\u003e\u003cp\u003eA new approach to certifying the quality and utility of the validated NIR models is proposed, based on the analysis of the adequacy of the errors (RMSEP) and the preservation of the data distribution, as assessed by the differences between the parameters of maximum, minimum, median, first quartile (Q1), and third quartile (Q3) between the reference results and the prediction results of the validation samples.\u003c/p\u003e\u003cp\u003eThis study represents a significant contribution to the field of meat product processing, as studies involving 'sous vide' technology and NIR spectroscopy are scarce. The results demonstrate that the developed PLS-NIR multivariate calibration models enable the implementation of printing nutritional tables on the packaging of 'sous vide' beef tenderloins with greater frequency, on a per-production-lot basis, thereby generating more accurate and reliable information. Objective quality measurements of the products will also enable industrial managers to achieve higher levels of quality for their products.\u003c/p\u003e\u003cp\u003eA complementary future study is suggested to evaluate non-pre-processed (seared) products, that is, without the interference caused by surface alterations, as it is believed that good results could be obtained for the intact product without packaging, enabling the implementation of non-destructive in-line inspection.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eDeclaration of Competing Interest\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\n\u003cp\u003eAcknowledgments:\u0026nbsp;IF Sudeste MG for the financial support; Brasil Gourmet Indústria e Comércio de Alimentos S/A; LADINA (Laboratory of Analysis, Development and Innovation of Foods) of the Federal University of Viçosa.\u003c/p\u003e\n\u003cp\u003eThis work was supported by the Instituto Nacional de Ciências e Tecnologias Analíticas Avançadas (INCTAA)/Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) [grant number 465768/2014-8], INCTAA/Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) [grant number 2014/50951-4].\u0026nbsp;MCH and CP are grateful to CNPq for the research fellowships [grants number 305649/2021-3 and 305406/2024-8, respectively]. LPF and KAMLC thank CAPES-PROCAD for the scholar fellowships [grant number 88887.808376/2023-00 and 88887.838359/2023-00, respectively].\u003c/p\u003e\n\u003cp\u003eThis work was carried out with the support of the Coordination for the Improvement of Higher Education Personnel – Brazil (CAPES) – Financing Code 001; the National Council for Scientific and Technological Development – CNPq.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCRediT authorship contribution statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eD.R. Ferreira:\u003c/strong\u003e Investigation, Methodology, Data curation, Writing - Original Draft, Writing - Review \u0026amp; Editing\u003cstrong\u003e. E.A.F. Fontes:\u003c/strong\u003e Resources, Writing - Original Draft, Writing - Review \u0026amp; Editing, Supervision, Project administration, Funding acquisition. \u003cstrong\u003eC. Pasquini\u003c/strong\u003e: Conceptualization, Formal analysis, Writing - Original Draft, Writing - Review \u0026amp; Editing, Funding acquisition. \u003cstrong\u003eM. C. Hespanhol\u003c/strong\u003e: Conceptualization, Formal analysis, Resources, Writing - Original Draft, Writing - Review \u0026amp; Editing. \u003cstrong\u003eS.S. Pereira\u003c/strong\u003e: Investigation, Methodology, Data curation. \u003cstrong\u003eL. P. Foli\u003c/strong\u003e: Investigation, Methodology, Data curation. \u003cstrong\u003eK. A. M. L. Cruz\u003c/strong\u003e: Investigation, Methodology, Data curation.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe data supporting the findings of this study may be obtained under request to the corresponding author.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAleixandre-Tud\u0026oacute; JL, Castell\u0026oacute;-Cogollos L, Aleixandre JL, Aleixandre-Benavent R (2020) Bibliometric insights into the spectroscopy research field: A food science and technology case study. 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Technometrics 46(1):108\u0026ndash;110. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1198/004017004000000167\u003c/span\u003e\u003cspan address=\"10.1198/004017004000000167\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"food-analytical-methods","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Food Analytical Methods](https://www.springer.com/journal/12161)","snPcode":"12161","submissionUrl":"https://submission.nature.com/new-submission/12161/3","title":"Food Analytical Methods","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"sous vide meat, near-infrared spectroscopy, chemometrics, variable selection, quality characteristics","lastPublishedDoi":"10.21203/rs.3.rs-7776526/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7776526/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u0026lsquo;Sous vide\u0026rsquo; is a cooking process that uses long time and low temperatures, affecting the quality and composition of the product. This study aimed to develop and validate prediction models for the proximate composition of sous vide beef tenderloin using near-infrared reflectance spectroscopy (NIRS) and to compare the performance of two portable NIR spectrometers. Original spectra were pretreated using the Standard Normal Variate (SNV) method, followed by the 1st derivative. Models using partial least squares regression (PLS) were constructed with all spectral variables, and after the jack-knife algorithm performed wavelength selection. The centesimal composition of the ground samples was accurately determined by the models, except for the carbohydrate content. The prediction errors resulting from external validation (RMSEP) for the InnoSpectra and NeoSpectra evaluated compact instruments were, respectively, 0.92% and 0.65% for moisture, 0.72% and 0.93% for fat, 0.93% and 0.60% for protein, and 0.12% and 0.03% for ash. Conversely, poor results were obtained for samples where readings were taken from whole roasters with or without packaging. A new method for assessing the quality and usefulness of multivariate models was proposed based on RMSEP and comparing the distributions of the reference and validation data. The NIRS-based method is fast, requires simple sample preparation, does not require the use of chemicals, and employs low-cost instruments.\u003c/p\u003e","manuscriptTitle":"Composition assessment of sous vide beef meat by near-infrared spectroscopy based on compact spectrophotometers, multivariate regression, and jack-knife variable selection","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-10-28 17:34:36","doi":"10.21203/rs.3.rs-7776526/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2025-11-20T12:46:01+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-26T08:17:16+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-10-15T12:28:21+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"340241107411017287763729502609910625512","date":"2025-10-14T21:10:06+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"308715448226611239096798529906358766975","date":"2025-10-14T17:38:35+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"126576721756258528653660623453840418387","date":"2025-10-14T14:35:24+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-10-14T11:46:13+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-10-07T05:21:08+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-10-07T05:19:47+00:00","index":"","fulltext":""},{"type":"submitted","content":"Food Analytical Methods","date":"2025-10-03T22:54:25+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"food-analytical-methods","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Food Analytical Methods](https://www.springer.com/journal/12161)","snPcode":"12161","submissionUrl":"https://submission.nature.com/new-submission/12161/3","title":"Food Analytical Methods","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"8313c383-f9d5-46ce-b814-28d6336f8623","owner":[],"postedDate":"October 28th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2025-12-14T16:38:43+00:00","versionOfRecord":[],"versionCreatedAt":"2025-10-28 17:34:36","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7776526","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7776526","identity":"rs-7776526","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}