Impact of the pretreatment of ATR-FTIR signals on the figures of merit when PLS is used

Journal Pre-proof Impact of the pretreatment of ATR-FTIR signals on the figures of merit when PLS is used C. Mas, L. Rubio, L. Valverde-Som, L.A. Sarabia, M.C. Ortiz PII: S0169-7439(19)30816-0 DOI: https://doi.org/10.1016/j.chemolab.2020.104006 Reference: CHEMOM 104006 To appear in: Chemometrics and Intelligent Laboratory Systems Received Date: 13 December 2019 Revised Date: 17 March 2020 Accepted Date: 19 March 2020 Please cite this article as: C. Mas, L. Rubio, L. Valverde-Som, L.A. Sarabia, M.C. Ortiz, Impact of the pretreatment of ATR-FTIR signals on the figures of merit when PLS is used, Chemometrics and Intelligent Laboratory Systems (2020), doi: https://doi.org/10.1016/j.chemolab.2020.104006. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V. Credit Author Statement: C. Mas: Analytical methodology L. Rubio: Investigation, Analytical Methodology Writing - Original Draft, Writing, Supervision L. Valverde-Som: Investigation, Analytical Methodology, Supervision, Writing - Review & Editing L.A. Sarabia Conceptualization, Methodology,Formal analysis, Software, Supervision, Writing - Review & Editing M.C. Ortiz: Conceptualization, Supervision, Writing - Review & Editing 1 IMPACT OF THE PRETREATMENT OF ATR-FTIR SIGNALS ON THE FIGURES OF MERIT WHEN PLS IS USED C. Mas a , L. Rubio a , L. Valverde-Som a , L.A. Sarabia b , M.C. Ortiz a,1 a Department of Chemistry, b Department of Mathematics and Computation Faculty of Sciences, Universidad de Burgos Plaza Misael Bañuelos s/n, 09001 Burgos (Spain) Abbreviations 2 Abstract The efficiency of the analytical methods based on vibrational spectroscopy has been widely verified in a high number of publications. In addition, it has been recognized that the pretreatment of the original signals is absolutely necessary to obtain enough quality in the subsequent classification and/or regression models. In fact, an inappropriate pretreatment makes the results worse. It is also impossible to give “a priori” rules that guarantee the adequacy of a pretreatment for specific data. The effect of the pretreatments is evaluated through their impact on the quality of the classification and /or regression models built from them due to the double dependence (on the data and on the purpose of the analysis). The effect of the pretreatment has been evaluated using partial least squares regression (PLSR) in some works and the root mean squares in prediction or in cross-validation has been always used as a criterion to evaluate the regression in all these cases. However, it seems appropriate to use quality criteria of the calibration of the analytical method through the figures of merit: the significance of the regression, the absence of constant or proportional bias, the residual standard deviation, the mean of the absolute values of the relative errors and the capability of detection. In this work, the use of these analytical criteria in a desirability function is proposed for the first time with calibration data of oxybenzone obtained by ATR-FTIR and PLSR. 1 Corresponding author. Telephone number: +34-947-259571. E-mail address: [email protected] (M.C. Ortiz). 2 Attenuated total reflectance-Fourier transform infrared (ATR-FTIR), oxybenzone (BP3), capability of detection (CCβ) data preprocessing (DP), design of experiments (DoE), direct orthogonal signal correction (DOSC), extended multiplicative scatter correction (EMSC), infrared (IR), latent variable (LV), multiplicative scatter correction (MSC), near infrared (NIR), orthogonal signal correction (OSC), partial least squares regression (PLSR), root mean square error (RMSEC), root mean square error of cross-validation (RMSEC_CV), Standard error in prediction ( SEP), standard normal variate (SNV). 2 This desirability function enables to choose the best pretreatment among the 39 possibilities studied. In addition, it is shown that the same optimum is not obtained if the minimum of RMSEC_CV is considered as a criterion. Keywords Pretreatment data; ATR-FTIR; PLS; oxybenzone; desirability function; figures of merit 1. Introduction Data preprocessing (DP) has been recognized as a critical stage for high dimensional data analysis, particularly for data obtained using vibrational spectroscopy techniques. There are a lot of scientific works about different DP methods which can be classified in two large groups: i) pretreatment by means of orthogonal projections to extract the relevant information of a training set [1] using pure spectra and information extracted from experimental design and calibration datasets that includes the Orthogonal Signal Correction (OSC) family; ii) pretreatment by transformation of the spectral signal removing undesired physical phenomena [2,3]. This last group can be divided into two categories. The first one, scatter correction, includes Multiplicative Scatter Correction (MSC), Inverse MSC, Extended MSC (EMSC) [4,5], Extended Inverse MSC, normalization, and Standard Normal Variate (SNV). The second group belongs to the spectral derivatization group which includes the Norris-Williams derivatives and Savitzky-Golay polynomial derivatives. The relation between MSC and SNV [6] has been studied because are the pretreatments most employed in practice, also their effect on the signals [7] and the chemical interpretability of pretreated spectra [8]. At the same time, there are different review articles [5,9] and many tutorials that have been published to show the practical aspects of using DP, for example with near infrared (NIR) [2], Raman and infrared (IR) [3,5,10,11] or attenuated total reflectance-Fourier transform infrared (ATR-FTIR) [12] data. However, despite the emphasis on the importance of the pretreatment of spectra data, there are few contributions on the search of the optimal pretreatment for a data set. The critical revision of the most common three strategies used for the data pretreatment concludes that "all three have serious drawbacks: they may be time-consuming beyond practicability or may provide misleading results" [13]. Then, it is necessary to consider jointly successive types of pretreatment. For this reason, J. Engel et al. [13] have used a search space formed by 7x10x10x7 pretreatments for baseline, scatter, noise, smoothing and scaling/transformations, respectively. Other 7 pretreatments are added for OSC and Direct Orthogonal Signal Correction (DOSC). A similar strategy includes binning, smoothing, normalization and baseline correction with 3528 different pretreatments that could be partially permuted [14]. In other work, experimental design (DoE), specifically a full factorial (2 4 ), is used as a strategy to explore the effect of these same types of pretreatments [15]. In reference [16] this strategy for pretreatment is linked with 3 variable selection to improve the interpretation and the predictive capacity of a regression model. On the other hand, a factorial design 2 4 is used with three different methods applied in variable selection to the four pretreatments selected in [17]. A Doptimal design to optimize the pretreatment in three intermediate stages is also used for a metabolomic data fusion of urine and serum in [18]. Many works analyse or optimise the data pretreatment before applying a classification technique. In general, a criterion to evaluate the classifier (e.g. the % of misclassification) is used. Only H.J. Butler et al. [14] used several criteria combined additively in one unique value. The need for carrying out a pretreatment of the spectra provided by vibrational spectroscopic techniques before applying a regression method, which is usually a Partial Least Squares Regression (PLSR), is completely accepted. In the literature consulted, the effect of changing the pretreatment is analysed through the change caused in the PLSR quality parameters. In this case, Root Mean Square Error of Prediction (RMSEP) [15,17], Root Mean Square Error of Cross-Validation (RMSEC_CV) [16] and a estimation of Root Mean Square Error (RMSEC) based on bootstrap [2] are used. In these works, the use of quality criteria of an analytical method evaluated by means of the regression “predicted concentration with PLSR versus true concentration of the test sample”, which is named as the accuracy line in prediction, is not tackled. This work proposes to study the effect of the pretreatment on the quality parameters of the PLSR model and on the accuracy line in prediction by means of ATR-FTIR data of the determination of oxybenzone, benzophenone-3 (BP3). BP3 is an additive used in the manufacture of sunscreen cosmetic creams and its determination by ATR-FTIR is possible due to the amount found in creams. 2. Material and methods 2.1 Chemicals 2-hydroxy-4-methoxybenzophenone (oxybenzone, CAS no. 131-57-7, 98% purity) was purchased from Sigma-Aldrich (Steinheim, Germany). Ethanol (96% vol., CAS no. 64-17-5, HiPerSolv CHROMANORM®, gradient grade for HPLC) was supplied by VWR International (Radnor, Pennsylvania, USA) and acetone (CAS no. 67-64-1) for liquid chromatography Lichrosolv® was from Merck KGaA (Darmstadt, Germany). 2.2 Standard solutions A stock solution of BP3 at 30275 mg L -1 was prepared in ethanol and intermediate solutions at concentrations of 5000, 10000, 15000 and 20000 mg L -1 were prepared from that stock solution in ethanol as calibration standards. All solutions, whose 4 weights were controlled to verify that the solvent had not evaporated, were stored in crimp vials at 4ºC and protected from light. The stability of the solutions of BP3 has been verified by GC/MS, being the stock and intermediate solutions of BP3 stable for 15 days as can be seen in ref. [19]. 2.3. Instrumental An Agilent Cary 630 FTIR spectrometer coupled to a ZnSe ATR module for measuring liquids samples (Agilent Technologies, Santa Clara, CA, USA) was used to perform the analyses. The number of reflections of the crystal with this module was 5. The main optical unit dimensions were only 16 × 22 × 13 cm. The Cary 630 FTIR spectrometer contained a unique Michelson interferometer. The spectral range to collect the absorbance signal was from 650 to 4000 cm -1 with 32 scans and the spectral resolution was fixed to 4 cm -1 using Happ-Genzel as apodization function [20]. The method gain was set at 255. 2.4. Steps to measure the sample First, air collection as background was selected with 16 scans. The background was collected at the beginning of the sequence and it was not measured again between samples. Then, a volume of 100 µL of the sample was put on the crystal. In this step, the absorbance signal was collected. Finally, two solvents (ethanol and acetone) were used to clean the crystal using delicate task wipers (Kimwipes®, from Sigma-Aldrich). A volume of 100 µL of ethanol was put on the crystal and the signal was recorded to check if the crystal was clean. 2.5. Software MicroLab PC, version 5.3.1748 (Agilent Technologies, Inc.) with Data Analysis software was used for acquiring data. The different pretreatments of the signals and PLSR models were performed with the PLS_Toolbox [21] used under MATLAB environment [22]. The regression models were fitted and validated using STATGRAPHICS Centurion XVI [23]. Capability of detection (CCβ) was calculated using the DETARCHI program [24]. 3. Calculations 3.1. Data A wide calibration range and few concentration levels were used as in routine analyses. The calibration set was made up of four samples at concentrations of 5000, 10000, 15000 and 20000 mg L -1 of BP3 and a blank. The test set was made up of other samples of the same concentrations of BP3 which were prepared again and independently of the calibration standards. The matrix dimensions in both cases are 5×1798. 5 3.2. Pretreatment The introduction section described different data pretreatments. In this work, the most common data pretreatment is chosen for ATR-FTIR spectroscopy data with liquid samples: 1) Multiplicative Scatter Correction (MSC) or Standard Normal Variate (SNV) to correct the scattering signal. 2) Savitzky-Golay smoothing (SG) with windows of 15 (or 25) points, a second order polynomial and second derivative. 3) Mean centering or Autoscaling for scale correction. In addition, the possibility of applying only one, two or no correction has been included. Scaling is the only pretreatment of the three ones described above that is not directly related to the elimination of any signal artefact. If scaling is used, it should be the last step of the pretreatment because its effect is to unify the statistical scale of the variables (mean and/or variances). Therefore, if scaling is used prior to scatter correction, the scaling effect will be partially attenuated by the scatter correction method. However, the other two steps may be changed in order. This may be important, e.g., the effect of exchanging the MSC and SG pretreatments is checked in ref. [25]. Table 1 shows the code of the different pretreatments used. By way of example, the code "253" means that SNV has been applied in the first step, Savitzky-Golay smoothing with windows of 15 points in the second step, and Autoscaling in the last step. The code “141” means that no pretreatment has been performed. When the change of order between scatter and smoothing is considered, duplication must be avoided when one of them is not applied. By way of example, the pretreatment “153” (which means using the code of Table 1: do not apply scatter correction, SG with 15 points and autoscaling) would be the same pretreatment as "513". Therefore, only a total of 39 different pretreatments have been applied. Given a set of spectra S i , i=1,.., n (e.g. a set of calibration samples), ref. [6] shows that there is a linear relationship between each spectrum transformed by SNV and the one transformed by MSC, although that linear relationship is different for each S i . Therefore, the pretreated spectra are similar except for a rotation and an offset correction and it is generally assumed that “MSC and SNV are the same for the most practical applications” [9,26] but the results are not always very similar. Fearn et al. [7] obtained “very different results when NIR spectral data were pre-treated with SNV and MSC, the former leading to a striking ellipsoidal structure in a plot of principal component scores and the latter to a plot with many extreme outliers”. In addition, ref. [8] shows that MSC (and other pretreatments of the same family including non-linear approaches as EMSC) produces a shift along the signal profile which leads to artefacts in the principal component analysis of the spectra. Both pretreatments have been included since the aim of this work is the analysis of the effect of the pretreatments on 6 the PLSR calibrations and there are no comparative studies in literature about the differences caused by SNV and MSC in the figures of merit. <Table 1> 3.3. PLSR model The PLSR model is built with the training data set and each of the 39 different pretreatments. The number of latent variables is the one that provides the minimum RMSEC_CV with leave-one-out as cross-validation. Then, the model is applied to the test set. In both cases, Hotelling's T 2 and Q-residual statistic at a 95% confidence level are used to check if there is any outlier. No outlier data was found in the built models. 4. Results and discussion 4.1. Effect of the pretreatment on PLSR models Table 2 shows all the pretreatments with different information about the PLSR models. The second column of this table indicates the number of latent variables in the model, whereas root mean square in calibration (RMSEC) and in cross-validation (RMSEC_CV) are collected in the third and fourth columns, respectively. In addition, standard error in prediction (SEP) has been calculated. <Table 2> The pretreatments with Savitzky-Golay smoothing with windows of 15 points and without scaling (codes 151, 251 and 351) show the greatest values of RMSEC_CV, SEP and RMSEC. On the other hand, the pretreatments without Savitzky-Golay smoothing and no autoscaling (codes 342, 341, 241, 242, 142 and 141) show the lowest values of RMSEC_CV with values between 2881.7 and 3002.9, but intermediate values of RMSEC (between 900 and 1000). In those cases, the selection of scatter correction (1, 2 or 3 in the first position of the code) is indifferent. The effect of no scaling or mean centering (1 or 2 in the third position of the code) is very small and it is only observed when the scatter correction is used, in which case mean centering provides better values of RMSEC, RMSEC_CV and SEP, but increases ERROR, s yx , and CCβ. The absolute minimum is achieved with a value of 2881.7 of RMSEC_CV with the pretreatment 342. 4.2. Effect of the pretreatment on the figures of merit of the analytical method In the scope of chemical analysis, it is important to validate the calibration model of an analytical method as well as to obtain the figures of merit. The statistical procedure for this task can be found in reference [27]. It is interesting to know, through the PLSR 7 model, the impact on these figures of merit to evaluate the different pretreatments carried out. First, the PLSR model is built; then, the regression line "predicted concentration with PLSR versus true concentration of BP3" which is known as accuracy line is validated. The test set samples of these regressions were not used to build the previous PLSR model. Table 2 shows the parameters of the accuracy lines in columns 6, 7, 8 and 9 such as the correlation coefficient (r), residual standard deviation (s yx ), intercept (b 0 ) and slope (b 1 ), respectively. 4.2.1. Significance of the accuracy line The hypothesis test to evaluate the significance of the accuracy line involves: H 0 : the regression does not explain a variance bigger than the residual. H a : the regression explains the variability of the response, so the regression is significant. The null hypothesis (H 0 ) is rejected if the p-value of test is lower than 0.05, in which case the alternative hypothesis (H a ) is accepted. Table 2 shows the p-values of the significance test (p-s, column 10) which are significant and H 0 is rejected. These results are coherent with the correlation coefficients which have values between 0.96 and 1.00 (Table 2, column 6). 4.2.2. Bias of the accuracy line The accuracy line should have the intercept equal to zero and the slope equal to one. Otherwise, the analytical procedure has constant and/or proportional bias. The hypothesis test is the following one (page 141 of ref. [27]): H 0 : intercept and slope are equal to zero and one, respectively (b 0 =0 and b 1 =1). H a : is not the case, the accuracy line is biased. The null hypothesis (H 0 ) is rejected if the p-value is lower than 0.05, in which case the alternative hypothesis (H a ) is accepted. Table 2 shows the p-values (p-F, column 11). The nine pretreatments with Savitzky-Golay smoothing with windows of 15 points (all of them marked with number 5 in the second position of the code in PRET of Table 2) show values lower than 0.05, therefore, H 0 is rejected. These pretreatments (151, 152, 153, 251, 252, 253, 351, 352 and 353) are not considered acceptable from an analytical point of view; in addition, the greatest values of RMSEC_CV and SEP are among them. 4.2.3. Relative error 14 [26] T. Fearn, The effect of spectral pre-treatments on interpretation, NIR News 20 (2009) 15.16. 15e16, https://doi.org/10.1255/nirn.1146. [27] M.C. Ortiz, M.S. Sánchez, L.A. Sarabia, Quality of analytical measurements: univariate regression, in: S.D. Brown, R. Tauler, B. Walczak (Eds.), Comprehensive chemometrics. Chemical and biochemical data analysis. Elsevier, v1, Amsterdam, 2009, pp. 127-169. https://doi.org/10.1016/B978-0444527011.00091-0. [28] International Organization for Standardization, ISO 11843-1:1997, Capability of detection - Part1: Terms and definitions, Genève, Switzerland, 1997. [29] International Organization for Standardization, ISO 11843-2:2000, Capability of detection – Part2: Methodology in the linear calibration case, Genève, Switzerland, 2000. [30] J. Inczédy, T. Lengyel, A.M. Ure, A. Gelencsér, A. Hulanicki, International Union of Pure and Applied Chemistry, IUPAC Compendium of analytical nomenclature, third ed., Baltimore, Port City Press Inc., 2000. [31] G. Derringer, R. Suich, Simultaneous optimization of several response variables, J. Qual. Technol. 12 (1980) 214-219. [32] M.C. Ortiz, L.A. Sarabia, M.S. Sánchez, Tutorial on evaluation of type I and type II errors in chemical analyses: From the analytical detection to authentication of products and process control, Anal. Chim. Acta 674 (2010) 123-142, https://doi.org/10.1016/j.aca.2010.06.026 [33] R.G. Brereton, The use and misuse of p values and related concepts, Chemom. Intell. Lab. Syst. 195 (2019) 103884 https://doi.org/10.1016/j.chemolab.2019.103884 15 FIGURE CAPTIONS Figure 1 Parallel coordinates plot of the values of the quality variables of the PLSR model and the accuracy line. The codification of variables is the same as in Table 2. Figure 2 Principal component analysis of the variables RMSEC, RMSEC_CV, SEP, r, s yx , b 0 , b 1 , ERROR and CCβ of Table 2. A) Loadings on the first and second PC and B) loadings on the first and third PC. Table 1 Pretreatments and their codification. Code / Scatter correction Code / Noise correction Code / Scaling 1 No scatter correction 4 No noise removal 1 No scaling 2 SNV 5 S-G smoothing, window 15 points 2 Mean centering 3 MSC 6 S-G smoothing, window 25 points 3 Autoscaling SNV, Standard Normal Variate; MSC, Multiplicative Scatter Correction; S-G, Savitzky-Golay. Table 2 PLS models and accuracy line (see the pretreatments codification in Table 1) PRET L.V. RMSEC RMSEC_CV SEP r s yx b 0 b 1 p-s p-F ERROR CCβ 141 3 994.02 3002.91 2422.31 0.9709 1703.7 4020 0.757 0.00590 0.118 24.4 12687 142 2 990.57 2967.13 2367.66 0.9705 1746.1 3976 0.770 0.00610 0.126 24.9 12790 143 2 1098.44 3487.76 1776.56 0.9853 1310.0 2755 0.827 0.00210 0.154 16.0 8928 151 2 1779.22 6266.01 4965.47 0.9650 943.3 7150 0.380 0.00780 0.004 38.1 13975 152 2 167.99 5684.47 3880.48 0.9747 1096.7 5884 0.524 0.00480 0.013 33.8 11796 153 2 89.47 4343.81 3089.47 0.9803 1160.6 4476 0.630 0.00330 0.031 22.0 10376 161 2 912.70 4717.50 2375.71 0.9806 1346.0 3334 0.738 0.00320 0.100 11.8 10279 162 1 660.33 4061.57 1734.71 0.9885 1146.9 2509 0.820 0.00150 0.141 12.8 7883 163 2 738.88 3751.92 2276.04 1.0000 63.7 0 1.000 0.00001 1.000 14.5 359 241 3 899.14 2889.14 2272.84 0.9766 1542.7 3795 0.767 0.00430 0.108 22.7 11331 242 2 900.19 2889.48 2271.66 0.9766 1541.8 3794 0.768 0.00430 0.108 22.7 11323 243 2 865.46 3864.61 2480.90 0.9686 1762.8 4225 0.753 0.00660 0.113 27.4 13202 251 2 1740.41 6257.89 4939.87 0.9666 927.7 7101 0.383 0.00730 0.004 37.8 13637 252 2 105.20 5974.19 4230.66 0.9734 1024.5 6322 0.477 0.00520 0.008 34.2 12113 253 2 84.07 4316.10 3148.11 0.9797 1163.6 4534 0.623 0.00350 0.030 22.1 10533 261 2 928.66 4726.40 2361.94 0.9807 1348.1 3310 0.740 0.00320 0.103 11.5 10265 262 1 811.85 4480.37 2033.53 0.9863 1189.3 2851 0.778 0.00190 0.109 11.3 8614 263 2 20.53 3759.02 2462.69 1.000 26.50 0 1.000 0.00001 1.000 15.3 88 341 3 899.52 2881.97 2273.51 0.9767 1539.4 3801 0.767 0.00430 0.107 22.7 11312 342 2 899.62 2881.71 2273.52 0.9767 1539.4 3801 0.767 0.00430 0.107 22.7 11312 343 2 790.41 3861.69 2408.57 0.9714 1692.4 4140 0.758 0.00580 0.107 27.3 12581 351 2 1743.09 6254.58 4943.96 0.9667 925.6 7112 0.383 0.00730 0.004 37.8 13626 352 2 113.70 5969.39 4236.79 0.9726 1038.6 6340 0.476 0.00540 0.008 34.4 12292 353 2 84.28 4308.06 3151.74 0.9798 1157.6 4554 0.622 0.00340 0.029 22.2 10490 361 2 919.48 4720.54 2363.63 0.9808 1343.9 3319 0.740 0.00320 0.101 11.5 10240 362 2 53.54 4535.90 2110.54 0.9889 3103.8 3102 0.759 0.00140 0.501 13.7 23062 363 2 721.44 3755.32 2461.20 1.0000 63.7 0 1.000 0.00001 1.000 15.4 359 521 3 36.13 6145.40 4518.96 0.9767 46.64 0 1.000 0.00001 1.000 34.2 263 522 2 36.29 6144.19 4519.84 0.9767 46.85 0 1.000 0.00001 1.000 34.3 264 523 2 84.34 4383.23 3070.23 0.9999 108.89 1 1.000 0.00001 1.000 22.5 614 621 2 1679.93 6227.64 4906.01 0.9714 2105.97 522 0.944 0.00580 0.917 37.1 12581 622 2 74.31 4859.11 2353.86 1.0000 15.63 0 1.000 0.00001 1.000 12.5 88 623 2 34.57 6144.32 3104.53 0.9999 108.74 1 1.000 0.00001 1.000 22.3 613 531 2 958.31 4742.01 2355.93 0.9908 1225.76 185 0.982 0.00110 0.974 11.1 7039 532 2 958.60 4742.02 2355.93 0.9908 1226.13 184 0.982 0.00110 0.974 11.1 7041 533 2 12.10 3788.33 2577.24 1.0000 15.62 0 1.000 0.00001 1.000 17.6 88 631 2 957.54 4741.76 2355.06 0.9908 1224.79 181 0.982 0.00110 0.974 11.1 7033 632 2 74.41 4850.72 2345.98 0.9999 96.06 1 1.000 0.00001 1.000 12.6 542 633 2 12.12 3779.46 2530.69 1.0000 15.64 0 1.000 0.00001 1.000 17.5 88 PRET, spectra data pretreatment (see the codification in Table 1); LV, number of latent variable in the PLS model; RMSEC, Root Mean Squares Error in Calibration and the same in cross validation, RMSEC_CV; SEP, Standard Error in Prediction; r, correlation coefficient; s yx residual standard deviation; b 0 , intercept ; b 1 , slope; p-s, p-value of the significance test; p-b 0 &b 1 , p-value to jointly test the intercept = 0 and slope = 1; ERROR (%), mean of the absolute values of the relative error; CCβ (mg L -1 ), capability of detection with the probabilities of false positive and false negative fixed to 0.05. Table 3 Principal component analysis of the variables RMSEC, RMSEC_CV, SEP, s yx , b 0 , b 1 , ERROR and CCβ Principal Component Eigenvalue Explained variance (%) Accumulated variance (%) 1 3.943 49.29 49.29 2 2.317 28.96 78.25 3 0.773 9.66 87.91 Table 4 Global desirability (D) for each pretreatment (PRET) PRET D PRET D PRET D 141 0.0000 241 0.0000 341 0.0000 142 0.0000 242 0.0000 342 0.0000 143 0.2898 243 0.0000 343 0.0000 151 0.0000 251 0.0000 351 0.0000 152 0.0000 252 0.0000 352 0.0000 153 0.0000 253 0.0000 353 0.0000 161 0.2511 261 0.2521 361 0.2556 162 0.4269 262 0.3965 362 0.0000 163 0.9188 263 0.9105 363 0.8969 521 0.0000 531 0.4284 522 0.0000 532 0.4281 523 0.6529 533 0.8486 621 0.0000 631 0.4290 622 0.9761 632 0.9497 623 0.6618 633 0.8515 FIGURE 1 RMSEC r S yx b0 b1 p-s p-F ERROR CCβ RMSEC_CV SEP 288112 1734 0.97 15.6 0.0 0.38 0.0 0.0 11.1 88 62661780 4965 1.00 3104 7150 1.00 0.01 1.00 38.1 23062 FIGURE 2 Component 1 - 0.47 - 0.27 - 0.07 0.13 0.33 0.5 - 0.47 - 0.27 - 0.07 0.13 0.33 0.53 Component 2 Component 1 RMSEC RMSEC_CV SEP ERROR b0 CCβ A) syx b1 RMSEC RMSEC_CV s yx b 0 b 1 ERROR SEP - - 0.27 - 0.07 0.13 0.33 0.53 Component 1 - 0.4 - 0.1 0.2 0.5 0.8 1.1 Component 3 CCβ B) HIGHLIGHTS Signal pretreatment mostly influences the vibrational spectroscopy methods A procedure to obtain the best pretreatment is developed for PLSR calibration The procedure is a multicriteria strategy that models the accuracy line quality The performance of the procedure has been proved for calibration of BP3 by ATR-FTIR