Multi-way chromatographic calibration—A review

An optimized methodology for the determination of multiclass organic ultraviolet sunscreens and metabolites in human milk through chromatographic and chemometric resolution

Organic UV filters (UVFS) are used to mitigate the dermal effects associated with health risks from UV radiation, making them essential in personal care products. UVFS are frequently identified in environmental samples due to their high lipophilicity and persistence, underscoring the urgency of comprehensive assessments and regulatory measures aimed at safeguarding ecosystems and human health. The present study reports a multiclass analytical method for determining 16 UV sunscreens and metabolites in breast milk based on an ultrasound-assisted-dispersive liquid-liquid micro-extraction (UA-DLLME) with further chromatographic and chemometric resolution. The experimental conditions of the UA-DLLME were optimized through the implementation of the Design of Experiment tools. To model the responses, least-squares and artificial neural network methodologies were implemented. The optimal conditions were found by employing the desirability function. The samples were analyzed through reverse-phase liquid chromatographic separation, UV diode array, and fast-scanning fluorescence detection. The chromatographic analysis enabled the resolution of 16 analytes in a total time of 13.0 min. Multivariate curve resolution-alternating least-square (MCR-ALS) modelling was implemented to resolve analytes that were not fully resolved and to determine analytes that coeluted with endogenous components of the breast milk samples. An enrichment factor of 5-fold concentration was obtained with this methodology, reaching recoveries between 65 % and 105 % for 13 multiclass UV sunscreens and metabolites in breast milk samples with RSD % and REP % lower than 12 %.

Enhanced efficiency of MS/MS all-ion fragmentation for non-targeted analysis of trace contaminants in surface water using multivariate curve resolution and data fusion

Data-independent acquisition-all-ion fragmentation (DIA-AIF) mode of mass spectrometry can facilitate wide-scope non-target analysis of contaminants in surface water due to comprehensive spectral identification. However, because of the complexity of the resulting MS2 AIF spectra, identifying unknown pollutants remains a significant challenge, with a significant bottleneck in translating non-targeted chemical signatures into environmental impacts. The present study proposes to process fused MS1 and MS2 data sets obtained from LC-HRMS/MS measurements in non-targeted AIF workflows on surface water samples using multivariate curve resolution-alternating least squares (MCR-ALS). This enables straightforward assignment between precursor ions obtained from resolved MS1 spectra and their corresponding MS2 spectra. The method was evaluated for two sets of tap water and surface water contaminated with 14 target chemicals as a proof of concept. The data set of surface water samples consisting of 3506 MS1 and 2170 MS2 AIF mass spectral features was reduced to 81 components via a fused MS1-MS2 MCR model that describes at least 98.8% of the data. Each component summarizes the distinct chromatographic elution of components together with their corresponding MS1 and MS2 spectra. MS2 spectral similarity of more than 82% was obtained for most target chemicals. This highlights the potential of this method for unraveling the composition of MS/MS complex data in a water environment. Ultimately, the developed approach was applied to the retrospective non-target analysis of an independent set of surface water samples.

Open-Source Chromatographic Data Analysis for Reaction Optimization and Screening

Automation and digitalization solutions in the field of small molecule synthesis face new challenges for chemical reaction analysis, especially in the field of high-performance liquid chromatography (HPLC). Chromatographic data remains locked in vendors' hardware and software components, limiting their potential in automated workflows and data science applications. In this work, we present an open-source Python project called MOCCA for the analysis of HPLC-DAD (photodiode array detector) raw data. MOCCA provides a comprehensive set of data analysis features, including an automated peak deconvolution routine of known signals, even if overlapped with signals of unexpected impurities or side products. We highlight the broad applicability of MOCCA in four studies: (i) a simulation study to validate MOCCA's data analysis features; (ii) a reaction kinetics study on a Knoevenagel condensation reaction demonstrating MOCCA's peak deconvolution feature; (iii) a closed-loop optimization study for the alkylation of 2-pyridone without human control during data analysis; (iv) a well plate screening of categorical reaction parameters for a novel palladium-catalyzed cyanation of aryl halides employing O-protected cyanohydrins. By publishing MOCCA as a Python package with this work, we envision an open-source community project for chromatographic data analysis with the potential of further advancing its scope and capabilities.

Development and Optimization of a New UPLC-UV/MS Method through DoE and MLR for Detecting Substandard Drug Products to Treat Tuberculosis

Drug products used for treating tuberculosis are one of the most widely reported medicines to be classified as falsified or substandard in low- and middle-income countries, representing a major hazard to health. The aim of this study was, firstly, to develop an ultra-performance liquid chromatography (UPLC) method which is able to analyze fixed combination tablets with up to four active pharmaceutical ingredients, including isoniazid, pyrazinamide, rifampicin, and ethambutol. Secondly, we aimed to optimize it through the design of experiments and multi-linear regression based on a central composite design and to validate it according to the guidelines of the International Conference on Harmonization. The application of this tools enabled the identification of the influential factors (flow rate, formic acid, and temperature) and their effects on the studied responses (retention factor and percentage for each drug) as part of the quality by design approach. The method proved to be to be linear in the range from 5.0 to 15 µg/mL for isoniazid, pyrazinamide, and rifampicin, being precise (<1%) and accurate (97−101%). In addition, the method validated for ethambutol proved to be linear from 1.4 to 4.2 µg/mL, as well as precise (0.54%) and accurate (97.3%). The method was stability indicated for all the active pharmaceutical ingredients studied and was able to detect two substandard formulations sampled on the African market.

Advances in Fingerprint Analysis for Standardization and Quality Control of Herbal Medicines

Herbal drugs or herbal medicines (HMs) have a long-standing history as natural remedies for preventing and curing diseases. HMs have garnered greater interest during the past decades due to their broad, synergistic actions on the physiological systems and relatively lower incidence of adverse events, compared to synthetic drugs. However, assuring reproducible quality, efficacy, and safety from herbal drugs remains a challenging task. HMs typically consist of many constituents whose presence and quantity may vary among different sources of materials. Fingerprint analysis has emerged as a very useful technique to assess the quality of herbal drug materials and formulations for establishing standardized herbal products. Rather than using a single or two marker(s), fingerprinting techniques take great consideration of the complexity of herbal drugs by evaluating the whole chemical profile and extracting a common pattern to be set as a criterion for assessing the individual material or formulation. In this review, we described and assessed various fingerprinting techniques reported to date, which are applicable to the standardization and quality control of HMs. We also evaluated the application of multivariate data analysis or chemometrics in assisting the analysis of the complex datasets from the determination of HMs. To ensure that these methods yield reliable results, we reviewed the validation status of the methods and provided perspectives on those. Finally, we concluded by highlighting major accomplishments and presenting a gap analysis between the existing techniques and what is needed to continue moving forward.

Stationary Phases for Green Liquid Chromatography

Industrial research, including pharmaceutical research, is increasingly using liquid chromatography techniques. This involves the production of large quantities of hazardous and toxic organic waste. Therefore, it is essential at this point to focus interest on solutions proposed by so-called “green chemistry”. One such solution is the search for new methods or the use of new materials that will reduce waste. One of the most promising ideas is to perform chromatographic separation using pure water, without organic solvents, as a mobile phase. Such an approach requires novel stationary phases or specific chromatographic conditions, such as an elevated separation temperature. The following review paper aims to gather information on stationary phases used for separation under purely aqueous conditions at various temperatures.

Chromatographic Applications in the Multi-Way Calibration Field

In this review, recent advances and applications using multi-way calibration protocols based on the processing of multi-dimensional chromatographic data are discussed. We first describe the various modes in which multi-way chromatographic data sets can be generated, including some important characteristics that should be taken into account for the selection of an adequate data processing model. We then discuss the different manners in which the collected instrumental data can be arranged, and the most usually applied models and algorithms for the decomposition of the data arrays. The latter activity leads to the estimation of surrogate variables (scores), useful for analyte quantitation in the presence of uncalibrated interferences, achieving the second-order advantage. Recent experimental reports based on multi-way liquid and gas chromatographic data are then reviewed. Finally, analytical figures of merit that should always accompany quantitative calibration reports are described.

Application of alternating trilinear decomposition-assisted multivariate curve resolution to gas chromatography-mass spectrometric data for the quantification of polycyclic aromatic hydrocarbons in aerosols

For the first time, alternating trilinear decomposition-assisted multivariate curve resolution (ATLD-MCR) was applied to analyse complex gas chromatography-mass spectrometric (GC-MS) data with severe baseline drifts, serious co-elution peaks and slight retention time shifts for the simultaneous identification and quantification of polycyclic aromatic hydrocarbons (PAHs) in aerosols. It was also compared with the classic multivariate curve resolution-alternating least-squares (MCR-ALS) and the GC-MS-based external standard method. In validation samples, average recoveries of five PAHs were within the range from (96.2 ± 6.8)% to (106.5 ± 4.1)% for ATLD-MCR, near to the results of MCR-ALS ((98.0 ± 1.5)% to (106.7 ± 4.3)%). In aerosol samples, the concentrations of pyrene provided by ATLD-MCR were not significantly different from those of MCR-ALS. The other four PAHs including chrysene, benzo[a]anthracene, fluoranthene and benzo[b]fluoranthene were not detected by ATLD-MCR and the GC-MS-based external standard method. The results of figures of merit further demonstrated that ATLD-MCR achieved high sensitivities (8.9 × 104 to 1.7 × 106 mAU ml µg-1) and low limits of detection (0.003 to 0.087 µg ml-1), which were better than or similar to MCR-ALS, presenting a great choice to deal with complex GC-MS data for the simultaneous determination of targeted PAHs in aerosols.

Application of Chemometrics-assisted HPLC-DAD Strategies for Simultaneous Determination of Paracetamol, Pseudoephedrine HCl, Dextromethorphan HBr, Doxylamine Succinate and Saccharin in Syrup Formulation

Introduction:

This study introduces an effective strategy, which combines high performance liquid chromatography coupled with diode array detection (HPLC-DAD) with multivariate calibration methods for the simultaneous determination of paracetamol (PAR), pseudoephedrine HCl (PSE), dextromethorphan HBr (DEX) and doxylamine succinate (DOX) along with sweetener saccharin (SAC) in syrup formulation.

Methods:

PLS-2 and PCR calibration algorithms were selected for data processing. Based on the strategy, all target analytes were rapidly quantified within 5.3 min under the simple isocratic elution (water: methanol, 20/80, v/v) without a complete separation. The performances of the proposed methods were confirmed by analyzing a series of synthetic solutions including different concentrations of analytes.

Results:

The average recovery values were in the range of 100.33 to 103.70%, and the REP (relative error of prediction) values ranged from 1.96 to 4.36% showed that these methods could provide satisfactory predictions.

Conclusion:

Novel HPLC methods coupled with PLS and PCR algorithm enable a simple, fast and low-cost analysis of similar pharmaceutical products for simultaneous determination of the target compounds.

Multilinear Mathematical Separation in Chromatography

Chromatography is a powerful and generally applicable method for the analytical separation and quantification of the chemical constituents in complex mixtures because chromatographic separation can provide high selectivity by isolating all analytes from interferences. Multiway analysis based on the multilinear model is an increasingly widely used method for interference-free and fast determination of the chemical constituents also in complex mixtures because multilinear mathematical separation can provide high selectivity by extracting the pure signal of the analyte from the mixed signal of a real sample. By combining chromatographic separation with mathematical separation, multiway calibration method, multiway standard additions method, and multiway internal standard method can be established. Chromatography assisted by multiway analysis can reduce the requirements for complete chromatographic separation, save elution time, and decrease the consumption of the mobile phase, particularly when the peak coelution problem is difficult to solve. This review presents the fundamentals and analytical applications of multilinear mathematical separation in chromatography.

Three-way calibration using PARAFAC and MCR-ALS with previous synchronization of second-order chromatographic data through a new functional alignment of pure vectors for the quantification in the presence of retention time shifts in peak position and shape

In the present contribution is shown the application of the recently developed functional alignment of pure vectors (FAPV) as a proper algorithm to align second-order chromatographic data with severe retention time shifts in peak position and shape. FAPV decomposed a three-way chromatographic data array in their three modes (sample, spectral and elution time vectors), using a basis function to pre-process the non-linear mode (elution time) and then it aligns the functionalized pure vectors and reshapes the transformed vectors into matrices, restoring the trilinearity of second-order chromatographic data. The well-aligned three-way chromatographic data array is then successfully decomposed by advanced chemometric models such as parallel factor analysis (PARAFAC) and multivariate curve resolution - alternating least-squares (MCR-ALS) with the trilinearity constraint. The performance of this innovative analytical strategy based on PARAFAC and MCR-ALS with previous synchronization of data through FAPV algorithm is properly evaluated using real second-order chromatographic data with multiple artifacts, i.e., shifts in peak position and shape for the simultaneous quantification of amoxicillin and potassium clavulanate in commercial medicinal drugs. The present contribution compares some analytical results achieved by: (1) the usual MCR-ALS as a bilinear model applied in augmented data matrix without previous synchronization and with interval correlation optimized shifting (ICOSHIFT) and FAPV and (2) trilinear models using PARAFAC with ICOSHIFT and FAPV and trilinearity constraint in MCR-ALS with FAPV. Available results suggest that these strongly shifted and warped elution time profiles cause for the loss of trilinearity, which can be adequately restored by FAPV algorithm. PARAFAC performed a successful trilinear decomposition of three-way chromatographic data array with law values of relative prediction error (REP) in the order of 1.34-1.42% in both analytes.

Assessment of the Kernel Gram Matrix Representation of Data in Order to Avoid the Alignment of Chromatographic Signals

This article discusses the possibility of exploratory data analysis of samples described by second-order chromatographic data affected by peak shifts. In particular, the potential of the kernel Gram matrix representation as an alternative to the necessary and time-consuming alignment step is evaluated. It was demonstrated through several simulation studies and comparisons that even small peak shifts can be a substantial source of data variance, and they can easily hamper the interpretation of chromatographic data. When peak shifts are small, their negative effect is far more destructive than the impact of relatively large levels of the Gaussian noise, heteroscedastic noise, and signal's baseline. The Gram principal component analysis approach has proven to be a well-suited tool for exploratory analysis of chromatographic signals collected using the diode-array detector in which sample-to-sample peak shifts were observed.

A down-to-earth analyst view of rotational ambiguity in second-order calibration with multivariate curve resolution - a tutorial

Rotational ambiguity is a phenomenon with the potential of generating an uncertainty in the estimation of analyte concentrations in protocols based on matrix instrumental data processed by multivariate curve resolution - alternating least-squares (MCR-ALS). This is particularly relevant when the second-order advantage is to be achieved, i.e., when selected analytes are determined in unknown samples having unexpected constituents, not considered in the calibration set of samples. It is therefore imperative that analytical chemists developing second-order multivariate calibration methods using MCR-ALS acknowledge the relevance of this issue, and more importantly, have access to the required tools to size the relative impact of this potential source of uncertainty on the estimated analyte concentrations. The purpose of this tutorial is to provide a down-to-earth view of rotational ambiguity, by studying in detail a synthetic example mimicking a typical chromatographic-spectral experiment, where a set of calibration samples is joined with an unknown sample having an uncalibrated interference. After explaining the background information needed to understand the origin of the phenomenon, the available tools for the estimation of the feasible MCR-ALS solutions and the derived uncertainty on analyte predictions will be discussed. A multi-component experimental system will also be discussed, stressing the fact that rotational ambiguity uncertainties, however small, should always be estimated and reported.

Sampling unit for efficient signal detection and application to liquid chromatography-Raman spectroscopy

A new sampling unit design enhances the signal intensity and is available to combine Raman spectrometer with liquid chromatography.

HPLC-DAD fingerprints combined with chemometric techniques for the authentication of plucking seasons of Laoshan green tea

Laoshan green teas plucked in summer and autumn were measured by high performance liquid chromatography-diode array detector (HPLC-DAD). After baseline correction, the fingerprints data were resolved by multivariate curve resolution-alternating least squares (MCR-ALS) and a total of 57 components were acquired. Relative concentrations of these components were afterwards applied to distinguish plucking seasons using principal component analysis (PCA), support vector machines (SVM) and partial least squares-discriminant analysis (PLS-DA). For both SVM and PLS-DA models, the total recognition rates of training set, cross-validation and testing set were 100%, 91.3% and 100%, respectively. Besides, three variable selection methods were employed to determine characteristic components for the authentication of summer and autumn teas. Results showed that PLS-DA model based on three characteristic components selected by VIP possesses identical predictive ability as the original model. This study demonstrated that our proposed strategy is competent for the authentication of plucking seasons of Laoshan green tea.

Online Liquid Chromatography-Raman Spectroscopy Using the Vertical Flow Method

Liquid chromatography and Raman spectroscopy (LC-Raman system) were combined and developed with the aid of the vertical flow method that enhances the Raman signal intensity. The LC-Raman system enabled the online acquisition of the nonresonance Raman spectrum of LC eluates. We employed singular value decomposition (SVD) and subsequent reconstruction of the components for the analysis of two-dimensional (temporal and spectral) data. The obtained components were consistent with the Raman spectra and elution patterns of the samples, indicating the appropriateness of the SVD-based procedure. The rise and fall times of the elution band of the temporal component were considered as the instrumental function. D₂O mixed with H₂O exhibited increased full width at half maximum of the elution band of up to 30% in comparison to the calculated value because of diffusion. Band broadening was less significant in the case in which an immiscible solute (pentane) was mixed with H₂O. The limits of detection and quantitation were 1.2 ± 0.1, 2.1 ± 0.1, and 2.7 ± 0.1 mM and 4.1 ± 0.1, 6.9 ± 0.1, and 9.1 ± 0.2 mM for the ortho-, meta-, and para-isomers of methoxyphenol, respectively. The nonresonance Raman experiment provides the molecular specificity to LC on the basis of the inherent properties of eluates.

Simultaneous Determination of Medicinal Drugs with Overlapping Profiles Contained in Low Chromatographic Resolution Data using HPLC-DAD and Multivariate Curve Resolution

Background:

The increasing demand of effective pharmaceutical products directed to fight against malaria lead to the combination of at least two antimalarial drugs. This combination aims to minimize the Plasmodium falciparum resistance which is found when the most frequently used drugs are taken individually. Within this context, proguanil hydrochloride and chloroquine phosphate which have independent modes of action are taken together to prevent malaria. This paper aims to develop a fast and powerful analytical method for the simultaneous determination of proguanil hydrochloride and chloroquine phosphate in the commercial Paludrine/Avloclor dosage forms using a multi-way chromatographic calibration based on high-performance liquid chromatography with diode array detection (HPLC-DAD) and multivariate curve resolution – alternating leastsquares (MCR-ALS).

Methods:

A rapid and powerful analytical method based on HPLC-DAD and MCR-ALS was developed for the simultaneous quantification of proguanil hydrochloride and chloroquine phosphate in the commercial Paludrine/Avloclor antimalarial drugs. An isocratic mobile phase composed by 0.2 M ammonium acetate, acetonitrile, and methanol (40:25:35) and a flow rate of 1.2 mL min-1 were employed in the chromatographic runs with an elution time about 5 min.

Results:

This approach demonstrates that chromatographic analysis may become considerably simpler and economical in terms of time, cost, and organic solvent consumption when coupled to multiway calibration models such as MCR-ALS. In fact, this multi-way chromatographic calibration based on second-order HPLC-DAD data matrices (with extremely low chromatographic resolution) and MCR-ALS allows the development of greener analytical methods for complex samples. The proposed analytical method allowed the simultaneous quantification of two antimalarial APIs present in the commercial Paludrine/Avloclor drugs with low REP values below 8% for the simultaneous determination of proguanil hydrochloride and chloroquine phosphate.

Conclusion:

The proposed multi-way chromatographic strategy can be used for routine control of pharmaceutical dosage forms. It should be highlighted that MCR-ALS allowed to: (a) achieve the second- order advantage and the quantification of analytes in the presence of uncalibrated compounds such as coeluted profile measured in different magnitude of the signal in each successive chromatographic run and significant overlapping profiles and (b) separate the contribution of several components from chromatographic runs with extremely low separation of peaks through the deconvolution of the signal obtained, performing the so-called mathematical chromatography.

Classification of quinoa varieties based on protein fingerprinting by capillary electrophoresis with ultraviolet absorption diode array detection and advanced chemometrics

Quinoa (Chenopodium quinoa Willd.) is an andean grain with exceptional nutritional properties that has been progressively introduced in western countries as a protein-rich super food with a broad amino acid spectrum. Quinoa is consumed as whole grain, but it is also milled to produce high-value flour, which is susceptible to adulteration. Therefore, there is a growing interest in developing novel analytical methods to get further information about quinoa at the chemical level. In this study, we developed a rapid and simple capillary electrophoresis-ultraviolet absorption diode array detection (CE-UV-DAD) method to obtain characteristic multiwavelength electrophoretic profiles of soluble protein extracts from different quinoa grain varieties. Then, advanced chemometric methods (i.e. multivariate curve resolution alternating least squares, MCR-ALS, followed by principal component analysis, PCA, and partial least squares discriminant analysis, PLS-DA) were applied to deconvolute the components present in the electropherograms and classify the quinoa varieties according to their differential protein composition.

Quantitative Analysis of Food Additives in a Beverage using High Performance Liquid Chromatography and Diode Array Detection Coupled with Chemometrics

BACKGROUND

In many countries, the levels of synthetic food additives causing harm to humans have been determined and their use has been controlled by legal regulations. Sensitive, accurate and low-cost analysis methods are required for food additive determination.

OBJECTIVE

In this study, a fast high performance liquid chromatography-diode array detection (HPLC-DAD) analytical methodology for quantification of sodium benzoate, potassium sorbate, ponceau 4R, and carmoisine in a beverage was proposed.

METHODS

Partial least squares (PLS) and principal component regression (PCR) multivariate calibration methods applied to chromatograms with overlapped peaks were used to establish a green and smart method with short isocratic elution. A series of synthetic solutions including different concentrations of analytes were used to test the prediction ability of the developed methods.

CONCLUSIONS

The average recoveries for all target analytes were in the range of 98.27-101.37% with average relative prediction errors of less than 3%. The proposed chemometrics-assisted HPLC-DAD methods were implemented to a beverage successfully. Analysis results from sodium benzoate, potassium sorbate, ponceau 4R, and carmoisine in a beverage by PLS-2 and PCR were statistically compared with conventional HPLC.

HIGHLIGHTS

The HPLC methods coupled with the PLS-2 and PCR algorithm could provide a simple, quick and accurate strategy for simultaneous determination of sodium benzoate, potassium sorbate, ponceau 4R, and carmoisine in a beverage sample.

Analytical Figures of Merit for Multisensor Arrays

Multisensor arrays employing various sensing principles are a rapidly developing field of research as they allow simple and inexpensive quantification of various parameters in complex samples. Quantitative analysis with such systems is based on multivariate regression techniques, and deriving of traditional analytical figures of merit (e.g., sensitivity, selectivity, limit of detection, and limit of quantitation) for such systems is not obvious and straightforward. Nevertheless, it is absolutely needed for further development of the multisensor research field and for introducing these instruments into the general context of analytical chemistry. Here, we report on the protocol for calculation of sensitivity, selectivity, and detection limits for multisensor arrays. The results are provided and discussed in detail for several real-world data sets.

Comparison of Pre-Processing and Variable Selection Strategies in Group-Based GC×GC-TOFMS Analysis

Chemometric analysis of comprehensive two-dimensional chromatography coupled to time-of-flight mass spectrometry (GC×GC-TOFMS) data has been reported with various workflows, yet little effort has been devoted to evaluating the impacts of workflow variation on study conclusions. The report presented herein aims to investigate the effects of different pre-processing and variable selection strategies on the scores’ plot outputs from GC×GC-TOFMS data acquired from lavender and tea tree essential oils. Our results suggest that pre-processing, such as applying log transformation to the data set, can result in significant differentiation of sample clustering when compared to only mean centering. Additionally, exploring differences between analysis of variance, Fisher-ratio, and partial least squares-discriminant analysis feature selection resulted in little variation in scores plots. This work highlights the effects different chemometric workflows can have on results to help facilitate harmonization efforts.

Four- and five-way excitation-emission luminescence-based data acquisition and modeling for analytical applications. A review

The latest advances in both theory and experimental procedures on third-order/four-way and fourth-order/five-way calibration methods are discussed. This report is focused on excitation-emission (fluorescence and phosphorescence) matrices generation, employing different variables as the third data mode (time retention in chromatography, pH gradient, fluorescence/phosphorescence lifetime, kinetics, or other chemical treatments). Fully capitalizing on the second-order advantage, it has been possible to develop appealing analytical applications in spite of the complexity of the data. Extraction of the significant chemical information about the system under study as well as the individual abundance of the contributing constituents after proper higher-order data decomposition has allowed to analytical researchers performing quantitative analysis of complex samples. The experimental works reported up to the present are introduced and discussed in order to illustrate concepts. Throughout this work, the analytical benefits achieved by modeling third- and fourth-order data are exposed, attempting to contribute to the ongoing debate in the chemometric community regarding the existence and the true nature of the third-order advantage.