ANOVA-simultaneous Component Analysis Research Articles

Comparative analysis of features extraction protocols for LC-HRMS untargeted metabolomics in mountain cheese ‘identitation’

This study presents a comprehensive metabolomic analysis of Parmigiano Reggiano samples to differentiate between those designated as Mountain Quality Certification (QC) and conventional Protected Designation of Origin (PDO). Despite following the same production protocol, these cheese varieties differ in the cows’ feeding regimes and milk stable locations, with mountain-certified samples adhering to specific requirements regarding milk origin and feed composition. An untargeted approach with Liquid Chromatography-High Resolution Mass Spectrometry (LC-HRMS) was proposed to characterize the cheese metabolome. High-resolution LC-MS data can generate gigabyte-sized files, making data compression essential for manageable multivariate analysis and noise reduction. This study employs the Region of Interest-Multivariate Curve Resolution (ROI-MCR) protocol to achieve effective data compression and chromatographic resolution, thereby extracting the most informative features. This method was compared with a classical approach for feature extraction from chromatographic data, namely Compound Discoverer (CD) software. The features extracted by both methods were analysed through Principal Component Analysis (PCA) and ASCA (ANOVA Simultaneous Component Analysis). The comparison of ROI-MCR and CD approaches demonstrated that while both methods yielded similar overall conclusions, ROI-MCR provided a more streamlined and manageable dataset, facilitating easier interpretation of the metabolic differences. Both approaches indicated that amino acids, fatty acids, and bacterial activity-related compounds played significant roles in distinguishing between the two sample types.

The effect of process parameters on a continuous blending process monitored in-line by near-infrared spectroscopy

The continuous feeding-mixing system ensures the composition uniformity down to the tableting continuous manufacturing line so that a quality end-product is consistently delivered. Near-infrared spectroscopy (NIRS) enables in-line assessment of the blend's critical quality attributes in real-time. In this study, the effect of total feed rate and impeller speed on the continuous blending process monitored in-line by NIRS was examined by principal component analysis (PCA), ANOVA simultaneous component analysis (ASCA) and partial least squares (PLS) regression. Process data were generated by a factorial experimental design with process parameters and a constant formulation comprised of: 30 % (wt/wt) ibuprofen, 67.5 % (wt/wt) microcrystalline cellulose, 2 % (wt/wt) of sodium starch glycolate and 0.5 % (wt/wt) of magnesium stearate. The PCA hinted at the prevalence of impeller speed effect on ibuprofen concentration due to path length variation of the NIR light caused by the fluidized behaviour in the powder blend as a result of high speed ranges (>300 rpm). The ASCA model indicated that while both impeller speed and total feed rate effects were statistically significant (p-value=0.004), the impeller speed was the factor that contributed the most to the spectral variance (55.5 %). The PLS regression model for the ibuprofen content resulted in a RMSECV of 1.3 % (wt/wt) and showed that impeller speed was yet again the factor that exerted the major influence on spectral variance, owing to its wavelength-dependent effect that prevents common pre-processing techniques from eliminating it across the entire NIR range. The best sample presentation to the NIR probe was achieved at low impeller speed ranges (<600 rpm) and low total feed rates (<15 kg/h), such that it enhanced the PLS model ability to predict the ibuprofen concentration in the blend.

Population Power Curves in ASCA With Permutation Testing

ABSTRACTIn this paper, we revisit the power curves in ANOVA simultaneous component analysis (ASCA) based on permutation testing and introduce the population curves derived from population parameters describing the relative effect among factors and interactions. The relative effect has important practical implications: The statistical power of a given factor depends on the design of other factors in the experiment and not only of the sample size. Thus, understanding the relative power in a specific experimental design can be extremely useful to maximize our capability of success when planning the experiment. In the paper, we derive relative and absolute population curves, where the former represent statistical power in terms of the normalized effect size between structure and noise, and the latter in terms of the sample size. Both types of population curves allow us to make decisions regarding the number and nature (fixed/random) of factors, their relationships (crossed/nested), and the number of levels and replicates, among others, in an multivariate experimental design (e.g., an omics study) during the planning phase of the experiment. We illustrate both types of curves through simulation.

Non-invasive exploration of malting barley (Hordeum vulgare) in vitro germination and varietal effects using short wave infrared spectral imaging and ANOVA simultaneous component analysis

ANOVA-simultaneous component analysis (ASCA) was applied to short-wave infrared spectral fingerprints of 5 malting barley varieties collected using a hyperspectral imaging system to determine the effect of germination, the influence of time and the influence of barley by means of a full factorial experimental design. ASCA indicated that there was a significant (p < 0.0001) effect of the germination status, the germination time and interaction on the spectral data for all varieties. The biochemical and physiological modification of the samples were characterised by visualisation of the longitudinal scores obtained from simultaneous component analysis for the germination time factor. This resulted in the visualisation and explanation of biochemical change over the course of barley germination as a factor of time. The relevant loadings indicated a significant change to the proteome, lipid and starch structure as driven by the uptake of water over time. The ASCA model were extrapolated to include the effect of barley variety to the already mentioned germination status and germination time factors, resulting once again in all the effects being significant (p < 0.0001). Here it was shown that all the barley varieties are significantly different from one another pre- and post-modification, based on the molecular vibrations observed in the short wave-infrared (SWIR) spectra, suggesting that the detection of biotic stress factors, such as pre-harvest germination, also differ for each variety, by indicating that the germination profile of each barley variety varies as a function of germination time. Thus, also the malting performance, germinative energy and chemical profile of each barley variety tested will vary before, during and after imbibition and germination – indicating the importance of malting commercial barley malt true to variety. These results indicate that (SWIR) spectral imaging instrumentation can possibly be used to monitor controlled germination of barley grain. Due to the shown ability of SWIR spectral imaging to detect small biochemical changes over time of barley grain during germination.

Permutation Strategies for Inference in ANOVA‐Based Models for Nonorthogonal Designs Including Continuous Covariates

ABSTRACTAnalysis of variance and linear models is undoubtedly one of the most useful statistical contributions to experimental and observational science. With the ability to characterize a system through multivariate responses, these methods have emerged to be general tools regardless of response dimensionality. Contemporary methods for establishing statistical inference, such as ANOVA simultaneous component analysis (ASCA), are based on Monte Carlo sampling; however, a flat uniform resampling scheme may violate the structure of the uncertainty for unbalanced designs as well as for observational data. In this work, we provide permutation strategies for inferential testing for unbalanced designs including interaction models and establish nonuniform randomization based on the concept of propensity score matching. Lastly, we provide a general method for modelling continuous covariates based on kernel smoothers. All methods are characterized on their ability to provide unbiased Type I error results.

Non-invasive VOCs detection to monitor the gut microbiota metabolism in-vitro

This work implemented a non-invasive volatile organic compounds (VOCs) monitoring approach to study how food components are metabolised by the gut microbiota in-vitro. The fermentability of a model food matrix rich in dietary fibre (oat bran), and a pure prebiotic (inulin), added to a minimal gut medium was compared by looking at global changes in the volatilome. The substrates were incubated with a stabilised human faecal inoculum over a 24-h period, and VOCs were monitored without interfering with biological processes. The fermentation was performed in nitrogen-filled vials, with controlled temperature, and tracked by automated headspace-solid-phase microextraction coupled with gas chromatography–mass spectrometry. To understand the molecular patterns over time, we applied a multivariate longitudinal statistical framework: repeated measurements—ANOVA simultaneous component analysis. The methodology was able to discriminate the studied groups by looking at VOCs temporal profiles. The volatilome showed a time-dependency that was more distinct after 12 h. Short to medium-chain fatty acids showed increased peak intensities, mainly for oat bran and for inulin, but with different kinetics. At the same time, alcohols, aldehydes, and esters showed distinct trends with discriminatory power. The proposed approach can be applied to study the intertwined pathways of gut microbiota food components interaction in-vitro.

Characterisation of Position‐Dependant Ripening Dynamics of Nectarines Using Near‐Infrared Spectroscopy and ASCA

ABSTRACTNectarines, a popular pit fruit closely related to peaches, are renowned for their nutritional value and associated health benefits. However, challenges arise in maintaining optimal organoleptic properties during harvest and handling, eventually leading to production waste and heterogeneous quality in the fruit that arrives to the consumer. This study investigates the impact of nectarine position on trees during the whole ripening process using non‐destructive near‐infrared (NIR) spectroscopy. Nectarines exposed to more sunlight mature faster and this influences sugar content and acidity, emphasising the significance of considering height, prominence and orientation in ripening dynamics of the fruit. Different data unfolding strategies were compared, using ANOVA‐Simultaneous Component Analysis (ASCA) to reveal the significance of in‐tree position factors at different ripening stages, and observing high significance at harvest. This underscores the necessity for growers and handlers to consider these factors for reducing waste. NIR spectroscopy, with adequate data analysis, is a valuable tool for the holistic analysis of fruit ripening, providing crucial insights for maintaining optimal fruit organoleptic properties from harvest to consumer.

Influence of regional and yearly weather patterns on multi-mycotoxin occurrence in Austrian wheat: a liquid chromatographic-tandem mass spectrometric and multivariate statistics approach.

Mycotoxin surveys play an essential role in our food safety system. The obtained occurrence data form the basis for the assessment of the exposure of humans and animals to these toxic fungal secondary metabolites. Liquid chromatography coupled with tandem mass spectrometry (LC-MS/MS) has become the gold standard for mycotoxin determination because it enables selective and sensitive multi-toxin analysis. Simultaneous determination of several hundreds of secondary fungal metabolites is feasible using this technique. In this study, we combined a targeted dilute-and-shoot LC-MS/MS-based multi-analyte approach with multivariate statistics for the analysis of Austrian wheat from two different years and different geographical origins. We quantified 47 secondary fungal metabolites, including regulated emerging and masked mycotoxins. The resulting multi-mycotoxin occurrence data were further analyzed using both multivariate and univariate statistics. Principal component analysis (PCA) and analysis of variance (ANOVA) simultaneous component analysis (ASCA) were employed to identify regional and yearly trends within the dataset and to quantify the variance in metabolite occurrence attributed to the different effects. In addition, secondary fungal metabolites significantly impacted by these factors were selected via ANOVA. Of the 47 secondary metabolites identified, 39 were affected by the year, region or a combined effect. Moreover, our findings show that 43 of the secondary fungal metabolites were significantly influenced by the weather conditions. The results presented in this study underline the added value of combining targeted LC-MS/MS with multivariate statistics for monitoring a broad spectrum of secondary fungal metabolites in food crops. Through multivariate statistics, trends associated with the year or region can be readily studied. The approach presented could pave the way for a better understanding of the impact of climate change on plant pathogenic fungi and its implications for food safety. © 2024 The Author(s). Journal of The Science of Food and Agriculture published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry.

Flow-modulation comprehensive two-dimensional enantio-gas chromatography: A valid and flexible alternative to heart-cutting multidimensional enantio-gas chromatography

The present research is focused on the proposal of use of flow-modulation comprehensive two-dimensional enantio-gas chromatography (FM eGC × GC) as a valid, flexible, and possibly superior alternative to heart-cutting multidimensional enantio-GC (eMDGC). The latter, a technique of demonstrated utility, is used specifically for the targeted separation of chiral compounds, whereas FM eGC × GC can produce both targeted and high-resolution untargeted information in a single run. It is clearly possible to use eMDGC for untargeted analysis, often with a flame ionization detector (stand-by analysis), to monitor a first-dimension (1D) separation, of much lower peak capacity compared to FM eGC × GC. If eMDGC is used with mass spectrometry (MS), it is normally exploited to monitor the second-dimension (2D) separation.The analytical instrument consisted of automated solid-phase microextraction (SPME), and a low duty-cycle FM eGC × GC system (with time-of-flight MS), equipped with an enantioselective 1D column (2,3-di-O-methyl-6-t-butyl silyl β-cyclodextrin derivative) and a 2D polyethylene glycol one. Ten Marsala wines were subjected to analysis, for the determination of chiral lactones (many at the low ppb level, due to the high concentration capacity of SPME) and for general analyte profiling. In many instances, highly complex chromatograms were attained, with statistical analysis (ANOVA-simultaneous component analysis and partial least squares discriminant analysis) used for sample differentiation.

First comprehensive untargeted metabolomics study of suramin-treated Trypanosoma brucei: an integrated data analysis workflow from multifactor data modelling to functional analysis.

Human African trypanosomiasis, commonly known as sleeping sickness, is a vector-borne parasitic disease prevalent in sub-Saharan Africa and transmitted by the tsetse fly. Suramin, a medication with a long history of clinical use, has demonstrated varied modes of action against Trypanosoma brucei. This study employs a comprehensive workflow to investigate the metabolic effects of suramin on T. brucei, utilizing a multimodal metabolomics approach. The primary aim of this study is to comprehensively analyze the metabolic impact of suramin on T. brucei using a combined liquid chromatography-mass spectrometry (LC-MS) and nuclear magnetic resonance spectroscopy (NMR) approach. Statistical analyses, encompassing multivariate analysis and pathway enrichment analysis, are applied to elucidate significant variations and metabolic changes resulting from suramin treatment. A detailed methodology involving the integration of high-resolution data from LC-MS and NMR techniques is presented. The study conducts a thorough analysis of metabolite profiles in both suramin-treated and control T. brucei brucei samples. Statistical techniques, including ANOVA-simultaneous component analysis (ASCA), principal component analysis (PCA), ANOVA 2 analysis, and bootstrap tests, are employed to discern the effects of suramin treatment on the metabolomics outcomes. Our investigation reveals substantial differences in metabolic profiles between the control and suramin-treated groups. ASCA and PCA analysis confirm distinct separation between these groups in both MS-negative and NMR analyses. Furthermore, ANOVA 2 analysis and bootstrap tests confirmed the significance of treatment, time, and interaction effects on the metabolomics outcomes. Functional analysis of the data from LC-MS highlighted the impact of treatment on amino-acid, and amino-sugar and nucleotide-sugar metabolism, while time effects were observed on carbon intermediary metabolism (notably glycolysis and di- and tricarboxylic acids of the succinate production pathway and tricarboxylic acid (TCA) cycle). Through the integration of LC-MS and NMR techniques coupled with advanced statistical analyses, this study identifies distinctive metabolic signatures and pathways associated with suramin treatment in T. brucei. These findings contribute to a deeper understanding of the pharmacological impact of suramin and have the potential to inform the development of more efficacious therapeutic strategies against African trypanosomiasis.

Uv–Vis molecular spectral resolution of multi-level mixture design-fingerprints of yerba mate leaves by chemometric methods

This study proposes the use of multivariate curve resolution with alternating least squares (MCR-ALS) to comprehensively analyze mixture design-fingerprints in yerba mate leaves, investigating the influence of multi-level factors such as sexual dimorphism (male and female plants) and cultivation systems (monoculture and agroforestry). Plant extracts were obtained according to a mixture design with ethanol, dichloromethane, and hexane and their binary and ternary combinations. Through simultaneous resolution of the diverse profiles obtained using these different solvents, seven components were successfully identified, collectively explaining 98.57% of the data variance. Each component was associated with distinct absorption bands indicative of their chemical composition with compounds such as chlorogenic acids, xanthophylls, catechin, caffeine, kaempferol, lycopene, carotene, and chlorophyll. The MCR-ALS resolved profiles revealed significant variations in component concentrations across experimental conditions, facilitating the determination of the effects of sexual dimorphism and cultivation systems on yerba mate metabolism. The ANOVA-simultaneous component analysis (ASCA) highlighted the chemical differences of yerba mate leaves due to the cultivation system. Binary and ternary mixture extractants resulted to be more effective than pure solvents in determining the significance of effects on the chemical composition of yerba mate. Partial least squares discriminant analysis (PLS-DA) demonstrated the most distinct metabolic profiles of yerba mate leaves under monoculture and agroforestry conditions, with specific components playing crucial roles in their discrimination. This study shows the robustness of the MCR-ALS method in resolving complex chemical data, offering valuable insights into the diverse chemical composition of yerba mate under different experimental conditions. The congruence of results across various analyses reinforced the reliability and validity of the methodology, emphasizing its potential use for exploring the composition and properties of natural products.

Release kinetic modeling of Satureja Khuzestanica Jamzad essential oil from fish gelatin/succinic anhydride starch nanocomposite films: The effects of temperature and nanocellulose concentration

Fish gelatin (FG) and octenyl succinic anhydride starch (OSAS) composite films loaded with 1, 2, 3 and 4 wt% bacterial nanocellulose (BNC) and Satureja Khuzestanica Jamzad essential oil (SKEO) were achieved successfully and their physicochemical and release properties were investigated. The results revealed that incorporation of BNC improved the tensile strength which was associated with FE-SEM, FTIR and XRD. Moreover, this study focused on the release modeling of SKEO in 4, 25 and 37 °C from nanocomposite films using different release kinetic and Arrhenius models. Also, analysis of variance-simultaneous component analysis (ASCA) and exploratory data visualization by principal component analysis (PCA) were carried out to investigate the effects of two controlled factors. Consequently, the Peleg model showed the best fitting of experimental data. The activation energies decreased by increasing the BNC concentration. This research demonstrated the nanocomposite film containing SKEO would be a suitable candidate for active food packaging.

On the complementary nature of ANOVA simultaneous component analysis (ASCA+) and Tucker3 tensor decompositions on designed multi‐way datasets

AbstractThe complementary nature of analysis of variance (ANOVA) Simultaneous Component Analysis (ASCA+) and Tucker3 tensor decompositions is demonstrated on designed datasets. We show how ASCA+ can be used to (a) identify statistically sufficient Tucker3 models; (b) identify statistically important triads making their interpretation easier; and (c) eliminate non‐significant triads making visualization and interpretation simpler. For multivariate datasets with an experimental design of at least two factors, the data matrix can be folded into a multi‐way tensor. ASCA+ can be used on the unfolded matrix, and Tucker3 modeling can be used on the folded matrix (tensor). Two novel strategies are reported to determine the statistical significance of Tucker3 models using a previously published dataset. A statistically sufficient model was created by adding factors to the Tucker3 model in a stepwise manner until no ASCA+ detectable structure was observed in the residuals. Bootstrap analysis of the Tucker3 model residuals was used to determine confidence intervals for the loadings and the individual elements of the core matrix and showed that 21 out of 63 core values of the 3 × 7 × 3 model were not significant at the 95% confidence level. Exploiting the mutual orthogonality of the 63 triads of the Tucker3 model, these 21 factors (triads) were removed from the model. An ASCA+ backward elimination strategy is reported to further simplify the Tucker3 3 × 7 × 3 model to 36 core values and associated triads. ASCA+ was also used to identify individual factors (triads) with selective responses on experimental factors A, B, or interactions, A × B, for improved model visualization and interpretation.

Untargeted cannabinomics reveals the chemical differentiation of industrial hemp based on the cultivar and the geographical field location

Cannabis sativa has long been harvested for industrial applications related to its fibers. Industrial hemp cultivars, a botanical class of Cannabis sativa with a low expression of intoxicating Δ9-tetrahydrocannabinol (Δ9-THC) have been selected for these purposes and scarcely investigated in terms of their content in bioactive compounds. Following the global relaxation in the market of industrial hemp-derived products, research in industrial hemp for pharmaceutical and nutraceutical purposes has surged. In this context, metabolomics-based approaches have proven to fulfill the aim of obtaining comprehensive information on the phytocompound profile of cannabis samples, going beyond the targeted evaluation of the major phytocannabinoids. In the present paper, an HRMS-based metabolomics study was addressed to seven distinct industrial hemp cultivars grown in four experimental fields in Northern, Southern, and Insular Italy. Since the role of minor phytocannabinoids as well as other phytocompounds was found to be critical in discriminating cannabis chemovars and in determining its biological activities, a comprehensive characterization of phytocannabinoids, flavonoids, and phenolic acids was carried out by LC-HRMS and a dedicated data processing workflow following the guidelines of the metabolomics Quality Assurance and Quality Control Consortium. A total of 54 phytocannabinoids, 134 flavonoids, and 77 phenolic acids were annotated, and their role in distinguishing hemp samples based on the geographical field location and cultivar was evaluated by ANOVA-simultaneous component analysis. Finally, a low-level fused model demonstrated the key role of untargeted cannabinomics extended to lesser-studied phytocompound classes for the discrimination of hemp samples.

Investigation of Lactation Period and Technological Treatments on Mineral Composition and IR-Profiles of Donkey Milk by Chemometrics

Donkey milk represents an efficient substitute for human milk in infants’ diets being unlikely to cause allergic reactions. In this study, different donkey milks were collected at two lactation times (T0 and T1), subjected to freezing–thawing and freeze-drying, and analyzed by Inductively Coupled Plasma–Optical Emission Spectroscopy (ICP-OES) and ATR-FT-IR. The data collected on freeze–thaw (FT-) and reconstituted (R-)milks were investigated by ANOVA–Simultaneous Component Analysis (ASCA) and Principal Component Analysis (PCA). The following concentrations (µg/mL) for FT and R-milks, respectively, at T0, were found: Ca: 712 ± 71, 600 ± 72; Fe: 0.7 ± 0.3, 0.1 ± 0.1; K: 595 ± 49, 551 ± 59; Mg: 75 ± 5, 67 ± 4; Na: 117 ± 16, 114 ± 16; P: 403 ± 30, 404 ± 38; Zn: 1.6 ± 0.2, 1.6 ± 0.3. At T1, the concentrations (µg/mL for FT and R-milks, respectively) were: Ca: 692 ± 60, 583 ± 43; Fe: 0.13 ± 0.02, 0.13 ± 0.03; K: 641 ± 71, 574 ± 61; Mg: 72 ± 4, 63 ± 1; Na: 116 ± 9, 109 ± 8; P: 412 ± 30, 405 ± 24; Zn: 1.6 ± 0.3, 1.6 ± 0.3. ASCA demonstrated the treatment has a substantial effect, and PCA revealed that the largest quantities of metals, specifically Fe, Mg, and Ca for T0 and K, P, and Na for T1, are present in the FT-milk samples. The IR spectra of FT- and R-milks revealed no macroscopic changes among them or between lactation periods, indicating this technique may not suitably capture variability in lactation or conservation processes in donkey milk. Despite the relatively small sample size, this study offers insight on the mineral composition changes in donkey milk and emphasizes the significance of milk preprocessing and the lactation period on it.

Effect of wheat roasting conditions and wheat type on short-wave infrared (SWIR) spectral data of whole and milled wheat by ANOVA-simultaneous component analysis

ANOVA-simultaneous component analysis (ASCA) was used to investigate the effect of roasting and wheat type on shortwave-infrared (SWIR) spectra of whole wheat and flour through assessment of statistical significance and characterisation of the contributing spectral features. The full factorial experimental design included two wheat types, three roasting temperatures and three roasting frequencies. SWIR spectral images were collected from the two roasted wheat types and their two milled samples. Three ASCA models, one for each wheat conformation (kernel, whole wheat flour, white flour) were investigated. It was evidenced that all factors and interaction in the whole wheat flour model had a significant (p ≤ 0.05) effect on spectral data. Only the factor roasting frequency was not significant in white flour model and only the interaction between roasting frequency and wheat type was not significant for the kernel model. The main variations in the loading line plots were identified and characterised by chemical structural differences that occur within the sample. The effect of roasting frequency had a more adverse effect on protein stability, moisture evaporation, water soluble carbohydrates and aromatic amino acids, compared to roasting temperature. A Rapid Visco-Analyser (RVA) was used to further investigate difference in wheat type as almost all spectral data sets differed significantly. The most prominent difference between the two wheat types was observed as differences in amylase activity and presence of lipids. ASCA applied to SWIR whole wheat and flour spectral data effectively characterised the significant effect of roasting on wheat starch and protein structures.

Analysis of high-dimensional metabolomics data with complex temporal dynamics using RM-ASCA.

The intricate dependency structure of biological "omics" data, particularly those originating from longitudinal intervention studies with frequently sampled repeated measurements renders the analysis of such data challenging. The high-dimensionality, inter-relatedness of multiple outcomes, and heterogeneity in the studied systems all add to the difficulty in deriving meaningful information. In addition, the subtle differences in dynamics often deemed meaningful in nutritional intervention studies can be particularly challenging to quantify. In this work we demonstrate the use of quantitative longitudinal models within the repeated-measures ANOVA simultaneous component analysis+ (RM-ASCA+) framework to capture the dynamics in frequently sampled longitudinal data with multivariate outcomes. We illustrate the use of linear mixed models with polynomial and spline basis expansion of the time variable within RM-ASCA+ in order to quantify non-linear dynamics in a simulation study as well as in a metabolomics data set. We show that the proposed approach presents a convenient and interpretable way to systematically quantify and summarize multivariate outcomes in longitudinal studies while accounting for proper within subject dependency structures.

Redundancy analysis includes analysis of variance-simultaneous component analysis (ASCA) and outperforms its extensions

Chemometrics and statistical ecology share interest in the analysis of multivariate data. In ecology, unconstrained and constrained ordination are popular methods to analyze and visualize multivariate data, with principal component analysis (PCA) and redundancy analysis (RDA) as prototype methods. Constraints give more insight and power by focusing on the response of the variables to particular external predictors or experimental factors, after optional adjustment for covariates. In chemometrics, analysis of variance - simultaneous component analysis (ASCA) was proposed decades later, with particular emphasis on the multivariate main and interaction effects in factorial experiments. This paper shows the similarities and differences between ASCA, its extensions, and (partial) RDA, alias reduced-rank regression. ASCA and RDA (understood as a sequence of partial RDAs, just as ASCA uses a sequence of PCAs) are shown to be mathematically identical for equireplicated designed experiments. Differences appear with unequal replication. As a corollary we show that, with equal replication, a particularly attractive form of ASCA, which displays a main effect together with an interaction, is a special case of principal response curve analysis. RDA is a least-squares method and uses the optimal weights in the dimension reduction of the treatment effects, whereas ASCA extensions for unbalanced data use alternative, sub-optimal weights.

Limpca: An R package for the linear modeling of high‐dimensional designed data based on ASCA/APCA family of methods

SummaryMany modern analytical methods are used to analyze samples issued from an experimental design, for example, in medical, biological, chemical, or agronomic fields. Those methods generate most of the time, highly multivariate data like spectra or images, where the number of variables (descriptor responses) tends to be much larger than the number of experimental units. Therefore, multivariate statistical tools are necessary to identify variables that are consistently affected by experimental factors. In this context, two recent methods combining ANOVA and PCA, namely, ASCA (ANOVA‐Simultaneous Component Analysis) and APCA (ANOVA‐Principal Component Analysis), were developed. They provide powerful visualization tools for multivariate structures in the space of each effect of the statistical model linked to the experimental design. Their main limitation is that they produce biased estimators of the factor effects when the design of experiment is unbalanced. This article presents the R package limpca (for linear models with principal component effects analysis) that implements ASCA+ and APCA+, an enhanced version of ASCA and APCA methods based on several principles from the theory of general linear models (GLM). In this paper, the methodology is reviewed, the package structure and functions are presented, and a metabolomics data set is used to clearly demonstrate the potential of ASCA+ and APCA+ methods to highlight true biomarkers corresponding to effects of interest in unbalanced designs.

Direct NIR spectral determination of genetic improvement, light availability, and their interaction effects on chemically selected yerba-mate leaves

Monitoring plant chemical modifications provides useful information about plant genetic variability owing to environmental stresses. This allows determining if the pattern of chemical compounds of interest remains constant. Classically, chemical compounds are monitored through classical analytical procedures that are costly and environmentally harmful. Decaffeinated and high caffeine yerba-mate trees were selected based on their chemical profiles. Their behavior was evaluated at five different shading levels (0%, 40%, 51%, 76%, and 82%), imitating the environmental characteristics of yerba-mate in agroforestry systems. Near-infrared spectroscopy (NIR) fingerprints were obtained for yerba-mate leaves, and ANOVA-simultaneous component analysis (ASCA) models were developed for chemical monitoring. The preprocessing of NIR spectra was assessed with a three-level full factorial design. The best preprocessing set of conditions found was standard normal variate followed by second derivatives, computed according to the Savitzky–Golay method (11-points window and second-degree interpolating polynomial). The ASCA models satisfactorily showed significant differences in chemical behavior for genetic improvement and its interaction with light availibility effects. The genetic improvement effect had a variance of 44.30% over NIR fingerprints, indicating that the chemical differences are maintained at any light level. The interaction effect with 1.84% of the total variance illustrated that the behaviors of decaffeinated and high-caffeinated yerba mate were different when subjected to the same light level. The main absorptions indicated by the ASCA model were the O-H stretching and bending combination band at 1654 nm, and the –CH stretching aromatic 1st overtone at 1675 nm. The ASCA method offered a powerful tool for monitoring chemically selected plants combined with NIR spectroscopy. The method is cheap, fast, environmentally friendly, and can be used for field research.