Standard Partial Least Squares Research Articles

Analytical solution to partial least squares

Partial least squares (PLS) is a widely used multivariate statistical technique, which can be used in neuroimaging, process monitoring, economics, etc. Because the standard PLS is trained by nonlinear iterative partial least squares (NIPALS) algorithm, which can only obtain the numerical solution rather than the analytical solution. Therefore, it is hard for the subsequent theoretical analysis in PLS and the iterative optimization process is computationally intensive. This paper proposes an analytical solution to take the place of NIPALS. This determination meaningfully contributes to future theoretical analysis of PLS. In addition, the analytical solution demonstrates that the selection of initial vector in NIPALS does not affect the PLS training results. Moreover, the analytical solution avoids the multiple iterative calculations, so the divergence of the calculation process will be avoided and the computation burden will be reduced significantly.

Predicting soil carbon in granitic soils using Fourier-transform mid-infrared (FT-MIR) spectroscopy: the value of database disaggregation

Soil carbon (C) is an important component in quality assessments and efficient models are required to estimate C rapidly. Accurate C assessments are valuable in monitoring land-use changes. Fourier-transform mid-infrared (FT-MIR) spectroscopy has proved to be a powerful tool for assessing C. The potential of FT-MIR spectroscopy to estimate C was evaluated using the following techniques: (1) three algorithms [partial least squares (PLS)], principal component regression (PCR), and classical least squares (CLS); and (2) disaggregating the dataset into subgroups based on soil depth and texture. The C contents of samples collected in the Johannesburg Granite Dome were determined by dry combustion for comparison. The soils ranged considerably in C (0.123–2.650%), clay (2.80–41.20%), and silt content (8.56–23.75%). Using standard normal variant (SNV), Savitzky-Golay smoothing and PLS, the best-performing model was the horizons subgroup which provided values of root mean square error for prediction (RMSEP) between 0.079 and 0.095%, root mean square error for calibration (RMSEC) = 0.041 − 0.092, r 2 pre = 0.6174–0.8459, r 2 cal = 0.6599–0.9778, residual prediction variation (RPD) = 2.404–2.753, and ratio of performance to interquartile range (RPIQ) = 2.667–3.454. The pronounced accuracy of FT-MIR spectroscopy coupled with PLS, pre-processing techniques, and textural subgroups confirms the potential of infrared spectroscopy as an efficient tool for estimating C content. Future studies should investigate the combined effects of FT-MIR spectroscopy and subgroups grouped according to soil types and land-uses when predicting C.

Variable selection of spectroscopic data through monitoring both location and dispersion of PLS loading weights

High dimensional data sets against the small sample size is essential for most of the sciences. The variable selection contributes to a better prediction of real-life phenomena. A multivariate approach called partial least squares (PLS) has the potential to model the high dimensional data, where the sample size is usually smaller than the number of variables. Truncation for variables selection in PLS $$T-PLS$$ is considered a reference method. $$T-PLS$$ and many others only monitors the location of PLS loading weights for variable selection. In the current article, we propose to monitor both location and dispersion of PLS loading weights for variable selection over the high dimensional spectral data. The proposed PLS variants are based on location, dispersion, both location and dispersion and at least location or dispersion monitoring of $$PLS$$ loading weights, and are denoted by $$X-PLS$$ , $$S-PLS$$ , $$X \& S-PLS$$ and $$X|S-PLS$$ respectively. Proposed PLS variants are compared with standard PLS and $$T-PLS$$ through the Monte Carlo simulation of 100 runs on simulated and real data sets which includes corn, milk, and oil contents prediction based on spectroscopic data. $$X \& S-PLS$$ shows the best capability in selecting the real variables over the simulated data. The validated RMSE comparison indicates $$X|S-PLS$$ and $$X \& S-PLS$$ outperforms compared to other methods in predicting corn, milk, and oil contents. $$X \& S-PLS$$ selects the smallest number of variables. Interestingly, selected variables by $$X \& S-PLS$$ are more consistent compared to all other methods. Hence $$X \& S-PLS$$ appears a potential candidate for variable selection in high dimensional data.

A Novel Mutual Information and Partial Least Squares Approach for Quality-Related and Quality-Unrelated Fault Detection

Partial least squares (PLS) and linear regression methods are widely utilized for quality-related fault detection in industrial processes. Standard PLS decomposes the process variables into principal and residual parts. However, as the principal part still contains many components unrelated to quality, if these components were not removed it could cause many false alarms. Besides, although these components do not affect product quality, they have a great impact on process safety and information about other faults. Removing and discarding these components will lead to a reduction in the detection rate of faults, unrelated to quality. To overcome the drawbacks of Standard PLS, a novel method, MI-PLS (mutual information PLS), is proposed in this paper. The proposed MI-PLS algorithm utilizes mutual information to divide the process variables into selected and residual components, and then uses singular value decomposition (SVD) to further decompose the selected part into quality-related and quality-unrelated components, subsequently constructing quality-related monitoring statistics. To ensure that there is no information loss and that the proposed MI-PLS can be used in quality-related and quality-unrelated fault detection, a principal component analysis (PCA) model is performed on the residual component to obtain its score matrix, which is combined with the quality-unrelated part to obtain the total quality-unrelated monitoring statistics. Finally, the proposed method is applied on a numerical example and Tennessee Eastman process. The proposed MI-PLS has a lower computational load and more robust performance compared with T-PLS and PCR.

Improved prediction of fuel properties with near-infrared spectroscopy using a complementary sequential fusion of scatter correction techniques

Near-infrared (NIR) spectroscopy of fuels can suffer from scattering effects which may mask the signals corresponding to key analytes in the spectra. Therefore, scatter correction techniques are often used prior to any modelling so to remove scattering and improve predictive performances. However, different scatter correction techniques may carry complementary information so that, if jointly used, both model stability and performances could be improved. A solution to that is the fusion of complementary information from differently scatter corrected data. In the present work, the use of a preprocessing fusion approach called sequential preprocessing through orthogonalization (SPORT) is demonstrated for predicting key quality parameters in diesel fuels. In particular, the possibility of predicting four different key properties, i.e., boiling point (°C), density (g/mL), aromatic mass (%) and viscosity (cSt), was considered. As a comparison, standard partial least-squares (PLS) regression modelling was performed on data pretreated by SNV and 2nd derivative (which is a widely used preprocessing combination). The results showed that the SPORT models, based on the fusion of scatter correction techniques, outperformed the standard PLS models in the prediction of all the four properties, suggesting that selection and use of a single scatter correction technique is often not sufficient. Up to complete bias removal with 50% reduction in prediction error was obtained. The R2P was increased by up to 8%. The sequential scatter fusion approach (SPORT) is not limited to NIR data but can be applied to any other spectral data where a preprocessing optimization step is required.

Exploring relevant wavelength regions for estimating soil total carbon contents of rice fields in Madagascar from Vis-NIR spectra with sequential application of backward interval PLS

ABSTRACT Laboratory visible and near-infrared (Vis-NIR) spectroscopy with partial least squares (PLS) regression can be used to determine the soil carbon (C) content, and the waveband selection procedures can refine the predictive ability. However, individually selected wavebands are not always the same depending on the location, scale, and approach. To simplify the variable selection issue, some methods for selecting wavelength regions instead of individual wavebands have been proposed. In this study, we explore relevant wavelength regions for predicting the total carbon (TC) content of lowland and upland soils in Madagascar from Vis-NIR spectroscopy using a dynamic version of backward interval PLS (biPLS) regression. The predictive ability of dynamic biPLS was compared with that of standard full-spectrum PLS (FS-PLS) using the cross-validated coefficient of determination (R 2), root mean squared error (RMSE), and ratio of performance to interquartile distance (RPIQ). The biPLS models using reflectance (R 2 = 0.877, RMSE = 0.690) and first derivative reflectance (FDR) (R 2 = 0.940, RMSE = 0.494) data sets showed better predictive accuracy than the FS-PLS models using reflectance (R 2 = 0.826, RMSE = 0.809) and FDR (R 2 = 0.933, RMSE = 0.518) data sets, the spectral efficiency was improved. By using biPLS to predict soil TC, the model was simplified by using only four selected wavelength regions in the reflectance (400–490, 1402–1440, 1846–1980 and 2151–2283 nm) and FDR (652–687, 1322–1443, 1856–1985, and 2290–2400 nm) data sets, which yielded reliable (RPIQ > 2.5) predictions.

A comparative evaluation of the generalised predictive ability of eight machine learning algorithms across ten clinical metabolomics data sets for binary classification

IntroductionMetabolomics is increasingly being used in the clinical setting for disease diagnosis, prognosis and risk prediction. Machine learning algorithms are particularly important in the construction of multivariate metabolite prediction. Historically, partial least squares (PLS) regression has been the gold standard for binary classification. Nonlinear machine learning methods such as random forests (RF), kernel support vector machines (SVM) and artificial neural networks (ANN) may be more suited to modelling possible nonlinear metabolite covariance, and thus provide better predictive models.ObjectivesWe hypothesise that for binary classification using metabolomics data, non-linear machine learning methods will provide superior generalised predictive ability when compared to linear alternatives, in particular when compared with the current gold standard PLS discriminant analysis.MethodsWe compared the general predictive performance of eight archetypal machine learning algorithms across ten publicly available clinical metabolomics data sets. The algorithms were implemented in the Python programming language. All code and results have been made publicly available as Jupyter notebooks.ResultsThere was only marginal improvement in predictive ability for SVM and ANN over PLS across all data sets. RF performance was comparatively poor. The use of out-of-bag bootstrap confidence intervals provided a measure of uncertainty of model prediction such that the quality of metabolomics data was observed to be a bigger influence on generalised performance than model choice.ConclusionThe size of the data set, and choice of performance metric, had a greater influence on generalised predictive performance than the choice of machine learning algorithm.

Laboratory Visible and Near-Infrared Spectroscopy with Genetic Algorithm-Based Partial Least Squares Regression for Assessing the Soil Phosphorus Content of Upland and Lowland Rice Fields in Madagascar

As a laboratory proximal sensing technique, the capability of visible and near-infrared (Vis-NIR) diffused reflectance spectroscopy with partial least squares (PLS) regression to determine soil properties has previously been demonstrated. However, the evaluation of the soil phosphorus (P) content—a major nutrient constraint for crop production in the tropics—is still a challenging task. PLS regression with waveband selection can improve the predictive ability of a calibration model, and a genetic algorithm (GA) has been widely applied as a suitable method for selecting wavebands in laboratory calibrations. To develop a laboratory-based proximal sensing method, this study investigated the potential to use GA-PLS regression analyses to estimate oxalate-extractable P in upland and lowland soils from laboratory Vis-NIR reflectance data. In terms of predictive ability, GA-PLS regression was compared with iterative stepwise elimination PLS (ISE-PLS) regression and standard full-spectrum PLS (FS-PLS) regression using soil samples collected in 2015 and 2016 from the surface of upland and lowland rice fields in Madagascar (n = 103). Overall, the GA-PLS model using first derivative reflectance (FDR) had the best predictive accuracy (R2 = 0.796) with a good prediction ability (residual predictive deviation (RPD) = 2.211). Selected wavebands in the GA-PLS model did not perfectly match wavelengths of previously known absorption features of soil nutrients, but in most cases, the selected wavebands were within 20 nm of previously known wavelength regions. Bootstrap procedures (N = 10,000 times) using selected wavebands also confirmed the improvements in accuracy and robustness of the GA-PLS model compared to those of the ISE-PLS and FS-PLS models. These results suggest that soil oxalate-extractable P can be predicted from Vis-NIR spectroscopy and that GA-PLS regression has the advantage of tuning optimum bands for PLS regression, contributing to a better predictive ability.

Vis-NIR Spectroscopy and PLS Regression with Waveband Selection for Estimating the Total C and N of Paddy Soils in Madagascar

Visible and near-infrared (Vis-NIR) diffuse reflectance spectroscopy with partial least squares (PLS) regression is a quick, cost-effective, and promising technology for predicting soil properties. The advantage of PLS regression is that all available wavebands can be incorporated in the model, while earlier studies indicate that PLS models include redundant wavelengths, and selecting specific wavebands can refine PLS analyses. This study evaluated the performance of PLS regression with waveband selection using Vis-NIR reflectance spectra to estimate the total carbon (TC) and total nitrogen (TN) in soils collected mainly from the surface of upland and lowland rice fields in Madagascar (n = 59; after outliers were removed). We used iterative stepwise elimination-based PLS (ISE-PLS) to estimate soil TC and TN and compared the predictive ability with standard full-spectrum PLS (FS-PLS). The predictive abilities were assessed using the coefficient of determination (R2), the root mean squared error of cross-validation (RMSECV), and the residual predictive deviation (RPD). Overall, ISE-PLS using first derivative reflectance (FDR) showed a better predictive accuracy than ISE-PLS for both TC (R2 = 0.972, RMSECV = 0.194, RPD = 5.995) and TN (R2 = 0.949, RMSECV = 0.019, RPD = 4.416) in the soil of Madagascar. The important wavebands for estimating TC (12.59% of all wavebands) and TN (3.55% of all wavebands) were selected from all 2001 wavebands over the 400–2400 nm range using ISE-PLS. These findings suggest that ISE-PLS based on Vis-NIR diffuse reflectance spectra can be used to estimate soil TC and TN contents in Madagascar with an improved predictive accuracy.

A timescale decomposed threshold regression downscaling approach to forecasting South China early summer rainfall

A timescale decomposed threshold regression (TSDTR) downscaling approach to forecasting South China early summer rainfall (SCESR) is described by using long-term observed station rainfall data and NOAA ERSST data. It makes use of two distinct regression downscaling models corresponding to the interannual and interdecadal rainfall variability of SCESR. The two models are developed based on the partial least squares (PLS) regression technique, linking SCESR to SST modes in preceding months on both interannual and interdecadal timescales. Specifically, using the datasets in the calibration period 1915–84, the variability of SCESR and SST are decomposed into interannual and interdecadal components. On the interannual timescale, a threshold PLS regression model is fitted to interannual components of SCESR and March SST patterns by taking account of the modulation of negative and positive phases of the Pacific Decadal Oscillation (PDO). On the interdecadal timescale, a standard PLS regression model is fitted to the relationship between SCESR and preceding November SST patterns. The total rainfall prediction is obtained by the sum of the outputs from both the interannual and interdecadal models. Results show that the TSDTR downscaling approach achieves reasonable skill in predicting the observed rainfall in the validation period 1985–2006, compared to other simpler approaches. This study suggests that the TSDTR approach, considering different interannual SCESR-SST relationships under the modulation of PDO phases, as well as the interdecadal variability of SCESR associated with SST patterns, may provide a new perspective to improve climate predictions.

Study of an adaptable calibration model of near-infrared spectra based on KF-PLS

The key to the quantitative analysis of near-infrared spectra is the establishment of an accurate and adaptable model. In this paper, a calibration method of a dynamic evolutionary model combined with Kalman filter (KF) and partial least squares (PLS) algorithms is proposed. First, an initial quantitative calibration model is built by applying the method of PLS regression to calculate the spectral data samples and their chemical constituent concentrations. Second, inspired by the dynamic evolution characteristics of the KF, the main PLS factor coefficient iterative method is set up based on the KF, by which the calibration model is dynamically corrected. Finally, to prove the validity of the proposed method, a near-infrared spectral dataset from a real corn sample is tested, and the standard PLS method and KF-PLS method are compared. For the 40 external samples (2015), the root mean square error of prediction (RMSEP) of the PLS model was 0.7046% (moisture) and 0.9352% (protein), which is obviously worse than the effects of the KF-PLS model (moisture, 0.3726%, and protein, 0.5451%). Moreover, the R2val (validation decision coefficient) of the KF-PLS model was 0.9035 (moisture) and 0.8565 (protein), which is better than the result of the PLS model (moisture, 0.5659, and protein, 0.6654). Regarding the ability to adapt to equipment (disturbance factor equal to 15%), KF–PLS (RMSEP: moisture, 0.1942%, and protein, 0.3299%; R2val: moisture, 0.9221, and protein, 0.8936) had less prediction error than PLS (RMSEP: moisture, 0.8546%, and protein, 1.0881%; R2val: moisture, 0.5077, and protein, 0.4946). The proposed method has satisfactory accuracy in tracking the evolution of the near-infrared spectrometry measurement state. The novel algorithm can effectively detect the moisture and protein concentration in corn and is also more compatible with outdated equipment, environmental changes and external samples than the PLS algorithm. Thus, this study explores a new approach towards a highly adaptive near-infrared spectrum calibration model.

A MPRM-based approach for fault diagnosis against outliers

In practice industrial applications, the training dataset collected from production process usually contain some outliers. This is a difficult case for partial least squares (PLS) regression which is sensitive to outliers. In order to solve this problem, the paper presents a multivariate statistical process monitoring and diagnosis method based on modified partial robust M-regression (MPRM). MPRM can eliminate the effects of the outliers in the raw data and establish accurate model by down-weighting the outliers strategy. In industry application, the key performance indicator related prediction and fault diagnosis are important to ensure the product quality and enhance economic benefits. Although, the standard PLS is one kind of the most widely used method, it performs an oblique projection to the input space, and thus cannot well distinguish quality-related faults from quality-unrelated ones. To overcome this drawback, the paper proposes to use the singular value decomposition (SVD) on coefficient matrix to decompose input data into quality-related part and quality-unrelated part. Then, robust monitoring statistics and control limits are derived for process monitoring purposes. A numerical example illustrates that the proposed method shows superior process monitoring performance in comparison with standard PLS when the modeling dataset contains outliers.

Mixed-norm partial least squares

The partial least squares (PLS) method is designed for prediction problems when the number of predictors is larger than the number of training samples. PLS is based on latent components which are linear combinations of the original predictors, it automatically employs all predictors regardless of their relevance. This strategy will potentially degrade its performance, and make the obtained coefficients lack interpretability. Then, several sparse PLS (SPLS) methods are proposed to simultaneously conduct prediction and variable selection via sparsely combining original predictors. However, if information bleed across different components, common variables shared by these components should be selected with successive loadings. To address this issue, we propose a new SPLS model — mixed-norm PLS (MNPLS) — to select common variables during each deflation in this paper. More specifically, we introduced the ℓ2,1 norm to the direction matrix and then developed the corresponding solution to MNPLS. Moreover, we also conducted convergence analysis to mathematically support the proposed MNPLS. Experiments are conducted on four real datasets, experimental results verified our theoretical analysis, and also demonstrated that our MNPLS method can generally outperform the standard PLS and other existing methods in variable selection and prediction.

Short communication: Selecting the most informative mid-infrared spectra wavenumbers to improve the accuracy of prediction models for detailed milk protein content

The objective of this study was to investigate the ability of mid-infrared spectroscopy (MIRS) to predict protein fraction contents of bovine milk samples by applying uninformative variable elimination (UVE) procedure to select the most informative wavenumber variables before partial least squares (PLS) analysis. Reference values (n=114) of protein fractions were measured using reversed-phase HPLC and spectra were acquired through MilkoScan FT6000 (Foss Electric A/S, Hillerød, Denmark). Prediction models were built using the full data set and tested with a leave-one-out cross-validation. Compared with MIRS models developed using standard PLS, the UVE procedure reduced the number of wavenumber variables to be analyzed through PLS regression and improved the accuracy of prediction by 6.0 to 66.7%. Good predictions were obtained for total protein, total casein (CN), and α-CN, which included αS1- and αS2-CN; moderately accurate predictions were observed for κ-CN and total whey protein; and unsatisfactory results were obtained for β-CN, α-lactalbumin, and β-lactoglobulin. Results indicated that UVE combined with PLS is a valid approach to enhance the accuracy of MIRS prediction models for milk protein fractions.

Prediction of the distillation temperatures of crude oils using 1H NMR and support vector regression with estimated confidence intervals

This paper aims to estimate the temperature equivalent to 10% (T10%), 50% (T50%) and 90% (T90%) of distilled volume in crude oils using 1H NMR and support vector regression (SVR). Confidence intervals for the predicted values were calculated using a boosting-type ensemble method in a procedure called ensemble support vector regression (eSVR). The estimated confidence intervals obtained by eSVR were compared with previously accepted calculations from partial least squares (PLS) models and a boosting-type ensemble applied in the PLS method (ePLS). By using the proposed boosting strategy, it was possible to identify outliers in the T10% property dataset. The eSVR procedure improved the accuracy of the distillation temperature predictions in relation to standard PLS, ePLS and SVR. For T10%, a root mean square error of prediction (RMSEP) of 11.6°C was obtained in comparison with 15.6°C for PLS, 15.1°C for ePLS and 28.4°C for SVR. The RMSEPs for T50% were 24.2°C, 23.4°C, 22.8°C and 14.4°C for PLS, ePLS, SVR and eSVR, respectively. For T90%, the values of RMSEP were 39.0°C, 39.9°C and 39.9°C for PLS, ePLS, SVR and eSVR, respectively. The confidence intervals calculated by the proposed boosting methodology presented acceptable values for the three properties analyzed; however, they were lower than those calculated by the standard methodology for PLS.

Enhanced quality-related fault detection approach based on OSC and M-PLS

Partial least squares (PLS) is an efficient tool widely used in multivariate statistical process monitoring. Since standard PLS performs oblique projection to input space X, it has limitations in distinguishing quality-related and quality-unrelated faults. Several postprocessing modifications of PLS, such as total projection to latent structures (T-PLS), have been proposed to solve this issue. Further studies have found that these modifications fail to reduce false alarm rates (FARs) of quality-unrelated faults when fault amplitude increases. To cope with this problem, this paper proposes an enhanced quality-related fault detection approach based on orthogonal signal correction (OSC) and modified-PLS (M-PLS). The proposed approach removes variation orthogonal to output space Y from input space X before PLS modeling, and further decomposes X into two orthogonal subspaces in which quality-related and quality-unrelated statistical indicators are designed separately. Compared with T-PLS, the proposed approach has a more robust performance and a lower computational load. Two case studies, including a numerical example and the Tennessee Eastman (TE) process, show the effeteness of the proposed approach.

A Partial Least Squares Algorithm for Microarray Data Analysis Using the VIP Statistic for Gene Selection and Binary Classification

An important application of microarray technology is the assignment of new subjects to known clinical groups (class prediction), but the huge number of screened genes and the small number of samples make this task difficult. To overcome this problem, the usual approach has been to extract a small subset of significant genes (gene selection) or to use the whole set of genes to build latent components (dimension reduction), then applying some usual multivariate classification procedure. Alternatively, both aims -gene selection and class prediction- can be achieved at the same time by using methods based on Partial Least Squares (PLS), as reported in the present work. We present an iterative PLS algorithm based on backward variable elimination through the “Variable Influence on Projection” (VIP) statistic, which finds an optimal PLS model through training and test sets. It simultaneously manages to reduce the number of selected genes by an iterative procedure and finds the best number of PLS factors to reach an optimal classification performance. It is a simple approach that uses only one mathematical method, maintains the identification of discriminatory genes, and builds an optimal predicting model with a fast computation. The algorithm runs as a module of the SIMFIT statistical package, where the optimal model and datasets can be re-run to further interpret the system through additional PLS options, such as scores and loadings plots, or class assignment of new samples. The proposed algorithm was tested under different scenarios occurring in microarray analysis using simulated data. The results are also compared against different classification methods such as KNN, PAM, SVM, RF and standard PLS. Keywords: Classification, gene selection, microarray, partial least squares, PLS, VIP statistic.

MultiScale PLS Modeling for Industrial Process Monitoring

In the process monitoring procedure, Data-driven (statistical) methods usually rely on the process measurements. In most industrial process this measurements has a multi-scale substance in time and frequency. Therefore the statistical methods which are proper for one scale may not be able to detect events at several scales. A Multi-Scale Partial Least Squares (MSPLS) algorithm consists of Wavelet Transforms for extracting multiscale nature of measurements and Partial Least Squares (PLS) as a popular technique of statistical monitoring methods. In this paper the MSPLS algorithm is applied for monitoring of the Tennessee Eastman Process as a benchmark. To show the advantages of MSPLS, its process monitoring performance is compared with the standard PLS and is proved that MSPLS can be a more efficient technique than standard PLS for fault detection in industrial processes.

Sparse partial least-squares regression and its applications to high-throughput data analysis

The partial least-squares (PLS) method is designed for prediction problems where the number of predictors is larger than the number of training samples. PLS is based on latent components that are linear combinations of all of the original predictors, so it automatically employs all predictors regardless of their relevance. This will potentially compromise its performance, but it will also make it difficult to interpret the result. In this paper, we propose a new formulation of the sparse PLS (SPLS) procedure to allow both sparse variable selection and dimension reduction. We use the standard L 1-penalty and the unbounded penalty of [1]. We develop a computing algorithm for SPLS by modifying the nonlinear iterative partial least-squares (NIPALS) algorithm, and illustrate the method with an analysis of a cancer dataset. Through the numerical studies we find that our SPLS method generally performs better than the standard PLS and other existing methods in variable selection and prediction.

Improving the analysis of designed studies by combining statistical modelling with study design information

BackgroundIn the fields of life sciences, so-called designed studies are used for studying complex biological systems. The data derived from these studies comply with a study design aimed at generating relevant information while diminishing unwanted variation (noise). Knowledge about the study design can be used to decompose the total data into data blocks that are associated with specific effects. Subsequent statistical analysis can be improved by this decomposition if these are applied on selected combinations of effects.ResultsThe benefit of this approach was demonstrated with an analysis that combines multivariate PLS (Partial Least Squares) regression with data decomposition from ANOVA (Analysis of Variance): ANOVA-PLS. As a case, a nutritional intervention study is used on Apoliprotein E3-Leiden (APOE3Leiden) transgenic mice to study the relation between liver lipidomics and a plasma inflammation marker, Serum Amyloid A. The ANOVA-PLS performance was compared to PLS regression on the non-decomposed data with respect to the quality of the modelled relation, model reliability, and interpretability.ConclusionIt was shown that ANOVA-PLS leads to a better statistical model that is more reliable and better interpretable compared to standard PLS analysis. From a following biological interpretation, more relevant metabolites were derived from the model. The concept of combining data composition with a subsequent statistical analysis, as in ANOVA-PLS, is however not limited to PLS regression in metabolomics but can be applied for many statistical methods and many different types of data.