Investigation on reference value error in multivariate calibration

Leveraging multiple linear regression for wavelength selection

: The major objective of the present research is to compare the fairness measures obtained by the prediction error (PE) model with the Cleary model for female and black Soldiers utilizing the current Army aptitude area composites as predictors and Skill Qualifications Test (SOT) scores as the criteria. Fairness is traditionally defined as the absence of underpredictions for the minority groups that are considered potentially susceptible to discrimination. The Cleary model was chosen for comparison with the PE model because Cleary has been considered the gold standard of fairness measurement for more than three decades. The models are compared for selection and classification and evaluated by a common metric using the same robust Army database in a double cross-validation design permitting objective estimates of prediction fairness. The authors conclude that the results obtained for the PE and Cleary models are quite comparable for practical purposes for selection, but possibly not for classification. They find that the PE model is the better of the two because of the precision that comes with utilization and reliance upon individual test scores.

Mean Squared Prediction Error Reduction with Instrumental Variables

When paired with high-powered chemometric analysis, spectrometric methods offer great promise for the high-throughput analysis of complex systems. Effective classification or quantification often relies on signal preprocessing to reduce spectral interference and optimize the apparent performance of a calibration model. However, less frequently addressed by systematic research is the affect of preprocessing on the statistical accuracy of a calibration result. The present work demonstrates the effectiveness of two criteria for validating the performance of signal preprocessing in multivariate models in the important dimensions of bias and precision. To assess the extent of bias, we explore the applicability of the elliptic joint confidence region (EJCR) test and devise a new means to evaluate precision by a bias-corrected root mean square error of prediction. We show how these criteria can effectively gauge the success of signal pretreatments in suppressing spectral interference while providing a straightforward means to determine the optimal level of model complexity. This methodology offers a graphical diagnostic by which to visualize the consequences of pretreatment on complex multivariate models, enabling optimization with greater confidence. To demonstrate the application of the EJCR criterion in this context, we evaluate the validity of representative calibration models using standard pretreatment strategies on three spectral data sets. The results indicate that the proposed methodology facilitates the reliable optimization of a well-validated calibration model, thus improving the capability of spectrophotometric analysis.

To improve the quality of input data of multivariate calibration model, a new hybrid preprocessing algorithm (WPT-GA-OSC) was proposed, which is the combination of wavelet packet transform (WPT), genetic algorithm (GA) and orthogonal signal correction (OSC) algorithm. At first, WPT algorithm is applied to split the raw spectra into different frequency components. Then, based on the root mean square error of prediction models, the genetic algorithm is employed to select the WPT components related to analyte as the input data of regression model. At last, to further improve the quality of input data, OSC algorithm is applied to each GA-filtered component to eliminate the information irrelevant to analyte information. To validate the WPT-GA-OSC algorithm, it was applied to develop the calibration model for oil concentration measurement of corn. Compared with the conventional preprocessing algorithm, the WPT-GA-OSC algorithm can take full advantages of multiscale property of near infrared (NIR) spectra, and also can significantly decrease the prediction error by up to 48.3%, indicating that it is a promising way for filtering the spectral data to develop the NIR calibration model.

<div> <p>The latest generation of integrated hydrologic models provides new opportunities to better understand and hypothesize about the connections between hydrological, ecological and energy transfer processes across a range of scales. Parallel to this has been unprecedented growth in new technologies to observe components of Earth’s biophysical system through satellite remote sensing or on-the-ground instruments. However, along with growth in available data and advanced modelling platforms comes a challenge to ensure models are representative of catchment systems and are not unrealistically confident in their predictions. Many hydrologic and ecosystem variables are measured infrequently, measured with significant error, or are measured at a scale different to their representation in a model. In fact, the modelled variable of interest is frequently not directly observed but inferred from surrogate measurements. This introduces errors in model calibration that will affect whether our models are representative of the systems we seek to understand.</p> </div><div> <p>In recent years, Bayesian inference has emerged as a powerful tool in the environmental modeler’s toolbox, providing a convenient framework in which to model parameter and observational uncertainties. The Bayesian approach is ideal for multivariate model calibration, by defining proper prior distributions that can be considered analogous to the weighting often prescribed in traditional multi-objective calibration. </p> </div><div> <p>In this study, we develop a multi-objective Bayesian approach to hydrologic model inference that explicitly capitalises on a priori knowledge of observational errors to improve parameter estimation and uncertainty estimation. We introduce a novel error model, which partitions observation and model residual error according to prior knowledge of the estimated uncertainty in the calibration data. We demonstrate our approach in two case studies: an ecohydrologic model where we make use of the known uncertainty in satellite retrievals of Leaf Area Index (LAI), and a water quality model using turbidity as a proxy for Total Suspended Solids (TSS). Overall, we aim to demonstrate the need to properly account for known observational errors in proper hydrologic model calibration.</p> </div>

Calibration model maintenance is often overlooked but is a significant part of successful use of multivariate calibration models, for example, in process monitoring and optimization. In some cases, companies are maintaining tens or even hundreds of calibration models. This could be partial least squares (PLS) calibration models pertaining to different recipes or raw materials or neural network based models covering different production sites. Maintaining such a high number of models is cumbersome and expensive. Sometimes, a solution presented for this problem is to merge all the models into one, but this often comes at the expense of significantly higher prediction errors. In this paper, we suggest a new approach for rationally merging calibration models in order to optimally balance the prediction error and maintenance workload. We do this by systematically merging models that lower the error as much as possible and hence provide a sort of optimal clustering or fusion of calibration models. We showcase the new approach on a case based on infrared spectroscopy applied to dairy production.

Determination of free amino acid content in Radix Pseudostellariae using near infrared (NIR) spectroscopy and different multivariate calibrations

The paper presents multivariate partial least-squares calibration model defined for the identification and simultaneous determination of phenolic terpenoids—eugenol, carvacrol, and thymol—by means of the differential pulse voltammetry. For the first time, using boron-doped diamond electrode signal, electrochemical distinction of carvacrol and thymol, despite the short distance between the peaks (15 mV), was described. The analytes’ concentrations applied in the calibration model were selected using the 3-factorial central composite design. The multivariate partial least-squares model, with optimized data pre-processing, was used for determination of eugenol, carvacrol, and thymol in the concentration ranges of 0.77–13.86, 0.58–10.40, and 0.73–7.32 mg/dm3, respectively. The quality of the method, expressed by the root-mean-squared error of calibration was 0.55, 0.20, and 0.26 mg/dm3 for the specified analytes. The recovery in the analysis of the pure signals was 98.92%, 101.62%, and 101.46%, what confirmed the possibility of clearly distinguishing the thymol and carvacrol peaks. In the spiked honey samples, the accuracy of eugenol, carvacrol, and thymol determination, expressed by the root-mean-squared error of prediction, was in the range 0.20–0.83 mg/dm3, and recovery in the range 80.9–111.9%. Application of the presented model not only enables electrochemical identification and simultaneous determination of eugenol, carvacrol, and thymol, but also allows rapid, accurate, and low-cost verification of authenticity of the commercial products.Graphical abstract

The development of efficient algorithms for variable selection becomes important to deal with large and complex datasets. Most works in quantitative chemical analysis have used Genetic Algorithms (GAs) as a reference method to select variables. On the other hand, new advances in metaheuristic techniques provide novel possibilities in this task Moreover, the application of Multi-Objective Optimization (MOO) may significantly contribute to efficiently construct an accurate model in the context of multivariate calibration. MOO has showed itself as an efficiently and successful tool to dealing with conflicting objective-functions. For instance, the use of MOO may be considered as a good choice to treat the reducing of prediction error and the number of selected variables in a calibration model. In this paper, we present a modern metaheuristic implementation called Multi-Objective Firefly Algorithm (MOFA) for variable selection in multivariate calibration models. The goal is to propose an optimization to reduce the prediction error of the property of interest in the analysed sample as well as reducing the number of selected variables. However, the outcomes are remarkably promising compared with the previous work. Based on the results obtained, it is possible to demonstrate that our proposal is a viable alternative in order to deal with such conflicting objectives. Additionally, we compare MOFA with a traditional GA implementation and show that MOFA is more efficient for the variable selection problem.

It was shown that linear transformations are suitable for use in multivariate calibration in near infrared spectroscopy as data compression tools. Partial Least Squares calibration models were built using spectral data transformed by expansion in the series of classical orthogonal polynomials, Fourier and wavelet harmonics. These models allowed effective prediction of the cetane number of diesel fuels, Brix and pol parameters of syrup in sugar production and fat and total protein content in milk. Depending on the compression ratio, prediction errors were no larger than 30% of corresponding errors obtained by the use of the non-transformed models. Although selection of the most suitable transformation depends on the calibration data and on the cross-validation method, in many cases Fourier transform gave satisfactory results.

The transfer of multivariate calibration models is investigated between a primary (A) and two secondary Fourier transform near-infrared (near-IR) spectrometers (B, C). The application studied in this work is the use of bands in the near-IR combination region of 5000-4000 cm(-)(1) to determine physiological levels of glucose in a buffered aqueous matrix containing varying levels of alanine, ascorbate, lactate, triacetin, and urea. The three spectrometers are used to measure 80 samples produced through a randomized experimental design that minimizes correlations between the component concentrations and between the concentrations of glucose and water. Direct standardization (DS), piecewise direct standardization (PDS), and guided model reoptimization (GMR) are evaluated for use in transferring partial least-squares calibration models developed with the spectra of 64 samples from the primary instrument to the prediction of glucose concentrations in 16 prediction samples measured with each secondary spectrometer. The three algorithms are evaluated as a function of the number of standardization samples used in transferring the calibration models. Performance criteria for judging the success of the calibration transfer are established as the standard error of prediction (SEP) for internal calibration models built with the spectra of the 64 calibration samples collected with each secondary spectrometer. These SEP values are 1.51 and 1.14 mM for spectrometers B and C, respectively. When calibration standardization is applied, the GMR algorithm is observed to outperform DS and PDS. With spectrometer C, the calibration transfer is highly successful, producing an SEP value of 1.07 mM. However, an SEP of 2.96 mM indicates unsuccessful calibration standardization with spectrometer B. This failure is attributed to differences in the variance structure of the spectra collected with spectrometers A and B. Diagnostic procedures are presented for use with the GMR algorithm that forecasts the successful calibration transfer with spectrometer C and the unsatisfactory results with spectrometer B.

The influence of vegetation cover on the spectroscopic estimation of soil properties

Monitoring of multivariate calibration models in the absence of new reference values: The regression case

The aim of this study was the non-destructive assessment of ‘Ortanique’ (Citrus reticulata Blanco x Citrus sinensis (L) Osbeck) ripening, based on the prediction of internal quality attributes (IQA) by short-wave near-infrared reflectance spectroscopy (SW-NIRS) calibration models. Spectra from fruit of 50 trees located in two different orchards, were acquired on tree using a customized portable visible near-infrared (vis-NIR) system. Partial least squares (PLS) was used to build the various IQA calibration models. The models were tested through internal validation (IV) and external validation (EV). Generally, the IV results were always superior to those of EV: regarding IV, a high regression coefficient (R2) and low root mean square error of prediction (RMSEP) were achieved, revealing a good predictive performance for juice pH (R2 = 0.80; RMSEP = 0.10; SDR = 2.23), soluble solids content (SSC) (R2 = 0.79; RMSEP = 0.75 %; SDR = 2.27), titratable acidity (TA) (R² = 0.73; RMSEP = 0.24 % citric acid; SDR = 1.94) and the maturation index (MI) (R2 = 0.80; RMSEP = 1.38; SDR = 2.2). The best EV predictions were obtained for TA (R2 = 0.69; RMSEP = 0.38 % citric acid; SDR = 1.24), and MI (R2 = 0.69; RMSEP = 2.07; SDR = 1.49). Calibration models for glucose, fructose and sucrose showed medium-coarse predictions for both validation strategies. A detailed investigation of MI models was performed, to understand the causes of their poor EV results. In the context of EV, model updating strategies were explored by using some validation samples to improve the calibration model. The methods of bias correction and spiking were tested, showing a clear improvement in the predictions.