Quantitative analysis multivariate calibration

An important aspect of all methods to be discussed concerns the choice of the model complexity, i.e., choosing the right number of factors. This is especially relevant if the relations are developed for predictive purposes. Building validated predictive models for quantitative relations based on multiple predictors is known as multivariate calibration. The latter subject is of such importance in chemo-metrics that it will be treated separately in the next chapter (Chapter 36). The techniques considered in this chapter comprise Procrustes analysis (Section 35.2), canonical correlation analysis (Section 35.3), multivariate linear regression... 

D.M. Haaland, Multivariate Calibration Methods Applied to the Quantitative Analysis of Infrared Spectra, Chapter I in Computer-Enhanced Analytical Spectroscopy, Volume 3", edited by P.C. Jurs. Plenum Press, New York, 1992. 

Goodacre, R. Neal, M. J. Kell, D. B. Rapid and quantitative analysis of the pyrolysis mass spectra of complex binary and tertiary mixtures using multivariate calibration and artificial neural networks. Anal. Chem. 1994, 66,1070-1085. 

Timmins, E. M. Goodacre, R. Rapid quantitative analysis of binary mixtures of Escherichia coli strains using pyrolysis mass spectrometry with multivariate calibration and artificial neural networks J. Appl. Microbiol. 1997,83, 208-218. 

Samola and Urleb [15] reported qualitative and quantitative analysis of OTC using near-infrared (NIR) spectroscopy. Multivariate calibration was performed on NIR spectral data using principle component analysis (PCA), PLS-1, and PCR. 

Cahn, F. and S. Compton, Multivariate Calibration of Infrared Spectra for Quantitative Analysis Using Designed Experiments , Applied Spectroscopy, 42 865-872 (July, 1988). 

Recently, introductory books about chemometrics have been published by R. G. Brereton, Chemometrics—Data Analysis for the Laboratory and Chemical Plant (Brereton 2006) and Applied Chemometrics for Scientists (Brereton 2007), and by M. Otto, Chemometrics—Statistics and Computer Application in Analytical Chemistry (Otto 2007). Dedicated to quantitative chemical analysis, especially using infrared spectroscopy data, are A User-Friendly Guide to Multivariate Calibration and Classification (Naes et al. 2004), Chemometric Techniques for Quantitative Analysis (Kramer 1998), Chemometrics A Practical Guide (Beebe et al. 1998), and Statistics and Chemometrics for Analytical Chemistry (Miller and Miller 2000). 

Their increased application in light food and drink products has given a new impetus to develop fast and accurate method for their determination. Among computer-controlled instruments multivariate calibration methods and derivative techniques are playing very important role in the multicomponent analysis of mixtures by UV-VIS molecular absorption spectrophotometry [2]. Both approaches ate useful in the resolution of overlapping band in quantitative analysis [3, 4]. 

E.V. Thomas and D.M. Haaland, Comparison of multivariate calibration methods for quantitative spectral analysis. Anal. Chem., 62, 1091-1099 (1990). 

Andersson M, Folestad S, Gottfires J, Johansson MO, Josefson M, Wahlund KG. Quantitative analysis of film coating in a fluidized-bed process by in-line NIR spectroscopy and multivariate batch calibration. Anal Chem 2000 72 2099-2108. Vazquz Elizabeth Rivera Master of Science Thesis, Optimization of Drying-end-points. Measurements for the automation of a fluidized-bed dryer using FT-NIR Spectroscopy, Univ of Puerto Rico, 2004. 

Quantitative analysis in ICP-MS is typically achieved by several univariate calibration strategies external calibration, standard addition calibration or internal standardisation. Nevertheless multivariate calibration has also been applied, as will be presented in Chapters 3 and 4. 

M. L. Griffiths, D. Svozil, P. Worsfold, S. Denham and E. H. Evans, Variable reduction algorithm for atomic emission spectra application to multivariate calibration and quantitative analysis of industrial samples, J. Anal. At. Spectrom., 17, 2002, 800-812. 

Multivariate calibrations have become a commonly applied tool in the field of modern analytical chemistry and, specifically, in quantitative IR analysis [13,14]. PLS regression is one of several methods that utilize an entire spectral information band present in IR data, often referred to as full-spectrum calibrations. The advantages of full-spectrum calibrations, such as PLS and CLS, are improvements in precision and robustness over univariate calibrations owing to increased signal averaging from including more spectral intensities. The distinction between PLS and CLS manifests in the fact that PLS is a factor-based regression, which means the full spectra for the acquired... 

New methods for non-destructive quantitative analysis of additives based on MIR spectra and multivariate calibration have been presented [67, 68], One of the limitations in the determination of additive levels by MIR spectroscopy is encountered in the detection limit of this technique, which is usually above the low concentration of additive present, due to their heavy dilution in the polymer matrix. The samples are thin polymer films with small variations in thickness (due to errors in sample preparation). The differences in thickness cause a shift in spectra and if not eliminated or reduced they may produce non-reliable results. Methods for spectral normalisation become necessary. These methods were reviewed and compared by Karstang et al. [68]. MIR is more specific than UV but the antioxidant content may be too low to give a suitable spectrum [69]. However, this difficulty can be overcome by using an additive-free polymer in the reference beam [67, 68, 69, 70]. On the other hand, UV and MIR have been successfully applied to quantify additives in polymer extracts [71, 72, 66]. 

A limiting factor in noninvasive optical technology is variations in the optical properties of samples under investigation that result in spectral distortions44 8 and sampling volume (effective optical path length) variability 49-54 These variations will impact a noninvasive optical technique not only in interpretation of spectral features, but also in the construction and application of a multivariate calibration model if such variations are not accounted for. As a result, correction methods need to be developed and applied before further quantitative analysis. For Raman spectroscopy, relatively few correction methods appear in the literature, and most of them are not readily applicable to biological tissue.55-59... 

Partial Least Squares Regression (PLS) is a multivariate calibration technique, based on the principles of Latent Variable Regression. Originated in a slightly different form in the field of econometrics, PLS has entered the spectroscopic scene.46,47,48 It is mostly employed for quantitative analysis of mixtures with overlapping bands (e.g. mixture of glucose, fructose and sucrose).49,50... 

Schultz TP, Glasser WG (1986) Quantitative structural analysis of lignin by diffuse reflectance Fourier transform infrared spectromety Holzforschung 40 (Suppl) 37-44 Schultz TP, Nicholas DD (1987) Fourier transform infrared spectrometry Detection of incipient brown rot decay in wood Int Analyst 41 35-39 Sjostrom M, Wold, S, Lindberg W, Persson J-A, Martens H (1983) A multivariate calibration problem in analytical chemistry solved by partial least-squares models in latent variables Anal Chim Acta 150 61-70... 

The American Society for Testing and Materials (ASTM) recently published an official document providing a guide to spectroscopists for the multivariate calibration of infrared spectrometers. The scope of the publication, entitled Standard Practices for Infrared Multivariate Quantitative Analysis includes a description of multivariate calibration methods for the determination of physical or chemical characteristics of materials. This document is the first official standard for the application of chemometric multivariate analysis to near-infrared and infrared instruments. 

Although less important than peak frequencies, peak intensities obviously play a role in quantitative analysis and, in many cases, qualitative identification. Multivariate calibration techniques and their transferability depend on reproducible relative peak heights. A possibly lengthy method development procedure may fail when a different spectrometer is used, if the observed intensities vary. Reproducibility of absolute signal is difficult to achieve between labs or even between instruments of the same design, but it is important for a particular instrument. Absolute intensities can at least be used to evaluate day-to-day instrument performance and to detect hardware or alignment problems. 

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