Precision multivariate calibration method

For all the mentioned reasons, there is an ongoing tendency in spectroscopic studies to manipulate samples less and perform fewer experiments but to obtain more data in each of them and use more sophisticated mathematical techniques than simple univariate calibration. Hence multivariate calibration methods are being increasingly used in laboratories where instruments providing multivariate responses are of general use. Sometimes, these models may give less precise or less accurate results than those given by the traditional method of (univariate) analysis, but they are much quicker and cheaper than classical approaches. 

Finally, the precision of the multivariate calibration method can be estimated from the standard error of prediction (SEP) (also called standard error of performance), corrected for bias ... 

The least-squares procedure just described is an example of a univariate calibration procedure because only one response is used per sample. The process of relating multiple instrument responses to an analyte or a mixture of analytes is known as multivariate calibration. Multivariate calibration methods have become quite popular in recent years as new instruments become available that produce multidimensional responses (absorbance of several samples at multiple wavelengths, mass spectrum of chromatographically separated components, and so forth). Multivariate calibration methods are very powerful. They can be used to determine multiple components in mixtures simultaneously and can provide redundancy in measurements to improve precision. Recall that repeating a measurement N times provides a Vn improvement in the precision of the mean value. These methods can also be used to detect the presence of interferences that would not be identified in a univariate calibration. 

Multivariate calibration methods were used to establish a new method for measurement of three selected additives in LDPE. The determination of the concentration of silica, erucamide and butylhydroxytoluene was based on IR spectroscopy and a calibration model. The concentrations were between 20 and 1100 wt/ppm. Compared with traditional chemical analyses, the new method was shown to be both time- and cost-effective and to be more precise. The method has potential for quality control of PE. 8 refs. NORWAY SCANDINAVIA WESTERN EUROPE... 

Analysis precision, n - a statistical measure of the expected repeatability of results for an unchanging sample, produced by an analytical method or instrument for samples whose spectra represent an interpolation of a multivariate calibration. The reader is cautioned to refer to specific definitions for precision and repeatability based on the context of use. 

In order to construct a calibration model, the values of the parameters to be determined must be obtained by using a reference method. The optimum choice of reference method will be that providing the highest possible accuracy and precision. The quality of the results obtained with a multivariate calibration model can never exceed that of the method used to obtain the reference values, so the choice should be carefully made as the quality of the model will affect every subsequent prediction. The averaging of random errors inherent in regression methods can help construct models with a higher precision than the reference method. 

In order to overcome, or at least minimise, such drawbacks we can resort to the use of chemometric techniques (which will be presented in the following chapters of this book), such as multivariate experimental design and optimisation and multivariate regression methods, that offer great possibilities for simplifying the sometimes complex calibrations, enhancing the precision and accuracy of isotope ratio measurements and/or reducing problems due to spectral overlaps. 

As in traditional methods that use univariate calibrations, the description of a method of analysis that uses multivariate calibration must also include the corresponding estimated figures of merit, including accuracy (trueness and precision), selectivity, sensitivity, linearity, limit of detection (LOD), limit of quantification (LOQ) and robustness. In this chapter, only the most common figures of merit are described. For a more extensive review, see [55]. Also, for a practical calculation of figures of merit in an atomic spectroscopic application, see [12]. 

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... 

Sections 8.9 to 8.11 have given a brief description of methods for making a regression model for multivariate calibration. To summarize, MLR would rarely be used because it cannot be carried out when the number of predictor variables is greater than the number of specimens. Rather than select a few of the predictor variables, it is better to reduce their number to just a few by using PCR or PLS. These methods give satisfactory results when there is correlation between the predictor variables. The preferred method in a given situation will depend on the precise nature of the data an analysis can be carried out by each method and the results evaluated in order to find which method performs better. For example, for the data in Table 8.4 PCR performed better than PLS as measured by the PRESS statistic. 

The second part of this chapter presents a novel method for improving the precision of multivariate calibration with NIR spectra from scanning and filter-wheel spectrometers. Optical regression (OR) employs the regression model to determine the optimal operational parameters for the scanning monochrometer or filter-wheel that maximizes the analytically useful signal-to-noise ratio. The theory of OR is presented is Section 10.6 and the method is applied to mixtures of dense nonaqueous phase liquids. 

The simple idea that we can actually use all the variables we measure and calculate in chemistry is a powerful one, and is the basis of projection methods such as PLS. We do not any more need awkward schemes for reducing the number of variables down to just a few, thus actually throwing away most of our information. Rather, by utilizing the information in the full set of variables we can deal with more complicated systems and processes, and also increase the precision of the results even in simple situations, as shown by the use of PLS, in multivariate calibration. 

The strengths of the factor-based methods lie in the fact that they are multivariate. The diagnostics are excellent in both the calibration and prediction phases. Improved precision and accuracy over univariate methods can often be realized because of the multivariate advantage. Ultimately, PLS and PCR are able to model complex data and identify when the models are no longer valid. This is an extremely powerful combination. 

CONTENTS 1. Chemometrics and the Analytical Process. 2. Precision and Accuracy. 3. Evaluation of Precision and Accuracy. Comparison of Two Procedures. 4. Evaluation of Sources of Variation in Data. Analysis of Variance. 5. Calibration. 6. Reliability and Drift. 7. Sensitivity and Limit of Detection. 8. Selectivity and Specificity. 9. Information. 10. Costs. 11. The Time Constant. 12. Signals and Data. 13. Regression Methods. 14. Correlation Methods. 15. Signal Processing. 16. Response Surfaces and Models. 17. Exploration of Response Surfaces. 18. Optimization of Analytical Chemical Methods. 19. Optimization of Chromatographic Methods. 20. The Multivariate Approach. 21. Principal Components and Factor Analysis. 22. Clustering Techniques. 23. Supervised Pattern Recognition. 24. Decisions in the Analytical Laboratory. 

Rodriguez-Otero et al. (46) tried to measure cheese composition by NIR in cheese. They tried to analyze cheese without any prior sample manipulation (not even grating) on the basis of increased knowledge in calibration techniques based on multivariate analysis. Repeatability of NIR moisture determination was approximately double in comparison with the reference method. Repeatability of determination of protein by reference (Kjeldahl) and NIR methods was higher for the NIR spectroscopy, probably because of the large sample size rather than to a lack of method precision. The repeatability of fat determination by reference (gravimetric extraction) and NIR methods was 0.31% for reference and 0.40% for NIRS. 

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