Multivariate approaches

The methods in Section 5.3.2 could be extended to all 10 PAHs, and with appropriate choice of 10 wavelengths may give reasonable estimates of concentrations. However, all the wavelengths contain some information and there is no reason why most of the spectrum cannot be employed. 

There is a fairly confusing literature on the use of multiple linear regression for calibration in chemometrics, primarily because many workers present their arguments in a very formalised manner. However, the choice and applicability of any method depends on three main factors  

die number of compounds in die mixture (N = 10 in diis case) or responses to be estimated  

the number of experiments (/ = 25 in tills case), often spectra or chromatograms  

In order to have a sensible model, the number of compounds must be less than or equal to the smaller of the number of experiments or number of variables. In certain specialised cases this limitation can be infringed if it is known that there are correlations between concentrations of different compounds. This may happen, for example, in environmental chemistry, where there could be tens or hundreds of compounds in a sample, but the presence of one (e.g. a homologous series) indicates the presence of another, so, in practice there are only a few independent factors or groups of compounds. Also, correlations can be built into the design. In most real world situations there definitely will be correlations in complex multicomponent mixtures. However, the methods described below are for die case where die number of compounds is smaller than the number of experiments or number of detectors. 

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Some methods that paitly cope with the above mentioned problem have been proposed in the literature. The subject has been treated in areas like Cheraometrics, Econometrics etc, giving rise for example to the methods Partial Least Squares, PLS, Ridge Regression, RR, and Principal Component Regression, PCR [2]. In this work we have chosen to illustrate the multivariable approach using PCR as our regression tool, mainly because it has a relatively easy interpretation. The basic idea of PCR is described below. 

S Hellberg, M Sjostrom, B Skagerberg, S Wold. Peptide quantitative structure-activity relationships, a multivariate approach. I Med Chem 30 1126-1135, 1987. 

The aim of all the foregoing methods of factor analysis is to decompose a data-set into physically meaningful factors, for instance pure spectra from a HPLC-DAD data-set. After those factors have been obtained, quantitation should be possible by calculating the contribution of each factor in the rows of the data matrix. By ITTFA (see Section 34.2.6) for example, one estimates the elution profiles of each individual compound. However, for quantitation the peak areas have to be correlated to the concentration by a calibration step. This is particularly important when using a diode array detector because the response factors (absorptivity) may considerably vary with the compound considered. Some methods of factor analysis require the presence of a pure variable for each factor. In that case quantitation becomes straightforward and does not need a multivariate approach because full selectivity is available. 

There are four main types of data that frequently occur in sensory analysis pair-wise differences, attribute profiling, time-intensity recordings and preference data. We will discuss in what situations such data arise and how they can be analyzed. Especially the analysis of profiling data and the comparison of such data with chemical information calls for a multivariate approach. Here, we can apply some of the techniques treated before, particularly those of Chapters 35 and 36. 

A table of correlations between the variables from the instrumental set and variables from the sensory set may reveal some strong one-to-one relations. However, with a battery of sensory attributes on the one hand and a set of instrumental variables on the other hand it is better to adopt a multivariate approach, i.e. to look at many variables at the same time taking their intercorrelations into account. An intermediate approach is to develop separate multiple regression models for each sensory attribute as a linear function of the physical/chemical predictor variables. 

Wavelength database libraries of >32000 analytical lines can be used for fast screening of the echellogram. Such databases allow the analyst to choose the best line(s) for minimum interferences, maximum sensitivity and best dynamic range. Further extension of the wavelength range (from 120 to 785 nm) is desirable for alkali metals, Cl, Br, Ga, Ge, In, B, Bi, Pb and Sn, and would allow measurement of several emission lines in a multivariate approach to spectral interpretation [185]. 

Use of multivariate approaches based on classification modelling based on cluster analysis, factor analysis and the SIMCA technique [98,99], and the Kohonen artificial neural network [100]. All these methods, though rarely implemented, lead to very good results not achievable with classical strategies (comparisons, amino acid ratios, flow charts) and, moreover it is possible to know the confidence level of the classification carried out. 

Thomsen M, Dobel S, Lassen P, Carlsen L, Mogensen BB, Hansen PE (2002) Reverse quantitative structure-activity relationship for modelling the sorption of esfenvalerate to dissolved organic matter. A multivariate approach. Chemosphere 49 1317-1325... 

As already mentioned, an experimental design approach is preferred to evaluate method robusmess. It is a multivariate approach, evaluating the factor effects on the responses by varying the factors simultaneously, according to the experimental conditions defined by the design. 

The advent of analytical techniques capable of providing data on a large number of analytes in a given specimen had necessitated that better techniques be employed in the assessment of data quality and for data interpretation. In 1983 and 1984, several volumes were published on the application of pattern recognition, cluster analysis, and factor analysis to analytical chemistry. These treatises provided the theoretical basis by which to analyze these environmentally related data. The coupling of multivariate approaches to environmental problems was yet to be accomplished. 

PLS was advantageous when studying the relationship of the toxicity of thiify triazines on Daphnia magna (25), and in a comparison between Hansch analysis and PLS analysis, using the same data set, it was shown that tiie multivariate approach of PLS provided more useful models than the Hansch type approach (26). 

Kent, M., Oehlenschlager, J., Mierke-Klemeyer, S., Manthey-Karl, M., Knoechel, R., Daschner, E, Schimmer, O. (2004) New multivariate approach to the problem of fish quality estimation. Food Chem. 87 531-535. 

Tollsten, L. (1993). A multivariate approach to post-pollination changes in the floral scent of Platanthera bifolia (Orchidaceae). Nordic Journal of Botany 13 495-499. 

Clement, A., Dorais, M., and Vernon, M. (2008). Multivariate approach to the measurement of tomato maturity and gustatory attributes and their rapid assessment by Vis-NIR spectroscopy. ]. Agric. Food Chem. 56,1538-1544. 

As noted above, Raman images of skin are usually derived from hundreds to thousands of spectra. Examination of each individual spectrum is evidently impractical. Multivariate approaches are required to condense the information into a small set of components with a minimum loss of spectral information. We have found initial evaluation by principal component analysis (PCA) followed by factor analysis to be useful for this purpose. 

This chapter constitutes an attempt to demonstrate the utility of multivariate statistics in several stages of the scientific process. As a provocation, it is suggested that the multivariate approach (in experimental design, in data description and in data analysis) will always be more informative and make generalizations more valid than the univariate approach. Finally, the multivariate strategy can be really enjoyable, not the least for its capacity to reveal hidden treasures in data that in a univariate analysis look like a set of random numbers. 

S. Hellberg, A multivariate approach to QSAR, Thesis, Univ. UmeS, Sweden (1986). 

Castro, I.A., Barroso, L.P., and Sinnecker, P. 2005. Functional foods for coronary heart disease risk reduction A meta-analysis using a multivariate approach. Am. J. Clin. Nutr. 82, 32-40. 

Reynoldson, T.B., Day, K.E. and Norris, R.H. (1995) Biological guidelines for freshwater sediment based on BEnthic Assessment of SedimenT (BEAST) using a multivariate approach for predicting biological state, Australian Journal of Ecology 20, 198-219. 

FIGURE 1 Multivariate approaches for omics data integration. (A) The RV coefficient is a correlation measure between datasets that can be used as distance metric. (B) The 02PLS method dissects gene expression and metabolomics datasets for shared and data type-specific variation. (C) The N-way approach accommodates experimental factors in a multidimensional block. Tucker3 is used to study intradataset covariation and NPLS analyzes between-block covariation. Panel (B) Reproduced from Bylesjo et al. (23). Panel (C) Reproduced from Conesa et al. (24). 

Canuel, E.A. (2001) Relations between river flow, primary production and fatty acid composition of particulate organic matter in San Francisco and Chesapeake Bays a multivariate approach. Qrg. Geochem. 32, 563-583. 

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. 

Using artificial neural networks to develop calibration models is also possible. The reader is referred to the literature [68-70] for further information. Neural networks are commonly utilized when the data set maintains a large degree of nonlinearity. Additional multivariate approaches for nonlinear data are described in the literature [71, 72],... 

Hoen B, Viel JF, Paquot C et al. (1995) Multivariate approach to differential diagnosis of acute meningitis. European Journal of Clinical Microbiology and Infectious Diseases 14 267-274. 

It is now a simple task to perform PLS (or indeed any other multivariate approach), as discussed above. The 30 variables are centred and the predictions of the concentrations performed when increasing number of components are used (note that three is the maximum permitted for column centred data in this case, so this example is somewhat simple). All the methods described above can be applied. 

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