Indicators analysis, multivariate method

To reduce the dimensionality of multivariate datasets, PCA or similar ordination methods are commonly used to reduce the number of variables in a dataset with minimal information loss (Wackernagel, 2003). Canonical correlation analysis (CCA) (Goovaerts, 1994 Wackemagel, 2003) is another method suited for multivariate indicator analysis with the aim to analyze relationships between sets of variables. 

Multivariate methods of data analysis are touted as the mathematical equilavent of wonder drugs they are supposed to cure all ills. Indeed, they go a long way in that direction. However, the side effects of their use have not been widely investigated what preliminary results exist [20] indicate that the whole story is not yet known there is considerable variation in the principal components that are computed when different sets of nominally the same noise are added to the same initial set of data. 

Beilken et al. [ 12] have applied a number of instrumental measuring methods to assess the mechanical strength of 12 different meat patties. In all, 20 different physical/chemical properties were measured. The products were tasted twice by 12 panellists divided over 4 sessions in which 6 products were evaluated for 9 textural attributes (rubberiness, chewiness, juiciness, etc.). Beilken etal. [12] subjected the two sets of data, viz. the instrumental data and the sensory data, to separate principal component analyses. The relation between the two data sets, mechanical measurements versus sensory attributes, was studied by their intercorrelations. Although useful information can be derived from such bivariate indicators, a truly multivariate regression analysis may give a simpler overall picture of the relation. 

The results show that DE-MS alone provides evidence of the presence of the most abundant components in samples. On account of the relatively greater difficulty in the interpretation of DE-MS mass spectra, the use of multivariate analysis by principal component analysis (PCA) of DE-MS mass spectral data was used to rapidly differentiate triterpene resinous materials and to compare reference samples with archaeological ones. This method classifies the spectra and indicates the level of similarity of the samples. The output is a two- or three-dimensional scatter plot in which the geometric distances among the various points, representing the samples, reflect the differences in the distribution of ion peaks in the mass spectra, which in turn point to differences in chemical composition of... 

A method has been offered to characterize variations in the retention properties of RPLC by column-eluent combinations by using retention indices of a set of reference compounds, toluene, nitrobenzene, p-cresol, and 2-naphthylethanol [96]. These compounds were selected by multivariate analysis to give optimum discrimination between eluents and columns. 

The separation of synthetic red pigments has been optimized for HPTLC separation. The structures of the pigments are listed in Table 3.1. Separations were carried out on silica HPTLC plates in presaturated chambers. Three initial mobile-phase systems were applied for the optimization A = n-butanol-formic acid (100+1) B = ethyl acetate C = THF-water (9+1). The optimal ratios of mobile phases were 5.0 A, 5.0 B and 9.0 for the prisma model and 5.0 A, 7.2 B and 10.3 C for the simplex model. The parameters of equations describing the linear and nonlinear dependence of the retention on the composition of the mobile phase are compiled in Table 3.2. It was concluded from the results that both the prisma model and the simplex method are suitable for the optimization of the separation of these red pigments. Multivariate regression analysis indicated that the components of the mobile phase interact with each other [79],... 

In traditional method validation, assessment of the calibration has been discussed in terms of linear calibration models for univariate systems, with an emphasis on the range of concentrations that conform to a linear model (linearity and the linear range). With modern methods of analysis that may use nonlinear models or may be multivariate, it is better to look at the wider picture of calibration and decide what needs to be validated. Of course, if the analysis uses a method that does conform to a linear calibration model and is univariate, then describing the linearity and linear range is entirely appropriate. Below I describe the linear case, as this is still the most prevalent mode of calibration, but where different approaches are required this is indicated. 

As it turns out, methods using quantum chemical parameters alone have been applied successfully only to very restricted structural types (Reddy, 1996). When applied to a larger variety of structures, non-quantum chemical parameters, such as an indicator for alkanes and a simple count of hetero atoms, are required (Bodor, 1992), and multivariate regression analysis of a database of measured values determines the contribution of each parameter. This certainly undermines any claim to a superior theoretical basis for quantum calculations. 

Fig. 2 NMR-based metabolomics can be used to quickly identify changes in the global NMR pattern. In this case, the red peaks between 2.5-0.5 ppm are indicative of metabolic differences that are specific to the disease state. Actual data is not nearly as clear as this schematic. The analysis of typical NMR metabolomics datasets requires the use of multivariate analysis methods, such as principle components analysis (PCA), in order to use the metabolome to classify samples...

Another problem that has been tackled by multivariate statistical methods is the characterization of the solvation capability of organic solvents based on empirical parameters of solvent polarity (see Chapter 7). Since such empirical parameters of solvent polarity are derived from carefully selected, strongly solvent-dependent reference processes, they are molecular-microscopic parameters. The polarity of solvents thus defined cannot be described by macroscopic, bulk solvent characteristics such as relative permittivities, refractive indices, etc., or functions thereof. For the quantitative correlation of solvent-dependent processes with solvent polarities, a large variety of empirical parameters of solvent polarity have been introduced (see Chapter 7). While some solvent polarity parameters are defined to describe an individual, more specific solute/solvent interaetion, others do not separate specific solute/solvent interactions and are referred to as general solvent polarity scales. Consequently, single- and multi-parameter correlation equations have been developed for the description of all kinds of solvent effects, and the question arises as to how many empirical parameters are really necessary for the correlation analysis of solvent-dependent processes such as chemical equilibria, reaction rates, or absorption spectra. 

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