Multivariate statistical analysis applications

Liardon R., Ott U. and Daget N. (1984) Analysis of coffee headspace profiles by multivariate statistics. Analysis of volatiles. Methods and Applications. P. Schreier Ed., W. de Gruyter, Berlin, New York, 447-59. 

Geographical dependences of wines in samples from Italy, France, Australia, California, and Korea have been reported, and the application of NMR-based multivariate statistical analysis has successfully allowed the association of wine metabolites with wine quality not only on the basis of geography, but also depending on climate, soU, sun exposition, or rainfalls ( terroir effect) [13,43 6]. 

In all statistical modeling, including multivariate data analysis, it is crucially important to determine the applicability of the derived model, and for several reasons ... 

Bakraji, E. H., Othman, I., Sarhil, A., and Al-Somel, N. (2002). Application of instrumental neutron activation analysis and multivariate statistical methods to archaeological Syrian ceramics. Journal of Trace and Microprobe Techniques 20 57-68. 

Despite the broad definition of chemometrics, the most important part of it is the application of multivariate data analysis to chemistry-relevant data. Chemistry deals with compounds, their properties, and their transformations into other compounds. Major tasks of chemists are the analysis of complex mixtures, the synthesis of compounds with desired properties, and the construction and operation of chemical technological plants. However, chemical/physical systems of practical interest are often very complicated and cannot be described sufficiently by theory. Actually, a typical chemometrics approach is not based on first principles—that means scientific laws and mles of nature—but is data driven. Multivariate statistical data analysis is a powerful tool for analyzing and structuring data sets that have been obtained from such systems, and for making empirical mathematical models that are for instance capable to predict the values of important properties not directly measurable (Figure 1.1). 

A principal components multivariate statistical approach (SIMCA) was evaluated and applied to interpretation of isomer specific analysis of polychlorinated biphenyls (PCBs) using both a microcomputer and a main frame computer. Capillary column gas chromatography was employed for separation and detection of 69 individual PCB isomers. Computer programs were written in AMSII MUMPS to provide a laboratory data base for data manipulation. This data base greatly assisted the analysts in calculating isomer concentrations and data management. Applications of SIMCA for quality control, classification, and estimation of the composition of multi-Aroclor mixtures are described for characterization and study of complex environmental residues. 

In the past few years, PLS, a multiblock, multivariate regression model solved by partial least squares found its application in various fields of chemistry (1-7). This method can be viewed as an extension and generalization of other commonly used multivariate statistical techniques, like regression solved by least squares and principal component analysis. PLS has several advantages over the ordinary least squares solution therefore, it becomes more and more popular in solving regression models in chemical problems. 

Among the multivariate statistical techniques that have been used as source-receptor models, factor analysis is the most widely employed. The basic objective of factor analysis is to allow the variation within a set of data to determine the number of independent causalities, i.e. sources of particles. It also permits the combination of the measured variables into new axes for the system that can be related to specific particle sources. The principles of factor analysis are reviewed and the principal components method is illustrated by the reanalysis of aerosol composition results from Charleston, West Virginia. An alternative approach to factor analysis. Target Transformation Factor Analysis, is introduced and its application to a subset of particle composition data from the Regional Air Pollution Study (RAPS) of St. Louis, Missouri is presented. 

In the present time with almost unlimited computer facilities in the analytical laboratory, analytical chemists should be able to obtain substantial benefits from the application of time series, information theory, multivariate statistics, a.o. factor analysis and pattern recognition, operations research, numerical analysis, linear algebra, computer science, artificial intelligence, etc. This is in fact what chemo-metricians have been doing for the past decades. 

The molecular specificity of Fourier transform infrared (FTIR) lends itself quite well to applications in pharmaceutical development labs, as pointed out in a review article with some historical perspective.10 One of the more common applications of mid-IR in development is a real-time assessment of reaction completion when used in conjunction with standard multivariate statistical tools, such as partial least squares (PLS) and principal component analysis (PCA).18,19 Another clever use of FTIR is illustrated in Figure 9.1, where the real-time response of a probe-based spectroscopic analyzer afforded critical control in the charge of an activating agent (trifluoroacetic anhydride) to activate lactol. Due to stability and reactivity concerns, the in situ spectroscopic approach was... 

Because data analysis is of central interest, particularly in the application of chemometric methods in the field of environmental research, a rough list of important multivariate statistical methods is given below (Tab. 1-1). 

Fax, L. Angewandte Statistik, Springer, Berlin, Heidelberg, New York, 1978 Flury, B., Riedwyl, H. Multivariate Statistics A Practical Approach, Chapman and Hall, 1988 Goldstein, M., Dillon, W.R. Multivariate Analysis Methods and Applications, Wiley, New York, 1984 Graham, R.C. Data Analysis for the Chemical Sciences A Guide to Statistical Techniques, VCH, New York, Weinheim, Cambridge, 1993... 

To demonstrate the accuracy, two dust and two soil reference materials were analyzed with the described method. The mean value of the correlation coefficients between the certified and the analyzed amounts of the 16 elements in the samples is r = 0.94. By application of factor analysis (see Section 5.4) the square root of the mean value of the communahties of these elements was computed to be approximately 0.84. As frequently happens in the analytical chemistry of dusts several types of distribution occur [KOM-MISSION FUR UMWELTSCHUTZ, 1985] these can change considerably in proportion to the observed sample size. In the example described the major components are distributed normally and most of the trace components are distributed log-normally. The relative ruggedness of multivariate statistical methods against deviations from the normal distribution is known [WEBER, 1986 AHRENS and LAUTER, 1981] and will be tested using this example by application of factor analysis. 

The application of methods of multivariate statistics (here demonstrated with examples of cluster analysis, multivariate analysis of variance and discriminant analysis, and principal components analysis) enables clarification of the lateral structure of the types of feature change within a test area. 

In soil science, the empirical description of soil horizons predominates. Only a few applications of statistical methods in this scientific field are described. SCHEFFER and SCHACHTSCHABEL [1992] give an example for the classification of different soils into soil groups using cluster analysis. They claim the objectivity of the results to be one advantage of multivariate statistical methods. 

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