Multiple component analysis methods

A method successfully used for chromatographic data and capable to answer this and related questions is the SIMCA method (Statistical Isolinear Multiple Component Analysis). It has been constructed and developed by Svante Wold and his group at the University of Umea, Sweden. 

Unfortunately, the utility of this method for many of the more interesting enzymes is restricted by the complexity of the protein. If more than one type of cluster is present, the multiple component analysis on the extruded mixture may lead to ambiguous conclusions. In addition non-metallochromophores may interfere. Holm and co-workers (Wong et ai, 1979) circumvented some of these problems for Fe S proteins by their choice of spectral analysis and exogenous thiolate ligand. Namely, they used F NMR spectroscopy to analyze the products of thiolate extrusion with /)-trifluoromethylbenzenethiol. Contact shifts for the fluorine resonances are considerably different for 2Fe and 4Fe clusters. Important restrictions on the use of the F NMR detection are the quantity of protein needed, the synthesis of the ligand, and access to the spectrometer. 

To gain insight into chemometric methods such as correlation analysis, Multiple Linear Regression Analysis, Principal Component Analysis, Principal Component Regression, and Partial Least Squares regression/Projection to Latent Structures... 

Multiple linear regression is strictly a parametric supervised learning technique. A parametric technique is one which assumes that the variables conform to some distribution (often the Gaussian distribution) the properties of the distribution are assumed in the underlying statistical method. A non-parametric technique does not rely upon the assumption of any particular distribution. A supervised learning method is one which uses information about the dependent variable to derive the model. An unsupervised learning method does not. Thus cluster analysis, principal components analysis and factor analysis are all examples of unsupervised learning techniques. 

Other chemometrics methods to improve caUbration have been advanced. The method of partial least squares has been usehil in multicomponent cahbration (48—51). In this approach the concentrations are related to latent variables in the block of observed instmment responses. Thus PLS regression can solve the colinearity problem and provide all of the advantages discussed earlier. Principal components analysis coupled with multiple regression, often called Principal Component Regression (PCR), is another cahbration approach that has been compared and contrasted to PLS (52—54). Cahbration problems can also be approached using the Kalman filter as discussed (43). 

We now consider a type of analysis in which the data (which may consist of solvent properties or of solvent effects on rates, equilibria, and spectra) again are expressed as a linear combination of products as in Eq. (8-81), but now the statistical treatment yields estimates of both a, and jc,. This method is called principal component analysis or factor analysis. A key difference between multiple linear regression analysis and principal component analysis (in the chemical setting) is that regression analysis adopts chemical models a priori, whereas in factor analysis the chemical significance of the factors emerges (if desired) as a result of the analysis. We will not explore the statistical procedure, but will cite some results. We have already encountered examples in Section 8.2 on the classification of solvents and in the present section in the form of the Swain et al. treatment leading to Eq. (8-74). 

Input-output analysis methods that project the inputs on a nonlocal hypersurface have also been developed, such as BPNs with multiple hidden layers and regression based on nonlinear principal components. 

Principal component analysis (PCA) of the soil physico-chemical or the antibiotic resistance data set was performed with the SPSS software. Before PCA, the row MPN values were log-ratio transformed (ter Braak and Smilauer 1998) each MPN was logio -transformed, then, divided by sum of the 16 log-transformed values. Simple linear regression analysis between scores on PCs based on the antibiotic resistance profiles and the soil physico-chemical characteristics was also performed using the SPSS software. To find the PCs that significantly explain variation of SFI or SEF value, multiple regression analysis between SFI or SEF values and PC scores was also performed using the SPSS software. The stepwise method at the default criteria (p=0.05 for inclusion and 0.10 for removal) was chosen. 

In a paper that addresses both these topics, Gordon et al.11 explain how they followed a com mixture fermented by Fusarium moniliforme spores. They followed the concentrations of starch, lipids, and protein throughout the reaction. The amounts of Fusarium and even com were also measured. A multiple linear regression (MLR) method was satisfactory, with standard errors of prediction (SEP) for the constituents being 0.37% for starch, 4.57% for lipid, 4.62% for protein, 2.38% for Fusarium, and 0.16% for com. It may be inferred from the data that PLS or PCA (principal components analysis) may have given more accurate results. 

There are several potential sources of error. Both methods of analysis use a binary model mixture, composed of sulfidic and thiophenic components. Thickness effects in the XANES of these model systems would alter the calibrations. There may be contributions from species not adequately represented by a simple dibenzothiophene-dibenzylsulfide model. While the XPS data are represented by 163.3 eV and 164.1 eV components, the model compound data base is as yet limited and not sufficient for a definitive interpretation in terms of alkyl sulfide and thiophenic forms. Examination by both XPS and XANES of a wider variety of model compounds and multiple component model compound mixtures will better define the sulfur species represented by these quantification methods. 

---