Guidance for the selection of a factor analysis method

The first step in analysing a data table is to determine how many pure factors have to be estimated. Basically, there are two approaches which we recommend. One starts with a PCA or else either with OPA or SIMPLISMA. PCA yields the number of factors and the significant principal components, which are abstract factors. OPA yields the number of factors and the purest rows (or columns) (factors) in the data table. If we suspect a certain order in the spectra, we preferentially apply evolutionary techniques such as FSWEFA or HELP to detect pure zones, or zones with two or more components. 

Depending on the way the analysis was started, either the abstract factors found by a PCA or the purest rows found by OPA, should be transformed into pure factors. If no constraints can be formulated on the pure factors, the purest rows 

Although the decomposition of a data table yields the elution profiles of the individual compounds, a calibration step is still required to transform peak areas into concentrations. Essentially we can follow two approaches. The first one is to start with a decomposition of the peak cluster by one of the techniques described before, followed by the integration of the peak of the analyte. By comparing the peak area with those obtained for a number of standards we obtain the amount. One should realize that the decomposition step is necessary because the interfering compound is unknown. The second approach is to directly calibrate the method by RAFA, RBL or GRAFA or to decompose the three-way table by Parafac. A serious problem with these methods is that the data sets measured for the sample and for the standard solution should be perfectly synchronized. 

Kaiser, The varimax criterion for analytic rotation in factor analysis. Psychometrika, 23 (1958) 187-200. 

Forina, C. Armanino, S. Lanteri and R. Leardi, Methods of Varimax rotation in factor analysis with applications in clinical and food chemistry. J. Chemom., 3 (1988) 115-125. 

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