Use of eigenvalues for determining the number of components in window factor analysis of spectroscopic and chromatographic data

Three methods for determining eigenvalues, namely (1) mean-centred sequential scores, (2) mean-centred sequential loadings and (3) uncentred data, are described, and compared on simulations and real data of two-way data matrices. The sequential direction may be time (high-performance liquid chromatography (HPLC)) or wavelength (infrared spectroscopy (IR)), with the non-sequential direction wavelength (HPLC) or sample number (IR). It is shown that method 1 is very dependent on peak shapes. Method 2 works well except when there is low variability in the non-sequential direction. Method 3 performs poorly in the presence of heteroscedastic noise. It is concluded that standard statistical approaches for eigenanalysis must be used with caution in chemometric methods for window factor analysis (WFA).