Critical comparison of methods predicting the number of components in spectroscopic data

Determining the number of chemical components in a mixture is a first important step to further analysis in spectroscopy. The accuracy of 13 statistical indices for estimation of the number of components that contribute to spectra was critically tested on simulated and on experimental data sets using algorithm INDICES in S-Plus. All methods are classified into two categories, precise methods based upon a knowledge of the instrumental error of the absorbance data, sinst (A), and approximate methods requiring no such knowledge. Most indices always predict the correct number of components even a presence of the minor one when the signal-to-error ratio (SER) is higher than 10 but in case of RESO and IND higher than 6. On base of SER the detection limit of every index method is estimated. Two indices, RESO and IND, correctly predict a minor component in a mixture even if its relative concentration is 0.5‐1% and solve an ill-defined problem with severe collinearity. For more than four components in a mixture the modifications of Elbergali et al. represent a useful resolution tool of a correct number of components in spectra for all indices. The Wernimont‐Kankare procedure performs reliable determination of the instrumental standard deviation of spectrophotometer used. In case of real experimental data the RESO, IND and indices methods based on knowledge of instrumental error should be preferred. © 2000 Elsevier Science B.V. All rights reserved.