MULTIVARIATE ANALYSIS, CHEMOMETRICS, AND THE FUTURE OF SPECTROSCOPY: HOW STATISTICS CAN COMPLEMENT SPECTROSCOPY AT ANY WAVELENGTH (Invited Presentation)

Many different analytical techniques are fundamentally based on spectroscopic measurements in which peak intensities or counts are related to concentration. In practice, this relationship is often complicated by factors such as chemical interactions of species, peak overlaps, sampling depths, varying mass absorption coefficients, and many other factors. In some cases, these effects can be dealt with using a first-principles approach; for example, electron microprobe data are routinely corrected using Z (atomic number) A (absorption correction) F (fluorescence correction) or phi-rho-z models. However, in many types of spectroscopy the interactions between the incident energy and the atoms are not so well characterized. In such cases, the techniques must depend on empirical methods for interpretation. Increasingly, multivariate statistical methods are being used to extract subtle details from complicated spectra of all types.

For example, laser-induced breakdown spectroscopy (LIBS) is based on atomic emissions from within a superheated plasma. Univariate analyses that relate individual peaks to concentration do not yield quantitative calibrations. Use of partial least-squares (PLS) techniques developed for situations where highly collinear explanatory (p) variables significantly outnumber the observations (N) ( p >> N) has made it possible to derive quantitative elemental analyses from LIBS data, outperforming univariate analyses in geological samples by an order of magnitude in accuracy. X-ray Absorption Near-Edge Spectroscopy (XANES) has also benefitted from implementation of these multivariate techniques; in those data, the pre-edge spectral region traditionally used for valence state measurements has been shown to be less accurate for predicting valence state than the main edge. Also used in the FTIR community, the PLS technique and other related shrunken regression methods have tremendous potential for extracting subtle details out of complicated spectral data.