Graphics for linearity and selectivity and prediction diagnostics for multicomponent spectra

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Abstract
Modern scanning infrared reflectance/absorption spectroscopes measure absorptions or reflectance at a sequence of around 1000 wavelengths. Training data may consist of 10–100 carefully designed sample mixtures whose true compositions are either known by formulation or accurately determined by wet chemistry. In future, one wishes to predict the true composition of a newly presented sample from its spectrum. Varying compositions of a mixture of three sugars in water are used for illustration of several different graphical techniques; the spectral measurements here are near‐infrared (NIR) absorbances, but there is nothing exclusively infrared about the methodology. Graphs display the adequacy of a linear explanation of absorbance variability at each wavelength by wavelength linearity plots. These highlight regions of the spectrum where non‐linearities and interaction effects are substantial. By selecting out these substantially non‐linear regions, one can concentrate on linear formulae for prediction with resultant robust linear modelling. Such selections are further aided by plots which identify the component sugar for which each wavelength is most selective. Such plots offer rather natural pre‐screening as an alternative or supplement to the wavelength selection method of Brown.We also display prediction diagnostics (R, Rx) which on a sample‐by‐sample basis may diagnose a particularly unusual presented spectrum. These diagnostics are shown to have predictive import for a validation data set.

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