GRAPHICS FOR LINEARITY AND SELECTIVITY AND PREDICTION DIAGNOSTICS FOR MULTICOMPONENT SPECTRA

Modern scanning infrared reflectance/absorption spectroscopes measure absorptions or reflectance at asequence of around 1000 wavelengths. Training data may consist of 10-100 carefully designed samplemixtures whose true compositions are either known by formulation or accurately determined by wetchemistry. In future, one wishes to predict the true composition of a newly presented sample from itsspectrum. Varying compositions of a mixture of three sugars in water are used for illustration of severaldifferent graphical techniques; the spectral measurements here are near-infrared (NIR) absorbances, butthere is nothing exclusively infrared about the methodology. Graphs display the adequacy of a linearexplanation of absorbance variability at each wavelength by wavelength linearity plots. These highlightregions of the spectrum where non-linearities and interaction effects are substantial. By selecting out thesesubstantially non-linear regions, one can concentrate on linear formulae for prediction with resultantrobust linear modelling. Such selections are further aided by plots which identify the component sugarfor which each wavelength is most selective. Such plots offer rather natural pre-screening as an alternativeor supplement to the wavelength selection method of Brown. We also display prediction diagnostics (R, Rx) which on a sample-by-sample basis may diagnose aparticularly unusual presented spectrum. These diagnostics are shown to have predictive import for avalidation data set.

GRAPHICS FOR LINEARITY AND SELECTIVITY AND PREDICTION DIAGNOSTICS FOR MULTICOMPONENT SPECTRA

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.