A New Method for Multivariate Calibration

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Abstract
A new method for multivariate calibration is described that combines the best features of “classical” (also called “physical” or “K-matrix”) calibration and “inverse” (or “statistical” or “P-matrix”) calibration. By estimating the spectral signal in the physical way and the spectral noise in the statistical way, so to speak, the prediction accuracy of the inverse model can be combined with the low cost and ease of interpretability of the classical model, including “built-in” proof of specificity of response. The cost of calibration is significantly reduced compared to today's standard practice of statistical calibration using partial least squares or principal component regression, because the need for lab-reference values is virtually eliminated. The method is demonstrated on a data set of near-infrared spectra from pharmaceutical tablets, which is available on the web (so-called Chambersburg Shoot-out 2002 data set). Another benefit is that the correct definitions of the “limits of multivariate detection” become obvious. The sensitivity of multivariate measurements is shown to be limited by the so-called “spectral noise,” and the specificity is shown to be limited by potentially existing “unspecific correlations.” Both limits are testable from first principles, i.e. from measurable pieces of data and without the need to perform any calibration.