Detecting and adjusting for non‐linearities in calibration of near‐infrared data using principal components

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Abstract
A new regression method for non‐linear near‐infrared spectroscopic data is proposed. The technique is based on a model which is linear in the principal components and simple functions (squares and products) of them. Added variable plots are used to determine which squares and products to incorporate into the model. The regression coefficients are estimated by a Stein estimate which shrinks towards the estimate determined by the first several principal components and the selected non‐linear terms. The technique is not computationally intensive and is appropriate for routine predictions of chemical concentrations. The method is tested on three data sets and in all cases gives more accurate predictions than does linear principal components regression.