Calibration Methods for NIRS Instruments: A Theoretical Evaluation and Comparisons by Data Splitting and Simulations

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Abstract
The properties of the recently proposed calibration method called restricted principal component regression (RPCR) were evaluated and compared with partial least-squares regression (PLSR) and two types of principal component regression (PCR1, selected according to the size of the eigenvalues, and PCR2, selected according to the t-value). RPCR can be considered a compromise between PCR and PLSR, since the first component of RPCR is equivalent to the first component of PLSR, while the rest can be regarded as principal components on a space orthogonal to the first. The methods showed almost the same properties when the irrelevant components had small eigenvalues. The prediction error of RPCR selected according to the size of the eigenvalues was intermediate to those of PCR1 and PLSR when the number of components was low, while RPCR and PCR1 nearly coincided when the number of components exceeded the number of relevant ones. The prediction error minimum was about the same for RPCR, PCR1, and PLSR, but the minimum of PLSR was obtained when a lower number of components were included in the calibration model.