Descriptive Definition of Multivariate Calibration Model Vector

Multivariate calibration relates a dependent variable such as a chemical or physical property to independent variables such as spectroscopic measurements via the model vector. The model vector is commonly estimated by the methods of partial least squares (PLS), the Tikhonov regularization (TR) variant of ridge regression (RR), or principal component regression (PCR). However, multivariate calibration models often fail to extrapolate beyond the calibration samples because of changes associated with the instrumental response, environmental condition, or sample matrix. Most of the current methods used to adapt a source calibration model to a target domain exclusively apply to calibration transfer between similar analytical devices, while generic methods for calibration model adaptation are largely missing. Considering that the calibration model vector carries on all information of the calibration model. In fact, the calculation of model vector b is the core of all different first-order multivariate calibration methods. So we have focused on basic properties of model vector b for proposing a clear descriptive definition of this magic vector in first-order multivariate calibrations. This magic vector carries on the most information of calibration samples related to analyte and non-analyte constituents behaviors. This vector is sensitive and selective to its related analyte and can exploits the analyte concentration from the measured spectrum of unknown samples in almost same conditions of calibration samples. Clear imagine and understanding of model vector b can help analytical chemist to improve the multivariate calibration methods for more accurate and precise prediction of analyte concentrations in unknown samples. Descriptive definition of model vector b can create a new calibration transfer method via adopting the proposed procedure to inconsistency problem for two different measurement instruments. We have simulated a three-component data set for investigating regression coefficients of different methods (PCR, PLS and the proposed descriptive method). This data (64×221) is divided to calibration/prediction sets (38/26). The results are shown in figure 1 and table 1. Also, a real data set (corn data) is used for comparing our descriptive method and calibration transfer method [1].