Multivariate calibration models transfer

R.D. Guenard, C.M. Wehlberg, R.J. Pell and D.M. Haaland, Importance of prediction outlier diagnostics in determining a successful inter-vendor multivariate calibration model transfer, Appl. Spectrosc., 61, 747 (2007). 

In the direct standardization introduced by Wang et al. [42] one finds the transformation needed to transfer spectra from the child instrument to the parent instrument using a multivariate calibration model for the transformation matrix = ZgF. The transformation matrix F (qxq) translates spectra Zg that are actually measured on the child instrument B into spectra Z that appear as if they were measured on instrument A. Predictions are then obtained by applying the old calibration model to these simulated spectra Z ... 

This method can be considered a calibration transfer method that involves a simple instrument-specific postprocessing of the calibration model outputs [108,113]. It requires the analysis of a subset of the calibration standards on the master and all of the slave instmments. A multivariate calibration model built using the data from the complete calibration set obtained from the master instrument is then applied to the data of the subset of samples obtained on the slave instruments. Optimal multiplicative and offset adjustments for each instrument are then calculated using linear regression of the predicted y values obtained from the slave instrument spectra versus the known y values. 

Transfer of Multivariate Calibration Models Based on Near-Infrared Spectroscopy... 

Multivariate calibration models are capable of enhancing the selectivity and reliability and thereby greatly reducing the effort of sample preparation. Some drawbacks of this approach, however, hinder the acceptance as analytical reference methods (a) calibration is sometimes heavily matrix-dependent (b) statistical evaluation is difficult or impossible (c) transfer of the calibration model to other instruments or changed experimental conditions usually is impossible (d) the process of data treatment is not evident enough. 

Several approaches have been investigated recently to achieve this multivariate calibration transfer. All of these require that a small set of transfer samples is measured on all instruments involved. Usually, this is a small subset of the larger calibration set that has been measured on the parent instrument A. Let Z indicate the set of spectra for the transfer set, X the full set of spectra measured on the parent instrument and a suffix Aor B the instrument on which the spectra were obtained. The oldest approach to the calibration transfer problem is to apply the calibration model, b, developed for the parent instrument A using a large calibration set (X ), to the spectra of the transfer set obtained on each instrument, i.e. and Zg. One then regresses the predictions (=Z b ) obtained for the parent instrument on those for the child instrument yg (=Z b ), giving... 

Calibration transfer, n - a method of applying a multivariate calibration developed on one instrument to data measured on a different instrument, by mathematically modifying the calibration model or by a process of instmment standardization. 

In the multivariate calibration field, Khayatzadeh et al. [65] compared ANNs with PLS to determine U, Ta, Mn, Zr and W by ICP in the presence of spectral interferences. For ANN modelling, a PCA preprocessing was found to be very effective and, therefore, the scores of the first five dominant PCs were input to an ANN. The network had a linear transfer function on both the hidden and output layers. They used only 20 samples for training. 

In this situation, it would be ideal to produce a calibration on only one of the analyzers, and simply transfer it to all of the other analyzers. There are certainly cases where this can be done effectively, especially if response variability between different analyzers is low and the calibration model is not very complex. However, the numerous examples illustrated above show that multivariate (chemometric) calibrations could be particularly sensitive to very small changes in the analyzer responses. Furthermore, it is known that, despite the great progress in manufacturing reproducibility that process analyzer vendors have made in the past decade, small response variabilities between analyzers of the same make and... 

Data preprocessing is important in multivariate calibration. Indeed, the relationship between even basic procedures such as centring the columns is not always clear, most investigators following conventional methods, that have been developed for some popular application but are not always appropriately transferable. Variable selection and standardisation can have a significant influence on the performance of calibration models. 

Another issue is that of transferability of the calibration model among instruments. This has been a significant obstacle to more widespread use of NIR methods. Transferability is especially important to multisite facilities, because it is needed to avoid time-consuming recalibration procedures. Calibration errors may occur among instruments because of slight differences in instrument response, especially if full-spectrum multivariate models are used. Shenk and Westerhaus addressed the problem and proposed a standardization algorithm, which was modified by others. ... 

Technically valid calibrations transfer is not the trivial process that some would propose. In fact, due to advancing calibration mathematics such as PCR, PLS, and spectral matching/search algorithms, it becomes even more critical that transfer technologies be scientifically scrutinized. To date, the most successful approach for transferring calibrations for use with all multivariate mathematical modeling techniques is found in a three-pronged approach ... 

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