Multivariate calibration validation

A solvent free, fast and environmentally friendly near infrared-based methodology was developed for the determination and quality control of 11 pesticides in commercially available formulations. This methodology was based on the direct measurement of the diffuse reflectance spectra of solid samples inside glass vials and a multivariate calibration model to determine the active principle concentration in agrochemicals. The proposed PLS model was made using 11 known commercial and 22 doped samples (11 under and 11 over dosed) for calibration and 22 different formulations as the validation set. For Buprofezin, Chlorsulfuron, Cyromazine, Daminozide, Diuron and Iprodione determination, the information in the spectral range between 1618 and 2630 nm of the reflectance spectra was employed. On the other hand, for Bensulfuron, Fenoxycarb, Metalaxyl, Procymidone and Tricyclazole determination, the first order derivative spectra in the range between 1618 and 2630 nm was used. In both cases, a linear remove correction was applied. Mean accuracy errors between 0.5 and 3.1% were obtained for the validation set. 

An important aspect of all methods to be discussed concerns the choice of the model complexity, i.e., choosing the right number of factors. This is especially relevant if the relations are developed for predictive purposes. Building validated predictive models for quantitative relations based on multiple predictors is known as multivariate calibration. The latter subject is of such importance in chemo-metrics that it will be treated separately in the next chapter (Chapter 36). The techniques considered in this chapter comprise Procrustes analysis (Section 35.2), canonical correlation analysis (Section 35.3), multivariate linear regression... 

The reliability of multispecies analysis has to be validated according to the usual criteria selectivity, accuracy (trueness) and precision, confidence and prediction intervals and, calculated from these, multivariate critical values and limits of detection. In multivariate calibration collinearities of variables caused by correlated concentrations in calibration samples should be avoided. Therefore, the composition of the calibration mixtures should not be varied randomly but by principles of experimental design (Deming and Morgan [1993] Morgan [1991]). 

This chapter deals with the necessity of representative sampling in the context of PAT. All PAT sensors need to be calibrated with respect to relevant, reliable reference data (Y data). This presupposes that representative samples are at hand for this characterization - but sampled howl Additionally, X signals (X measurements) need to be qualified as representative of the same volume as was extracted for Y characterization, or at least a sufficiently well-matching volume. How does one demonstrate this in a quantitative manner If the quality of both X and Y data involved is suspect, how can a multivariate calibration be expected to be trustworthy This also includes the issue regarding proper validation of the chemometric multivariate calibration(s) involved, which can only be resolved based on proper understanding of the phenomenon of heterogeneity. The TOS delivers answers to all these issues. The TOS constitutes the missing link in PAT. 

Figure 3.10 Hallmark signature of significant sampling bias as revealed in chemometric multivariate calibrations (shown here as a prediction validation). Crab sampling results in an unacceptably high, irreducible RMSEP. While traditionally ascribed to measurement errors, it is overwhelmingly due to ISE.

AU multivariate calibrations must be based on empirical training and validation data sets obtained in fully realistic situations acoustic chemometrics is no exception. Many models are in addition based on indirect multivariate calibration. All industrial applications must always be evaluated only based on test set validation. Reference [2] deals extensively with the merits of the various validation methods, notably when it is admissible, and when not, to use cross-validation. See also Chapters 3 and 12, which give further background for the test set imperative in light of typical material heterogeneity and the Theory of Sampling . 

One of the most powerful advantages of multivariate calibration is that the predictions can be validated. That is, it is possible to evaluate the reliability of the concentration estimates. Four prediction diagnostic tools are discussed below and a summarv is found at the end of the section in Table 5.4. 

In multivariate calibration, accuracy reports the closeness of agreement between the reference value and the value found by the calibration model and is generally expressed as the root mean square error of prediction (RMSEP, as described in section 4.5.6) for a set of validation samples ... 

N. M. Faber and R. Rajko, How to avoid over-fitting in multivariate calibration the conventional validation approach and an alternative. Anal. Chim. Acta, 595, 2007, 98-106. 

Luo et al. [83] used an ANN to perform multivariate calibration in the XRF analysis of geological materials and compared its predictive performance with cross-validated PLS. The ANN model yielded the highest accuracy when a nonlinear relationship between the characteristic X-ray line intensity and the concentration existed. As expected, they also found that the prediction accuracy outside the range of the training set was bad. 

Multivariate calibration models are often built on an underdetermined data set, that is, more wavelengths than samples. The use of powerful data reduction techniques, such as PCR and PLS, makes assessing the model validity an extremely important aspect of the analysis procedure. Here, we present four important criteria on which to judge the validity of results from multivariate calibration. 

The term chemometrics was hrst coined in 1971 to describe the growing use of mathematical models, statistical principles, and other logic-based methods in the held of chemistry and, in particular, the held of analytical chemistry. Chemometrics is an interdisciplinary held that involves multivariate statistics, mathematical modeling, computer science, and analytical chemistry. Some major application areas of chemometrics include (1) calibration, validation, and signihcance testing (2) optimization of chemical measurements and experimental procedures and (3) the extraction of the maximum of chemical information from analytical data. 

Traditionally, data was a single numerical result from a procedure or assay for example, the concentration of the active component in a tablet. However, with modem analytical equipment, these results are more often a spectrum, such as a mid-infrared spectrum for example, and so the use of multivariate calibration models has flourished. This has led to more complex statistical treatments because the result from a calibration needs to be validated rather than just a single value recorded. The quality of calibration models needs to be tested, as does the robustness, all adding to the complexity of the data analysis. In the same way that the spectroscopist relies on the spectra obtained from an instrument, the analyst must rely on the results obtained from the calibration model (which may be based on spectral data) therefore, the rigor of testing must be at the same high standard as that of the instrument... 

As with univariate and multivariate calibration, three-way calibration assumes linear additivity of signals. When the sample matrix influences the spectral profiles or sensitivities, either care must be taken to match the standard matrix to those of the unknown samples, or the method of standard additions must be employed for calibration. Employing the standard addition method with three-way analysis is straightforward only standard additions of known analyte quantity are needed [42], When the standard addition method is applied to nonbilinear data, the lowest predicted analyte concentration that is stable with respect to the leave-one-out cross-validation method is unique to the analyte. 

It is important that calibration models are rigorously validated and in the first instance that all variations are accounted for in the model using diverse samples that are expected to be observed in future bioprocess runs. Some investigators attempt to keep process conditions very reproducible but such conditions are uncommon in an industrial environment. In addition, multivariate calibration models will work well if identical media (composition) and process conditions are used on each successive run. Simple modifications such as use of a different media supplier can affect the spectral background. The predictive ability of the models will then be affected as they will be challenged with samples which they have not been trained to recognise [74]. 

The similarity between the diffuse reflectance FTIR spectra of aristeromycin and neplanocin A (Figure 2) and the complexity of the supernatant background FTIR spectra (see Figure 3) necessitates the use of multivariate methods for quantitative analysis of the components. Training data for the construction of multivariate calibration models and test data for model validation were provided by HPLC and FTIR analysis of the S. citricolor mutant fermentation supernatants with a total of 48 samples taken from duplicate fermentations after 3 and 6 days incubation. 

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