Chemometric calibrations

Figure 3 Chemometric calibration of the elastic modulus (left) and the yield stress (right) of a series of polyethylenes. Reproduced from Gabriel et al. [23], Copyright 2003, with permission from Wiley-VCH Verlag GmbH.

What we were trying to do in the column was to ascertain the behavior of a mathematical (not physical ) system in the face of a certain type of (simulated) physical behavior. There is nothing wrong with trying to come up with empirical methods for improving the practical performance of chemometric calibration, but one of the philosophical problems with the current state of chemometrics is that nobody is trying to do anything else, that is to determine the fundamental behavior of these mathematical systems. 

In creating chemometric calibrations, it is common to transform the spectrum, for any of various reasons, from the measured format, which is usually absorbance, into a different format. One common, widely used transformation is to compute a derivative of the spectrum. First (dA/dA) and second (d2A/dA2) derivatives are often used. Hence, in our next few chapters we will be discussing the properties and behavior of derivatives. 

The empirical modeling element indicates an increased emphasis on data-driven rather than theory-driven modeling of data. This is not to say that appropriate theories and prior chemical knowledge are ignored in chemometrics, only that they are not relied upon completely to model the data. In fact, when one builds a chemometric calibration model for a process analyzer, one is likely using prior knowledge or theoretical relations of some sort regarding the chemistry of the sample or the physics of the analyzer. One example... 

There is a failure to recognize the plant-site requirements for NIR calibration and validation, snch as the existence of appropriate sampling valves, well-designed sampling protocols, good laboratory reference methods, and variability in the analyte concentrations of interest. More details on these chemometric calibration issues can be found in Chapter 12. 

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... 

Saurina J, Hemandez-Cassou S, Quantitative determinations in conventional flow injection analysis based on different chemometric calibration statregies a review, Analytica Chimica Acta, 2001, 438, 335-352. 

C H, O H and N—H overtones can be observed. Strong overlaps of different absorption bands are usually too sophisticated for univariate quantification. Instead, chemometric calibration is necessary in most cases. 

Zhang, X. et al (2012) Application of hyperspectral imaging and chemometric calibrations for variety... 

The various calibration strategies available with ICP-MS are summarized in Table 4, along with implications of the above-mentioned limitations. (More elaborate chemometric calibration procedures have also been developed by a few groups.) In general, unless the sample matrix is simple, internal standardization (or frequent calibration) will be required for quantitative analysis using external calibration with a series of standard solutions. The choice of the internal standard(s) depends on the instrument, the sample, etc. For the best results, an element with properties similar to that of the analyte (so that it will behave similarly in ICP-MS) is needed, so several internal standards may be required for a multielemental analysis spanning the entire mass range. 

For many applications, quantitative band shape analysis is difficult to apply. Bands may be numerous or may overlap, the optical transmission properties of the film or host matrix may distort features, and features may be indistinct. If one can prepare samples of known properties and collect the FTIR spectra, then it is possible to produce a calibration matrix that can be used to assist in predicting these properties in unknown samples. Statistical, chemometric techniques, such as PLS (partial least-squares) and PCR (principle components of regression), may be applied to this matrix. Chemometric methods permit much larger segments of the spectra to be comprehended in developing an analysis model than is usually the case for simple band shape analyses. 

We will explore the two major families of chemometric quantitative calibration techniques that are most commonly employed the Multiple Linear Regression (MLR) techniques, and the Factor-Based Techniques. Within each family, we will review the various methods commonly employed, learn how to develop and test calibrations, and how to use the calibrations to estimate, or predict, the properties of unknown samples. We will consider the advantages and limitations of each method as well as some of the tricks and pitfalls associated with their use. While our emphasis will be on quantitative analysis, we will also touch on how these techniques are used for qualitative analysis, classification, and discriminative analysis. 

Because of peak overlappings in the first- and second-derivative spectra, conventional spectrophotometry cannot be applied satisfactorily for quantitative analysis, and the interpretation cannot be resolved by the zero-crossing technique. A chemometric approach improves precision and predictability, e.g., by the application of classical least sqnares (CLS), principal component regression (PCR), partial least squares (PLS), and iterative target transformation factor analysis (ITTFA), appropriate interpretations were found from the direct and first- and second-derivative absorption spectra. When five colorant combinations of sixteen mixtures of colorants from commercial food products were evaluated, the results were compared by the application of different chemometric approaches. The ITTFA analysis offered better precision than CLS, PCR, and PLS, and calibrations based on first-derivative data provided some advantages for all four methods. ... 

E. Vigneau, D. Bertrand and E.M. Qannari, Application of latent root regression for calibration in near-infrared spectroscopy. Comparison with principal component regression and partial least squares. Chemometr. Intell. Lab. Syst., 35 (1996) 231-238. 

T. Fearn, Flat or natural A note on the choice of calibration samples, pp. 61-66 in Ref. [1]. T. Naes and T. Isaksson, Splitting of calibration data by cluster-analysis. J. Chemometr, 5 (1991)49-65. 

In chemometrics, the inverse calibration model is also denoted as the P-matrix model (the dimension of P is m x n) ... 

Lorber A, Kowalski BR (1988) Estimation of prediction error for multivariate calibration. J Chemometrics 2 93... 

Currie LA (1997) Detection International update, and some emerging dilemmas involving calibration, the blank, and multiple detection decisions. Chemometrics Intell Lab Syst 37 151... 

So, overall the chemometrics bridge between the lands of the overly simplistic and severely complex is well under construction one may find at least a single lane open by which to pass. So why another series Well, it is still our labor of love to deal with specific issues that plague ourselves and our colleagues involved in the practice of multivariate qualitative and quantitative spectroscopic calibration. Having collectively worked with hundreds of instrument users over 25 combined years of calibration problems, we are compelled, like bees loaded with pollen, to disseminate the problems, answers, and questions brought about by these experiences. Then what would a series named Chemometrics in Spectroscopy hope to cover which is of interest to the readers of Spectroscopy ... 

This leads us to the other hand, which, it should be obvious, is that we feel that Chemometrics should be considered a subfield of Statistics, for the reasons given above. Questions currently plaguing us, such as How many MLR/PCA/PLS factors should I use in my model , Can I transfer my calibration model (or more importantly and fundamentally How can I tell if I can transfer my calibration model ), may never be answered in a completely rigorous and satisfactory fashion, but certainly improvements in the current state of knowledge should be attainable, with attendant improvements in the answers to such questions. New questions may arise which only fundamental statistical/probabilistic considerations may answer one that has recently come to our attention is, What is the best way to create a qualitative (i.e., identification) model, if there may be errors in the classifications of the samples used for training the algorithm ... 

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