Calibration chemometrics

Multivariate calibration (chemometrics) methods must be used to develop acceptable methods. 

Diffuse reflectance FTIR in combination with a multivariate calibration chemometric approach to data analysis could be used to effect the rapid quantification of a pharmaceutical product (ampicillin) in a (variable) biological background E. coli cells), a situation representative of metabolite over-production in a screening or titre improvement programme... 

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... 

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.

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 ... 

I have always looked forward to reading your articles on Chemometrics in Spectroscopy. They are truly a valuable resource -1 usually cut them out and save them for future reference. However, I think your article Linearity in Calibration in the June 1998 issue of Spectroscopy leads the reader to an erroneous conclusion. This conclusion results largely because of the assumptions you make about the application of PLS and PCR. 

I recently read your column in the Spectroscopy issue of June 1998, which was dealing with Linearity in Calibration . First, I have to tell you that I really like your monthly column. You do a good job at explaining the basics and more of many topics related to chemometrics, and demistify the subjects. 

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. 

Real data, as we have seen, is far too complicated to work with to try to obtain fundamental understanding, just as the physical world is often too complicated to study directly in toto. Therefore work such as was presented in the Linearity in Calibration chapter is needed, creating a simplified system where the characteristic of interest can be isolated and studied - just as physical experiments often work with a simplified portion of the physical world for the same reason. This might be categorized as Experimental Chemometrics , controlling the nature of the data in a way that allows us to relate the properties of the data to the behavior of the model. Does this mimic the real world No, but it does provide a window into the inner workings of the calibration calculations, and we need as many such windows as we can get. 

Nonlinearity is a subject the specifics of which are not prolifically or extensively discussed as a specific topic in the multivariate calibration literature, to say the least. Textbooks routinely cover the issues of multiple linear regression and nonlinearity, but do not cover the issue with full-spectrum methods such as PCR and PLS. Some discussion does exist relative to multiple linear regression, for example in Chemometrics A Textbook by D.L. Massart et al. [6], see Section 2.1, Linear Regression (pp. 167-175) and Section 2.2, Non-linear Regression, (pp. 175-181). The authors state,... 

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. 

There are other mysteries in NIR (and other applications of chemometrics) that nonlinearity can also explain. For example, as indicated above, one is the difficulty of transferring calibration models between instruments, even of the same type. Where would our technological world be if a manufacturer of, say, rulers could not reliably transfer the calibration of the unit of length from one ruler to the next ... 

The second critical fact that comes from equation 70-20 can be seen when you look at the Chemometric cross-product matrices used for calibrations (least-squares regression, for example, as we discussed in [1]). What is this cross-product matrix that is often so blithely written in matrix notation as ATA as we saw in our previous chapter Let us write one out (for a two-variable case like the one we are considering) and see ... 

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