Univariate calibration problem

The quality of a model depends on the quality of the samples used to calculate it (or, to say it using the univariate approach, the quality of any traditional univariate calibration cannot be better than the quality of the standards employed to measure the analyte). Although this statement is trivial, the discussion on how many samples and which samples are required to develop a good predictive model is still open, so only general comments will be given. Below, we consider that the quality of the measurement device fits the purpose of the analytical problem. 

Chapter three presents the basic ideas of classical univariate calibration. These constitute the standpoint from which the natural and intuitive extension of multiple linear regression (MLR) arises. Unfortunately, this generalisation is not suited to many current laboratory tasks and, therefore, the problems associated with its use are explained in some detail. Such problems justify the use of other more advanced techniques. The explanation of what the... 

Classical calibration. There is a huge literature on univariate calibration.19 23 One of the simplest problems is to determine the concentration of a single compound using the... 

Figure 1 (A) An ideal chemical measurement where (y) is linearly related to ). (B) How selectivity and interference problems limit the effectiveness of univariate calibration methods causing nonlinearity.

As an example of the simple case, consider the analytical problem of determining the concentration of a specific, known compound in a sample. If the pure compound is available, then a univariate calibration can be calculated using the above approach. The absorption observed is plotted as a function of concentration, and if the relationship is linear, then a linear fit will suffice. 

The second chapter reviews univariate calibration. Although this might seem trivial for researchers it is observed too frequently, even in papers published in prestigious journals, that fundamental issues have been overlooked and, therefore, the results might be questionable. Chemists must be aware of some fundamental problems caused by the way in which we use the regression line obtained using the well-known ( ) least-squares criterion. It happens that we do not have an exact mathematical solution and, therefore, we are forced to use approximations, which are acceptable under some restricted conditions. Further, different equations are published in literature and their differences/similarities not always explained. We have tried to present a unified approach. In this... 

Under-fitting and over-fitting were discussed in some detail in Section 5.4. There, it was explained that over-fitting is much more likely to occur than under-fitting. The same can be argued for ANN-based models, although one should keep in mind that they are very much prone to over-fitting. In effect, the intrinsic behaviour of the ANNs leads them to predict the (limited number of) calibrators as closely as possible. Therefore, if any unexpected phenomenon appears in the unknown samples we want to predict (e.g. a spectral artefact or a new component), it may well happen that the net does not predict these samples properly. This is in fact also a problem with any classical (univariate) calibration, but it is exacerbated when ANNs are used." ... 

While in classical statistics (univariate methods) modelling regards only quantitative problems (calibration), in multivariate analysis also qualitative models can be created in this case classification is performed. 

In this chapter the fundamentals of chemometrics will be presented by means of a quick overview of the most relevant techniques for data display, classification, modeling, and calibration. The goal of the chapter is to make people aware of the great superiority of multivariate analysis over the commonly used univariate approach. Mathematical and algorithmical details will not be presented, since the chapter is mainly focused on the general problems to which chemometrics can be successfully applied in the field of environmental chemistry. 

Analytical chemists always face a problem in comparison of the performance between analytical instruments. There is no simple rule to justify which one is better because of the variations between the instrumental responses. In order to correct this, a standardization approach is generally adopted. However, a calibration model as developed on an instrument cannot be employed for the other instrument in the real situation. Walczak et al. [28] suggested a new standardization method for comparing the performance between two near-infrared (NIR) spectrometers in the wavelet domain. In their proposed method, the NIR spectra from two different spectrometers were transformed to the wavelet domain at resolution level (J — 1). Suppose and correspond to the NIR spectra from Instruments 1 and 2, respectively, in the wavelet domain. A univariate linear model is applied to determine the transfer parameters t between and... 

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