Inverse methods interferent modeling

How can the inverse method correct for the interferent when it was not explicitly included in the model For this example, it is easy to see. Recall that the spectrum of the interferent is ij - [3 0 0]. The estimated regression vectors (b) in Figure 5.63c have zeros for the variable on which the interferent responds (variable 1). In this case, the inverse approach has implicitly modeled the presence of the interferent by ignoring the response variable that is assooiated With the interfering component. This example demonstrates that, for this weU-... 

Multivariate techniques are inverse calibration methods. In normal least-squares methods, often called classical least-squares methods, the system response is modeled as a function of analyte concentration. In inverse methods, the concentrations are treated as functions of the responses. The latter has some advantages in that concentrations can be accurately predicted even in the presence of chemical and physical sources of interference. In classical methods, all components in the system need to be considered in the mathematical model produced (regression equation). 

The advantage of the inverse calibration approach is that we do not have to know all the information on possible constituents, analytes of interest and inter-ferents alike. Nor do we need pure spectra, or enough calibration standards to determine those. The columns of C (and P) only refer to the analytes of interest. Thus, the method can work in principle when unknown chemical interferents are present. It is of utmost importance then that such interferents are present in the Ccdibration samples. A good prediction model can only be derived from calibration data that are representative for the samples to be measured in the future. 

The multivariate quantitative spectroscopic analysis of samples with complex matrices can be performed using inverse calibration methods, such as ILS, PCR and PLS. The term "inverse" means that the concentration of the analyte of interest is modelled as a function of the instrumental measurements, using an empirical relationship with no theoretical foundation (as the Lambert Bouguer-Beer s law was for the methods explained in the paragraphs above). Therefore, we can formulate our calibration like eqn (3.3) and, in contrast to the CLS model, it can be calculated without knowing the concentrations of all the constituents in the calibration set. The calibration step requires only the instrumental response and the reference value of the property of interest e.g. concentration) in the calibration samples. An important advantage of this approach is that unknown interferents may be present in the calibration samples. For this reason, inverse models are more suited than CLS for complex samples. 

In practice this simple additive model may not describe the situation completely. There are two reasons for this. The first is that the substances of interest may interfere with each other chemically in a way that affects their spectra. The second is that the specimens from real-life sources may well contain substances other than those of interest, which make a contribution to the absorbance. In these cases it is better to use inverse calibration and calibrate with real-life specimens. The term inverse calibration means that the analyte concentration is modelled as a function of the spectrum (i.e. the reverse of the classical method). For the data in Table 8.4 the regression equations take the form q = fooi + + 2/ 2 + + Inverse... 

Inverse least squares in an example of a multivariate method. In this type of model, the dependent variable (concentration) is solved by calculating a solution from multiple independent variables (in this case, the responses at the selected wavelengths). It is not possible to work backwards from the concentration value to the independent spectral response values because an infinite number of possible solutions exist. However, the main advantage of a multivariate method is the ability to calibrate for a constituent of interest without having to account for any interferences in the spectra. 

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