Multivariate inverse models squares model

The improvement in computer technology associated with spectroscopy has led to the expansion of quantitative infrared spectroscopy. The application of statistical methods to the analysis of experimental data is known as chemometrics [5-9]. A detailed description of this subject is beyond the scope of this present text, although several multivariate data analytical methods which are used for the analysis of FTIR spectroscopic data will be outlined here, without detailing the mathematics associated with these methods. The most conunonly used analytical methods in infrared spectroscopy are classical least-squares (CLS), inverse least-squares (ILS), partial least-squares (PLS), and principal component regression (PCR). CLS (also known as K-matrix methods) and PLS (also known as P-matrix methods) are least-squares methods involving matrix operations. These methods can be limited when very complex mixtures are investigated and factor analysis methods, such as PLS and PCR, can be more useful. The factor analysis methods use functions to model the variance in a data set. 

Spectrophotometric monitoring with the aid of chemometrics has also been applied to more complex mixtures. To solve the mixtures of corticosteroid de-xamethasone sodium phosphate and vitamins Bg and Bi2, the method involves multivariate calibration with the aid of partial least-squares regression. The model is evaluated by cross-validation on a number of synthetic mixtures. The compensation method and orthogonal function and difference spectrophotometry are applied to the direct determination of omeprazole, lansoprazole, and pantoprazole in grastroresistant formulations. Inverse least squares and PCA techniques are proposed for the spectrophotometric analyses of metamizol, acetaminophen, and caffeine, without prior separation. Ternary and quaternary mixtures have also been solved using iterative algorithms. 

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. 

Multiwavelength methods. Least squares curve fitting techniques may be used in the determination of multicomponent mixtures with overlapping spectral features. Two classical quantitation methods, the Classical Least Squares (CLS) mode and the Inverse Least Squares (ILS) model, are applied when wavelength selection is not a problem. CLS is based on Beer s law and uses large regions of the spec-tram for calibration but cannot cope with mixtures of interacting constituents. ILS (multivariate method) can accurately build models for complex mixtures when only some of the constituent concentrations are known. 

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). 

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