Multivariate calibration techniques component regression

In more recent development, chemometric or multivariate calibration techniques have been applied into spectrophotometric methods. As reported by Palabiyik and Onur [24], principal component regression and partial least square were used to determine ezetimibe in combination with simvastatin. This method offers advanfages such as no chemical prefreafmenf prior to analysis as well as no need to observe graphical spectra and calculations as with the derivative method. In addition, the instrumentation used is also simpler. 

On the other hand, atomic emission spectra are inherently well suited for multivariate analysis due to the fact that the intensity data can be easily recorded at multiple wavelengths. The only prerequisite is that the cahbration set encompasses all likely constituents encountered in the real sample matrix. Calibration data are therefore acquired by a suitable experimental design. Not surprisingly, many of the present analytical schemes are based on multivariate calibration techniques such as multiple linear regression (MLR), principal components regression (PCR), and partial least squares regression (PLS), which have emerged as attractive alternatives. 

NIR spectral bands are normally broad and often overlapping. There are rarely clean spectral bands that allow simple correlation with analyte concentration. Instead. multivariate calibration techniques are used." Most commonly, partial least squares, principal components regression, and artificial neural networks are em-... 

Regression techniques. Principal components are sometimes called abstract factors, and are primarily mathematical entities. In multivariate calibration the aim is to convert these to compound concentrations. PCR uses regression (sometimes called transformation or rotation) to convert PC scores onto concentrations. This process is often loosely called factor analysis, although terminology differs according to author and discipline. 

In chemometrics, multivariate calibration methods provide a convenient way to determine several components in a mixture within one experimental step, without the tedious operation of separation of these components. The method of calculation usually used is PLS method. Artificial neural network is also often used especially when the data set exhibits obvious nonlinearity. But it is prone to overfitting. Therefore, several types of techniques have been developed to prevent overfitting. At the same time, support vector regression, as a method suitable to treat nonlinear data without serious overfitting, can be used as a new method of computation in multivariate calibration. An example of using SVR in multivariate calibration will be described as follows. 

Quantitative analysis for one or more analytes through the simultaneous measurement of experimental parameters such as molecular UV or infrared absorbance at multiple wavelengths can be achieved even where clearly defined spectral bands are not discernible. Standards of known composition are used to compute and refine quantitative calibration data assuming linear or nonlinear models. Principal component regression (PCR) and partial least squares (PLS) regression are two multivariate regression techniques developed from linear regression (Topic B4) to optimize the data. 

CONTENTS 1. Chemometrics and the Analytical Process. 2. Precision and Accuracy. 3. Evaluation of Precision and Accuracy. Comparison of Two Procedures. 4. Evaluation of Sources of Variation in Data. Analysis of Variance. 5. Calibration. 6. Reliability and Drift. 7. Sensitivity and Limit of Detection. 8. Selectivity and Specificity. 9. Information. 10. Costs. 11. The Time Constant. 12. Signals and Data. 13. Regression Methods. 14. Correlation Methods. 15. Signal Processing. 16. Response Surfaces and Models. 17. Exploration of Response Surfaces. 18. Optimization of Analytical Chemical Methods. 19. Optimization of Chromatographic Methods. 20. The Multivariate Approach. 21. Principal Components and Factor Analysis. 22. Clustering Techniques. 23. Supervised Pattern Recognition. 24. Decisions in the Analytical Laboratory. 

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). 

Chapter 4 retrieves the basic ideas of classical univariate calibration as the standpoint from which the natural and intuitive extension of multiple linear regression (MLR), arises. Unfortunately, this generalization is not suited to many 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 multivariate space looks like and how principal components analysis can tackle it is the next step forward. This constitutes the root of the regression methodology presented in the following chapter. 

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