Principal component regression chemometrical analysis

To gain insight into chemometric methods such as correlation analysis, Multiple Linear Regression Analysis, Principal Component Analysis, Principal Component Regression, and Partial Least Squares regression/Projection to Latent Structures... 

Other chemometrics methods to improve caUbration have been advanced. The method of partial least squares has been usehil in multicomponent cahbration (48—51). In this approach the concentrations are related to latent variables in the block of observed instmment responses. Thus PLS regression can solve the colinearity problem and provide all of the advantages discussed earlier. Principal components analysis coupled with multiple regression, often called Principal Component Regression (PCR), is another cahbration approach that has been compared and contrasted to PLS (52—54). Cahbration problems can also be approached using the Kalman filter as discussed (43). 

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. ... 

The main goal of this chapter is to present the theoretical background of some basic chemometric methods as a tool for the assessment of surface water quality described by numerous chemical and physicochemical parameters. As a case study, long-term monitoring results from the watershed of the Struma River, Bulgaria, are used to illustrate the options offered by multivariate statistical methods such as CA, principal components analysis, principal components regression (models of source apportionment), and Kohonen s SOMs. 

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. 

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. 

Several factors are important in quantitative work. First, an internal reference band is needed for calculating relative intensity (either area or peak) of the band being used in quantitation. Although an external standard can be used, the internal band-ratio calculation is more reliable. However, if a chemometrics approach (e.g., principal components analysis [PCA], principal components regression [PCR], or PLS) is used, a standard is not required. 

Paracetamol, propiphenazone and caffeine First to fourth derivative spectra of components were subjected to chemometric analysis (principal component regression, PCR partial least squares with one dependent variable, PLS-1 three dependent variables, PLS2) and adopted for multicomponent analysis. The third derivative spectra of aU ingredients became a basis of quantification method. 39... 

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. 

Other study was carried out to develop a method based on FTIR spectroscopy combined with chemometrics of multivariate calibrations (partial least square and principal component regression) as well as discriminant analysis for quantification and discrimination of canola oil in virgin coconut oil (Che Man Rohman 2013). 

Fig. 4 Different chemometric tools used in the development of BioETs clear bars) in comparison with those mostly used for generic ET systems dark bars). PCA principal component analysis, LDA linear discriminant analysis, ANN artificial neural network, PLS partial least squares, PCR. principal component regression, k-NN k-nearest neighbours, MCR multiple component regression. Data obtained from the literature search on the period 1996-2015 using SCOPUS database (Elsevier)...

Chemometrics can also be used to overcome some of the intrinsic deficiencies of sequential extraction, such as non-specificity. Barona and Romero (1996a) used principal components analysis (PCA) to establish relationships between the amounts of metals released at each stage of a sequential extraction procedure and bulk soil properties, and demonstrated that carbonates played a dominant role in governing metal partitioning in the soil studied. The same workers employed multiple regression analysis to study soil remediation (see Section 10.11.1.1). Zufiaurre et al. (1998) also used PCA to confirm their interpretation of phase association and hence potential bioavailability of heavy metals in sewage sludge. 

The multivariate methods of data analysis, like discriminant analysis, factor analysis and principal component analysis, are often employed in chemometrics if the multiple regression method fails. Most popular in QSRR studies is the technique of principal component analysis (PCA). By PCA one reduces the number of variables in a data set by finding linear combinations of these variables which explain most of the variability [28]. Normally, 2-3 calculated abstract variables (principal components) condense most (but not all) of the information dispersed within the original multivariable data set. 

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