Partial least squares Subject

Some methods that paitly cope with the above mentioned problem have been proposed in the literature. The subject has been treated in areas like Cheraometrics, Econometrics etc, giving rise for example to the methods Partial Least Squares, PLS, Ridge Regression, RR, and Principal Component Regression, PCR [2]. In this work we have chosen to illustrate the multivariable approach using PCR as our regression tool, mainly because it has a relatively easy interpretation. The basic idea of PCR is described below. 

In their day, Principal Components and Partial Least Squares were each considered almost as the magic answer to all calibration problems . It took a long time for the realization to dawn that they contain no magic and are subject to most of the... 

Wajima and coauthors offer an alternative approach to utilize animal VD data to predict human VD [13]. Several compound descriptors that included both chemical structural elements as well as animal VDSS values were subject to multiple linear regression and partial least squares statistical analyses, with human VDSS as the independent parameter to be predicted using a dataset of 64 drugs. Methods derived in this manner were compared to simple allometry for overall accuracy. Their analyses yielded the following regressions ... 

The feasibility of using FTIR-ATR spectroscopy for qualitative and quantitative analysis was investigated using the three known polymorphs of ganciclovir as a model system.65 Definitive identification of each polymorph was obtained from materials that did not need to be subjected to any sample handling or preparation. Quantitation of mixtures was carried out using a partial least-squares procedure, with mean absolute errors of less than 3% being reported for Form-I and Form-II, and about 6% for Form-Ill. 

Figure 13.3-5. Partial least-squares discriminant analysis model for the classification of blood plasma samples in terms of coronary artery disease, based on their NMR spectra with visualization of the degree of coronary artery occlusion. Each point is based on data from a NMR spectrum of human blood plasma from subjects with different degrees of coronary artery occlusion. Circles—no stenosis, triangles—stenosis of one artery, inverted triangles—stenosis of two arteries, and squares—stenosis of three arteries. (This figure is available in full color at ftp //ftp.wiley.com/public/sci tech med/pharmaceutical biotech/.)...

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 second example represents a large-scale human metabolomics study that was performed with LC/MS [54]. The aim of this study was to identify potential biomarkers from lipid profiles of some 600 human plasma samples. Lipids were extracted from plasma samples and subjected to LC/ESI-MS analysis. Several different classes of lipids, such as phosphatidylcholines, lysophosphatidyl-cholines, triglycerides, diglycerides, sphingomyelins, and cholesterol esters were the target of this study. To detect small differences in metabolic profiles, statistical methods were used to process this large set of data. Partial least-squares discriminant analysis of the data could locate potential biomarkers. 

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. 

The latter relationship is shown in Fig. 21.2A it is not very accurate, partially because act/d proves to vary in a number of cases during the pyrolysis (least squares fit leads to act/d = 0-6Td,i/2 — 149 with cc = 0.68). The relation between Td/i/2 and Td/0 is shown in Fig. 21.2B. The amount of char residue will be subject of a separate discussion. 

The enthalpy of formation was obtained from the equilibrium data of Brewer and Lofgren (1 ). They studied the reaction x Cu(cr) + X HCl(g) Cu2Cl2(g) + x/2 H2(g) by measuring the amount of CuCl formed when various ratios of HC1 H2 were passed over heated copper. Brewer and Lofgren analyzed the data by a least squares fitting technique and deduced partial pressures of monomer and triraer. The monomer pressures were subjected to 2nd and 3rd law analysis and gave A H (298.15 K) = 46.85 3.2 and 43.83... 

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