Partial least squares regression, analytical

Cd2+ and the Pb2+ and all electrodes display the two peaks but to different extents. Despite the peak overlap, the electrode array can be calibrated for each metal ion using a three-way partial least squares regression (AT-PLS) [53]. The electrode array was employed to analyse three test samples of known concentration of Cu2+, Cd2+ and Pb2+ and the concentrations of each analyte predicted by the calibrated electrode array are shown in Table 10.1. As can be seen from Table 10.1 there is reasonable agreement between the actual and predicted values despite the fact that all electrodes respond to all analytes and that the electrochemical responses to lead and cadmium overlap. Further improvements would be expected if the calibrations were performed with a box experimental design, which encompassed the linear range of all the sensors. 

The calibration methods most frequently used to relate the property to be measured to the analytical signals acquired in NIR spectroscopy are MLR,59 60 principal component regression (PCR)61 and partial least-squares regression (PLSR).61 Most of the earliest quantitative applications of NIR spectroscopy were based on MLR because spectra were then recorded on filter instruments, which afforded measurements at a relatively small number of discrete wavelengths only. However, applications involving PCR and PLSR... 

Small GW, Arnold MA, Marquardt LA. Strategies for coupling digital filtering with partial least-squares regression application to the determination of glucose in plasma by Fourier-transform near-infrared spectroscopy. Analytical Chemistry 1993, 65, 3279-3289. 

NIR spectroscopy became much more useful when the principle of multiple-wavelength spectroscopy was combined with the deconvolution methods of factor and principal component analysis. In typical applications, partial least squares regression is used to model the relation between composition and the NIR spectra of an appropriately chosen series of calibration samples, and an optimal model is ultimately chosen by a procedure of cross-testing. The performance of the optimal model is then evaluated using the normal analytical performance parameters of accuracy, precision, and linearity. Since its inception, NIR spectroscopy has been viewed primarily as a technique of quantitative analysis and has found major use in the determination of water in many pharmaceutical materials. 

The calibration model referred to a partial least squares regression (PLSR) is a relatively modem technique, developed and popularized in analytical science by Wold. The method differs from PCR by including the dependent variable in the data compression and decomposition operations, i.e. both y and x data are actively used in the data analysis. This action serves to minimize the potential effects of jc variables having large variances but which are irrelevant to the calibration model. The simultaneous use of X and y information makes the method more complex than PCR as two loading vectors are required to provide orthogonality of the factors. 

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. 

Bangalore, A. S., Shaffer, R. E., Small, G. W. and Arnold, M. (1996) Genetic algorithm-based method for selecting wavelengths and model size for use with partial least squares regression. Application to near infrared spectroscopy. Analytical Chemistry, 68, 4200-12. 

Partial least-squares regression (PLSR) is a multivariate data analytical technique designed to handle intercorrelated regressors. It is based on Herman Wold s general PLS principle [1], in which complicated, multivariate systems analysis problems are solved by a sequence of simple least-squares regressions. 

Fourier transform infrared (FTIR) spectroscopy of coal low-temperature ashes was applied to the determination of coal mineralogy and the prediction of ash properties during coal combustion. Analytical methods commonly applied to the mineralogy of coal are critically surveyed. Conventional least-squares analysis of spectra was used to determine coal mineralogy on the basis of forty-two reference mineral spectra. The method described showed several limitations. However, partial least-squares and principal component regression calibrations with the FTIR data permitted prediction of all eight ASTM ash fusion temperatures to within 50 to 78 F and four major elemental oxide concentrations to within 0.74 to 1.79 wt % of the ASTM ash (standard errors of prediction). Factor analysis based methods offer considerable potential in mineral-ogical and ash property applications. 

If the system is not simple, an inverse calibration method can be employed where it is iKst necessary to obtain the spectra of the pure analytes. The three inverse methods discussed later in this chapter include multiple linear regression (MLR), jirincipal components regression (PCR), and partial least squares (PLS). Wlien using. MLR on data sees found in chemlstiy, variable. sciectson is... 

The method of PLS, also known as Partial Least Squares, is a highly utilized regression tool in the chemometrics toolbox,1 and has been successfully used for many process analytical applications. Like the PCR method, PLS uses the exact same mathematical models for the compression of the X-data and the compression of the Y-data ... 

Finally it is important to note that modern analytical equipment frequently offers opportunities for measuring several or many characteristics of a material more or less simultaneously. This has encouraged the development of multivariate statistics methods, which in principle permit the simultaneous analysis of several components of the material. Partial least squares methods and principal component regression are examples of such techniques that are now finding extensive uses in several areas of analytical science. ... 

There is an approach in QSRR in which principal components extracted from analysis of large tables of structural descriptors of analytes are regressed against the retention data in a multiple regression, i.e., principal component regression (PCR). Also, the partial least square (PLS) approach with cross-validation 29 finds application in QSRR. Recommendations for reporting the results of PC A have been published 130). 

The multiple regression method is most often employed to derive predictive QSRR. However, good predictions of GC retention were obtained by means of factorial methods of data analysis. The PLS (partial least squares) treatment of 17 simple descriptors of analytes, such as the number of atoms of each element, of multiple bonds, of functional groups, etc., made predictions of retention of 100 substituted benzenes and pyridines 188],... 

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