Multivariate partial least squares

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. 

Sections 9A.2-9A.6 introduce different multivariate data analysis methods, including Multiple Linear Regression (MLR), Principal Component Analysis (PCA), Principal Component Regression (PCR) and Partial Least Squares regression (PLS). 

Mancozeb is a dithiocarbamate pesticide with a very low solubility in organic and inorganic solvent. In this work we have developed a solvent free, accurate and fast photoacoustic FTIR-based methodology for Mancozeb determination in commercial fungicides. The proposed procedure was based on the direct measurement of the solid samples in the middle infrared region using a photoacoustic detector. A multivariate calibration approach based on the use of partial least squares (PLS) was employed to determine the pesticide content in commercially available formulations. 

Capitan-Vallvey, L.F. et al.. Simultaneous determination of the colorants tartrazine, ponceau 4R and sunset yellow FCF in foodstuffs by solid phase spectrophotometry using partial least square multivariate calibration, Talanta, 47, 861, 1998. 

Bozdogan, A., Ozgur, U.M., and Koyuncu, L, Simultaneous determination of sunset yellow and Ponceau 4R in gelatin powder by derivative spectrophotometry and partial least-squares multivariate spectrophotometric calibration, Anal. Lett., 33, 2975, 2000. 

A difficulty with Hansch analysis is to decide which parameters and functions of parameters to include in the regression equation. This problem of selection of predictor variables has been discussed in Section 10.3.3. Another problem is due to the high correlations between groups of physicochemical parameters. This is the multicollinearity problem which leads to large variances in the coefficients of the regression equations and, hence, to unreliable predictions (see Section 10.5). It can be remedied by means of multivariate techniques such as principal components regression and partial least squares regression, applications of which are discussed below. 

Manne R (1987) Analysis of two partial-least-squares algorithms for multivariate calibration. Chemom Intell Lab Syst 2 187... 

Partial least squares (PLS) projections to latent structures [40] is a multivariate data analysis tool that has gained much attention during past decade, especially after introduction of the 3D-QSAR method CoMFA [41]. PLS is a projection technique that uses latent variables (linear combinations of the original variables) to construct multidimensional projections while focusing on explaining as much as possible of the information in the dependent variable (in this case intestinal absorption) and not among the descriptors used to describe the compounds under investigation (the independent variables). PLS differs from MLR in a number of ways (apart from point 1 in Section 16.5.1) ... 

Galego and Arroyo [14] described a simultaneous spectrophotometric determination of OTC, hydrocortisone, and nystatin in the pharmaceutical preparations by using ratio spectrum-zero crossing derivate method. The calculation was performed by using multivariate methods such as partial least squares (PLS)-l, PLS-2, and principal component regression (PCR). This method can be used to resolve accurately overlapped absorption spectra of those mixtures. 

A total of 185 emission lines for both major and trace elements were attributed from each LIBS broadband spectrum. Then background-corrected, summed, and normalized intensities were calculated for 18 selected emission lines and 153 emission line ratios were generated. Finally, the summed intensities and ratios were used as input variables to multivariate statistical chemometric models. A total of 3100 spectra were used to generate Partial Least Squares Discriminant Analysis (PLS-DA) models and test sets. 

The four-volume Handbook of Chemoinformatics—From Data to Knowledge (Gasteiger 2003) contains a number of introductions and reviews that are relevant to chemometrics Partial Least Squares (PLS) in Cheminformatics (Eriksson et al. 2003), Inductive Learning Methods (Rose 1998), Evolutionary Algorithms and their Applications (von Homeyer 2003), Multivariate Data Analysis in Chemistry (Varmuza 2003), and Neural Networks (Zupan 2003). 

Multivariate calibration has the aim to develop mathematical models (latent variables) for an optimal prediction of a property y from the variables xi,..., jcm. Most used method in chemometrics is partial least squares regression, PLS (Section 4.7). An important application is for instance the development of quantitative structure—property/activity relationships (QSPR/QSAR). 

In this work, two methods for the determination of caffeine in energy drinks by derivative spectrophotometry and by partial least-squares multivariate spectropho-tometric calibration (PLS-1) are described. Proposed methods involve background correction methods that interferences from vitamins, taurin and food colours were minimized by treating the sample with basic lead acetate and NaHC03 for the arralysis of caffeine in energy drinks. 

Under eonstant experimental conditions, the number of Raman seattered photons is proportional to analyte eoneentration. Quantitative methods can be developed with simple peak height measurements [1]. Just as with infrared calibrations, multiple components in eomplex mixtures ean be quantified if a distinet wavelength for each component can be identified. When isolated bands are not readily apparent, advaneed multivariate statistical tools (chemometrics) like partial least squares (PLS) ean help. These work by identifying all of the wavelengths correlated to, or systematically changing with, the eoneentration of a eomponent [2], Raman speetra also can be correlated to other properties, sueh as stress in semieonduetors, polymer erystal-linity, and particle size, because these parameters are refleeted in the loeal moleeular environment. 

M. Sjostrom, S. Wold, W. Lindberg, J.A. Persson and H. Martens, A multivariate calibration problem in analytical chemistry solved by partial least squares models in latent variables. Anal. Chim. Acta, 150, 61-70 (1983). 

The multivariate techniques which reveal underlying factors such as principal component factor analysis (PCA), soft Independent modeling of class analogy (SIMCA), partial least squares (PLS), and cluster analysis work optimally If each measurement or parameter Is normally distributed In the measurement space. Frequency histograms should be calculated to check the normality of the data to be analyzed. Skewed distributions are often observed In atmospheric studies due to the process of mixing of plumes with ambient air. 

---