Partial regression

CONSTANTINIDES, Applied Numerical Methods with Personal Computers, McGraw-Hill, 1987. Nonlinear regression, partial deferential equations, matrix manipulations, and a mere flexible program for simultaneous ODEs. 

The enantiomeric composition of methyl lactate ester mixtures was measured by an array of S- and it-sensors and the data were evaluated by chemo-metric tools (multiple line regression, partial component analysis and principal component regression). The ability to distinguish the enantiomeric composition of various mixtures of N-TFA-Ala-OMe or lactates quantitatively with octyl-Chirasil-Val was demonstrated [18]. 

Chemometrics is the discipline concerned with the application of statistical and mathematical methods to chemical data [2.18], Multiple linear regression, partial least squares regression and the analysis of the main components are the methods that can be used to design or select optimal measurement procedures and experiments, or to provide maximum relevant chemical information from chemical data analysis. Common areas addressed by chemometrics include multivariate calibration, visualisation of data and pattern recognition. Biometrics is concerned with the application of statistical and mathematical methods to biological or biochemical data. 

The common multivariate calibration methods are multiple linear regression, partial least-squares regression, and principal components regression. 

S Wold, A Ruhe, H Wold, and WJ Dunn. The collinearity problem in linear regression. Partial least squares PLS approach to generalized inverses. SIAM J. Sci. Stat. Comput., 3(5) 735-743, 1984. 

Farkas, O. and Heberger, K (2005) Comparison of ridge regression, partial least-squares, pairwise correlation, forward and best subset selection methods for prediction of retention indices for aliphatic alcohols. /. Chem. Inf. Model., 45, 339-346. 

Determination of model least squares multi-linear regression weighted multi-linear regression robust regression ridge regression partial least squares generalised inverse... 

Once the descriptors have been selected, investigators need to select the statistical approach for developing the QSAR model. This can involve a number of techniques, such as multiple linear regression, partial least squares analysis, neural networks, and a variety of others [9]. These techniques need to be applied to both the training set (model development) and the validation set (assessment of predictability). 

In this section we shall consider the rather general case where for a series of chemical compounds measurements are made in a number of parallel biological tests and where a set of descriptor variables is believed to be related to the biological potencies observed. In order to imderstand the data in their entirety and to deal adequately with the mathematical properties of such data, methods of multivariate statistics are required. A variety of such methods is available as, for example, multivariate regression, canonical correlation, principal component analysis, principal component regression, partial least squares analysis, and factor analysis, which have all been applied to biological or chemical problems (for reviews, see [1-11]). Which method to choose depends on the ultimate objective of an analysis and the property of the data. We have found principal component and factor analysis particularly useful. For this reason and also since many multivariate methods make use of components for factors we will start with these methods in some detail, while the discussion of other approaches will be less extensive. 

Principal Component Regression, Partial Least Squares, and Continuum Regression... 

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