Multivariate regression analysis approach

A set of 120 atom types was proposed. The corresponding hydrophobic constants were evaluated by multivariate regression analysis using a training set of 893 compounds, = 0.856 and s = 0.496. This approach is actually called the ALOGP method [Viswanadhan et al, 1993], and a similar approach was also proposed for - molar refractivity. As in the Broto-Moreau-Vandycke approach, correction factors are avoided, while hydrogen atoms are considered instead. 

Fig. 3. Comparison of some multivariate methods used in QSAR relating a matrix of biologieal variables, Y, to a matrix of deseriptor variables, X PCRA (prineipal component regression analysis) PLS (partial least-squares method) PCA (principal component analysis according to the Weiner/Malinowski approach) MRA (multivariate regression analysis) and CCA (canonical correlation analysis).

In Table 14.3, we have listed five topics that we will briefly review. The first is closely related to the notion of aromaticity, one of the central concepts of chemistry that appears to be elusive even though, as we will see, its conceptual clarification for the case of hydrocarbons was outlined over 35 years ago [6,7]. The second topic relates to the oldest statistical method, the method that has remained even today one of the most widely used tools for analysis of experimental data the multivariate regression analysis (MR A) [8]. The third topic also relates to MR A, but rather than dealing with the method itself, it is concerned with construction and selection of molecular descriptors [9]. Next, we will consider one of the topics of bioinformatics How to extract useful quantitative information from qualitative proteome maps [7]. Finally, we will address the topic of protein and DNA sequence alignments by describing, in contrast to the current computer manipulations of bio-sequences, an alternative a non-empirical graphical approach to protein and DNA sequence alignments [8-10]. 

N.B Vogt, Polynomial principal component regression an approach to analysis and interpretation of complex mixture relationships in multivariate environmental data, Chemom. Intell. Lab. Syst, 7, 119-130 (1989). 

In many chemical studies, the measured properties of the system can be regarded as the linear sum of the fundamental effects or factors in that system. The most common example is multivariate calibration. In environmental studies, this approach, frequently called receptor modeling, was first applied in air quality studies. The aim of PCA with multiple linear regression analysis (PCA-MLRA), as of all bilinear models, is to solve the factor analysis problem stated below ... 

The adaptive least squares (ALS) method [396, 585 — 588] is a modification of discriminant analysis which separates several activity classes e.g. data ordered by a rating score) by a single discriminant function. The method has been compared with ordinary regression analysis, linear discriminant analysis, and other multivariate statistical approaches in most cases the ALS approach was found to be superior to categorize any numbers of classes of ordered data. ORMUCS (ordered multicate-gorial classification using simplex technique) [589] is an ALS-related approach which... 

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. 

Part V will cover several techniques for working on prevention that apply multiple factor models. Multiple factor models may use quantitative or qualitative analysis. Statistical techniques, such as factor analysis, multiple regression analysis and other multivariate methods may be useful. Fault tree analysis, failure mode and effects analysis and other approaches help identify characteristics that together can lead to undesired events. 

Regression analysis can be used to extract information from NIR spectra. Multivariate discriminant analysis enables to separate samples into different classes. There are two mathematical approaches... 

Linear or nonlinear multiple regression analysis is used as a statistical tool to derive quantitative models, to check the significance of these models and of each individual term in the regression equation. Other statistical methods, such as discriminant analysis, principal component analysis (PCA), or partial least squares (PLS) analysis (see Partial Least Squares Projections to Latent Structures (PLS) in Chemistry) are alternatives to regression analysis (see Che mo me tries Multivariate View on Chemical Problems)Newer approaches compare the similarity of molecules with respect to different physicochemical or other properties with their biological activities. 

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