Partial Least Squares PLS Analysis and Other Multivariate Statistical Methods

Partial Least Squares (PLS) Analysis and Other Multivariate Statistical Methods 

COMPACT (computer-optimized molecular parametric analysis of chemical toxicity) [582, 583], a discriminant analysis approach, is described to predict carcinogenicity and other forms of toxicity involving the formation of reactive intermediates by determining the structural criteria for substrate specificity towards cytochrome P-450 enzymes it is claimed that the method is about 75% predictive for rodent carcinogenicity [583]. Recently, a discriminant-regression model was described [584]. It applies stepwise discriminant analysis to form clusters of compounds for which quantitative relationships are derived by multiple regression analysis. 

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 

The most promising new approach in multivariate statistical methods is the PLS (partial least squares in latent variables) method [26, 27, 38, 607 — 610]. Many, even hundreds or thousands of independent variables (the X block) can be correlated with one or several dependent variables (the Y block). PLS analysis is a principal component-like method, with the main difference that the vectors are not indepen- 

The results of a PLS analysis can be transformed to regression coefficients of the X block variables, most often leading to the curious result that more regression coefficients than objects are obtained. It should be mentioned that in the case of one dependent variable and a number of X variables that equals the number of PLS components, the results from regression analysis and, after appropriate transformation, from PLS analysis are numerically identical. 

---

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. 

In the past few years, PLS, a multiblock, multivariate regression model solved by partial least squares found its application in various fields of chemistry (1-7). This method can be viewed as an extension and generalization of other commonly used multivariate statistical techniques, like regression solved by least squares and principal component analysis. PLS has several advantages over the ordinary least squares solution therefore, it becomes more and more popular in solving regression models in chemical problems. 

---