Interpretation of partial least squares regression models by means of target projection and selectivity ratio plots

• Published in: Journal of chemometrics 2010-07, Vol.24 (7-8), p.496-504
• Main Author: Kvalheim, Olav M.
• Format: Article
• Language: English
• Subjects: Chemistry; Displays; Equivalence; Exact sciences and technology; General and physical chemistry; General. Nomenclature, chemical documentation, computer chemistry; Least squares method; Mathematical models; Measurement; model interpretation; Parameter estimation; partial least squares; Projection; Regression; Regression analysis; Selectivity; target projection; Theory of reactions, general kinetics. Catalysis. Nomenclature, chemical documentation, computer chemistry; variable selection; Variables
• ISSN: 0886-9383; 1099-128X; 1099-128X
• DOI: 10.1002/cem.1289

Displays of latent variable regression models in variable and object space are provided to reveal model parameters useful for interpretation and to reveal the most influential x‐variables with respect to the predicted response. Although the target projected (TP) component obtained from a standard partial least square, or equivalently, the predictive component from orthogonal partial least squares (OPLS) or partial least squares + similarity transform (PLS + ST) is maximally co‐varying with the response, the corresponding loadings are not necessarily the best choice for model interpretation and disclosure of the most important variables with respect to explaining the response. Selectivity ratio plot represents a bridge from co‐variance‐based TP loadings to correlation‐like localized information suitable for interpretation. Copyright © 2010 John Wiley & Sons, Ltd. The usefulness of the partial least squares (PLS) weight vector, the predictive target projected (TP) component and the regression vector for model interpretation is assessed and the information content in these vectors is compared with the vector of the correlation‐like selectivity ratios. The conclusion is that the selectivity ratios displayed with the sign of the corresponding TP loadings represent a more reliable presentation for revealing the most influential x‐variables in a regression model than the traditional PLS vectors.