Multivariate analysis of aquatic toxicity data with PLS

A common task in data analysis is to model the relationships between two sets of variables, the descriptor matrixX and the response matrixY. A typical example in aquatic science concerns the relationships between the chemical composition of a number of samples (X) and their toxicity to a number of different aquatic species (Y). This modelling is done in order to understand the variation ofY in terms of the variation ofX, but also to lay the ground for predictingY of unknown observations based on their knownX-data. Correlations of this type are usually expressed as regression models, and are rather common in aquatic science. Often, however, the multivariateX andY matrices invalidate the use of multiple linear regression (MLR) and call for methods which are better suited for collinear data. In this context, multivariate projection methods represent a highly useful alternative, in particular, partial least squares projections to latent structures (PLS). This paper introduces PLS, highlights its strengths and presents applications of PLS to modelling aquatic toxicity data. A general discussion of regression, comparing MLR and PLS, is provided.