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 matrix X and the response matrix Y. 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 of Y in terms of the variation of X, but also to lay the ground for predicting Y of unknown observations based on their known X-data. Correlations of this type are usually expressed as regression models, and are rather common in aquatic science. Often, however, the multivariate X and Y 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.