Partial Least Squares for Compositional Data: an approach based on the splines

The constrained nature of compositional data gives many difficulties when one performs a multivariate data analysis technique. In literature, to respect the nature of compositional data Partial Least Squares (PLS) based on a Logcontrast PLS was suggesting by Hinkle and Rayen (1995). Moreover this approach presents two principal problems: a very strong assumption of strict positive and the curvature that generally the compositional data present. To resolve them, we present an alternative method based on a particular spline transformation of the compositional data and a constrained version of the PLS. Finally an application on Customer Satisfaction (CS) data is given.