Compositional data and three-mode analysis

For the exploratory analysis of three-way data, the Tucker3 is one of the most applied models to study three-way arrays when the data are approximately trilinear. It is a three-way generalization of the PCA (Principal Component Analysis). Like the PCA, the Tucker3 yields component matrices for the objects and for variables, but it also yields a component matrix for the occasions. When the data consist of vectors of positive values summing to a unit, as in the case of compositional data, this model should consider the special problems that compositional data analysis brings. The aim of this work is to describe how to do a Tucker3 analysis of compositional data and how to read the results correctly in a low-dimensional space such as joint biplots