Tucker3 Model for Compositional Data

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 quadrilinear. 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 specific problems that compositional data analysis brings. The main purpose of this paper is to describe how to do a Tucker3 analysis of compositional data, and to show the relationships between the loading matrices when different preprocessing procedures are used.