Three-mode Analysis of Compositional Data: Some Graphical Displays

Modeling higher order arrays of data has gained importance in many sci- ences, and graphical procedures are frequently applied to study three-way arrays when the data are approximately trilinear. When the data consist of vectors of pos- itive values summing to some fixed constant, as in the case of compositional data, this model should consider the special problems that compositional data analysis brings. Gallo (2012) has shown how the Tucker3 model can be used to analyze compositional data. In this work, the aim is to describe how the different versions of the Tucker models can be applied to compositional data and how to read the results correctly.