Three-way Compositional Data Analysis

For the exploratory analysis of three-way data, e.g., measurements of a number of objects, on a number of variables at different points in time, Tucker analysis is one of the most applied technique to study three-way array when the data are approximately trilinear. It can be considered a three way generalization of PCA (Principal Component Analysis). Like PCA, to interpret the results from these methods, it is possible, in addition to inspecting the loadings matrices and core array, inspect visual representation of the outcome. When the data are particular ratios, as in the case of compositional data, these models should consider the special problems that compositional data gives. Aim of this work is describe how an analysis of compositional data by Tucker analysis is possible and how the results should be interpreted. Moreover, a procedure for displaying the results for objects, variables and occasions will be give