Factor Analysis of Compositional Data with a Total

The sample space of a manifest random vector is of crucial importance for a latent variable model. Compositional data require an appropriate statistical analysis because they provide the relative importance of the parts of a whole. Any statistical model including variables created using the original parts should be formulated according to the geometry of the simplex. Methods based on log-ratio coordinates give a consistent framework for analyzing this type of data. Here, we introduce an approach that includes both the orthonormal log-ratio coordinates and an auxiliary variable carrying absolute information and illustrate it through the factor analysis of two real datasets.