Units recovery methods in compositional data analysis

Compositional data carry relative information. Hence, their statistical analysis has to be performed on coordinates with respect to a log-ratio basis. Frequently, the modeler is required to back-transform the estimates obtained with the modeling to have them in the original units such as euros, kg or mg/liter. Approaches for recovering original units need to be formally introduced and its properties explored. Here, we formulate and analyze the properties of two procedures: a simple approach consisting of adding a residual part to the composition and an approach based on the use of an auxiliary variable. Both procedures are illustrated using a geochemical data set where the original units are recovered when spatial models are applied.