Regression Models with Compositional Regressors in Case of Structural Zeros

In many real-life situations, it may happen to consider a regression model with compositional explanatory variables. Compositional data describe parts of some whole, having the feature to sum to a fixed value, so they are commonly presented as vectors of proportions, percentages, or frequencies. In the compositional framework, the presence of structural zeros is problematic, since a composition is not allowed to have a part equal to zero. In the recent years, a few techniques have been introduced in the literature to address the issue. In this paper, three methods (the replacement, the conditioning, and projection approach) are described and illustrated by an example of application.