Regression Models with Compositional Covariates and Structural Zeros

In the last few years, the regression models with compositional explanatory variables have been approached in the literature, and some procedures to manage them have been developed. One issue requiring more investigation regards the presence of structural zeros in the explanatory variables. A structural zero is a value that is intrinsically zero because of a physical limitation: it is not a rounded zero, it is not a value below a certain detection limit, and it is not related to then variability of the selected sampling procedure. It is a sort of ”true” zero. It follows that the presence of structural zeros is problematic in the compositional framework, since a composition is not allowed to have a part equal to zero. Moreover, a quite standard approach used for compositional regression models is to transform the compositional explanatory variables by applying a (isometric log-ratio, usually) transformation keeping as much as possible the information represented by the compositional nature of them (see, for example, Hron et al., 2012): unfortunately, such transformation is not allowed in the case of null parts. Beyond the well-known naive practice of replacing the zeros with an arbitrary small positive value, which represents an easy and intuitive but sometimes non-suitable procedure, in recent years a couple of more sophisticated methodologies to overcome this blocking issue have been proposed in the literature (see Verbelen et al. 2018). The aim of this talk is to illustrate these two procedures, describing in detail how they work. Moreover, it will be shown that they can be seen as special cases of a more general model already known in the literature as the ANCOVA model (Analysis of Covariance Model).