Resumen de Covariates impacts in compositional models and simplicial derivatives
Joanna Morais, Christine Thomas-Agnan
Compositions can be used as variables in regression models, either as explanatory variables (see Hron et al. (2012)) or as dependent variables (see Egozcue et al. (2012)), or both (see Chen et al. (2016), Morais et al. (2018b) and Nguyen T.H.A (2018)). However, measuring the marginal impacts of covariates in these types of models is not straightforward, as the change in one component of a composition may affect the rest of the composition. Morais et al. (2018a) have shown how to measure, compute and interpret these marginal impacts in the case of linear regression models with a dependent composition (Y) by compositional explanatory variables (X). The resulting natural interpretation is in terms of an elasticity, commonly used in econometrics and marketing applications. Morais et al. (2018a) also demonstrate the link between these elasticities and simplicial derivatives as defined in Egozcue et al. in Pawlowsky-Glahn and Buccianti (2011), chapter 12 and Barcelo-Vidal et al. in PawlowskyGlahn and Buccianti (2011), chapter 13. The aim of this contribution is to show how to compute these semi-elasticites and simplicial derivatives in other situations, namely first when the dependent variable is a composition and the explanatory variables are non-compositional, and second when the dependent variable is noncompositional and at least one of the explanatory variables is a composition. Moreover we also consider the case where a total is used or not as an explanatory variable, with several possible interpretations of the total. Finally, we discuss how to compute confidence intervals for these elasticities or semi-elasticities, which significantly improves the interpretability of the compositional regression models. This contribution will be illustrated by real-data applications.
