Impact of Covariates in Compositional Models and Simplicial Derivatives

In the framework of Compositional Data Analysis, vectors carrying relative information, also called compositional vectors, can appear in regression models either as dependent or explanatory variables. some situations, they be on both sides equation. Measuring marginal impacts covariates these types is not straightforward since a change one component closed composition automatically affects rest composition. Previous work by authors has shown how to measure, compute and interpret case linear with compositions The resulting natural interpretation terms an elasticity, quantity commonly used econometrics marketing applications. They demonstrate link between elasticities simplicial derivatives. aim this contribution extend results other namely when vector single side cases, impact related semi-elasticity linked derivative. Moreover we consider possibility that total variable variable, several possible interpretations derive elasticity formulas case.