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Title: Assessing the impact of covariates in compositional regression models Authors:  Christine Thomas-Agnan - Universite Toulouse (France) [presenting]
Abstract: Regression models are considered which involve compositional vectors (i.e. carrying relative information) either as the dependent variable, as explanatory variables or on both sides of the regression equation. Measuring the marginal impacts of covariates in these models is not straightforward since a change in one component of a closed composition automatically affects the rest of the composition. A natural tool for this assessment is the concept of elasticity or semi-elasticity, depending on the model. Indeed the elasticity (respectively the semi-elasticity) is linked to the simplicial derivative of the expected value of the dependent variable with respect to the covariate in the case both the dependent and the explanatory variables are compositional (respectively in the case one of them is compositional). We present examples of derivations of such relationships. After recalling the formulas for evaluating these (semi-) elasticities as a function of parameters estimates, we illustrate their use on several examples. We contrast with alternative interpretations of these models. We describe several extensions for example to models including a total variable among the explanatory variables, with possibly several definitions of the total, and models involving a spatial dimension.