Covariates impacts in compositional models and simplicial derivatives

Christine Thomas-Agnan and Joanna Morais

No 19-1057, TSE Working Papers from Toulouse School of Economics (TSE)

Abstract: In the framework of Compositional Data Analysis, vectors carrying relative information, also called compositional vectors, can appear in regression models either as dependent or as explanatory variables. In some situations, they can be on both sides of the regression equation. Measuring the marginal impacts of covariates in these types of models is not straightforward since a change in one component of a closed composition automatically affects the rest of the composition. J. Morais, C. Thomas-Agnan and M. Simioni [Austrian Journal of Statistics, 47(5), 1-25, 2018] have shown how to measure, compute and interpret these marginal impacts in the case of linear regression models with compositions on both sides of the equation. The resulting natural interpretation is in terms of an elasticity, a quantity commonly used in econometrics and marketing applications. They also demonstrate the link between these elasticities and simplicial derivatives. The aim of this contribution is to extend these results to other situations, namely when the compositional vector is on a single side of the regression equation. In these cases, the marginal impact is related to a semi-elasticity and also linked to some simplicial derivative. Moreover we consider the possibility that a total variable is used as an explanatory variable, with several possible interpretations of this total and we derive the elasticity formulas in that case.

Keywords: compositional regression model; marginal effects; simplicial derivative; elasticity; semi-elasticity. (search for similar items in EconPapers)
JEL-codes: C10 C25 C35 C46 D12 M31 (search for similar items in EconPapers)
Date: 2019-12
New Economics Papers: this item is included in nep-ecm and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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