Pairwise share-ratio interpretations of compositional regression models

Lukas Dargel and Christine Thomas-Agnan ()
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Lukas Dargel: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Christine Thomas-Agnan: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement

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Abstract: The interpretation of regression models with compositional vectors as dependent and/or independent variables has been approached from different perspectives. The first approaches that appeared in the literature are done in coordinate space after some log-ratio transformation of the share vectors. Considering the fact that these models are non-linear with respect to classical operations of the real space, another approach has been proposed based on infinitesimal increments or derivatives understood in a simplex sense, leading to elasticities or semi-elasticities interpretations in the original space that have the advantage of being independent of any log-ratio transformations. After briefly reviewing these two points of view, we show that some functions of elasticities or semi-elasticities are constant throughout the sample observations, which makes them natural parameters for interpreting CoDa models. We derive approximations of share ratio variations and link them to these parameters leading to transformatio-free interpretations in the original shares space. We use a real data set on the French presidential election to illustrate each type of interpretation in detail.

Date: 2026-03-10
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