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 response and/or explanatory variables has been approached from different perspectives. The initial approaches are performed in coordinate space subsequent to applying a log-ratio transformation to the compositional vectors. Given that these models exhibit non-linearity concerning classical operations within real space, an alternative approach has been proposed. This approach relies on infinitesimal increments or derivatives, interpreted within a simplex framework. Consequently, it offers interpretations of elasticities or semi-elasticities in the original space of shares which are independent of any log-ratio transformations. Some functions of these elasticities or semi-elasticities turn out to be constant throughout the sample observations, making them natural parameters for interpreting CoDa models. These parameters are linked to relative variations of pairwise share ratios of the response and/or of the explanatory variables. Approximations of share ratio variations are derived and linked to these natural parameters. A real dataset on the French presidential election is utilized to illustrate each type of interpretation in detail.

Date: 2024-07
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Published in Computational Statistics and Data Analysis, 2024, vol.195 (107945), ⟨10.1016/j.csda.2024.107945⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-05471784

DOI: 10.1016/j.csda.2024.107945

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