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Impact of covariates in compositional models and simplicial derivatives

Author

Listed:
  • Joanna Morais

    (Avisia, Bordeaux)

  • Christine Thomas-Agnan

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université 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)

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. Previous work by the authors has 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.

Suggested Citation

  • Joanna Morais & Christine Thomas-Agnan, 2021. "Impact of covariates in compositional models and simplicial derivatives," Post-Print hal-03180682, HAL.
    • Handle: RePEc:hal:journl:hal-03180682
    DOI: 10.17713/ajs.v50i2.1069
    Note: View the original document on HAL open archive server: https://hal.science/hal-03180682
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    References listed on IDEAS

    as
    1. T. H. A. Nguyen & T. Laurent & C. Thomas-Agnan & A. Ruiz-Gazen, 2022. "Analyzing the impacts of socio-economic factors on French departmental elections with CoDa methods," Journal of Applied Statistics, Taylor & Francis Journals, vol. 49(5), pages 1235-1251, April.
    2. Jiajia Chen & Xiaoqin Zhang & Shengjia Li, 2017. "Multiple linear regression with compositional response and covariates," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(12), pages 2270-2285, September.
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    Cited by:

    1. Dargel, Lukas & Thomas-Agnan, Christine, 2023. "Share-ratio interpretations of compositional regression models," TSE Working Papers 23-1456, Toulouse School of Economics (TSE), revised 20 Sep 2023.
    2. Thibault Laurent & Christine Thomas-Agnan & Anne Ruiz-Gazen, 2023. "Covariates impacts in spatial autoregressive models for compositional data," Journal of Spatial Econometrics, Springer, vol. 4(1), pages 1-23, December.

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    More about this item

    Keywords

    Compositional regression model; Marginal effects; Simplicial derivative; Elasticity; Semi-elasticity;
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