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Share-ratio interpretations of compositional regression models

Author

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  • Dargel, Lukas
  • Thomas-Agnan, Christine
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.

Suggested Citation

  • 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.
    • Handle: RePEc:tse:wpaper:128262
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    References listed on IDEAS

    as
    1. Thi Huong An Nguyen & Christine Thomas-Agnan & Thibault Laurent & Anne Ruiz-Gazen, 2021. "A simultaneous spatial autoregressive model for compositional data," Spatial Economic Analysis, Taylor & Francis Journals, vol. 16(2), pages 161-175, April.
    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.
    3. Berta Ferrer-Rosell & Germà Coenders & Glòria Mateu-Figueras & Vera Pawlowsky-Glahn, 2016. "Understanding Low-Cost Airline Users' Expenditure Patterns and Volume," Tourism Economics, , vol. 22(2), pages 269-291, April.
    4. Thomas-Agnan, Christine & Laurent, Thibault & Ruiz-Gazen, Anne & Nguyen, T.H.A & Chakir, Raja & Lungarska, Anna, 2020. "Spatial simultaneous autoregressive models for compositional data: Application to land use," TSE Working Papers 20-1098, Toulouse School of Economics (TSE).
    5. K. Hron & P. Filzmoser & K. Thompson, 2012. "Linear regression with compositional explanatory variables," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(5), pages 1115-1128, November.
    6. Joanna Morais & Christine Thomas-Agnan & Michel Simioni, 2017. "Interpretation of explanatory variables impacts in compositional regression models," Working Papers hal-01563362, HAL.
    7. 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.
    8. Joanna Morais & Christine Thomas-Agnan, 2021. "Impact of covariates in compositional models and simplicial derivatives," Post-Print hal-03180682, HAL.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    JEL classification:

    • C39 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Other
    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software

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