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Pairwise share ratio interpretations of compositional regression models

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  • Dargel, Lukas
  • Thomas-Agnan, Christine

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.

Suggested Citation

  • Dargel, Lukas & Thomas-Agnan, Christine, 2024. "Pairwise share ratio interpretations of compositional regression models," Computational Statistics & Data Analysis, Elsevier, vol. 195(C).
    • Handle: RePEc:eee:csdana:v:195:y:2024:i:c:s016794732400029x
    DOI: 10.1016/j.csda.2024.107945
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    References listed on IDEAS

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    1. Lukas Dargel & Christine Thomas-Agnan, 2024. "The link between multiplicative competitive interaction models and compositional data regression with a total," Journal of Applied Statistics, Taylor & Francis Journals, vol. 51(14), pages 2929-2960, October.
    2. 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.
    3. 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.
    4. Ruiz-Gazen, Anne & Thomas-Agnan, Christine & Laurent, Thibault & Mondon, Camille, 2022. "Detecting outliers in compositional data using Invariant Coordinate Selection," TSE Working Papers 22-1320, Toulouse School of Economics (TSE).
    5. 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.
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    8. Joanna Morais & Christine Thomas-Agnan & Michel Simioni, 2017. "Interpretation of explanatory variables impacts in compositional regression models," Working Papers hal-01563362, HAL.
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