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Covariates impacts in compositional models and simplicial derivatives

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  • Thomas-Agnan, Christine
  • Morais, Joanna

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. J. Morais, C. Thomas-Agnan and M. Simioni [Austrian Journal of Statistics, 47(5), 1-25, 2018] have 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

  • Thomas-Agnan, Christine & Morais, Joanna, 2019. "Covariates impacts in compositional models and simplicial derivatives," TSE Working Papers 19-1057, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:123765
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    References listed on IDEAS

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    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. 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.
    3. Petra Kynčlová & Peter Filzmoser & Karel Hron, 2015. "Modeling Compositional Time Series with Vector Autoregressive Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 34(4), pages 303-314, July.
    4. 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.
    5. Masao Nakanishi & Lee G. Cooper, 1982. "Technical Note—Simplified Estimation Procedures for MCI Models," Marketing Science, INFORMS, vol. 1(3), pages 314-322.
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    Cited by:

    1. 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).

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    More about this item

    Keywords

    compositional regression model; marginal effects; simplicial derivative; elasticity; semi-elasticity.;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • M31 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising - - - Marketing
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis

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