IDEAS home Printed from https://ideas.repec.org/p/tse/wpaper/123765.html
   My bibliography  Save this paper

Covariates impacts in compositional models and simplicial derivatives

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.tse-fr.eu/sites/default/files/TSE/documents/doc/wp/2019/wp_tse_1057.pdf
    File Function: Full Text
    Download Restriction: no
    ---><---

    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. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jacob Fiksel & Scott Zeger & Abhirup Datta, 2022. "A transformation‐free linear regression for compositional outcomes and predictors," Biometrics, The International Biometric Society, vol. 78(3), pages 974-987, September.
    2. Dargel, Lukas & Thomas-Agnan, Christine, 2024. "Pairwise share ratio interpretations of compositional regression models," Computational Statistics & Data Analysis, Elsevier, vol. 195(C).
    3. Morais, Joanna & Simioni, Michel & Thomas-Agnan, Christine, 2016. "A tour of regression models for explaining shares," TSE Working Papers 16-742, Toulouse School of Economics (TSE).
    4. Defever, F. & Riaño, A., 2022. "Firm-Destination Heterogeneity and the Distribution of Export Intensity," Working Papers 22/01, Department of Economics, City University London.
    5. 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.
    6. Juan José Egozcue & Vera Pawlowsky-Glahn, 2019. "Compositional data: the sample space and its structure," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 599-638, September.
    7. Monique Graf, 2020. "Regression for compositions based on a generalization of the Dirichlet distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(4), pages 913-936, December.
    8. 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.
    9. Joanna Morais & Christine Thomas-Agnan, 2021. "Impact of covariates in compositional models and simplicial derivatives," Post-Print hal-03180682, HAL.
    10. Nikola Štefelová & Andreas Alfons & Javier Palarea-Albaladejo & Peter Filzmoser & Karel Hron, 2021. "Robust regression with compositional covariates including cellwise outliers," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(4), pages 869-909, December.
    11. Leenheer, J. & Bijmolt, T.H.A. & van Heerde, H.J. & Smidts, A., 2002. "Do Loyalty Programs Enhance Behavioral Loyalty : An Empirical Analysis Accounting for Program Design and Competitive Effects," Discussion Paper 2002-65, Tilburg University, Center for Economic Research.
    12. Mauricio Velasquez, 2016. "Compositions vs Gini: A new metric to evaluate the effects of land-income disparities," 2016 Papers pve364, Job Market Papers.
    13. Janina Janurek & Sascha Abdel Hadi & Andreas Mojzisch & Jan Alexander Häusser, 2018. "The Association of the 24 Hour Distribution of Time Spent in Physical Activity, Work, and Sleep with Emotional Exhaustion," IJERPH, MDPI, vol. 15(9), pages 1-14, September.
    14. J. A. Martín-Fernández, 2021. "“Compositional Data Analysis in Practice” by Michael Greenacre Universitat Pompeu Fabra (Barcelona, Spain), Chapman and Hall/CRC, 2018," Journal of Classification, Springer;The Classification Society, vol. 38(1), pages 109-111, April.
    15. Andriansyah, Andriansyah & Messinis, George, 2016. "Intended use of IPO proceeds and firm performance: A quantile regression approach," Pacific-Basin Finance Journal, Elsevier, vol. 36(C), pages 14-30.
    16. Roberto Casarin & Stefano Grassi & Francesco Ravazzolo & Herman K. van Dijk, 2020. "A Bayesian Dynamic Compositional Model for Large Density Combinations in Finance," Working Paper series 20-27, Rimini Centre for Economic Analysis.
    17. Brockett, Patrick L. & Charnes, Abraham & Cooper, William W. & Learner, David & Phillips, Fred Y., 1995. "Information theory as a unifying statistical approach for use in marketing research," European Journal of Operational Research, Elsevier, vol. 84(2), pages 310-329, July.
    18. 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.
    19. Lau, K. & Kagan, A. & Post, G. V., 1997. "Market share modeling within a switching regression framework," Omega, Elsevier, vol. 25(3), pages 345-353, June.
    20. Zhao, T.; & Sutton, M.; & Meacock, M.;, 2023. "Use of compositional covariates in linear regression: problems and solutions," Health, Econometrics and Data Group (HEDG) Working Papers 23/16, HEDG, c/o Department of Economics, University of York.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tse:wpaper:123765. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/tsetofr.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.