IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v195y2024ics016794732400029x.html
   My bibliography  Save this article

Pairwise share ratio interpretations of compositional regression models

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016794732400029X
    Download Restriction: Full text for ScienceDirect subscribers only.

    File URL: https://libkey.io/10.1016/j.csda.2024.107945?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    6. 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.
    7. 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.
    8. Katz, Jonathan N. & King, Gary, 1999. "A Statistical Model for Multiparty Electoral Data," American Political Science Review, Cambridge University Press, vol. 93(1), pages 15-32, March.
    9. Joanna Morais & Christine Thomas-Agnan & Michel Simioni, 2017. "Interpretation of explanatory variables impacts in compositional regression models," Working Papers hal-01563362, HAL.
    10. 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.
    Full references (including those not matched with items on IDEAS)

    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. 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. 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.
    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. Thomas-Agnan, Christine & Morais, Joanna, 2019. "Covariates impacts in compositional models and simplicial derivatives," TSE Working Papers 19-1057, 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.
    6. Defever, F. & Riaño, A., 2022. "Firm-Destination Heterogeneity and the Distribution of Export Intensity," Working Papers 22/01, Department of Economics, City University London.
    7. 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.
    8. Thomas-Agnan, Christine & Simioni, Michel & Trinh, Thi-Huong, 2023. "Discrete and Smooth Scalar-on-Density Compositional Regression for Assessing the Impact of Climate Change on Rice Yield in Vietnam," TSE Working Papers 23-1410, Toulouse School of Economics (TSE), revised Apr 2024.
    9. Thi Huong An Nguyen & Anne Ruiz-Gazen & Christine Thomas-Agnan & Thibault Laurent, 2019. "Multivariate Student versus Multivariate Gaussian Regression Models with Application to Finance," JRFM, MDPI, vol. 12(1), pages 1-21, February.
    10. 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.
    11. Joanna Morais & Christine Thomas-Agnan, 2021. "Impact of covariates in compositional models and simplicial derivatives," Post-Print hal-03180682, HAL.
    12. 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.
    13. Julia Cage & Edgard Dewitte, 2021. "It Takes Money to Make MPs: Evidence from 150 Years of British Campaign Spending," SciencePo Working papers Main hal-03384143, HAL.
    14. Arzheimer, Kai & Evans, Jocelyn, 2010. "Bread and butter à la française: Multiparty forecasts of the French legislative vote (1981-2007)," International Journal of Forecasting, Elsevier, vol. 26(1), pages 19-31, January.
    15. Mauricio Velasquez, 2016. "Compositions vs Gini: A new metric to evaluate the effects of land-income disparities," 2016 Papers pve364, Job Market Papers.
    16. Alessandro Gavazza & Mattia Nardotto & Tommaso Valletti, 2019. "Internet and Politics: Evidence from U.K. Local Elections and Local Government Policies," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(5), pages 2092-2135.
    17. Bogatyrev, Konstantin & Stoetzer, Lukas, 2024. "Synthetic Control Methods for Proportions," OSF Preprints brhd3_v1, Center for Open Science.
    18. 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.
    19. Julia Cage & Edgard Dewitte, 2021. "It Takes Money to Make MPs: Evidence from 150 Years of British Campaign Spending," SciencePo Working papers hal-03384143, HAL.
    20. Gerdes, Christer & Wadensjö, Eskil, 2008. "The Impact of Immigration on Election Outcomes in Danish Municipalities," IZA Discussion Papers 3586, Institute of Labor Economics (IZA).

    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:eee:csdana:v:195:y:2024:i:c:s016794732400029x. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.