IDEAS home Printed from https://ideas.repec.org/p/hal/wpaper/hal-01563362.html
   My bibliography  Save this paper

Interpretation of explanatory variables impacts in compositional regression models

Author

Listed:
  • Joanna Morais

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

  • Christine Thomas-Agnan

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique)

  • Michel Simioni

    (UMR MOISA - Marchés, Organisations, Institutions et Stratégies d'Acteurs - Cirad - Centre de Coopération Internationale en Recherche Agronomique pour le Développement - INRA - Institut National de la Recherche Agronomique - Montpellier SupAgro - Centre international d'études supérieures en sciences agronomiques - CIHEAM-IAMM - Centre International de Hautes Etudes Agronomiques Méditerranéennes - Institut Agronomique Méditerranéen de Montpellier - CIHEAM - Centre International de Hautes Études Agronomiques Méditerranéennes - Montpellier SupAgro - Institut national d’études supérieures agronomiques de Montpellier)

Abstract

We are interested in modeling the impact of media investments on automobile manufacturer's market shares. Regression models have been developed for the case where the dependent variable is a vector of shares. Some of them, from the marketing literature, are easy to interpret but quite simple (Model A). Other models, from the compositional data analysis literature, allow a large complexity but their interpretation is not straightforward (Model B). This paper combines both literatures in order to obtain a performing market share model and develop relevant interpretations for practical use. We prove that Model A is a particular case of Model B, and that an intermediate specification is possible (Model AB). A model selection procedure is proposed. Several impact measures are presented and we show that elasticities are particularly useful: they can be computed from the transformed or from the original model, and they are linked to the simplicial derivatives.

Suggested Citation

  • Joanna Morais & Christine Thomas-Agnan & Michel Simioni, 2017. "Interpretation of explanatory variables impacts in compositional regression models," Working Papers hal-01563362, HAL.
  • Handle: RePEc:hal:wpaper:hal-01563362
    Note: View the original document on HAL open archive server: https://hal.science/hal-01563362
    as

    Download full text from publisher

    File URL: https://hal.science/hal-01563362/document
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Joanna Morais & Christine Thomas-Agnan & Michel Simioni, 2018. "Using compositional and Dirichlet models for market share regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 45(9), pages 1670-1689, July.
    2. 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).
    3. 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)

    Citations

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


    Cited by:

    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. Morais, Joanna & Thomas-Agnan, Christine & Simioni, Michel, 2018. "Impact of advertizing on brand’s market-shares in the automobile market:: a multi-channel attraction model with competition and carry-over effects," TSE Working Papers 18-878, Toulouse School of Economics (TSE).
    4. 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.
    5. Mitch Kunce, 2023. "Age Cohort Affects on U.S. State-Level Alcohol Consumption Shares: Insights Using Attraction CODA," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 12(3), pages 1-1.
    6. 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.
    7. Dargel, Lukas & Thomas-Agnan, Christine, 2024. "Pairwise share ratio interpretations of compositional regression models," Computational Statistics & Data Analysis, Elsevier, vol. 195(C).
    8. Joscha Krause & Jan Pablo Burgard & Domingo Morales, 2022. "Robust prediction of domain compositions from uncertain data using isometric logratio transformations in a penalized multivariate Fay–Herriot model," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(1), pages 65-96, February.

    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. 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. 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.
    3. Morais, Joanna & Trinh, Thi-Huong, 2017. "Impact of socioeconomic factors on nutritional diet in Vietnam from 2004 to 2014: new insights using compositional data analysis," TSE Working Papers 17-825, Toulouse School of Economics (TSE).
    4. Mitch Kunce, 2023. "Age Cohort Affects on U.S. State-Level Alcohol Consumption Shares: Insights Using Attraction CODA," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 12(3), pages 1-1.
    5. 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.
    6. Morais, Joanna & Thomas-Agnan, Christine & Simioni, Michel, 2018. "Impact of advertizing on brand’s market-shares in the automobile market:: a multi-channel attraction model with competition and carry-over effects," TSE Working Papers 18-878, Toulouse School of Economics (TSE).
    7. Thomas-Agnan, Christine & Morais, Joanna, 2019. "Covariates impacts in compositional models and simplicial derivatives," TSE Working Papers 19-1057, Toulouse School of Economics (TSE).
    8. 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).
    9. Jasper Dijkstra & Tracy Durrant & Jesús San-Miguel-Ayanz & Sander Veraverbeke, 2022. "Anthropogenic and Lightning Fire Incidence and Burned Area in Europe," Land, MDPI, vol. 11(5), pages 1-19, April.
    10. Takahiro Yoshida & Morito Tsutsumi, 2018. "On the effects of spatial relationships in spatial compositional multivariate models," Letters in Spatial and Resource Sciences, Springer, vol. 11(1), pages 57-70, March.
    11. Haixiang Zhang & Jun Chen & Zhigang Li & Lei Liu, 2021. "Testing for Mediation Effect with Application to Human Microbiome Data," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 13(2), pages 313-328, July.
    12. Defever, F. & Riaño, A., 2022. "Firm-Destination Heterogeneity and the Distribution of Export Intensity," Working Papers 22/01, Department of Economics, City University London.
    13. Candau, Fabien & Regnacq, Charles & Schlick, Julie, 2022. "Climate change, comparative advantage and the water capability to produce agricultural goods," World Development, Elsevier, vol. 158(C).
    14. Lisa-Marie Schröder & Vito Bobek & Tatjana Horvat, 2021. "Determinants of Success of Businesses of Female Entrepreneurs in Taiwan," Sustainability, MDPI, vol. 13(9), pages 1-23, April.
    15. 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.
    16. Morais, Joanna & Thomas-Agnan, Christine & Simioni, Michel, 2017. "Interpreting the impact of explanatory variables in compositional models," TSE Working Papers 17-805, Toulouse School of Economics (TSE).
    17. Berta Ferrer-Rosell & Eva Martin-Fuentes & Estela Marine-Roig, 2020. "Diverse and emotional: Facebook content strategies by Spanish hotels," Information Technology & Tourism, Springer, vol. 22(1), pages 53-74, March.
    18. Chunmei Zhang & Lingen Wang, 2023. "Evaluating the Health of Urban Human Settlements," Sustainability, MDPI, vol. 15(4), pages 1-15, February.
    19. Gao, Cheng & Wang, Dan & Sun, Yuying & Wang, Wei & Zhang, Xiuyu, 2023. "Optimal load dispatch of multi-source looped district cooling systems based on energy and hydraulic performances," Energy, Elsevier, vol. 274(C).
    20. Dargel, Lukas & Thomas-Agnan, Christine, 2024. "Pairwise share ratio interpretations of compositional regression models," Computational Statistics & Data Analysis, Elsevier, vol. 195(C).

    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:hal:wpaper:hal-01563362. 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: CCSD (email available below). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    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.