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A tour of regression models for explaining shares

Author

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  • Morais, Joanna
  • Simioni, Michel
  • Thomas-Agnan, Christine

Abstract

This paper aims to present and compare statistical modeling methods adapted for shares as dependent variables. Shares are characterized by the following constraints: positivity and sum equal to 1. Four types of models satisfy this requirement: multinomial logit models widely used in discrete choice models of the econometric literature, market-share models from the marketing literature, Dirichlet covariate models and compositional regression models from the statistical literature. We highlight the properties, the similarities and the differences between these models which are coming from the assumptions made on the distribution of the data and from the estimation methods. We prove that all these models can be written in an attraction model form, and that they can be interpreted in terms of direct and cross elasticities. An application to the automobile market is presented where we model brand market-shares as a function of media investments in 6 channels in order to measure their impact, controlling for the brands average price and a scrapping incentive dummy variable. We propose a cross-validation method to choose the best model according to different quality measures.

Suggested Citation

  • 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).
  • Handle: RePEc:tse:wpaper:31265
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    References listed on IDEAS

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    2. J. L. Scealy & A. H. Welsh, 2011. "Regression for compositional data by using distributions defined on the hypersphere," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(3), pages 351-375, June.
    3. Kumar, V., 1994. "Forecasting performance of market share models: an assessment, additional insights, and guidelines," International Journal of Forecasting, Elsevier, vol. 10(2), pages 295-312, September.
    4. Javier Palarea-Albaladejo & Josep Martín-Fernández & Jesús Soto, 2012. "Dealing with Distances and Transformations for Fuzzy C-Means Clustering of Compositional Data," Journal of Classification, Springer;The Classification Society, vol. 29(2), pages 144-169, July.
    5. 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.
    6. Masao Nakanishi & Lee G. Cooper, 1982. "Technical Note—Simplified Estimation Procedures for MCI Models," Marketing Science, INFORMS, vol. 1(3), pages 314-322.
    7. Wang, Huiwen & Liu, Qiang & Mok, Henry M.K. & Fu, Linghui & Tse, Wai Man, 2007. "A hyperspherical transformation forecasting model for compositional data," European Journal of Operational Research, Elsevier, vol. 179(2), pages 459-468, June.
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    Cited by:

    1. 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).
    2. Joanna Morais & Christine Thomas-Agnan & Michel Simioni, 2017. "Interpretation of explanatory variables impacts in compositional regression models," Working Papers hal-01563362, HAL.
    3. 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).

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    More about this item

    Keywords

    Multinomial logit; Market-shares models; Compositional data analysis; Dirichlet regression;
    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
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis
    • M31 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Marketing and Advertising - - - Marketing

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