Interpretation of Explanatory Variables Impacts in Compositional Regression Models

  • Joanna Morais Toulouse School of Economics, University of Toulouse 1 Capitole
  • Christine Thomas-Agnan Toulouse School of Economics, University of Toulouse 1 Capitole
  • Michel Simioni INRA, UMR 1110 MOISA, 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). Alternative models, from the compositional data analysis literature, allow a large complexity but their interpretation is not straightforward (Model B).  This paper combines both approaches 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.

Author Biographies

Joanna Morais, Toulouse School of Economics, University of Toulouse 1 Capitole

PhD student in applied mathematics at Toulouse School of Economics (last year).

Data scientist consultant at BVA Group.

Christine Thomas-Agnan, Toulouse School of Economics, University of Toulouse 1 Capitole
Professor in mathematics
Michel Simioni, INRA, UMR 1110 MOISA, Montpellier
Professor in economics

References

Chen J, Zhang X, Li S (2016). Multiple linear regression with compositional response and covariates." Journal of Applied Statistics, pp. 1-16.

Hron K, Filzmoser P, Thompson K (2012). Linear regression with compositional explanatory variables." Journal of Applied Statistics, 39(5), 1115-1128.

Morais J, Thomas-Agnan C, Simioni M (2016). A tour of regression models for explaining shares."

TSE Working Paper, (16-742). URL https://www.tse-fr.eu/fr/publications/tour-regression-models-explaining-shares.

Morais J, Thomas-Agnan C, Simioni M (2017). Using compositional and Dirichlet models for market-share regression." Working paper, URL https://hal.archives-ouvertes.fr/hal-01558527.

Pawlowsky-Glahn V, Buccianti A (2011). Compositional data analysis: Theory and applications. John Wiley & Sons.

Pawlowsky-Glahn V, Egozcue JJ, Tolosana-Delgado R (2015). Modeling and Analysis of Compositional Data. John Wiley & Sons.

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Analysing Compositional Data with R. Springer.

Wang H, Shangguan L, Wu J, Guan R (2013). Multiple linear regression modeling for compositional data.

Neurocomputing, 122, 490-500.

Published
2018-09-08
How to Cite
Morais, J., Thomas-Agnan, C., & Simioni, M. (2018). Interpretation of Explanatory Variables Impacts in Compositional Regression Models. Austrian Journal of Statistics, 47(5), 1-25. https://doi.org/10.17713/ajs.v47i5.718
Section
CoDaWork 2017