Interpretation of explanatory variables impacts in compositional regression models

Joanna Morais (), Christine Thomas-Agnan and Michel Simioni ()
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Joanna Morais: TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - UT - Université de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, BVA
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

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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 (ModelB).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.

Keywords: media investments impact; elasticity; model selection; odds ratio; marginal effect; market-shares; compositional model; compositional differential calculus (search for similar items in EconPapers)
Date: 2018
Note: View the original document on HAL open archive server: https://hal.inrae.fr/hal-02617783v1
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Citations: View citations in EconPapers (7)

Published in Austrian Journal of Statistics, 2018, 47 (5), pp.1-25. ⟨10.17713/ajs.v47i5.718⟩

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Related works:
Working Paper: Interpretation of explanatory variables impacts in compositional regression models (2017)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-02617783

DOI: 10.17713/ajs.v47i5.718

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