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Interpretation of explanatory variables impacts in compositional regression models

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.
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Joanna Morais, Christine Thomas-Agnan, Michel Simioni. Interpretation of explanatory variables impacts in compositional regression models. Austrian Journal of Statistics, 2018, 47 (5), pp.1-25. ⟨10.17713/ajs.v47i5.718⟩. ⟨hal-02617783⟩



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