Using compositional and Dirichlet models for market share regression

When the aim is to model market shares, the marketing literature proposes some regression models which can be qualified as attraction models. They are generally derived from an aggregated version of the multinomial logit model. But aggregated multinomial logit models (MNL) and the so-called generalized multiplicative competitive interaction models (GMCI) present some limitations: in their simpler version they do not specify brand-specific and cross effect parameters. In this paper, we consider alternative models: the Dirichlet model (DIR) and the compositional model (CODA). DIR allows to introduce brand-specific parameters and CODA allows additionally to consider cross effect parameters. We show that these two models can be written in a similar fashion, called attraction form, as the MNL and the GMCI models. As market share models are usually interpreted in terms of elasticities, we also use this notion to interpret the DIR and CODA models. We compare the properties of the models in order to explain why CODA and DIR models can outperform traditional market share models. An application to the automobile market is presented where we model brands market shares as a function of media investments, controlling for the brands price and scrapping incentive. We compare the quality of the models using measures adapted to shares.