| Abstract: |
When the aim is to model market-shares as a function of explanatory variables,
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 widely used in econometrics for
discrete choice modeling. But aggregated multinomial logit models (MNL) and
the so-called market-share models or generalized multiplicative competitive
interaction models (GMCI) present some limitations: in their simpler version
they do not specify brand-specific and cross-effect parameters. Introducing
all possible cross effects is not possible in the MNL and would imply a very
large number of parameters in the case of the GMCI. In this paper, we consider
alternative models which are the Dirichlet covariate 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 last 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 main properties of the models in order to
explain why CODA and DIR models can outperform traditional market-share
models. The benefits of highlighting these relationships is on one hand to
propose new models to the marketing literature and on the other hand to
improve the interpretation of the CODA and DIR models using the elasticities
of the econometrics literature. Finally, an application to the automobile
market is presented where we model brands market-shares as a function of media
investments, controlling for the brands average price and a scrapping
incentive dummy variable. We compare the goodness-of-fit of the various models
in terms of quality measures adapted to shares. |