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            <title xml:lang="en">Using compositional and Dirichlet models for market-share regression</title>
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                <title xml:lang="en">Using compositional and Dirichlet models for market-share regression</title>
                <title xml:lang="fr">Utiliser les modèles de composition et de Dirichlet pour la régression de parts de marché</title>
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                <term xml:lang="en">Dirichlet regression</term>
                <term xml:lang="en">marketing</term>
                <term xml:lang="en">market-shares models</term>
                <term xml:lang="en">compositional data analysis</term>
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              <p>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.</p>
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              <p>Lorsque l'objectif est de modéliser des parts de marché, la littérature marketing propose des modèles de régression qui peuvent être qualifié de modèles d'attraction. Ils sont généralement dérivés d'une version agrégée du modèle multinomial logit. Mais le logit multinomial agrégé et le modèle d'attraction appelé generalized multiplicative competitive interaction models (GMCI) présentent quelques limitations : dans leur version simple, ils ne spécifient pas de paramètres propres aux marques ni d'effets croisés. Dans ce papier, nous considérons des modèles alternatifs : le modèle de Dirichlet (DIR) et le modèle de composition (CODA). DIR permet d'introduire des paramètres propres aux marques et CODA permet en plus de considérer des effets croisés. Nous montrons que ces deux modèles peuvent être exprimés sous une forme similaire, appelée formulation en attraction, comme les modèles MNL et GMCI.  Les modèles de parts de marché étant habituellement interprétés en termes d’élasticités, nous utilisons également cette notion pour interpréter les modèles DIR et CODA. Nous comparons les propriétés des modèles de manière à expliquer pourquoi les modèles CODA et DIR peuvent être plus performants que les modèles de parts de marché traditionnels. Une application au marché automobile est présentée où nous modélisons les parts de marché des marques en fonction des investissements médias, en contrôlant pour le prix des marques et l’existence ou non de prime à la casse. Nous comparons la qualité des modèles en utilisant des mesures adaptées aux données de parts.</p>
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