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Impact of media investments on brands' market shares: a compositional data analysis approach
Abstract
The aim of this CIFRE thesis, realized with the market research institute BVA in collaboration with the automobile manufacturer Renault, is to build a model in order to measure the impact of media investments of several channels (television, outdoor, etc.) on the brands' market shares, taking into account the competition et the potential cross effects and synergies between brands, as well as controlling for average price and regulatory context (scrapping incentive).Market share models have been developed in the marketing literature, especially the GMCI model (generalized multiplicative competitive interaction model), inspired from the aggregated conditional MNL (multinomial logit) model. In the statistical literature, the compositional data analysis (CODA) allows to analyze share data respecting their nature (a vector of D shares subject to the unit sum constraint is a composition and belongs to the dimension D simplex space). Regression models for dependent and explanatory compositional variables exist but are rarely used in practice. Finally, the Dirichlet covariate model allows to model a simplex valued dependent variable.In the first chapter, these different models avec compared from a theoretical and empirical point of view. It is shown that all of them can be expressed with a similar formulation using the notions of attraction and of simplicial expected value. The GMCI model appears to be a particular case of the CODA model, such that these two specifications can be combined into a unique model. The complexity of Dirichlet and CODA models turns out to be necessary in order to capture the diversity of competitive relationships. In the second chapter, emphasis is given to the interpretation of models which is not very well developed in the CODA literature. Different types of interpretations are presented, but it is demonstrated that the calculation of the elasticities of market shares relative to media investments in particularly relevant from a mathematical point of view and from a practical perspective. Indeed, we prove that elasticities are consistent with C-derivatives of simplex valued functions of another simplex. Moreover, these elasticities can be easily interpreted by car manufacturers and can be used for advertising budgeting optimization (Dorfman-Steiner theorem). In the third chapter, a practical application to the B segment of the French automobile market is presented for the purpose of measuring the impact of the different advertising channels on the market shares of the three leaders of this segment and of the group of other brands, taking into account the lagged effects of advertising (adstock function) and the competitive cross effects. The media investments elasticity of the brand market share varies from one brand to another and from one channel to another. Synergies between some brands can be highlighted. The last chapter opens the discussion on different directions to be explored in order to improve the proposed model and to provide further answers to the considered issue.
... , x D summing to 1. (Aitchison, 1986) Compositional data are common in economics, and more particularly the study of shares, initiated by Woodland (1979) and completed by . Recently, Morais (2017) proposes an analysis of compositional time series and Fry (2011) a panorama of compositional data applications in economics. ...
L'économétrie permet de formaliser et de styliser un phénomène économique. Au fil du temps, les économètres font face à de nouveaux problèmes liés à l'évolution des données. À titre d'exemple, la prédominance de données massives ou les nouvelles réformes sur la protection des données font évoluer la nature, la forme ou encore la disponibilité des données. Cette transformation soulève de nouveaux défis et problèmes pratiques dans la prise en compte de ces données par les économètres. L'objectif de cette thèse est de proposer et d'étudier des méthodologies adaptées aux données imparfaites, plus particulièrement, les variables agrégées et les variables dépendantes limitées à travers deux phénomènes économiques : premièrement, les mesures d'inégalités, et deuxièmement, l'indemnisation des dommages corporels. Dans chaque contexte, un ensemble de méthodes pertinentes est proposé afin d'appréhender les données disponibles et d'expliquer chaque phénomène. Dans le cadre des données agrégées, elle fournit une étude des variables compositionnelles liée à l’agrégation des données catégorielles (Chapitre I) et une méthode d’estimation des mesures d’inégalités à partir des données quantiles (Chapitre II). Dans le cadre des données censurées, elle propose une méthode d’analyse des montants d’indemnisation pour les préjudices corporels (Chapitre III).
... Finally for a function f from S D X , to S D Y , a similar approximation has been obtained in Morais (2017) for the particular case D X = D Y . Combining the above two results, we obtain easily that the Taylor approximation of a function f from S D X to S D Y is given by ...
In the framework of Compositional Data Analysis, vectors carrying relative information, also called compositional vectors, can appear in regression models either as dependent or as explanatory variables. In some situations, they can be on both sides of the regression equation. Measuring the marginal impacts of covariates in these types of models is not straightforward since a change in one component of a closed composition automatically affects the rest of the composition.
Previous work by the authors has shown how to measure, compute and interpret these marginal impacts in the case of linear regression models with compositions on both sides of the equation. The resulting natural interpretation is in terms of an elasticity, a quantity commonly used in econometrics and marketing applications. They also demonstrate the link between these elasticities and simplicial derivatives.
The aim of this contribution is to extend these results to other situations, namely when the compositional vector is on a single side of the regression equation. In these cases, the marginal impact is related to a semi-elasticity and also linked to some simplicial derivative. Moreover we consider the possibility that a total variable is used as an explanatory variable, with several possible interpretations of this total and we derive the elasticity formulas in that case.
Previous research suggests that a multinomial logit model of market share can be used in optimization or equilibrium analyses of marketing decision making. However, there are significant problems with the solutions obtained from such an analysis. The authors show that for any firm with less than a 50% market share, the profit maximizing solution is to increase advertising as much as possible. The same holds true for any other positively signed marketing mix variable. The exponential property of the MNL model precludes reasonable descriptions of firm behavior in this case. Thus, the MNL market share model is inappropriate for equilibrium analysis of marketing competition.
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). Alternative models, from the compositional data analysis literature, allow a large complexity but their interpretation is not straightforward (Model B). This paper combines both approaches 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.
Logical consistency of market share models has received considerable attention in the recent marketing literature. The reports suggest that, at least theoretically, attraction-type specifications are more easily justified than the ones commonly used in empirical work. The authors examine whether the theoretical superiority also implies a better predictive performance. The empirical results give a tentatively affirmative answer.
It is difficult to imagine that the statistical analysis of compositional data has been a major issue of concern for more than 100 years. It is even more difficult to realize that so many statisticians and users of statistics are unaware of the particular problems affecting compositional data, as well as their solutions. The issue of spurious correlation'', as the situation was phrased by Karl Pearson back in 1897, affects all data that measures parts of some whole, such as percentages, proportions, ppm and ppb. Such measurements are present in all fields of science, ranging from geology, biology, environmental sciences, forensic sciences, medicine and hydrology. This book presents the history and development of compositional data analysis along with Aitchison's log-ratio approach. Compositional Data Analysis describes the state of the art both in theoretical fields as well as applications in the different fields of science. Key Features: • Reflects the state-of-the-art in compositional data analysis. • Gives an overview of the historical development of compositional data analysis, as well as basic concepts and procedures. • Looks at advances in algebra and calculus on the simplex. • Presents applications in different fields of science, including, genomics, ecology, biology, geochemistry, planetology, chemistry and economics. • Explores connections to correspondence analysis and the Dirichlet distribution. • Presents a summary of three available software packages for compositional data analysis. • Supported by an accompanying website featuring R code. Applied scientists working on compositional data analysis in any field of science, both in academia and professionals will benefit from this book, along with graduate students in any field of science working with compositional data.
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.