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). 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.
Highlights
We are interested in modeling the impact of media investments on the distribution of automobile manufacturer sales
Car manufacturers spend millions of euros in media investments to enhance their image, giving rise to the following question: do the media investments have an impact on brands market-shares8? In order to answer this question in the present paper, we model brands market-shares of the B segment of the French automobile market9 as a function of brand media investments, of brand average catalogue price and of a scrapping incentive dummy variable
All explanatory variables are significant at 0.1% according to the analysis of variance (ANOVA)
Summary
We are interested in modeling the impact of media investments on the distribution of automobile manufacturer sales. From the marketing or econometric literature, are perfectly adapted to model market-shares and to interpret direct and cross impacts of media investments, but the proposed models are quite simple and do not allow the specification of cross effects between brands. Elasticities are useful to isolate the impact of an explanatory variable on a particular share as they correspond to the relative variation of a component with respect to the relative variation of an explanatory variable, ceteris paribus (in a simplex sense) We show that they can be computed from the transformed model or equivalently from the model in the simplex. The models are interpreted using marginal effects, elasticities and odds ratios, and they are compared using the Fisher test and in terms of (out-of-sample) goodness-of-fit using quality measures adapted for share data. The last section concludes on the findings and on further directions to be investigated
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