The Dirichlet Model: Analysis of a Market and Comparison of Estimation Procedures

This paper examines the Dirichlet model describing consumer behaviour. The model estimates brand performance measures in the case of repeat purchases over a set of brands. The Dirichlet model relies on some assumptions such as stationarity and the fact that the market is unsegmented. Its formulation derives from a combination of the Negative Binomial and the Dirichlet distributions. Various estimation methods have been proposed. The original one is an iterative procedure based on the method of moments and requires as inputs only aggregated quantities, such as brand penetrations and average purchase rates. There is also an estimation method based on likelihood maximization which requires raw individual or household panel data. The method of moments deserves attention, since raw panel data are frequently not available to researchers and/or enterprises. In this paper, the Dirichlet model is used to analyze the Italian beer market as a by-product of the main objective, which is to compare two estimation procedures available on-line for the method of moments: one based on an Excel Workbook and the other written in R. Neither procedures are very robust in the presence of atypical brands in the market.