Flexible Mixture-Amount Models for Business and Industry Using Gaussian Processes

Tinbergen Institute Discussion Paper 16-075/III

38 Pages Posted: 13 Sep 2016

See all articles by Aiste Ruseckaite

Aiste Ruseckaite

Erasmus University Rotterdam (EUR) - Department of Econometrics

D. Fok

Econometric Institute - Erasmus University Rotterdam; Erasmus Research Institute of Management (ERIM); Tinbergen Institute Rotterdam

Peter Goos

University of Antwerp; KU Leuven

Date Written: September 9, 2016

Abstract

Many products and services can be described as mixtures of ingredients whose proportions sum to one. Specialized models have been developed for linking the mixture proportions to outcome variables, such as preference, quality and liking. In many scenarios, only the mixture proportions matter for the outcome variable. In such cases, mixture models suffice. In other scenarios, the total amount of the mixture matters as well. In these cases, one needs mixture- amount models. As an example, consider advertisers who have to decide on the advertising media mix (e.g. 30% of the expenditures on TV advertising, 10% on radio and 60% on online advertising) as well as on the total budget of the entire campaign. To model mixture-amount data, the current strategy is to express the response in terms of the mixture proportions and specify mixture parameters as parametric functions of the amount. However, specifying the functional form for these parameters may not be straightforward, and using a flexible functional form usually comes at the cost of a large number of parameters.

In this paper, we present a new modeling approach which is flexible but parsimonious in the number of parameters. The model is based on so-called Gaussian processes and avoids the necessity to a-priori specify the shape of the dependence of the mixture parameters on the amount. We show that our model encompasses two commonly used model specifications as extreme cases. Finally, we demonstrate the model’s added value when compared to standard models for mixture-amount data. We consider two applications. The first one deals with the reaction of mice to mixtures of hormones applied in different amounts. The second one concerns the recognition of advertising campaigns. The mixture here is the particular media mix (TV and magazine advertising) used for a campaign. As the total amount variable, we consider the total advertising campaign exposure.

Keywords: Gaussian process prior, Nonparametric Bayes, Advertising mix, In- gredient proportions, Mixtures of ingredients

JEL Classification: C01, C02, C11, C14, C51, C52

Suggested Citation

Ruseckaite, Aiste and Fok, Dennis and Goos, Peter, Flexible Mixture-Amount Models for Business and Industry Using Gaussian Processes (September 9, 2016). Tinbergen Institute Discussion Paper 16-075/III. Available at SSRN: https://ssrn.com/abstract=2837626 or http://dx.doi.org/10.2139/ssrn.2837626

Aiste Ruseckaite (Contact Author)

Erasmus University Rotterdam (EUR) - Department of Econometrics ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Dennis Fok

Econometric Institute - Erasmus University Rotterdam ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Erasmus Research Institute of Management (ERIM) ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands
+31 10 408 1333 (Phone)
+31 10 408 9162 (Fax)

Tinbergen Institute Rotterdam ( email )

P.O. Box 1738
3000 DR Rotterdam
Netherlands

Peter Goos

University of Antwerp ( email )

Prinsstraat 13
Antwerp, Antwerp 2000
Belgium

KU Leuven ( email )

Oude Markt 13
Leuven, Vlaams-Brabant 3000
Belgium

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