Exact MCMC for Choices from Menus -- Measuring Substitution and Complementarity among Menu Items

64 Pages Posted: 24 Apr 2017 Last revised: 8 May 2019

See all articles by Tetyana Kosyakova

Tetyana Kosyakova

Frankfurt School of Finance & Management gemeinnützige GmbH

Thomas Otter

Goethe University Frankfurt - Department of Marketing

Sanjog Misra

University of Chicago - Booth School of Business

Christian Neuerburg

GfK SE

Date Written: April 30, 2019

Abstract

Choice environments in practice are often more complicated than the well studied case of choice between perfect substitutes. Consumers choosing from menus or configuring products face choice sets that consist of substitutes, complements and independent items, and the utility maximizing choice corresponds to a particular item combination out of a potentially huge number of possible combinations. This reality is mirrored in menu-based choice experiments. The inferential challenge posed by data from such choices is in the calibration of utility functions that accommodate a mix of substitutes, complements, and independent items. We develop a model that not only accounts for heterogeneity in preferences but also in what consumers perceive to be substitutes and complements and show how to perform Bayesian inference for this model based on the exact likelihood, despite its practically intractable normalizing constant. We characterize the model from first principles and show how it structurally improves on the multivariate probit model (Liechty et al., 2001) and on models that include cross-price effects in the utility function (Orme, 2010). We find empirical support for our model in a menu-based discrete choice experiment investigating demand for game consoles and accessories. Finally, we illustrate substantial implications from modeling substitution and complementarity for optimal pricing.

Keywords: menu based choice, choice modeling, autologistic choice model, hierarchical Bayes

JEL Classification: C11, C51, M31,

Suggested Citation

Kosyakova, Tetyana and Otter, Thomas and Misra, Sanjog and Neuerburg, Christian, Exact MCMC for Choices from Menus -- Measuring Substitution and Complementarity among Menu Items (April 30, 2019). Available at SSRN: https://ssrn.com/abstract=2957105 or http://dx.doi.org/10.2139/ssrn.2957105

Tetyana Kosyakova

Frankfurt School of Finance & Management gemeinnützige GmbH ( email )

Adickesallee 32-34
Frankfurt am Main, 60322
Germany

Thomas Otter (Contact Author)

Goethe University Frankfurt - Department of Marketing ( email )

Frankfurt
Germany
++49.69.798.34646 (Phone)

HOME PAGE: http://www.marketing.uni-frankfurt.de/index.php?id=97?&L=1

Sanjog Misra

University of Chicago - Booth School of Business ( email )

5807 South Woodlawn Avenue
Chicago, IL 60637
United States

Christian Neuerburg

GfK SE ( email )

Nürnberg
Germany

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