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Market Share Constraints and the Loss Function in Choice-Based Conjoint Analysis

Mendoza College of Business, University of Notre Dame, Notre Dame, Indiana 46556
Stephen M. Ross School of Business, University of Michigan, Ann Arbor, Michigan 48109
The Modellers, LLC, Salt Lake City, Utah 84047
tgilbrid{at}nd.edu
plenk{at}umich.edu
jeff.brazell{at}themodellers.com

Choice-based conjoint analysis is a popular marketing research technique to learn about consumers' preferences and to make market share forecasts under various scenarios for product offerings. Managers expect these forecasts to be "realistic" in terms of being able to replicate market shares at some prespecified or "base-case" scenario. Frequently, there is a discrepancy between the recovered and base-case market share. This paper presents a Bayesian decision theoretic approach to incorporating base-case market shares into conjoint analysis via the loss function. Because defining the base-case scenario typically involves a variety of management decisions, we treat the market shares as constraints on what are acceptable answers, as opposed to informative prior information. Our approach seeks to minimize the adjustment of parameters by using additive factors from a normal distribution centered at 0, with a variance as small as possible, but such that the market share constraints are satisfied. We specify an appropriate loss function, and all estimates are formally derived via minimizing the posterior expected loss. We detail algorithms that provide posterior distributions of constrained and unconstrained parameters and quantities of interest. The methods are demonstrated using discrete choice models with simulated data and data from a commercial market research study. These studies indicate that the method recovers base-case market shares without systematically distorting the preference structure from the conjoint experiment.

Key Words: Bayesian decision theory; conjoint analysis; constrained optimization; cross-validation; hierarchical Bayes; loss function; market share prediction; penalized maximum likelihood; posterior risk
History: Received: December 1, 2006;