Polyhedral methods for choice-based conjoint analysis provide a means to adapt choice-based questions at the individual-respondent level and provide an alternative means to estimate partworths when there are relatively few questions per respondent as in a web-based questionnaire. However, these methods are deterministic and are susceptible to the propagation of response errors. They also assume, implicitly, a uniform prior on the partworths. In this paper we provide a probabilistic interpretation of polyhedral methods and propose improvements that incorporate response error and/or informative priors into individual-level question selection and estimation.
Monte Carlo simulations suggest that response-error modeling and informative priors improve polyhedral question-selection methods in the domains where they were previously weak. A field experiment with over 2,200 leading-edge wine consumers in the US, Australia, and New Zealand, suggests that the new question-selection methods show promise relative to existing methods.
Toubia, Olivier, John Hauser, and Rosanna Garcia. "Probabilistic Polyhedral Methods for Adaptive Choice-Based Conjoint Analysis: Theory and Application." Marketing Science 26, no. 5 (2007): 596-610.
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