Polyhedral Methods for Adaptive Choice-Based Conjoint Analysis
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Author(s)
Toubia, Olivier
Hauser, John
Simester, Duncan
Date Issued
February 26, 2003
Series/Report no.
MIT Sloan School of Management Working Paper;4285-03
Abstract
Choice-based conjoint analysis (CBC) is used widely in marketing for product design,
segmentation, and marketing strategy. We propose and test a new "polyhedral"
question-design method that adapts each respondent's choice sets based on previous
answers by that respondent. Individual adaptation appears promising because, as
demonstrated in the aggregate customization literature, question design can be
improved based on prior estimates of the respondent's partworths – information that is
revealed by respondents' answers to prior questions. The otherwise impractical
computational problems of individual CBC adaptation become feasible based on
recent polyhedral "interior-point" algorithms, which provide the rapid solutions
necessary for real-time computation. To identify domains where individual adaptation
is promising (and domains where it is not), we evaluate the performance of polyhedral
CBC methods with Monte Carlo experiments. We vary magnitude (response
accuracy), respondent heterogeneity, estimation method, and question-design method
in a 4x23 experiment. The estimation methods are Hierarchical-Bayes estimation (HB)
and Analytic-Center estimation (AC). The latter is a new individual-level estimation
procedure that is a by-product of polyhedral question design. The benchmarks for
individual adaptation are random designs, orthogonal designs, and aggregate
customization. The simulations suggest that polyhedral question design does well in
many domains, particularly those in which heterogeneity and partworth magnitudes are
relatively large. In the comparison of estimation methods, HB is strong across all
domains, but AC estimation shows promise when heterogeneity is high. We close by
describing an empirical application to the design of executive education programs in
which 354 web-based respondents answered stated-choice tasks with four service
profiles each. The profiles varied on eight multi-level features. With the help of this
study a major university is revising its executive education programs with new formats
and a new focus.
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