Abstract
The authors explore situations where consumers supplement their judgments with a measurement of uncertainty about their own preferences, either implicitly or explicitly, and develop two sets of hierarchical Bayesian conjoint models incorporating such measurements. The first set of models uses the relative location of a rating to determine the importance or weight given to the rating, in a regression setting. The second set uses interval judgment as a dependent variable in a regression setting. After specifying the models, the authors perform a theoretical comparison with a basic Bayesian regression model. They show that, under different conditions, the proposed models will yield more precise individual-level partworth estimates. Two simulated data examples and data from a conjoint study are used to illustrate the gains that could be obtained from modeling uncertainty. In the empirical application, the authors show that model fit improves when ratings for items that respondents do not like are given more weight compared to ratings for items that they do like.
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Notes
We make the assumption that essentially all of the relevant probability mass for each y ip is within a fixed interval (e.g., between 1 and 100). This assumption also holds for the scores given by the two different interval models. Clearly, there may be settings in which this assumption is not valid; in these cases, it is fairly straightforward to replace the normal density for the error term with a truncated normal density. The resulting model requires more sophisticated sampling strategies for the Markov chain Monte Carlo (MCMC) algorithms. One sampling strategy that would work well for relaxing this error assumption is the slice sampler, which we discuss in the Appendix.
One limitation of our modeling approaches is that the models cannot distinguish between uncertainty in the judgment scores and uncertainty in the utilities; stated differently, the covariance matrix of β i does not depend on the uncertainty measurements. Extending the models so that Λ is a function of uncertainty could distinguish between uncertainty in preference statements and uncertainty about the utility vector, which represents a fruitful area for further research.
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Liechty, J.C., Fong, D.K.H., Huizingh, E.K.R.E. et al. Hierarchical Bayesian conjoint models incorporating measurement uncertainty. Market Lett 19, 141–155 (2008). https://doi.org/10.1007/s11002-007-9026-x
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DOI: https://doi.org/10.1007/s11002-007-9026-x