Abstract
Discrete-choice experiments are commonly used to measure subjects’ preference structures and are often preferred to other measurement methods because they better align with actual choice behavior and avoid some of the well-documented biases inherent in alternative elicitation methods. A limitation of discrete-choice methods is the loss of inter-subject comparability because preference estimates are invariant to linear transformations necessitating indentifying constraints that remove a common, between-subjects utility scale. This constraint limits the application of discrete-choice results to situations where within-subject comparisons are meaningful. They enable one to sort options for each subject but not to sort subjects according to the relative intensity of their preferences. This paper uses auxiliary data to recover a common preference scale for between-subject comparisons. The model combines discrete-choice data with ratings data while adjusting for response biases due to method effects. The joint model moves the identification constraints from the sub-model for the discrete-choice data to the sub-model for the ratings data. The proposed methodology is complementary to willingness-to-pay computations when studies lack price or its economic foundation is untenable.
Notes
Note that the common scale origin we refer to is not necessarily an absolute origin. For instance, the utility scale from a cell-phone study may not be comparable to the utility scale from a career-choice study or to a medical procedure study. An absolute origin is not needed for comparing the utilities of different respondents in the same study. All that is required is that measurement be on a scale with the same origin for all respondents to be compared in the same study.
We assume here for explanatory purposes that the number of options is fixed across tasks, although our method does not require it.
Bayesians conflate fixed and random effects. We follow traditional terminology and call {φi} a “random effect” because we assume that it has a normal distribution across subjects. However, in estimating the model, we treat it as a fixed effect and estimate it for each subject instead of integrating it out of the likelihood function. The traditional approach to fixed effects does not assume a distribution for them.
We wish to thank Knowledge Networks for the data.
Best/Worst with 3 alternatives is equivalent to a full ranking.
We wish to thank Chris Chapman and Sawtooth Software for providing the data.
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Bacon, L., Lenk, P. Augmenting discrete-choice data to identify common preference scales for inter-subject analyses. Quant Mark Econ 10, 453–474 (2012). https://doi.org/10.1007/s11129-012-9124-9
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DOI: https://doi.org/10.1007/s11129-012-9124-9