On Bayesian Testing of Additive Conjoint Measurement Axioms Using Synthetic Likelihood
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This article introduces a Bayesian method for testing the axioms of additive conjoint measurement. The method is based on an importance sampling algorithm that performs likelihood-free, approximate Bayesian inference using a synthetic likelihood to overcome the analytical intractability of this testing problem. This new method improves upon previous methods because it provides an omnibus test of the entire hierarchy of cancellation axioms, beyond double cancellation. It does so while accounting for the posterior uncertainty that is inherent in the empirical orderings that are implied by these axioms, together. The new method is illustrated through a test of the cancellation axioms on a classic survey data set, and through the analysis of simulated data.
Keywordsaxiom testing conjoint measurement approximate Bayesian computation
The author is grateful for the detailed comments and suggestions by two anonymous reviewers and the Editor. They have helped improve the presentation of this article. Funding was provided by National Science Foundation (Grant Nos. SES-0242030 and SES-1156372).
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