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On Bayesian Testing of Additive Conjoint Measurement Axioms Using Synthetic Likelihood


  • George Karabatsos

    () (University of Illinois-Chicago)


Abstract 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.

Suggested Citation

  • George Karabatsos, 2018. "On Bayesian Testing of Additive Conjoint Measurement Axioms Using Synthetic Likelihood," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 321-332, June.
  • Handle: RePEc:spr:psycho:v:83:y:2018:i:2:d:10.1007_s11336-017-9581-x
    DOI: 10.1007/s11336-017-9581-x

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    References listed on IDEAS

    1. Tim Robertson & Giles Warrack, 1985. "An application of order restricted inference methodology to a problem in psychiatry," Psychometrika, Springer;The Psychometric Society, vol. 50(4), pages 421-427, December.
    2. J. Kruskal, 1964. "Nonmetric multidimensional scaling: A numerical method," Psychometrika, Springer;The Psychometric Society, vol. 29(2), pages 115-129, June.
    3. Hoffman, Peter B. & Beck, James L., 1974. "Parole decision-making: A salient factor score," Journal of Criminal Justice, Elsevier, vol. 2(3), pages 195-206.
    4. Ben Domingue, 2014. "Evaluating the Equal-Interval Hypothesis with Test Score Scales," Psychometrika, Springer;The Psychometric Society, vol. 79(1), pages 1-19, January.
    5. Jan Toporowski & Jo Michell, 2012. "Introduction," Chapters,in: Handbook of Critical Issues in Finance, pages i-ii Edward Elgar Publishing.
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