University of Illinois-Chicago, Chicago, IL, USA.
Psychometrika. 2018 Jun;83(2):321-332. doi: 10.1007/s11336-017-9581-x. Epub 2017 Aug 25.
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.
本文介绍了一种用于检验可加联合测量公理的贝叶斯方法。该方法基于一种重要性抽样算法，通过合成似然函数进行无似然、近似贝叶斯推断，以克服该检验问题的分析复杂性。与之前的方法相比，这种新方法有所改进，因为它提供了对整个取消公理层次结构的全面检验，超出了双重取消。它通过考虑这些公理所隐含的经验排序的固有后验不确定性来实现这一点。通过对经典调查数据集上的取消公理进行测试以及对模拟数据进行分析，说明了新方法的有效性。
