Bayesian Order-Constrained Analysis of Decision-Making Behavior

• Activity Number: 254
• Type: Contributed
• Date/Time: Tuesday, August 5, 2003 : 12:00 PM to 1:50 PM
• Sponsor: Section on Bayesian Stat. Sciences
• Author(s): In Jae Myung*+ and George Karabatsos
• Companies: The Ohio State University and University of Illinois, Chicago
• Keywords: axiomatic measurement theory ; order-constrained modeling ; MCMC ; isotonic regression ; Deviance Information Criterion ; posterior predictive p values

Abstract

Much of behavioral science data can be characterized by qualitative ordinal structures, which arise from research questions such as: "Does variable A increase or decrease with variable B" and "Do the subjects prefer object x over object y?" Measurement axioms are often used to summarize such structures as possible models of the behavior. However, it is difficult to test such axioms on data. Given that axioms are formulated in deterministic language, they cannot account for random error that confounds empirical data. The present study addresses this incompatibility by presenting a Bayes framework for axiom testing. Following the initial developments of Sedransk, et al. (1985), and using MCMC, the Bayesian approach infers the posterior distribution of a given axiom, conditional on a prior distribution that fully represents the order constraints implied by the axiom. The information provided by the posterior distribution then naturally lends to axiom testing via posterior predictive p values and axiom selection via DIC. We illustrate the approach by analyzing well-known axioms of decision-making such as consequence monotonicity and stochastic transitivity.