Bayesian Approaches for Testing Additivity Axioms

• 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): George Karabatsos*+ and In Jae Myung
• Companies: University of Illinois, Chicago and The Ohio State University
• Keywords: Bayesian inference ; order-restricted inference ; MCMC ; bagging ; axiom testing

Abstract

The assumption of additivity is ubiquitous in the quantitative sciences, as evidenced by the many linear models of applied statistics, and most models of behavioral decision making. A hierarchy of cancellation axioms characterizes this assumption, which specifies highly complex order-constraints on the dependent variable. With real data, this presentation illustrates two effective Bayesian approaches for empirically testing additivity axioms. The first approach specifies additivity order-constraints on the dependent variable, through the prior distribution of the parameters. We developed a Gibbs sampler that efficiently estimates the resulting order-constrained posterior distribution. The second approach, with the Bayesian bootstrap, implements bagging (bootstrap aggregation) to Kruskal's isotonic regression algorithm (MONANOVA) that transforms data (of the dependent variable) to predictions conforming to the additivity order-constraints. In order to empirically test the axioms, and to compare the data fit between different axioms, the first approach employs the deviance information criterion, and the second approach estimates generalization error.