Testing Measurement Theory Axioms within a Bayesian Framework

Abstract

Measurement theories are of fundamental importance for quantification within the social sciences. Probabilistic measurement theory translates measurement theory axioms formulated in algebraic terms into a form suited to empirical testing. The statistical issues that arise in testing these choice probabilities have not received much attention in the statistical community. To facilitate research interest in this area, this presentation proposes testing measurement theory axioms within a Bayesian framework, and illustrates it with models of nonparametric item response theory.