Hilbert space multidimensional theory

Abstract

A general theory of measurement context effects, called Hilbert space multidimensional (HSM) theory, is presented. A measurement context refers to a subset of psychological variables that an individual evaluates on a particular occasion. Different contexts are formed by evaluating different but possibly overlapping subsets of variables. Context effects occur when the judgments across contexts cannot be derived from a single joint probability distribution over the complete set of values of the observed variables. HSM theory provides a way to model these context effects by using quantum probability theory, which represents all the variables within a low dimensional vector space. HSM models produce parameter estimates that provide a simple and informative interpretation of the complex collection of judgments across contexts. Comparisons of HSM model fits with Bayesian network model fits are reported for a new large experiment, demonstrating the viability of this new model. We conclude that the theory is broadly applicable to measurement context effects found in the social and behavioral sciences.