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. (PsycINFO Database Record

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