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A Boundary Mixture Approach to Violations of Conditional Independence

Published online by Cambridge University Press:  01 January 2025

Johan Braeken
Johan Braeken*
Affiliation:
Tilburg University
*
Requests for reprints should be sent to Johan Braeken, Department of Methodology and Statistics, Tilburg University, Tilburg, The Netherlands. E-mail: j.braeken@uvt.nl
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Abstract

Conditional independence is a fundamental principle in latent variable modeling and item response theory. Violations of this principle, commonly known as local item dependencies, are put in a test information perspective, and sharp bounds on these violations are defined. A modeling approach is proposed that makes use of a mixture representation of these boundaries to account for the local dependence problem by finding a balance between independence on the one side and absolute dependence on the other side. In contrast to alternative approaches, the nature of the proposed boundary mixture model does not necessitate a change in formulation of the typical item characteristic curves used in item response theory. This has attractive interpretational advantages and may be useful for general test construction purposes.

Keywords

Fréchet–Hoeffding boundscopula functionlocal item dependenciesconditional independence
Type
Original Paper
Information
Psychometrika , Volume 76 , Issue 1 , January 2011 , pp. 57 - 76
Copyright
Copyright © 2010 The Psychometric Society

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