A Boundary Mixture Approach to Violations of Conditional Independence

Author: Braeken, Johan

Source: Psychometrika, Volume 76, Number 1, January 2011 , pp. 57-76(20)

Publisher: Springer

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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 bounds; conditional independence; copula function; local item dependencies

Document Type: Research Article

DOI: http://dx.doi.org/10.1007/s11336-010-9190-4

Affiliations: Department of Methodology and Statistics, Tilburg University, Tilburg, The Netherlands, Email: j.braeken@uvt.nl

Publication date: January 1, 2011

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