A Boundary Mixture Approach to Violations of Conditional Independence

Psychometrika volume 76, pages57–76(2011)Cite this article

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.

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  1. Department of Methodology and Statistics, Tilburg University, Tilburg, The Netherlands

    Johan Braeken

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  1. Johan Braeken
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Correspondence to Johan Braeken.

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Braeken, J. A Boundary Mixture Approach to Violations of Conditional Independence. Psychometrika 76, 57–76 (2011). https://doi.org/10.1007/s11336-010-9190-4

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Keywords

  • Fréchet–Hoeffding bounds
  • copula function
  • local item dependencies
  • conditional independence