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A boundary mixture approach to violations of conditional independence. (English) Zbl 1208.62182

Summary: 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.

MSC:

62P15 Applications of statistics to psychology
62H10 Multivariate distribution of statistics
65C60 Computational problems in statistics (MSC2010)
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