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Items Bundles

Published online by Cambridge University Press:  01 January 2025

Paul R. Rosenbaum
Paul R. Rosenbaum*
Affiliation:
University of Pennsylvania
*
Requests for reprints should be sent to Paul R. Rosenbaum, Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, PA 19104-6302.
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Abstract

An item bundle is a small group of multiple choice items that share a common reading passage or graph, or a small group of matching items that share distractors. Item bundles are easily identified by paging through a copy of a test. Bundled items may violate the latent conditional independence assumption of unidimensional item response theory (IRT), but such a violation would not typically suggest the existence of a new fundamental human ability to read one specific reading passage or to interpret one specific graph. It is important, therefore, to have theoretical concepts and empirical checks that distinguish between, on the one hand, anticipated violations of latent conditional independence within item bundles, and, on the other hand, violations that cannot be attributed to idiosyncratic features of test format and instead suggest departures from unidimensionalty. To this end, two theorems on unidimensional IRT are extended to describe observable item response distributions when there is conditional independence between but not necessarily within item bundles.

Keywords

item response theorylatent variable modelsassociated random variablesconditional associationstochastic partial order
Type
Article
Information
Psychometrika , Volume 53 , Issue 3 , September 1988 , pp. 349 - 359
Copyright
Copyright © 1988 The Psychometric Society

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Footnotes

The author is grateful to Ivo Molenaar and the referees for many helpful suggestions, and to D. Thayer for assistance with computing.

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