, Volume 53, Issue 3, pp 349–359 | Cite as

Items bundles

  • Paul R. Rosenbaum


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 independencebetween but not necessarilywithin item bundles.

Key words

item response theory latent variable models associated random variables conditional association stochastic partial order 


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Copyright information

© The Psychometric Society 1988

Authors and Affiliations

  • Paul R. Rosenbaum
    • 1
  1. 1.Department of Statistics, The Wharton SchoolUniversity of PennsylvaniaPhiladelphia

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