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A new item response theory modeling approach with applications to unidimensionality assessment and ability estimation

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Abstract

Using an infinite item test framework, it is argued that the usual assumption of local independence be replaced by a weaker assumption,essential independence. A fortiori, the usual assumption of unidimensionality is replaced by a weaker and arguably more appropriatestatistically testable assumption of essential unidimennsionality. Essential unidimennsionnality implies the existence of a “unique” unidimensional latent ability. Essential unidimensionality is equivalent to the “consistent” estimation of this latnet ability in an ordinal scaling sense using anyBalanced empirical scaling. A variation of this estimation approach allows consistent estimation of ability on the given latent ability scale.

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Authors and Affiliations

  1. Department of Statistics, University of Illinois at Urbana-Champaign, 725 South Wright Street, 61820, Champaign, IL

    William F. Strout

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  1. William F. Strout
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Additional information

I wish to thank Brian Junker for useful comments and discussions resulting from his careful and thoughtful reading of the manuscript. I wish to thank Charles Davis for useful comments that lead to several improvements, in particular in section 3 and 4. I wish to thank D. R. Divgi for an insight that lead to a useful reformulation of essential independence. Lloyd Humphreys' steadfast insistence that tests items are inherently “multiply determined” provided the empirical grounding for essential dimensionality. Remarks by Mark Reckase and Ming-mei Wang were also helpful.

This research was supported by Office of Naval Reserch Grant N00014-87-K-0277 and National Science Foundation Grant NSF-DMS-88-02556.

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Strout, W.F. A new item response theory modeling approach with applications to unidimensionality assessment and ability estimation. Psychometrika 55, 293–325 (1990). https://doi.org/10.1007/BF02295289

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