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A New Item Response Theory Modeling Approach with Applications to Unidimensionality Assessment and Ability Estimation

Published online by Cambridge University Press:  01 January 2025

William F. Strout
William F. Strout*
Affiliation:
Department of Statistics, University of Illinois at Urbana-Champaign
*
Requests for reprints should be sent to William F. Stout, Department of Statistics, University of Illinois at Urbana-Champaign, 725 South Wright Street, Champaign, IL 61820.
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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 appropriate statistically 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 any Balanced empirical scaling. A variation of this estimation approach allows consistent estimation of ability on the given latent ability scale.

Keywords

Local independenceessential independenceessential traitintrinsic ability scalemarginal item responnse functionlatent dimensionalitymultidimensionalityessential unidimensionnalityitem response theorylatent trait theoryability estimationnconsistent estimationnnonparametricbalanced linear formula scoreinfinite item pool
Type
Original Paper
Information
Psychometrika , Volume 55 , Issue 2 , June 1990 , pp. 293 - 325
Copyright
Copyright © 1990 The Psychometric Society

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Footnotes

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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