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Estimating Difficulty from Polytomous Categorical Data

Published online by Cambridge University Press:  01 January 2025

Javier Revuelta
Javier Revuelta*
Affiliation:
Autonoma University of Madrid
*
Requests for reprints should be sent to Javier Revuelta, Department of Social Psychology and Methodology, Autonoma University of Madrid, 28049 Madrid, Spain. E-mail: javier.revuelta@uam.es
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Abstract

A comprehensive analysis of difficulty for multiple-choice items requires information at different levels: the test, the items, and the alternatives. This paper introduces a new parameterization of the nominal categories model (NCM) for analyzing difficulty at these three levels. The new parameterization is referred to as the NE–NCM and is statistically equivalent to the NCM. The NE–NCM is applied to a sample of responses from a logical analysis test. The results suggest that the individuals execute a self-terminated response process that is mostly determined by working memory load.

Keywords

nested effects parameterizationnominal categories modelgeneralized logit-linear item response modelidentifiabilitypolytomous item response theory
Type
Original Paper
Information
Psychometrika , Volume 75 , Issue 2 , June 2010 , pp. 331 - 350
Copyright
Copyright © 2010 The Psychometric Society

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Footnotes

I would like to thank the editor and three anonymous reviewers for their comments, which contributed to improvements on earlier versions of this paper.

This work was supported by the Comunidad de Madrid (Spain) grant: CCG07-UAM/ESP-1615.

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