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Asymptotic Identifiability of Nonparametric Item Response Models

Published online by Cambridge University Press:  01 January 2025

Jeffrey A. Douglas
Jeffrey A. Douglas*
Affiliation:
Department of Statistics, University of Illinois
*
Requests for reprints should be sent to Jeffrey A. Douglas, 101 Illini Hall, 725 South Wright Street, Champaign, IL. E-Mail: [email protected]
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Abstract

The identifiability of item response models with nonparametrically specified item characteristic curves is considered. Strict identifiability is achieved, with a fixed latent trait distribution, when only a single set of item characteristic curves can possibly generate the manifest distribution of the item responses. When item characteristic curves belong to a very general class, this property cannot be achieved. However, for assessments with many items, it is shown that all models for the manifest distribution have item characteristic curves that are very near one another and pointwise differences between them converge to zero at all values of the latent trait as the number of items increases. An upper bound for the rate at which this convergence takes place is given. The main result provides theoretical support to the practice of nonparametric item response modeling, by showing that models for long assessments have the property of asymptotic identifiability.

Keywords

nonparametric item response theorylarge sample theoryidentifiability
Type
Articles
Information
Psychometrika , Volume 66 , Issue 4 , December 2001 , pp. 531 - 540
Copyright
Copyright © 2001 The Psychometric Society

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Footnotes

The research was partially supported by the National Institute of Health grant R01 CA81068-01.

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