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Identification of a Semiparametric Item Response Model

Published online by Cambridge University Press:  01 January 2025

Michael Peress
Michael Peress*
Affiliation:
University of Rochester
*
Requests for reprints should be sent to Michael Peress, Department of Political Science, University of Rochester, Rochester, NY, USA. E-mail: mperess@mail.rochester.edu
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Abstract

We consider the identification of a semiparametric multidimensional fixed effects item response model. Item response models are typically estimated under parametric assumptions about the shape of the item characteristic curves (ICCs), and existing results suggest difficulties in recovering the distribution of individual characteristics under nonparametric assumptions. We show that if the shape of the ICCs are unrestricted, but the shape is common across individuals and items, the individual characteristics are identified. If the shape of the ICCs are allowed to differ over items, the individual characteristics are identified in the multidimensional linear compensatory case but only identified up to a monotonic transformation in the unidimensional case. Our results suggest the development of two new semiparametric estimators for the item response model.

Keywords

item response theorynonparametric identification
Type
Original Paper
Information
Psychometrika , Volume 77 , Issue 2 , April 2012 , pp. 223 - 243
Copyright
Copyright © 2012 The Psychometric Society

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Footnotes

Electronic Supplementary Material The online version of this article (doi: 10.1007/s11336-012-9253-9) contains supplementary material, which is available to authorized users.

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