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Identifiability of Nonlinear Logistic Test Models

Published online by Cambridge University Press:  01 January 2025

Timo M. Bechger ,
Norman D. Verhelst  and
Huub H. F. M. Verstralen
Timo M. Bechger*
Affiliation:
National Institute for Educational Measurement (Cito)
Norman D. Verhelst
Affiliation:
National Institute for Educational Measurement (Cito)
Huub H. F. M. Verstralen
Affiliation:
National Institute for Educational Measurement (Cito)
*
Requests for reprints should be sent to Timo M. Bechger, National Institute of Educational Measurement (Cito), P.O. Box 1034, 6801 MG Arnhem, THE NETHERLANDS. E-Mail: [email protected]
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Abstract

The linear logistic test model (LLTM) specifies the item parameters as a weighted sum of basic parameters. The LLTM is a special case of a more general nonlinear logistic test model (NLTM) where the weights are partially unknown. This paper is about the identifiability of the NLTM. Sufficient and necessary conditions for global identifiability are presented for a NLTM where the weights are linear functions, while conditions for local identifiability are shown to require a model with less restrictions. It is also discussed how these conditions are checked using an algorithm due to Bekker, Merckens, and Wansbeek (1994). Several illustrations are given.

Keywords

linear logistic test modelidentifiabilityitem response theorycomponential item response theorynonlinear logistic test models
Type
Articles
Information
Psychometrika , Volume 66 , Issue 3 , September 2001 , pp. 357 - 371
Copyright
Copyright © 2001 The Psychometric Society

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Footnotes

This article was written while the first author was a post doctoral fellow at the university of Twente. He gratefully acknowledges the university's hospitality and the financial support by NWO (project nr. 30002).

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