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Equivalent MIRID Models

Published online by Cambridge University Press:  01 January 2025

Gunter Maris  and
Timo M. Bechger
Gunter Maris*
Affiliation:
CITO, National Institute for Educational Measurement
Timo M. Bechger
Affiliation:
CITO, National Institute for Educational Measurement
*
Requests for reprints should be sent to Dr. Gunter Marls, CITO, P.O. Box 1034, 6801 MG Arnhem, NETHERLANDS. E-mail: Gunter.Maris@citogroep.nl
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Abstract

It is shown that in the context of the Model with Internal Restrictions on the Item Difficulties (MIRID), different componential theories about an item set may lead to equivalent models. Furthermore, we provide conditions for the identifiability of the MIRID model parameters, and it will be shown how the MIRID model relates to the Linear Logistic Test Model (LLTM). While it is known that the LLTM is a special case of the MIRID, we show that it is possible to construct an LLTM that encompasses the MIRID. The MIRID model places a bilinear restriction on the item parameters of the Rasch model. It is explained how this fact is used to simplify the results of Bechger, Verhelst, and Verstralen (2001) and Bechger, Verstralen, and Verhelst (2002), and extend their scope to a wider class of models.

Keywords

MIRIDLLTMidentifiabilitymodel equivalence
Type
Theory And Methods
Information
Psychometrika , Volume 69 , Issue 4 , December 2004 , pp. 627 - 639
Copyright
Copyright © 2004 The Psychometric Society

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