Hostname: page-component-74656f9884-54qdv Total loading time: 0 Render date: 2026-11-09T17:07:15.919Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Information

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Bechger, T.M., Verhelst, N.D., Verstralen, H.H.F.M. (2001). Identifiability of nonlinear logistic test models. Psychometrika, 66, 357–372CrossRefGoogle Scholar
Bechger, T.M., Verstralen, H.H.F.M., Verhelst, N.D. (2002). Equivalent linear logistic test models. Psychometrika, 67, 123–13610.1007/BF02294712CrossRefGoogle Scholar
Butter, R. (1994). Item response model with internal restrictions on item difficulty. Unpublished doctoral dissertation, KU Leuven.Google Scholar
Butter, R., De Boeck, P., Verhelst, N.D. (1998). An item response model with internal restrictions on item difficulty. Psychometrika, 63, 47–6310.1007/BF02295436CrossRefGoogle Scholar
Embretson, S.E., Reise, S.P. (2000). Item response theory for psychologists, London: Lawrence ErlbaumGoogle Scholar
Fischer, G.H. (1983). Logistic latent trait models with linear constraints. Psychometrika, 48, 3–2610.1007/BF02314674CrossRefGoogle Scholar
Fischer, G.H. (1995). The linear logistic test model. In Fischer, G.H., Molenaar, I.W. (Eds.), Rasch models: Foundations, recent developments and applications (pp. 131–155). Berlin: Springer 10.1007/978-1-4612-4230-7_8CrossRefGoogle Scholar
Fischer, G.H. (2004). Remarks on ‘Equivalent linear logistic test models’ by Bechger, Verstralen, and Verhelst (2002). Psychometrika, 69, 305–31610.1007/BF02295946CrossRefGoogle Scholar
Pringle, R.M., Rayner, A.A. (1971). Generalized inverse matrices with applications to statistics, London: Charles Griffin & Co.Google Scholar
Schleiblechner, H. (1972).Das Lernen und Lösen komplexer Denkaufgaben [The learning and solving of complex reasoning items]. Zeitschrift für Experimentelle und Angewandte Psychologie, 3, 456–506Google Scholar