, Volume 69, Issue 4, pp 627–639

Equivalent MIRID models

Theory And Methods

DOI: 10.1007/BF02289859

Cite this article as:
Maris, G. & Bechger, T.M. Psychometrika (2004) 69: 627. doi:10.1007/BF02289859


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.

Key words

MIRID LLTM identifiability model equivalence 

Copyright information

© The Psychometric Society 2004

Authors and Affiliations

  1. 1.Cito, National Institute for Educational MeasurementThe Netherlands
  2. 2.CitoArnhemNetherlands

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