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Identifiability and Equivalence of GLLIRM Models

Published online by Cambridge University Press:  01 January 2025

Javier Revuelta
Javier Revuelta*
Affiliation:
Autonoma University of Madrid
*
Requests for reprints should be sent to Javier Revuelta, Department of Social Psychology and Methodology, Autonoma University of Madrid, 28049 Madrid, Spain. E-mail: javier.revuelta@uam.es
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Abstract

The generalized logit–linear item response model (GLLIRM) is a linearly constrained nominal categories model (NCM) that computes the scale and intercept parameters for categories as a weighted sum of basic parameters. This paper addresses the problems of the identifiability of the basic parameters and the equivalence between different GLLIRM models. It is shown that the identifiability of the basic parameters depends on the size and rank of the coefficient matrix of the linear functions. Moreover, two models are observationally equivalent if the product of the respective coefficient matrices has full column rank. Finally, the paper also explores the relations between the parameters of nested models.

Keywords

generalized logit–linear item response modelnominal categories modelidentifiabilityequivalenceitem-response theory
Type
Original Paper
Information
Psychometrika , Volume 74 , Issue 2 , June 2009 , pp. 257 - 272
Copyright
Copyright © 2008 The Psychometric Society

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Footnotes

I would like to express my gratitude to the editor and three anonymous reviewers for their helpful suggestions on earlier versions of the paper. This work was supported by the Comunidad de Madrid (Spain) grant: CCG07-UAM/ESP-1615.

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