Identifiability and Equivalence of GLLIRM Models |
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Authors: | Javier Revuelta |
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Institution: | (1) Department of Social Psychology and Methodology, Autonoma University of Madrid, 28049 Madrid, Spain |
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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.
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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Keywords: | generalized logit– linear item response model nominal categories model identifiability equivalence item-response theory |
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