On the Identifiability of 3- and 4-Parameter Item Response Theory Models From the Perspective of Knowledge Space Theory

Stefano Noventa (), Sangbeak Ye (), Augustin Kelava () and Andrea Spoto ()
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Stefano Noventa: Methods Center, Universität Tübingen
Sangbeak Ye: Methods Center, Universität Tübingen
Augustin Kelava: Methods Center, Universität Tübingen
Andrea Spoto: Department of General Psychology, University of Padova

Psychometrika, 2024, vol. 89, issue 2, No 6, 486-516

Abstract: Abstract The present work aims at showing that the identification problems (here meant as both issues of empirical indistinguishability and unidentifiability) of some item response theory models are related to the notion of identifiability in knowledge space theory. Specifically, that the identification problems of the 3- and 4-parameter models are related to the more general issues of forward- and backward-gradedness in all items of the power set, which is the knowledge structure associated with IRT models under the assumption of local independence. As a consequence, the identifiability problem of a 4-parameter model is split into two parts: a first one, which is the result of a trade-off between the left-side added parameters and the remainder of the Item Response Function, e.g., a 2-parameter model, and a second one, which is the already well-known identifiability issue of the 2-parameter model itself. Application of the results to the logistic case appears to provide both a confirmation and a generalization of the current findings in the literature for both fixed- and random-effects IRT logistic models.

Keywords: knowledge space theory; item response theory; identifiability; empirical indistinguishability; rasch models; 3PL; 4PL (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11336-024-09950-z

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