, Volume 44, Issue 2, pp 405–423 | Cite as

Identified and unidentified cases of the fixed-effects 3- and 4-parameter models in item response theory

  • Haruhiko Ogasawara
Original Paper


The 3-parameter logistic (3PL) model including guessing parameters is one of the popular models in item response theory. While the guessing parameters in the fixed-effects 3PL model with non-stochastic abilities have been believed to have identification, some counter examples with new ones given in this paper are currently available. In this paper, the concept of degeneracy for nested models is introduced. Some degenerate cases in the counter examples are shown to have model identification for guessing parameters, which are further shown to have model unidentification in a more degenerate model. Similar results in the fixed-effects 4-parameter logistic model are also derived.


3PL model 4PL model Guessing parameters Slipping parameters Model identification 



This work was partially supported by a Grant-in-Aid for Scientific Research from the Japanese Ministry of Education, Culture, Sports, Science and Technology (JSPS KAKENHI, Grant No. 17K00042).

Compliance with ethical standards

Conflict of interest

The author declares no conflict of interest.


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Copyright information

© The Behaviormetric Society 2017

Authors and Affiliations

  1. 1.Otaru University of CommerceMidoriJapan

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