Identified and unidentified cases of the fixed-effects three-parameter IRT model
Haruhiko Ogasawara · The Proceedings of the Annual Convention of the Japanese Psychological Association · 2020
It was believed until Maris （2002） that the guessing parameters （c-parameters） or lower asymptotes in the three-parameter logistic model in item response theory （IRT） have local identification. Maris’ unidentified case is special in that equal discrimination parameters are employed. Other examples without identification for c-parameters have been added by van der Linden and Barrett （2016） and Ogasawara （2017）. In this paper, Maris’ case is shown using a reformulated equivalent model. Then, the necessary and sufficient condition of the model identification for the fixed-effects three-parameter logistic model in IRT is given synthesizing known results. Some weak assumptions for associated models are introduced. Under these assumptions, it is shown that when two c-parameters are equal and the corresponding difficulty parameters are different, the IRT model is generally identifiable. References: Maris, G. （2002）. Concerning the identification of the 3PL model. Measurement and Research Department Reports 2002-3. Arnhem, the Netherlands: CITO National Institute for Educational Measurement; Ogasawara, H. （2017）. Identified and unidentified cases of the three- and four-parameter models in item response theory. Behaviormetrika, 44, 405-423; van der Linden, W. J., ＆ Barrett, M. D. （2016）. Linking item response model parameters. Psychometrika, 81, 650-673. （Erratum, 2017, 82, 273）.