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A Note on the Identifiability of Fixed-Effect 3PL Models

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  • Hao Wu

    (Boston College)

Abstract

In this note, we prove that the 3 parameter logistic model with fixed-effect abilities is identified only up to a linear transformation of the ability scale under mild regularity conditions, contrary to the claims in Theorem 2 of San Martín et al. (Psychometrika, 80(2):450–467, 2015a).

Suggested Citation

  • Hao Wu, 2016. "A Note on the Identifiability of Fixed-Effect 3PL Models," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 1093-1097, December.
    • Handle: RePEc:spr:psycho:v:81:y:2016:i:4:d:10.1007_s11336-016-9519-8
    DOI: 10.1007/s11336-016-9519-8
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    References listed on IDEAS

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    1. Ernesto Martín & Jorge González & Francis Tuerlinckx, 2015. "Erratum to: On the Unidentifiability of the Fixed-Effects 3PL Model," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 1146-1146, December.
    2. Hao Wu & Michael Neale, 2013. "On the Likelihood Ratio Tests in Bivariate ACDE Models," Psychometrika, Springer;The Psychometric Society, vol. 78(3), pages 441-463, July.
    3. Wim J. Linden & Michelle D. Barrett, 2016. "Linking Item Response Model Parameters," Psychometrika, Springer;The Psychometric Society, vol. 81(3), pages 650-673, September.
    4. Ernesto Martín & Jorge González & Francis Tuerlinckx, 2015. "On the Unidentifiability of the Fixed-Effects 3PL Model," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 450-467, June.
    5. Jing Qin & Kung-Yee Liang, 2011. "Hypothesis Testing in a Mixture Case–Control Model," Biometrics, The International Biometric Society, vol. 67(1), pages 182-193, March.
    6. Hao Wu & Ryne Estabrook, 2016. "Identification of Confirmatory Factor Analysis Models of Different Levels of Invariance for Ordered Categorical Outcomes," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 1014-1045, December.
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    Cited by:

    1. Haruhiko Ogasawara, 2021. "Maximization of Some Types of Information for Unidentified Item Response Models with Guessing Parameters," Psychometrika, Springer;The Psychometric Society, vol. 86(2), pages 544-563, June.
    2. Paula Fariña & Jorge González & Ernesto San Martín, 2019. "The Use of an Identifiability-Based Strategy for the Interpretation of Parameters in the 1PL-G and Rasch Models," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 511-528, June.

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