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The Use of an Identifiability-Based Strategy for the Interpretation of Parameters in the 1PL-G and Rasch Models

Author

Listed:
  • Paula Fariña

    (Universidad Diego Portales)

  • Jorge González

    (Pontificia Universidad Católica de Chile)

  • Ernesto San Martín

    (Pontificia Universidad Católica de Chile
    Université catholique de Louvain)

Abstract

Using the well-known strategy in which parameters are linked to the sampling distribution via an identification analysis, we offer an interpretation of the item parameters in the one-parameter logistic with guessing model (1PL-G) and the nested Rasch model. The interpretations are based on measures of informativeness that are defined in terms of odds of correctly answering the items. It is shown that the interpretation of what is called the difficulty parameter in the random-effects 1PL-G model differs from that of the item parameter in a random-effects Rasch model. It is also shown that the traditional interpretation of the guessing parameter in the 1PL-G model changes, depending on whether fixed-effects or random-effects versions of both models are considered.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:psycho:v:84:y:2019:i:2:d:10.1007_s11336-018-09659-w
    DOI: 10.1007/s11336-018-09659-w
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    References listed on IDEAS

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    1. Steven Rigdon & Robert Tsutakawa, 1983. "Parameter estimation in latent trait models," Psychometrika, Springer;The Psychometric Society, vol. 48(4), pages 567-574, December.
    2. Ernesto San Martín & Jean-Marie Rolin & Luis Castro, 2013. "Identification of the 1PL Model with Guessing Parameter: Parametric and Semi-parametric Results," Psychometrika, Springer;The Psychometric Society, vol. 78(2), pages 341-379, April.
    3. 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.
    4. Paul Holland, 1990. "On the sampling theory roundations of item response theory models," Psychometrika, Springer;The Psychometric Society, vol. 55(4), pages 577-601, December.
    5. Frederic Lord, 1970. "Item characteristic curves estimated without knowledge of their mathematical form—a confrontation of Birnbaum's logistic model," Psychometrika, Springer;The Psychometric Society, vol. 35(1), pages 43-50, March.
    6. Rizopoulos, Dimitris, 2006. "ltm: An R Package for Latent Variable Modeling and Item Response Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 17(i05).
    7. 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.
    8. 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.
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