IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v84y2019i2d10.1007_s11336-018-09659-w.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11336-018-09659-w
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11336-018-09659-w?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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).
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Yang Liu & Ji Seung Yang, 2018. "Bootstrap-Calibrated Interval Estimates for Latent Variable Scores in Item Response Theory," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 333-354, June.
    3. Justin L. Kern & Steven Andrew Culpepper, 2020. "A Restricted Four-Parameter IRT Model: The Dyad Four-Parameter Normal Ogive (Dyad-4PNO) Model," Psychometrika, Springer;The Psychometric Society, vol. 85(3), pages 575-599, September.
    4. M.-L. Feddag, 2016. "Pairwise likelihood estimation for the normal ogive model with binary data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(2), pages 223-237, April.
    5. Yang Yixin & Lü Xin & Ma Jian & Qiao Han, 2014. "A Robust Factor Analysis Model for Dichotomous Data," Journal of Systems Science and Information, De Gruyter, vol. 2(5), pages 437-450, October.
    6. Arulmani Thiyagarajan & Tyler G. James & Roy Rillera Marzo, 2022. "Psychometric properties of the 21-item Depression, Anxiety, and Stress Scale (DASS-21) among Malaysians during COVID-19: a methodological study," Palgrave Communications, Palgrave Macmillan, vol. 9(1), pages 1-8, December.
    7. Cees Glas, 1988. "The derivation of some tests for the rasch model from the multinomial distribution," Psychometrika, Springer;The Psychometric Society, vol. 53(4), pages 525-546, December.
    8. Robitzsch, Alexander, 2020. "About Still Nonignorable Consequences of (Partially) Ignoring Missing Item Responses in Large-scale Assessment," OSF Preprints hmy45, Center for Open Science.
    9. Christian A. Gregory, 2020. "Are We Underestimating Food Insecurity? Partial Identification with a Bayesian 4-Parameter IRT Model," Journal of Classification, Springer;The Classification Society, vol. 37(3), pages 632-655, October.
    10. Cervantes, Víctor H., 2017. "DFIT: An R Package for Raju's Differential Functioning of Items and Tests Framework," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i05).
    11. Andrew Karl & Randy Eubank & Jelena Milovanovic & Mark Reiser & Dennis Young, 2014. "Using RngStreams for parallel random number generation in C++ and R," Computational Statistics, Springer, vol. 29(5), pages 1301-1320, October.
    12. Sora Lee & Daniel M. Bolt, 2018. "Asymmetric Item Characteristic Curves and Item Complexity: Insights from Simulation and Real Data Analyses," Psychometrika, Springer;The Psychometric Society, vol. 83(2), pages 453-475, June.
    13. Nick Bailey & Anne-Catherine Guio, 2022. "Adaptive Deprivation Scales in a Multi-National Context: The European Child Deprivation Indicators," Child Indicators Research, Springer;The International Society of Child Indicators (ISCI), vol. 15(6), pages 2335-2362, December.
    14. Dawit G. Ayele & Temesgen Zewotir & Henry Mwambi, 2014. "Using Rasch Modeling to Re-Evaluate Rapid Malaria Diagnosis Test Analyses," IJERPH, MDPI, vol. 11(7), pages 1-11, June.
    15. Sandip Sinharay & Jens Ledet Jensen, 2019. "Higher-Order Asymptotics and Its Application to Testing the Equality of the Examinee Ability Over Two Sets of Items," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 484-510, June.
    16. Anders Christoffersson, 1975. "Factor analysis of dichotomized variables," Psychometrika, Springer;The Psychometric Society, vol. 40(1), pages 5-32, March.
    17. Stefano Noventa & Luca Stefanutti & Giulio Vidotto, 2014. "An Analysis of Item Response Theory and Rasch Models Based on the Most Probable Distribution Method," Psychometrika, Springer;The Psychometric Society, vol. 79(3), pages 377-402, July.
    18. Mark Alfano & Kathryn Iurino & Paul Stey & Brian Robinson & Markus Christen & Feng Yu & Daniel Lapsley, 2017. "Development and validation of a multi-dimensional measure of intellectual humility," PLOS ONE, Public Library of Science, vol. 12(8), pages 1-28, August.
    19. Francisco José Eiroa-Orosa & Laura Limiñana-Bravo, 2019. "An Instrument to Measure Mental Health Professionals’ Beliefs and Attitudes towards Service Users’ Rights," IJERPH, MDPI, vol. 16(2), pages 1-16, January.
    20. Jinshu Cui & Heather Rosoff & Richard S. John, 2017. "A Polytomous Item Response Theory Model for Measuring Near-Miss Appraisal as a Psychological Trait," Decision Analysis, INFORMS, vol. 14(2), pages 75-86, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:psycho:v:84:y:2019:i:2:d:10.1007_s11336-018-09659-w. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.