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An Improved Inferential Procedure to Evaluate Item Discriminations in a Conditional Maximum Likelihood Framework

Author

Listed:
  • Clemens Draxler

    (UMIT TIROL Private University for Health Sciences and Technology)

  • Andreas Kurz

    (University of Salzburg)

  • Can Gürer
  • Jan Philipp Nolte

    (UMIT TIROL Private University for Health Sciences and Technology)

Abstract

A modified and improved inductive inferential approach to evaluate item discriminations in a conditional maximum likelihood and Rasch modeling framework is suggested. The new approach involves the derivation of four hypothesis tests. It implies a linear restriction of the assumed set of probability distributions in the classical approach that represents scenarios of different item discriminations in a straightforward and efficient manner. Its improvement is discussed, compared to classical procedures (tests and information criteria), and illustrated in Monte Carlo experiments as well as real data examples from educational research. The results show an improvement of power of the modified tests of up to 0.3.

Suggested Citation

  • Clemens Draxler & Andreas Kurz & Can Gürer & Jan Philipp Nolte, 2024. "An Improved Inferential Procedure to Evaluate Item Discriminations in a Conditional Maximum Likelihood Framework," Journal of Educational and Behavioral Statistics, , vol. 49(3), pages 403-430, June.
    • Handle: RePEc:sae:jedbes:v:49:y:2024:i:3:p:403-430
    DOI: 10.3102/10769986231183335
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    References listed on IDEAS

    as
    1. Clemens Draxler, 2018. "Bayesian conditional inference for Rasch models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(2), pages 245-262, April.
    2. Clemens Draxler & Johannes Zessin, 2015. "The power function of conditional tests of the Rasch model," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(3), pages 367-378, July.
    3. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 149-174, June.
    4. Mair, Patrick & Hatzinger, Reinhold, 2007. "Extended Rasch Modeling: The eRm Package for the Application of IRT Models in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i09).
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    6. Clemens Draxler & Andreas Kurz, 2021. "Conditional Inference in Small Sample Scenarios Using a Resampling Approach," Stats, MDPI, vol. 4(4), pages 1-13, October.
    7. Anders Skrondal & Sophia Rabe-Hesketh, 2022. "The Role of Conditional Likelihoods in Latent Variable Modeling," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 799-834, September.
    8. Gerhard Fischer, 1981. "On the existence and uniqueness of maximum-likelihood estimates in the Rasch model," Psychometrika, Springer;The Psychometric Society, vol. 46(1), pages 59-77, March.
    9. Clemens Draxler & Rainer Alexandrowicz, 2015. "Sample Size Determination Within the Scope of Conditional Maximum Likelihood Estimation with Special Focus on Testing the Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 897-919, December.
    10. J. Pfanzagl, 1993. "On the consistency of conditional maximum likelihood estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(4), pages 703-719, December.
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    Full references (including those not matched with items on IDEAS)

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