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A Note on Weighted Likelihood and Jeffreys Modal Estimation of Proficiency Levels in Polytomous Item Response Models

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  • David Magis

Abstract

Warm (in Psychometrika, 54, 427–450, 1989 ) established the equivalence between the so-called Jeffreys modal and the weighted likelihood estimators of proficiency level with some dichotomous item response models. The purpose of this note is to extend this result to polytomous item response models. First, a general condition is derived to ensure the perfect equivalence between these two estimators. Second, it is shown that this condition is fulfilled by two broad classes of polytomous models including, among others, the partial credit, rating scale, graded response, and nominal response models. Copyright The Psychometric Society 2015

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  • David Magis, 2015. "A Note on Weighted Likelihood and Jeffreys Modal Estimation of Proficiency Levels in Polytomous Item Response Models," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 200-204, March.
    • Handle: RePEc:spr:psycho:v:80:y:2015:i:1:p:200-204
    DOI: 10.1007/s11336-013-9378-5
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    References listed on IDEAS

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    1. David Thissen & Lynne Steinberg, 1986. "A taxonomy of item response models," Psychometrika, Springer;The Psychometric Society, vol. 51(4), pages 567-577, December.
    2. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 149-174, June.
    3. David Magis & Gilles Raîche, 2012. "On the Relationships Between Jeffreys Modal and Weighted Likelihood Estimation of Ability Under Logistic IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 77(1), pages 163-169, January.
    4. R. Darrell Bock, 1972. "Estimating item parameters and latent ability when responses are scored in two or more nominal categories," Psychometrika, Springer;The Psychometric Society, vol. 37(1), pages 29-51, March.
    5. David Andrich, 1978. "A rating formulation for ordered response categories," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 561-573, December.
    6. Thomas Warm, 1989. "Weighted likelihood estimation of ability in item response theory," Psychometrika, Springer;The Psychometric Society, vol. 54(3), pages 427-450, September.
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    Cited by:

    1. Mathur, Maya B, 2024. "Meta-analysis with Jeffreys priors: Empirical frequentist properties," OSF Preprints 7jvrw, Center for Open Science.
    2. Sandip Sinharay, 2015. "The Asymptotic Distribution of Ability Estimates," Journal of Educational and Behavioral Statistics, , vol. 40(5), pages 511-528, October.
    3. David Magis & Norman Verhelst, 2017. "On the Finiteness of the Weighted Likelihood Estimator of Ability," Psychometrika, Springer;The Psychometric Society, vol. 82(3), pages 637-647, September.
    4. Sandip Sinharay, 2016. "Asymptotically Correct Standardization of Person-Fit Statistics Beyond Dichotomous Items," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 992-1013, December.
    5. Yang Liu & Jan Hannig & Abhishek Pal Majumder, 2019. "Second-Order Probability Matching Priors for the Person Parameter in Unidimensional IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 701-718, September.

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