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.
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Acknowledgements
The author wishes to thank Roger E. Millsap, Editor, and three anonymous reviewers for their helpful comments. This research was funded by a post-doctoral research grant “Chargé de recherches” of the National Funds for Scientific Research (FNRS, Belgium), the IAP Research Network P7/06 of the Belgian State (Belgian Science Policy), and the Research Funds of the KU Leuven, Belgium.
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Magis, D. A Note on Weighted Likelihood and Jeffreys Modal Estimation of Proficiency Levels in Polytomous Item Response Models. Psychometrika 80, 200–204 (2015). https://doi.org/10.1007/s11336-013-9378-5
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DOI: https://doi.org/10.1007/s11336-013-9378-5