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

Published online by Cambridge University Press:  01 January 2025

David Magis
David Magis*
Affiliation:
University of Liège and Ku Leuven, Belgium
*
Requests for reprints should be sent to David Magis, Department of Education (B32), University of Liège, Boulevard du Rectorat 5, 4000 Liège, Belgium. E-mail: david.magis@ulg.ac.be
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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.

Keywords

item response theorypolytomous modelsweighted likelihoodJeffreys modal
Type
Original Paper
Information
Psychometrika , Volume 80 , Issue 1 , March 2015 , pp. 200 - 204
Copyright
Copyright © 2013 The Psychometric Society

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References

Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika, 43, 561–573.CrossRefGoogle Scholar
Bock, R.D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37, 29–51.CrossRefGoogle Scholar
Embretson, S.E., & Reise, S.P. (2000). Item response theory for psychologists. Mahwah: Lawrence Erlbaum Associates.Google Scholar
Jeffreys, H. (1946). An invariant form for the prior probability in estimation problems. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 186, 453–461.Google ScholarPubMed
Magis, D., & Raîche, G. (2012). On the relationships between Jeffreys modal and weighted likelihood estimation of ability under logistic IRT models. Psychometrika, 77, 163–169.CrossRefGoogle Scholar
Masters, G.N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149–174.CrossRefGoogle Scholar
Muraki, E. (1990). Fitting a polytomous item response model to Likert-type data. Applied Psychological Measurement, 14, 59–71.CrossRefGoogle Scholar
Muraki, E. (1992). A generalized partial credit model: application of an EM algorithm. Applied Psychological Measurement, 16, 159–176.CrossRefGoogle Scholar
Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores.CrossRefGoogle Scholar
Samejima, F. (1998, April). Expansion of Warm’s weighted likelihood estimator of ability for the three-parameter logistic model to general discrete responses. Paper presented at the annual meeting of the National Council on Measurement in Education, San Diego, CA.Google Scholar
Thissen, D., & Steinberg, L. (1986). A taxonomy of item response models. Psychometrika, 51, 567–577.CrossRefGoogle Scholar
Warm, T.A. (1989). Weighted likelihood estimation of ability in item response models. Psychometrika, 54, 427–450.CrossRefGoogle Scholar