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Confidence Distribution for the Ability Parameter of the Rasch Model

Published online by Cambridge University Press:  01 January 2025

Piero Veronese Open the ORCID record for Piero Veronese [Opens in a new window]  and
Eugenio Melilli
Piero Veronese*
Affiliation:
Bocconi University
Eugenio Melilli
Affiliation:
Bocconi University
*
Correspondence should be made to Piero Veronese, Department of Decision Sciences, Bocconi University, via Roentgen 1, 20136 Milano, Italy. Email: piero.veronese@unibocconi.it
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Abstract

In this paper, we consider the Rasch model and suggest novel point estimators and confidence intervals for the ability parameter. They are based on a proposed confidence distribution (CD) whose construction has required to overcome some difficulties essentially due to the discrete nature of the model. When the number of items is large, the computations due to the combinatorics involved become heavy, and thus, we provide first- and second-order approximations of the CD. Simulation studies show the good behavior of our estimators and intervals when compared with those obtained through other standard frequentist and weakly informative Bayesian procedures. Finally, using the expansion of the expected length of the suggested interval, we are able to identify reasonable values of the sample size which lead to a desired length of the interval.

Keywords

asymptotic expansionconfidence intervalcoverageextreme scorefiducial distributionitem response theorynatural exponential familyobjective Bayesian inference
Type
Theory and Methods
Information
Psychometrika , Volume 86 , Issue 1 , March 2021 , pp. 131 - 166
Copyright
Copyright © 2021 The Psychometric Society

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