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Second-Order Probability Matching Priors for the Person Parameter in Unidimensional IRT Models
Stockholm University, Faculty of Science, Department of Mathematics.
Number of Authors: 32019 (English)In: Psychometrika, ISSN 0033-3123, E-ISSN 1860-0980, Vol. 84, no 3, p. 701-718Article in journal (Refereed) Published
Abstract [en]

In applications of item response theory (IRT), it is often of interest to compute confidence intervals (CIs) for person parameters with prescribed frequentist coverage. The ubiquitous use of short tests in social science research and practices calls for a refinement of standard interval estimation procedures based on asymptotic normality, such as the Wald and Bayesian CIs, which only maintain desirable coverage when the test is sufficiently long. In the current paper, we propose a simple construction of second-order probability matching priors for the person parameter in unidimensional IRT models, which in turn yields CIs with accurate coverage even when the test is composed of a few items. The probability matching property is established based on an expansion of the posterior distribution function and a shrinkage argument. CIs based on the proposed prior can be efficiently computed for a variety of unidimensional IRT models. A real data example with a mixed-format test and a simulation study are presented to compare the proposed method against several existing asymptotic CIs.

Place, publisher, year, edition, pages
2019. Vol. 84, no 3, p. 701-718
Keywords [en]
item response theory, test scoring, person parameter, objective Bayes, probability matching prior, data-dependent prior, higher-order asymptotics, Edgeworth expansion, confidence interval
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-171945DOI: 10.1007/s11336-019-09675-4ISI: 000477596000003PubMedID: 31264028OAI: oai:DiVA.org:su-171945DiVA, id: diva2:1348696
Available from: 2019-09-05 Created: 2019-09-05 Last updated: 2019-09-05Bibliographically approved

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