Second-Order Probability Matching Priors for the Person Parameter in Unidimensional IRT Models

Yang Liu (), Jan Hannig and Abhishek Pal Majumder
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Yang Liu: University of Maryland
Jan Hannig: The University of North Carolina at Chapel Hill
Abhishek Pal Majumder: Stockholm University

Psychometrika, 2019, vol. 84, issue 3, No 3, 718 pages

Abstract: Abstract 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.

Keywords: item response theory; test scoring; person parameter; objective Bayes; probability matching prior; data-dependent prior; higher-order asymptotics; Edgeworth expansion; confidence interval (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s11336-019-09675-4

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