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

Authors
  • Liu, Yang1
  • Hannig, Jan2
  • Pal Majumder, Abhishek3
  • 1 Department of Human Development and Quantitative Methodology, University of Maryland, College Park, USA. [email protected]
  • 2 Department of Statistics and Operations Research, The University of North Carolina at Chapel Hill, Chapel Hill, USA.
  • 3 Department of Mathematical Statistics, Stockholm University, Stockholm, Sweden. , (Sweden)
Type
Published Article
Journal
Psychometrika
Publication Date
Sep 01, 2019
Volume
84
Issue
3
Pages
701–718
Identifiers
DOI: 10.1007/s11336-019-09675-4
PMID: 31264028
Source
Medline
Keywords
Language
English
License
Unknown

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.

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