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The UMP Exact Test and the Confidence Interval for Person Parameters in IRT Models

Authors
  • Liu, Xiang1
  • Han, Zhuangzhuang1
  • Johnson, Matthew S.1
  • 1 Teachers College of Columbia University, Department of Human Development, 525 West 120th Street, New York, NY, 10027-6696, USA , New York (United States)
Type
Published Article
Journal
Psychometrika
Publisher
Springer US
Publication Date
Aug 23, 2017
Volume
83
Issue
1
Pages
182–202
Identifiers
DOI: 10.1007/s11336-017-9580-y
Source
Springer Nature
Keywords
License
Yellow

Abstract

In educational and psychological measurement when short test forms are used, the asymptotic normality of the maximum likelihood estimator of the person parameter of item response models does not hold. As a result, hypothesis tests or confidence intervals of the person parameter based on the normal distribution are likely to be problematic. Inferences based on the exact distribution, on the other hand, do not suffer from this limitation. However, the computation involved for the exact distribution approach is often prohibitively expensive. In this paper, we propose a general framework for constructing hypothesis tests and confidence intervals for IRT models within the exponential family based on exact distribution. In addition, an efficient branch and bound algorithm for calculating the exact p value is introduced. The type-I error rate and statistical power of the proposed exact test as well as the coverage rate and the lengths of the associated confidence interval are examined through a simulation. We also demonstrate its practical use by analyzing three real data sets.

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