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

Xiang Liu (), Zhuangzhuang Han and Matthew S. Johnson
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Xiang Liu: Teachers College of Columbia University
Zhuangzhuang Han: Teachers College of Columbia University
Matthew S. Johnson: Teachers College of Columbia University

Psychometrika, 2018, vol. 83, issue 1, No 9, 182-202

Abstract: 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.

Keywords: IRT; exponential family; UMP; exact distribution; algorithm; p value; sufficient statistic; confidence interval (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s11336-017-9580-y

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