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Optimal and Most Exact Confidence Intervals for Person Parameters in Item Response Theory Models

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  • Anna Doebler
  • Philipp Doebler
  • Heinz Holling

Abstract

The common way to calculate confidence intervals for item response theory models is to assume that the standardized maximum likelihood estimator for the person parameter θ is normally distributed. However, this approximation is often inadequate for short and medium test lengths. As a result, the coverage probabilities fall below the given level of significance in many cases; and, therefore, the corresponding intervals are no longer confidence intervals in terms of the actual definition. In the present work, confidence intervals are defined more precisely by utilizing the relationship between confidence intervals and hypothesis testing. Two approaches to confidence interval construction are explored that are optimal with respect to criteria of smallness and consistency with the standard approach. Copyright The Psychometric Society 2013

Suggested Citation

  • Anna Doebler & Philipp Doebler & Heinz Holling, 2013. "Optimal and Most Exact Confidence Intervals for Person Parameters in Item Response Theory Models," Psychometrika, Springer;The Psychometric Society, vol. 78(1), pages 98-115, January.
    • Handle: RePEc:spr:psycho:v:78:y:2013:i:1:p:98-115
    DOI: 10.1007/s11336-012-9290-4
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    References listed on IDEAS

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    1. Karl Klauer, 1991. "Exact and best confidence intervals for the ability parameter of the Rasch model," Psychometrika, Springer;The Psychometric Society, vol. 56(3), pages 535-547, September.
    2. Frederic Lord, 1983. "Unbiased estimators of ability parameters, of their variance, and of their parallel-forms reliability," Psychometrika, Springer;The Psychometric Society, vol. 48(2), pages 233-245, June.
    3. R. Bock & Murray Aitkin, 1981. "Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm," Psychometrika, Springer;The Psychometric Society, vol. 46(4), pages 443-459, December.
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    Cited by:

    1. Piero Veronese & Eugenio Melilli, 2021. "Confidence Distribution for the Ability Parameter of the Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 131-166, March.
    2. Yang Liu & Jan Hannig & Abhishek Pal Majumder, 2019. "Second-Order Probability Matching Priors for the Person Parameter in Unidimensional IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 701-718, September.
    3. Martin Biehler & Heinz Holling & Philipp Doebler, 2015. "Saddlepoint Approximations of the Distribution of the Person Parameter in the Two Parameter Logistic Model," Psychometrika, Springer;The Psychometric Society, vol. 80(3), pages 665-688, September.

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