Psychometrika

, Volume 78, Issue 1, pp 98–115 | Cite as

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

Article

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.

Key words

confidence intervals optimality item response theory monotone likelihood ratio adaptive testing 

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Copyright information

© The Psychometric Society 2012

Authors and Affiliations

  1. 1.Fachbereich Psychologie und Sportwissenschaft (FB 7), Institut für PsychologieWestfälische Wilhelms-UniversitätMünsterGermany

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