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

Published online by Cambridge University Press:  01 January 2025

Anna Doebler,
Philipp Doebler and
Heinz Holling
Anna Doebler*
Affiliation:
Fachbereich Psychologie und Sportwissenschaft (FB 7), Institut für Psychologie, Westfälische Wilhelms-Universität
Philipp Doebler
Affiliation:
Fachbereich Psychologie und Sportwissenschaft (FB 7), Institut für Psychologie, Westfälische Wilhelms-Universität
Heinz Holling
Affiliation:
Fachbereich Psychologie und Sportwissenschaft (FB 7), Institut für Psychologie, Westfälische Wilhelms-Universität
*
Requests for reprints should be sent to Anna Doebler, Fachbereich Psychologie und Sportwissenschaft (FB 7), Institut für Psychologie, Westfälische Wilhelms-Universität, Fliednerstr. 21, 48149 Münster, Germany. E-mail: anna.doebler@uni-muenster.de
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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.

Keywords

confidence intervalsoptimalityitem response theorymonotone likelihood ratioadaptive testing

Information

Type
Original Paper
Information
Psychometrika , Volume 78 , Issue 1 , January 2013, pp. 98 - 115
Copyright
Copyright © The Psychometric Society

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Footnotes

This work was supported by a Grant of the Studienstiftung des Deutschen Volkes.

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