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An Exact and Optimal Standardized Person Test for Assessing Consistency with the Rasch Model

Published online by Cambridge University Press:  01 January 2025

Karl Christoph Klauer
Karl Christoph Klauer*
Affiliation:
Freie Universität Berlin
*
Requests for reprints should be sent to Karl Christoph Klauer, FU Berlin, Institut für Psychologie, Habelschwerdter Allee 45, 1000 Berlin 33, FR GERMANY.
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Abstract

The Rasch model predicts that an individual's ability level is invariant over subtests of the total test, and thus, all subtests measure the same latent trait. A person test of this invariance hypothesis is discussed that is uniformly most powerful and standardized in the sense that the conditional distribution of the test statistic, given a particular level of ability, does not depend on the absolute value of the examinee's ability parameter. The test can be routinely performed by applying a computer program designed by and obtainable from the author. Finally, a suboptimal test is derived that is extremely easy to use, and an overall group test of the invariance hypothesis discussed. All tests considered do not rely on asymptotic approximations; hence, they may be applied when the test is of only moderate length and the group of examinees is small.

Keywords

item response theoryperson fitunidimensionality

Information

Type
Original Paper
Information
Psychometrika , Volume 56 , Issue 2 , June 1991, pp. 213 - 228
Copyright
Copyright © 1991 The Psychometric Society

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