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Asymptotic Null Distribution of Person Fit Statistics with Estimated Person Parameter

Published online by Cambridge University Press:  01 January 2025

Tom A. B. Snijders
Tom A. B. Snijders*
Affiliation:
University of Groningen
*
Requests for reprints should be sent to Tom A.B. Snijders, Department of Statistics, Measurement Theory, and Information Technology, University of Groningen, Grote Kruisstraat 2/1, 9712 TS Groningen, THE NETHERLANDS. E-Mail [email protected]
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Abstract

Person fit statistics are considered for dichotomous item response models. The asymptotic null distribution is derived for statistics which are linear in the item responses, and in which the ability parameter is replaced by an estimate. This allows the asymptotically correct standardization of linear person fit statistics with estimated ability parameter. The fact that the ability parameter is estimated usually decreases the asymptotic variance.

Keywords

item response theoryperson fitasymptotic approximations
Type
Articles
Information
Psychometrika , Volume 66 , Issue 3 , September 2001 , pp. 331 - 342
Copyright
Copyright © 2001 The Psychometric Society

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Footnotes

I am indebted to Herbert Hoijtink and three anonymous referees for their comments on a previous version.

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