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Exact Tests for the Rasch Model Via Sequential Importance Sampling

Published online by Cambridge University Press:  01 January 2025

Yuguo Chen  and
Dylan Small
Yuguo Chen
Affiliation:
Duke University
Dylan Small*
Affiliation:
University of Pennsylvania
*
Requests for reprints should be sent to Dylan Small, Department of Statistics, The Wharton School, University of Pennsylvania, 400 Jon M. Huntsman Hall, 3730 Locust Walk, Philadelphia, PA 19104, USA. E-mail: [email protected]
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Abstract

Rasch proposed an exact conditional inference approach to testing his model but never implemented it because it involves the calculation of a complicated probability. This paper furthers Rasch’s approach by (1) providing an efficient Monte Carlo methodology for accurately approximating the required probability and (2) illustrating the usefulness of Rasch’s approach for several important testing problems through simulation studies. Our Monte Carlo methodology is shown to compare favorably to other Monte Carlo methods proposed for this problem in two respects: it is considerably faster and it provides more reliable estimates of the Monte Carlo standard error.

Keywords

Rasch modelexact testsgoodness of fit testsMonte Carlo methodssequential importance sampling
Type
Original Paper
Information
Psychometrika , Volume 70 , Issue 1 , March 2005 , pp. 11 - 30
Copyright
Copyright © 2005 The Psychometric Society

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Footnotes

This Research was supported in part by National Science Foundation grant DMS-0203762 and a University of Pennsylvania Research Foundation grant.

The authors are grateful to Don Burdick for helpful comments. In addition, the authors wish to thank the editor, the associate editor, and the referees for their helpful suggestions.

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