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Rasch's Model for Reading Speed with Manifest Explanatory Variables

Published online by Cambridge University Press:  01 January 2025

Margo G. H. Jansen
Margo G. H. Jansen*
Affiliation:
University of Groningen
*
Requests for reprints should be sent to Margo G. H. Jansen, Grote Rozenstraat 38, Department of Education RUG, 9712 TJ Groningen, THE NETHERLANDS.
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Abstract

In educational and psychological measurement we find the distinction between speed and power tests. Although most tests are partially speeded, the speed element is usually neglected. Here we consider a latent trait model developed by Rasch for the response time on a (set of) pure speed test(s), which is based on the assumption that the test response times are approximately gamma distributed, with known shape parameters and scale parameters depending on subject “ability” and test “difficulty” parameters. In our approach the subject parameters are treated as random variables having a common gamma distribution. From this, maximum marginal likelihood estimators are derived for the test difficulties and the parameters of the latent subject distribution. This basic model can be extended in a number of ways. Explanatory variables for the latent subject parameters and for the test parameters can be incorporated in the model. Our methods are illustrated by the analysis of a simulated and an empirical data set.

Keywords

reading speed testsRasch modelexplanatory variables
Type
Original Paper
Information
Psychometrika , Volume 62 , Issue 3 , September 1997 , pp. 393 - 409
Copyright
Copyright © 1997 The Psychometric Society

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Footnotes

I wish to thank H. Bruning, E. Wekking and P. Dingemans who kindly made their data available. I also thank the members of the Dutch Raschgroup. In particular I thank I. W. Molenaar for reading an earlier version of this article, and N. D. Verhelst for many valuable suggestions.

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