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Extensions of Rasch's Multiplicative Poisson Model

Published online by Cambridge University Press:  01 January 2025

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

Consideration will be given to a model developed by Rasch that assumes scores observed on some types of attainment tests can be regarded as realizations of a Poisson process. The parameter of the Poisson distribution is assumed to be a product of two other parameters, one pertaining to the ability of the subject and a second pertaining to the difficulty of the test. Rasch's model is expanded by assuming a prior distribution, with fixed but unknown parameters, for the subject parameters. The test parameters are considered fixed. Secondly, it will be shown how additional between- and within-subjects factors can be incorporated. Methods for testing the fit and estimating the parameters of the model will be discussed, and illustrated by empirical examples.

Keywords

contingency tablesempirical Bayes methodsRasch model
Type
Original Paper
Information
Psychometrika , Volume 57 , Issue 3 , September 1992 , pp. 405 - 414
Copyright
Copyright © 1992 The Psychometric Society

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