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A Rasch Model for Continuous Ratings

Published online by Cambridge University Press:  01 January 2025

Hans Müller
Hans Müller*
Affiliation:
Johann Wolfgang Goethe-Universität
*
Requests for reprints should be sent to Hans Müller, Institut für Psychologie, Johann Wolfgang Goethe-Universität, Mertonstr. 17, D-6000 Frankfurt am Main 11, FEDERAL REPUBLIC OF GERMANY.
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Abstract

A unidimensional latent trait model for continuous ratings is developed. This model is an extension of Andrich's rating formulation which assumes that the response process at latent thresholds is governed by the dichotomous Rasch model. Item characteristic functions and information functions are used to illustrate that the model takes ceiling and floor effects into account. Both the dichotomous Rasch model and a linear model with normally distributed error can be derived as limiting cases. The separability of the structural and incidental parameters is demonstrated and a procedure for estimating the parameters is outlined.

Keywords

latent traitRasch modelthresholdsrating scalescontinuous responsesceiling and floor effectsnormal distribution
Type
Original Paper
Information
Psychometrika , Volume 52 , Issue 2 , March 1987 , pp. 165 - 181
Copyright
Copyright © 1987 The Psychometric Society

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Footnotes

†

The author wishes to thank the three anonymous reviewers for several valuable suggestions and Rose Marie Bambach for improving the English manuscript.

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