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An Extension of the Rating Scale Model with an Application to the Measurement of Change

Published online by Cambridge University Press:  01 January 2025

G. H. Fischer  and
P. Parzer
G. H. Fischer*
Affiliation:
University of Vienna
P. Parzer
Affiliation:
University of Vienna
*
Requests for reprints should be sent to G. H. Fischer, Department of Psychology, University of Vienna, Liebiggasse 5, A-1010 Wien (Vienna), AUSTRIA.
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Abstract

The polytomous unidimensional Rasch model with equidistant scoring, also known as the rating scale model, is extended in such a way that the item parameters are linearly decomposed into certain basic parameters. The extended model is denoted as the linear rating scale model (LRSM). A conditional maximum likelihood estimation procedure and a likelihood-ratio test of hypotheses within the framework of the LRSM are presented. Since the LRSM is a generalization of both the dichotomous Rasch model and the rating scale model, the present algorithm is suited for conditional maximum likelihood estimation in these submodels as well. The practicality of the conditional method is demonstrated by means of a dichotomous Rasch example with 100 items, of a rating scale example with 30 items and 5 categories, and in the light of an empirical application to the measurement of treatment effects in a clinical study.

Keywords

Rasch modelsrating scale modelsitem response theorystructural modelingassessment of treatment effectsmeasurement of change
Type
Original Paper
Information
Psychometrika , Volume 56 , Issue 4 , December 1991 , pp. 637 - 651
Copyright
Copyright © 1991 The Psychometric Society

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Footnotes

Work supported in part by the Fonds zur Förderung der Wissenschaftlichen Forschung under Grant No. P6414.

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