Hostname: page-component-f554764f5-c4bhq Total loading time: 0 Render date: 2025-04-16T08:50:32.661Z Has data issue: false hasContentIssue false
  • English
  • Français

Expanding the Rasch Model to a General Model having more than One Dimension

Published online by Cambridge University Press:  01 January 2025

Werner Stegelmann
Werner Stegelmann*
Affiliation:
Max-Planck-Institut Für Bildungsforschung
*
Requests for reprint should be addressed to Werner Stegelmann, Max-Planck-Institut für Bildungsforschung, 1 Berlin 33, Lantzeallee 94, West Germany.
Get access Rights & Permissions [Opens in a new window]

Abstract

The well-known Rasch model is generalized to a multicomponent model, so that observations of component events are not needed to apply the model. It is shown that the generalized model has retained the property of the specific objectivity of the Rasch model. For a restricted variant of the model, maximum likelihood estimates of its parameters and a statistical test of the model are given. The results of an application to a mathematics test involving six components are described.

Keywords

model testparameter estimationspecific objectivity
Type
Original Paper
Information
Psychometrika , Volume 48 , Issue 2 , June 1983 , pp. 259 - 267
Copyright
Copyright © 1983 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

Footnotes

*

A model with two kinds of parameters is said to have the specific objectivity property if the results of comparing parameters of one kind are independent of the parameters of the other kind. A consequence of requiring specific objectivity for statistical models is that inferential separation of the parameters should be possible.

References

Reference Notes

Stegelmann, W. On the complexity of a computational problem arising in a generalization of the Rasch model. Unpublished manuscript, Berlin.Google Scholar
Kempf, W. F. Parameterschätzung in einem mehrdimensionalem strukturellen logistischen Testmodell. (Unveröffentlichtes Manuskript) Kiel: 1976.Google Scholar

References

Andersen, E. B. Das mehrkategorielle logistische Testmodell. In Kempf, W. F. (Eds.), Probabilistische Modelle in der Sozialpsychologie, Bern: Hans Huber Verlag, 1974.Google Scholar
Andersen, E. B. Discrete statistical models with social science application, New York: North Holland Publishing Company, 1980.Google Scholar
Dienes, Z. P. An experimental study of mathematics-learning, London: Hutchinson & Co., 1964.Google Scholar
Fischer, G. H. The linear logistic test model as an instrument in educational research. Acta Psychologica, 1973, 37, 359–374.CrossRefGoogle Scholar
Hilke, R., Kempf, W. F. & Scandura, J. M. Deterministic and probabilistic theorizing in structural learning. In Spada, H., Kempf, W. F. (Eds.), Structural models of thinking and learning, Bern: Hans Huber Publishers, 1977.Google Scholar
Kempf, W. F. Dynamic models for the measurement of “traits” in social behavior. In Kempf, W. F. & Repp, B. (Eds.), Mathematical models for social psychology, Bern: Hans Huber Publishers, 1977.Google Scholar
Scheiblechner, H. Das Lernen und Lösen komplexer Denkaufgaben. Zeitschrift fuer Experimentelle und Angewandte Psychologie, 1972, 19, 476–505.Google Scholar
Whitely, S. E. Multicomponent latent trait models for ability tests. Psychometrika, 1980, 45, 479–494.CrossRefGoogle Scholar
Wilks, S. S. Mathematical statistics, New York: Wiley, 1963.Google Scholar