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Applications of Projective Transformations to Test Theory

Published online by Cambridge University Press:  01 January 2025

J. A. Keats
J. A. Keats*
Affiliation:
The University of Newcastle
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Extract

Various writers have suggested the use of projective transformations in psychological theories. Among them are Herbst [t970], Atkin [1972] and Levine [in press]. In general these suggestions relate to scaling problems in psychophysics and in social psychology. The purpose of the present note is to extend these applications to test theory. One of the models proposed by Rasch [1960] can be seen as a special case of the projective transformation and this fact has certain implications for the use of the model.

Type
Original Paper
Information
Psychometrika , Volume 39 , Issue 3 , September 1974 , pp. 359 - 360
Copyright
Copyright © 1974 The Psychometric Society

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Footnotes

*

This paper was prepared while the writer was a Visiting Professor at the University Kebangsaan of Malaysia. Helpful discussions with Dr. J. L. Cornette, University of Iowa, and Professor P. G. Herbst, University of Oslo are acknowledged. The opinions are those of the author.

References

Atkin, R. H. From cohomology in physics to φ-connectivity in social sicence. International journal of man-machine studies, 1972, 4, 139–167.CrossRefGoogle Scholar
Herbst, P. Behavioural Worlds—the study of individual cases, 1970, London: Tavistock.Google Scholar
Levine, M. V. Geometric interpretations of some psychological results. In Atkinson, R. C., David Krantz, R. Duncan, Luce, and Suppes, P. (Eds.). Contemporary Developments in Mathematical Psychology. In press, 1973.Google Scholar
Rasch, G. Probabilistic models for some intelligence and attainment tests, 1960, Copenhagen: Nielsen and Lydiche (for Danmark Paedagogiske Institut).Google Scholar
Struik, D. J. Lectures on analytic and projective geometry, 1952, Reading, Mass.: Addison-Wesley.Google Scholar