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Axiomatic Foundations of a Three-Set Guttman Simplex Model with Applicability to Longitudinal Data

Published online by Cambridge University Press:  01 January 2025

Linda M. Collins  and
Norman Cliff
Linda M. Collins*
Affiliation:
Health Behavior Research Institute, University of Southern California
Norman Cliff
Affiliation:
University of Southern California
*
Requests for reprints should be sent to Linda M. Collins, Health Behavior Research Institute, University of Southern California, 1985 Zonal Avenue, Los Angeles, CA 90033.
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Abstract

In this paper the usual two-set Guttman simplex model is extended to three sets. The axiomatic foundations of this extention are presented. Two cases are discussed. In Case 1 there is a three-set joint order, while in Case 2 there is a two-set joint order consistent across all levels of the third set. Case 2 represents the first clear formulation of a longitudinal developmental scale. The model is discussed in terms of its most straightforward application, longitudinal developmental data, and in terms of other possible applications.

Keywords

Guttman simplexThree-setThree-wayLongitudinal scaling
Type
Original Paper
Information
Psychometrika , Volume 50 , Issue 2 , June 1985 , pp. 147 - 158
Copyright
Copyright © 1985 The Psychometric Society

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Footnotes

This research was supported in part by NSF grant BNS 8108145.

References

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