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Additive Structure in Qualitative Data: An Alternating Least Squares Method with Optimal Scaling Features

Published online by Cambridge University Press:  01 January 2025

Jan de Leeuw,
Forrest W. Young and
Yoshio Takane
Jan de Leeuw
Affiliation:
Rijksuniversiteit Te Leiden
Forrest W. Young*
Affiliation:
University of North Carolina
Yoshio Takane
Affiliation:
University of North Carolina
*
Requests for reprints should be sent to Forrest W. Young, Psychometric Laboratory, University of North Carolina, Davie Hall 013 A, Chapel Hill, North Carolina 25714.
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Abstract

A method is developed to investigate the additive structure of data that (a) may be measured at the nominal, ordinal or cardinal levels, (b) may be obtained from either a discrete or continuous source, (c) may have known degrees of imprecision, or (d) may be obtained in unbalanced designs. The method also permits experimental variables to be measured at the ordinal level. It is shown that the method is convergent, and includes several previously proposed methods as special cases. Both Monte Carlo and empirical evaluations indicate that the method is robust.

Keywords

linear modelanalysis of variancemeasurementsuccessive block algorithmquantificationdata analysis

Information

Type
Original Paper
Information
Psychometrika , Volume 41 , Issue 4 , December 1976, pp. 471 - 503
Copyright
Copyright © 1976 The Psychometric Society

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Footnotes

This research was supported in part by grant MH-10006 from the National Institute of Mental Health to the Psychometric Laboratory of the University of North Carolina. We wish to thank Thomas S. Wallsten for comments on an earlier draft of this paper. Copies of the paper and of ADDALS, a program to perform the analyses discussed herein, may be obtained from the second author.

References

Reference Notes

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