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A Monotonically Convergent Algorithm for Factals

Published online by Cambridge University Press:  01 January 2025

Henk A. L. Kiers ,
Yoshio Takane  and
Ab Mooijaart
Henk A. L. Kiers*
Affiliation:
University of Groningen
Yoshio Takane
Affiliation:
McGill University
Ab Mooijaart
Affiliation:
Leiden University
*
Request for reprints should be sent to Henk A. L. Kiers, Department of Psychology, Grote Kruisstraat 2/1, 9712 TS Groningen, THE NETHERLANDS.
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Abstract

Takane, Young, and de Leeuw proposed a procedure called FACTALS for the analysis of variables of mixed measurement levels (numerical, ordinal, or nominal). Mooijaart pointed out that their algorithm does not necessarily converge, and Nevels proposed a new algorithm for the case of nominal variables. In the present paper it is shown that Nevels' procedure is incorrect, and a new procedure for handling nominal variables is proposed. In addition, a procedure for handling ordinal variables is proposed. Using these results, a monotonically convergent algorithm is constructed for FACTALS of any mixture of variables.

Keywords

FACTALSalternating least squaresmonotone regressionmajorization
Type
Original Paper
Information
Psychometrika , Volume 58 , Issue 4 , December 1993 , pp. 567 - 574
Copyright
Copyright © 1993 The Psychometric Society

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Footnotes

The authors are obliged to Jos ten Berge for stimulating comments on an earlier version of this paper. The research of H. A. L. Kiers has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. The research of Y. Takane has been supported by the Natural Sciences and Engineering Research Council of Canada, grant number A6394, and by the McGill-IBM Cooperative Grant.

References

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