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The Nonconvergence of Factals: A nonmetric Common Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Ab Mooijaart
Ab Mooijaart*
Affiliation:
Department of Psychology, Leiden University
*
Request for reprints should be sent to: Ab Mooijaart, Department of Psychology, Leiden University, Hooigracht 15, 2312 KM Leiden, The Netherlands.
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Abstract

FACTALS is a nonmetric common factor analysis model for multivariate data whose variables may be nominal, ordinal or interval. In FACTALS an Alternating Least Squares algorithm is utilized which is claimed to be monotonically convergent.

In this paper it is shown that this algorithm is based upon an erroneous assumption, namely that the least squares loss function (which is in this case a nonscale free loss function) can be transformed into a scalefree loss function. A consequence of this is that monotonical convergence of the algorithm can not be guaranteed.

Keywords

common factor analysisalternating least squares (ALS)loss functionconvergence

Information

Type
Notes And Comments
Information
Psychometrika , Volume 49 , Issue 1 , March 1984 , pp. 143 - 145
Copyright
Copyright © 1984 The Psychometric Society

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References

References notes

Mooijaart, A. and Pol, J. van der (1983). A nonmetric common factor analysis (in Preparation).Google Scholar

References

Harman, H. H. and Jones, W. H. (1966). Factor analysis by minimizing residuals (MINRES). Psychometrika, 31, 351–368.CrossRefGoogle ScholarPubMed
Takane, Y., Young, F. W. and de Leeuw, J. (1979). Non-metric common factor analysis: an alternating least squares method with optimal scaling features. Behaviormetrika, 6, 45–56.CrossRefGoogle Scholar