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A New Algorithm for the Least-Squares Solution in Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Masashi Okamoto  and
Masamori Ihara
Masashi Okamoto*
Affiliation:
Osaka University
Masamori Ihara
Affiliation:
Osaka University
*
Requests for reprints should be sent to Masashi Okamoto, Department of Applied Mathematics, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka 560, Japan.
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Abstract

A new algorithm to obtain the least-squares or MINRES solution in common factor analysis is presented. It is based on the up-and-down Marquardt algorithm developed by the present authors for a general nonlinear least-squares problem. Experiments with some numerical models and some empirical data sets showed that the algorithm worked nicely and that SMC (Squared Multiple Correlation) performed best among four sets of initial values for common variances but that the solution might sometimes be very sensitive to fluctuations in the sample covariance matrix.

Keywords

factor analysisleast-squaresMINRESsquared multiple correlation (SMC)up-and-down Marquardt algorithm
Type
Original Paper
Information
Psychometrika , Volume 48 , Issue 4 , December 1983 , pp. 597 - 605
Copyright
Copyright © 1983 The Psychometric Society

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Footnotes

Numerical computation was made on a NEAC S-1000 computer in the Computer Center, Osaka University.

References

Reference Note

Mattsson, A., Olsson, U. & Rosen, M. The maximum likelihood method in factor analysis with special consideration to the problem of improper solutions. Research Report, Institute of Statistics, University of Uppsala, 1966.Google Scholar

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