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A Newton-Raphson Algorithm for Maximum Likelihood Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Robert I. Jennrich  and
Stephen M. Robinson
Robert I. Jennrich
Affiliation:
University of California, Los Angeles United States Army
Stephen M. Robinson
Affiliation:
University of California, Los Angeles United States Army
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Abstract

This paper demonstrates the feasibility of using a Newton-Raphson algorithm to solve the likelihood equations which arise in maximum likelihood factor analysis. The algorithm leads to clean easily identifiable convergence and provides a means of verifying that the solution obtained is at least a local maximum of the likelihood function. It is shown that a popular iteration algorithm is numerically unstable under conditions which are encountered in practice and that, as a result, inaccurate solutions have been presented in the literature. The key result is a computationally feasible formula for the second differential of a partially maximized form of the likelihood function. In addition to implementing the Newton-Raphson algorithm, this formula provides a means for estimating the asymptotic variances and covariances of the maximum likelihood estimators.

Type
Original Paper
Information
Psychometrika , Volume 34 , Issue 1 , March 1969 , pp. 111 - 123
Copyright
Copyright © 1969 The Psychometric Society

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Footnotes

*

This research was supported by the Air Force Office of Scientific Research, Grant No. AF-AFOSR-4.59-66 and by National Institutes of Health, Grant No. FR-3.

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