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A Newton-Raphson algorithm for maximum likelihood factor analysis

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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.

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Authors and Affiliations

  1. University of California, Los Angeles

    Robert I. Jennrich & Stephen M. Robinson

  2. United States Army, USA

    Robert I. Jennrich & Stephen M. Robinson

Authors
  1. Robert I. Jennrich
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  2. Stephen M. Robinson
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Additional information

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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Jennrich, R.I., Robinson, S.M. A Newton-Raphson algorithm for maximum likelihood factor analysis. Psychometrika 34, 111–123 (1969). https://doi.org/10.1007/BF02290176

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  • DOI: https://doi.org/10.1007/BF02290176

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