, Volume 34, Issue 1, pp 111–123 | Cite as

A Newton-Raphson algorithm for maximum likelihood factor analysis

  • Robert I. Jennrich
  • Stephen M. Robinson


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.


Covariance Public Policy Local Maximum Statistical Theory Likelihood Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Psychometric Society 1969

Authors and Affiliations

  • Robert I. Jennrich
    • 1
    • 2
  • Stephen M. Robinson
    • 1
    • 2
  1. 1.University of CaliforniaLos Angeles
  2. 2.United States ArmyUSA

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