A Newton-Raphson algorithm for maximum likelihood factor analysis |
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Authors: | Robert I Jennrich Stephen M Robinson |
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Institution: | (1) University of California, Los Angeles;(2) United States Army, USA |
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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.
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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Keywords: | |
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