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A Reliability Coefficient for Maximum Likelihood Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Ledyard R Tucker  and
Charles Lewis
Ledyard R Tucker
Affiliation:
University of Illinois
Charles Lewis
Affiliation:
University of Illinois
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Abstract

Maximum likelihood factor analysis provides an effective method for estimation of factor matrices and a useful test statistic in the likelihood ratio for rejection of overly simple factor models. A reliability coefficient is proposed to indicate quality of representation of interrelations among attributes in a battery by a maximum likelihood factor analysis. Usually, for a large sample of individuals or objects, the likelihood ratio statistic could indicate that an otherwise acceptable factor model does not exactly represent the interrelations among the attributes for a population. The reliability coefficient could indicate a very close representation in this case and be a better indication as to whether to accept or reject the factor solution.

Keywords

Common FactorFactor ModelReliability CoefficientFactor SolutionLikelihood Ratio Statistic
Type
Original Paper
Information
Psychometrika , Volume 38 , Issue 1 , March 1973 , pp. 1 - 10
Copyright
Copyright © 1973 The Psychometric Society

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Footnotes

*

This research was supported by the Personnel and Training Research Programs Office of the Office of Naval Research under contract US NAVY/00014-67-A-0305-0003. Critical review of the development and suggestions by Richard Montanelli were most helpful.

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