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Determinants of Standard Errors of MLEs in Confirmatory Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Ke-Hai Yuan ,
Ying Cheng  and
Wei Zhang
Ke-Hai Yuan*
Affiliation:
University of Notre Dame
Ying Cheng
Affiliation:
University of Notre Dame
Wei Zhang
Affiliation:
University of Notre Dame
*
Requests for reprints should be sent to Ke-Hai Yuan, University of Notre Dame, Notre Dame, IN 46556, USA. E-mail: kyuan@nd.edu
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Abstract

This paper studies changes of standard errors (SE) of the normal-distribution-based maximum likelihood estimates (MLE) for confirmatory factor models as model parameters vary. Using logical analysis, simplified formulas and numerical verification, monotonic relationships between SEs and factor loadings as well as unique variances are found. Conditions under which monotonic relationships do not exist are also identified. Such functional relationships allow researchers to better understand the problem when significant factor loading estimates are expected but not obtained, and vice versa. What will affect the likelihood for Heywood cases (negative unique variance estimates) is also explicit through these relationships. Empirical findings in the literature are discussed using the obtained results.

Keywords

standard errorconfirmatory factor analysismaximum likelihoodimproper solution
Type
Original Paper
Information
Psychometrika , Volume 75 , Issue 4 , December 2010 , pp. 633 - 648
Copyright
Copyright © 2010 The Psychometric Society

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Footnotes

The research was supported by Grants DA00017 and DA01070 from the National Institute on Drug Abuse.

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