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September, 1990 Asymptotic Chi-Square Tests for a Large Class of Factor Analysis Models
Yasuo Amemiya, T. W. Anderson
Ann. Statist. 18(3): 1453-1463 (September, 1990). DOI: 10.1214/aos/1176347760

Abstract

Three types of asymptotic $\chi^2$ goodness-of-fit tests derived under the normal assumption have been used widely in factor analysis. Asymptotic behavior of the test statistics is investigated here for the factor analysis model with linearly or nonlinearly restricted factor loadings under weak assumptions on the factor vector and the error vector. In particular the limiting $\chi^2$ result for the three tests is shown to hold for the factor vector, either fixed or random with any distribution having finite second-order moments, and for the error vector with any distribution having finite second-order moments, provided that the components of the error vector are independent, not just uncorrelated. As special cases the result holds for exploratory and confirmatory factor analysis models and for certain nonnormal structural equation (LISREL) models.

Citation

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Yasuo Amemiya. T. W. Anderson. "Asymptotic Chi-Square Tests for a Large Class of Factor Analysis Models." Ann. Statist. 18 (3) 1453 - 1463, September, 1990. https://doi.org/10.1214/aos/1176347760

Information

Published: September, 1990
First available in Project Euclid: 12 April 2007

zbMATH: 0706.62056
MathSciNet: MR1062719
Digital Object Identifier: 10.1214/aos/1176347760

Subjects:
Primary: 62H25
Secondary: 62F05

Rights: Copyright © 1990 Institute of Mathematical Statistics

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Vol.18 • No. 3 • September, 1990
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