Annals of Statistics

Asymptotic Chi-Square Tests for a Large Class of Factor Analysis Models

Yasuo Amemiya and T. W. Anderson

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 18, Number 3 (1990), 1453-1463.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176347760

Digital Object Identifier
doi:10.1214/aos/1176347760

Mathematical Reviews number (MathSciNet)
MR1062719

Zentralblatt MATH identifier
0706.62056

JSTOR
links.jstor.org

Subjects
Primary: 62H25: Factor analysis and principal components; correspondence analysis
Secondary: 62F05: Asymptotic properties of tests

Keywords
Factor analysis goodness-of-fit test asymptotic robustness structural equation model

Citation

Amemiya, Yasuo; Anderson, T. W. Asymptotic Chi-Square Tests for a Large Class of Factor Analysis Models. Ann. Statist. 18 (1990), no. 3, 1453--1463. doi:10.1214/aos/1176347760. https://projecteuclid.org/euclid.aos/1176347760


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