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A Note on the Likelihood Ratio Test in High-Dimensional Exploratory Factor Analysis

Published online by Cambridge University Press:  01 January 2025

Yinqiu He ,
Zi Wang  and
Gongjun Xu Open the ORCID record for Gongjun Xu [Opens in a new window]
Yinqiu He
Affiliation:
University of Michigan
Zi Wang
Affiliation:
University of Michigan
Gongjun Xu*
Affiliation:
University of Michigan
*
Correspondence should be made to Gongjun Xu, Department of Statistics, University of Michigan, 456 West Hall, 1085 South University, Ann Arbor, MI48109, USA. Email: gongjun@umich.edu
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Abstract

The likelihood ratio test is widely used in exploratory factor analysis to assess the model fit and determine the number of latent factors. Despite its popularity and clear statistical rationale, researchers have found that when the dimension of the response data is large compared to the sample size, the classical Chi-square approximation of the likelihood ratio test statistic often fails. Theoretically, it has been an open problem when such a phenomenon happens as the dimension of data increases; practically, the effect of high dimensionality is less examined in exploratory factor analysis, and there lacks a clear statistical guideline on the validity of the conventional Chi-square approximation. To address this problem, we investigate the failure of the Chi-square approximation of the likelihood ratio test in high-dimensional exploratory factor analysis and derive the necessary and sufficient condition to ensure the validity of the Chi-square approximation. The results yield simple quantitative guidelines to check in practice and would also provide useful statistical insights into the practice of exploratory factor analysis.

Keywords

exploratory factor analysislikelihood ratio testChi-square approximation

Information

Type
Theory and Methods (T&M)
Information
Psychometrika , Volume 86 , Issue 2 , June 2021 , pp. 442 - 463
Copyright
Copyright © 2021 The Psychometric Society

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Footnotes

This research is partially supported by NSF CAREER SES-1846747, DMS-1712717, and SES-1659328

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