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

Yinqiu He1, Zi Wang1, Gongjun Xu2

  • 1Department of Statistics, University of Michigan, 456 West Hall, 1085 South University, Ann Arbor, MI, 48109, USA.

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|March 26, 2021
PubMed
Summary
This summary is machine-generated.

The likelihood ratio test (LRT) in exploratory factor analysis fails with high-dimensional data. This study provides conditions to ensure the Chi-square approximation

Keywords:
Chi-square approximationexploratory factor analysislikelihood ratio test

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Area of Science:

  • Statistics
  • Psychometrics
  • Data Science

Background:

  • The likelihood ratio test (LRT) is a standard method for assessing model fit in exploratory factor analysis (EFA).
  • The classical Chi-square approximation for the LRT statistic is known to fail when data dimensionality is high relative to sample size.
  • Existing research lacks clear guidelines on the validity of this approximation in high-dimensional EFA.

Purpose of the Study:

  • To investigate the failure of the Chi-square approximation of the LRT in high-dimensional EFA.
  • To derive the necessary and sufficient conditions for the validity of the Chi-square approximation.
  • To provide practical guidelines for researchers using EFA.

Main Methods:

  • Theoretical investigation of the LRT statistic under high-dimensional conditions.
  • Derivation of mathematical conditions for the Chi-square approximation's validity.
  • Analysis of the impact of data dimensionality on LRT performance.

Main Results:

  • Identified the precise conditions under which the Chi-square approximation of the LRT fails in high-dimensional EFA.
  • Derived a necessary and sufficient condition for the validity of the Chi-square approximation.
  • Developed simple, quantitative guidelines for practical use.

Conclusions:

  • The study addresses a critical limitation of LRT in high-dimensional EFA.
  • Provides essential statistical insights and practical guidance for researchers.
  • Enhances the reliability of model fit assessment in EFA with large datasets.