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Comparing Frequentist and Bayesian Methods for Factorial Invariance with Latent Distribution Heterogeneity.

Xinya Liang1, Ji Li1, Mauricio Garnier-Villarreal2

  • 1Department of Counseling, Leadership, and Research Methods, University of Arkansas, Fayetteville, AR 72703, USA.

Behavioral Sciences (Basel, Switzerland)
|April 26, 2025
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Summary
This summary is machine-generated.

Heterogeneity in latent factor variances significantly impacts measurement invariance testing more than mean differences. Likelihood ratio tests and cross-validation methods are more powerful for detecting noninvariance than fit indices.

Keywords:
Bayesian estimationfactorial invariancefit indiceslatent distribution heterogeneitymaximum likelihood estimationmeasurement invariancemodel selection methods

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Area of Science:

  • Psychometrics
  • Social Science Research Methodology
  • Statistical Modeling

Background:

  • Factorial invariance ensures valid comparisons across groups or time in social science.
  • Detecting factorial invariance is complicated by heterogeneity in latent factor distributions.
  • This study investigates the impact of latent mean and variance heterogeneity on invariance detection.

Purpose of the Study:

  • To examine how latent mean and variance differences affect measurement invariance detection.
  • To compare the performance of Bayesian and maximum likelihood fit measures.
  • To evaluate the effectiveness of different model selection methods.

Main Methods:

  • Simulation study with varying sample sizes, noninvariance levels, and latent factor distributions.
  • Comparison of Bayesian and maximum likelihood estimation approaches.
  • Assessment of goodness-of-fit indices, likelihood ratio tests (LRTs), information criteria (ICs), and leave-one-out cross-validation (LOO).

Main Results:

  • Differences in latent factor variance have a greater impact on measurement invariance than differences in latent means.
  • Latent variance heterogeneity more strongly affects scalar invariance testing than metric invariance testing.
  • LRTs, ICs (except BIC), and LOO demonstrated higher power in detecting noninvariance compared to goodness-of-fit indices.

Conclusions:

  • Latent factor variance heterogeneity poses a significant challenge to measurement invariance testing.
  • Likelihood ratio tests and cross-validation techniques offer superior performance for detecting noninvariance.
  • Researchers should consider the impact of latent variance heterogeneity and utilize appropriate statistical methods for robust invariance assessment.