Bayesian penalty methods for evaluating measurement invariance in moderated nonlinear factor analysis.

Area of Science:

• Psychometrics
• Statistical Modeling
• Educational Measurement

Background:

• Measurement invariance (MI) is crucial for comparing latent factor scores across diverse populations.
• Traditional differential item functioning (DIF) detection methods are limited in complex scenarios with multiple correlated grouping variables or covariates.
• Existing approaches often oversimplify practical applications involving numerous demographic and continuous variables.

Purpose of the Study:

• To propose and evaluate Bayesian Moderated Nonlinear Factor Analysis (BMNFA) for detecting DIF in complex settings.
• To investigate the utility of modern Bayesian shrinkage priors for identifying DIF items with multiple groups and covariates.
• To compare the performance of various shrinkage priors against standard and small variance priors.

Main Methods:

• Application of Bayesian Moderated Nonlinear Factor Analysis (BMNFA).
• Utilizing Bayesian shrinkage priors, including lasso-type, spike-and-slab, and horseshoe priors.
• Comparing performance against standard normal and small variance priors in simulations.
• Illustrating the approach with data from the PISA 2018 study.

Main Results:

• Spike-and-slab and lasso shrinkage priors demonstrated superior performance in detecting DIF compared to other methods.
• Horseshoe priors showed slightly lower power for DIF detection than lasso and spike-and-slab.
• Small variance priors exhibited very low power for DIF detection with sample sizes under 800.
• Normal priors were associated with inflated Type I error rates.

Conclusions:

• Bayesian shrinkage priors, particularly lasso and spike-and-slab, offer a powerful approach for detecting DIF in complex, real-world measurement scenarios.
• BMNFA provides a flexible framework for addressing limitations of traditional DIF detection methods.
• The findings support the use of advanced Bayesian techniques for ensuring measurement invariance in heterogeneous populations.