Accounting for Differential Item Functioning Using Bayesian Approximate Measurement Invariance.

Area of Science:

• Psychometrics
• Statistical Modeling
• Educational Measurement

Background:

• Establishing measurement invariance is crucial for cross-group comparisons in educational assessments.
• Traditional methods often require strict invariance criteria, which may not be met in real-world data.
• Alternative approaches are needed to reliably compare latent means when exact invariance fails.

Purpose of the Study:

• To apply Bayesian structural equation modeling (BSEM) for approximate measurement invariance (A-MI).
• To evaluate latent mean differences using A-MI criteria in Saudi Arabian national examination data.
• To compare the efficacy of exact versus relative evaluative criteria for measurement invariance.

Main Methods:

• Utilized Bayesian structural equation modeling (BSEM) to establish approximate measurement invariance (A-MI).
• Employed a novel prior-posterior predictive p-value (PPPP) for evaluating group differences.
• Compared latent mean comparisons using exact and relative evaluative-MI protocols with specified prior variances.

Main Results:

• The study demonstrated the utility of BSEM for A-MI as an alternative to strict invariance.
• The prior-posterior predictive p-value (PPPP) effectively identified meaningful group differences.
• Relative evaluative criteria proved valuable when exact measurement invariance was not achieved.

Conclusions:

• Bayesian structural equation modeling (BSEM) offers a flexible framework for approximate measurement invariance (A-MI).
• The prior-posterior predictive p-value (PPPP) is a robust tool for assessing latent mean differences.
• This methodology enhances the validity of cross-group comparisons in educational assessments, even without exact invariance.