Measurement bias detection through Bayesian factor analysis.

Area of Science:

• Psychometrics
• Statistical Modeling
• Psychological Measurement

Background:

• Measurement bias, a violation of measurement invariance, can distort research findings.
• Restricted factor analysis (RFA) is a statistical technique used to investigate potential sources of measurement bias.
• Detecting complex bias, such as nonuniform bias, requires advanced modeling techniques.

Purpose of the Study:

• To explore a Bayesian approach for estimating RFA models with interaction effects.
• To detect both uniform and nonuniform measurement bias using this Bayesian RFA framework.
• To evaluate the performance of bias detection procedures within the Bayesian RFA model.

Main Methods:

• A simulation study was conducted, varying bias type (uniform, nonuniform), violator type (observed continuous, observed dichotomous, latent continuous), and trait-violator correlation.
• Bayesian restricted factor analysis (RFA) models with interaction terms were estimated.
• Two bias detection procedures, utilizing the DIC fit statistic, were assessed.

Main Results:

• Parameter estimates in the Bayesian RFA models demonstrated satisfactory accuracy.
• Bias detection rates were high when the violator was observed.
• Bias detection remained satisfactory across all simulated conditions, including those with latent violators.

Conclusions:

• The Bayesian approach is effective for estimating complex RFA models, including those with interaction effects necessary for detecting nonuniform bias.
• This method provides accurate parameter estimates and reliable bias detection, enhancing the assessment of measurement invariance.
• The findings support the utility of Bayesian RFA for identifying and addressing measurement bias in various contexts.