Marginalized Measurement Variance Modeling and Bayes Factor Testing (RR 16-06)

Among the assumptions that should be met when applying an item response theory (IRT) model to the analysis of test data is measurement invariance. Measurement invariance requires that, after controlling for a test taker’s proficiency, group membership have no effect on the probability that that test taker will answer a test question correctly. Groups may be defined on the basis of many factors, including gender, race/ethnicity, and citizenship.

This research study proposes and evaluates a new method for detecting violations of the measurement invariance assumption. The method is evaluated through both data simulation and application to actual responses to an international survey. The results obtained by the proposed method are also compared to those obtained using the Mantel–Haenszel statistic, the industry standard for group membership comparisons. Promising results are reported, and plans for extended research are discussed.