Coherent Bayesian Regularization Methods in Measurement Invariance Evaluation

Psychological studies that involve heterogeneous groups need to evaluate scale items and account for any differential item performance in reflecting the underlying constructs. Classical methods to evaluate differential item functioning (DIF) require an anchor item set that remains invariant across groups, yet these methods tend to incur inflated error rates when the anchor item assumption is incorrect. Recent approaches use lasso regularization to simultaneously detect DIF in all items and avoid incorrect anchor item assumptions. Although promising, lasso methods cause other inferential issues such as invalid standard errors and incorrect p-values for regularized estimates. An effective alternative may be Bayesian regularization, which separates variable selection from estimate shrinkage. However, it remains unclear how to choose among various empirical Bayesian variable selection criteria in the DIF detection context. This study clarifies the limitations of empirical Bayesian variable selection criteria. We argue that a spike-and-slab prior with an inclusion probability criterion provides more theoretically coherent DIF selection over other empirical selection rules. We conducted simulation studies with item response theory (IRT) and moderated nonlinear factor analysis (MNLFA) models to demonstrate the advantageous DIF selection performance of the spike-and-slab prior selection rule in comparison to other Bayesian regularizing priors and frequentist lasso. We also compared inferential quality of these DIF selection models and provided practical recommendations for using the spike-and-slab prior rule in measurement invariance evaluation.Master of Art