Advantages of Spike and Slab Priors for Detecting Differential Item Functioning Relative to Other Bayesian Regularizing Priors and Frequentist Lasso

An important step in scale development and assessment is to evaluate differential item functioning (DIF) across segments of the population. Recent approaches use lasso regularization simultaneously detect DIF all items avoid incorrect anchor assumptions that incur inflated error rates for classical evaluation methods. Although promising, methods cause underestimated standard errors p-values. alternative Bayesian provides empirical errors. However, we point out using criteria such as credible intervals selecting parameters has limited validity. We argue a spike-and-slab prior with an inclusion probability criterion more theoretically coherent selection inference over regularizing priors rules or frequentist lasso. demonstrate this by simulation studies Multi-group Item Response Theory Moderated Nonlinear Factor Analysis models. Practical utility discussed.