Using Lasso and Adaptive Lasso to Identify DIF in Multidimensional 2PL Models

Differential item functioning (DIF) analysis refers to procedures that evaluate whether an item's characteristic differs for different groups of persons after controlling for overall differences in performance. DIF is routinely evaluated as a screening step to ensure items behave the same across groups. Currently, the majority DIF studies focus predominately on unidimensional IRT models, although multidimensional IRT (MIRT) models provide a powerful tool for enriching the information gained in modern assessment. In this study, we explore regularization methods for DIF detection in MIRT models and compare their performance to the classic likelihood ratio test. Regularization methods have recently emerged as a new family of methods for DIF detection due to their advantages: (1) they bypass the tedious iterative purification procedure that is often needed in other methods for identifying anchor items, and (2) they can handle multiple covariates simultaneously. The specific regularization methods considered in the study are: lasso with expectation-maximization (EM), lasso with expectation-maximization-maximization (EMM) algorithm, and adaptive lasso with EM. Simulation results show that lasso EMM and adaptive lasso EM hold great promise when the sample size is large, and they both outperform lasso EM. A real data example from PROMIS depression and anxiety scales is presented in the end.