Statistical inference for the penalized EM algorithm to test differential item functioning

Recent advancements in testing differential item functioning (DIF) have greatly relaxed restrictions made by the conventional multiple group item response theory (IRT) model with respect to the number of grouping variables and the assumption of predefined DIF-free anchor items. The application of the $L_1$ penalty in DIF detection has shown promising results in identifying a DIF item without a priori knowledge on anchor items while allowing the simultaneous investigation of multiple grouping variables. The least absolute shrinkage and selection operator (LASSO) is added directly to the loss function to encourage variable sparsity such that DIF parameters of anchor items are penalized to be zero. Therefore, no predefined anchor items are needed. However, DIF detection using LASSO requires a non-trivial model selection consistency assumption and is difficult to draw statistical inference. Given the importance of identifying DIF items in test development, this study aims to apply the decorrelated score test to test DIF once the penalized method is used. Unlike the existing regularized DIF method which is unable to test the statistical significance of a DIF item selected by LASSO, the decorrelated score test requires weaker assumptions and is able to provide asymptotically valid inference to test DIF. Additionally, the deccorrelated score function can be used to construct asymptotically unbiased normal and efficient DIF parameter estimates via a one-step correction. The performance of the proposed decorrelated score test and the one-step estimator are evaluated via a Monte Carlo simulation study.