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Recent advancements in testing differential item functioning (DIF) havegreatly relaxed restrictions made by the conventional multiple group itemresponse theory (IRT) model with respect to the number of grouping variablesand 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 DIFitem without a priori knowledge on anchor items while allowing the simultaneousinvestigation of multiple grouping variables. The least absolute shrinkage andselection operator (LASSO) is added directly to the loss function to encouragevariable sparsity such that DIF parameters of anchor items are penalized to bezero. Therefore, no predefined anchor items are needed. However, DIF detectionusing LASSO requires a non-trivial model selection consistency assumption andis difficult to draw statistical inference. Given the importance of identifyingDIF items in test development, this study aims to apply the decorrelated scoretest to test DIF once the penalized method is used. Unlike the existingregularized DIF method which is unable to test the statistical significance ofa DIF item selected by LASSO, the decorrelated score test requires weakerassumptions and is able to provide asymptotically valid inference to test DIF.Additionally, the deccorrelated score function can be used to constructasymptotically unbiased normal and efficient DIF parameter estimates via aone-step correction. The performance of the proposed decorrelated score testand the one-step estimator are evaluated via a Monte Carlo simulation study.

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