  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.
