Bayesian Adaptive Lasso for the Detection of Differential Item Functioning in Graded Response Models

The detection of differential item functioning (DIF) is important in psychological and behavioral sciences. Standard DIF detection methods perform an item-by-item test iteratively, often assuming that all items except the one under investigation are DIF-free. This article proposes a Bayesian adaptive Lasso method to detect DIF in graded response models (GRMs), where the DIF effects for all items can be identified simultaneously. The multiple-group GRMs are specified, and the possible DIF effects for each item are reparameterized using the increment components. Then, a Bayesian adaptive Lasso procedure is developed for parameter estimation, in which DIF effects can be automatically obtained. Our method is evaluated and compared with the commonly used likelihood ratio test method in a simulation study. The results show that our method can recover most model parameters well and has better control of false positive rates in almost all conditions. An application is presented using data from the National Longitudinal Study of Adolescent to Adult Health (Add Health).