Detecting Differential Item Functioning across Multiple Groups Using Group Pairwise Penalty

Abstract We introduce a novel regularization method for detecting differential item functioning (DIF) in two-parameter logistic (2PL) models. Existing regularization methods require choosing a reference group and using an $L_1$ penalty (LP) to shrink the item parameters of focal groups toward those of the reference. This approach has two key limitations: (1) shrinking all focal groups toward a reference is inherently unfair, as results are affected by the choice of reference and direct comparison among focal groups is unavailable and (2) the LP leads to biased estimates because it overly shrinks large nonzero parameters toward zero. These limitations are particularly problematic for intersectional DIF, where various identity aspects intersect to create multiple smaller groups. Our method addresses these issues by penalizing item parameter differences between all pairs of groups using a truncated LP, thereby treating groups equally and avoiding excessive penalization of large differences. Simulations demonstrate that the proposed method outperforms existing approaches by accurately identifying items exhibiting DIF even with multiple small groups. Application to two real-world datasets further illustrates its utility. We recommend this method as a more equitable and precise tool for DIF detection. The proposed method is available as D2PL_pair_em() in the R package VEMIRT ( https://map-lab-uw.github.io/VEMIRT ).