Detection of differential item functioning using the lasso approach

This paper proposes a novel approach to detect differential item functioning (DIF) among dichotomously scored items. Unlike standard DIF methods that perform an item-by-item analysis, we propose the “LR lasso DIF method”: logistic regression (LR) model is formulated for all item responses. The model contains item specific intercepts, an effect of the sum score and item-group interaction (i.e. DIF) effects, with a lasso penalty on all DIF parameters. Optimal penalty parameter selection is investigated through several known information criteria (AIC, BIC and cross-validation) as well as through a newly developed alternative. A simulation study was conducted to compare the global performance of the suggested “LR lasso DIF” method to the logistic regression and Mantel-Haenszel methods (in terms of false alarm and hit rates). It is concluded that for small samples the LR lasso DIF approach globally outperforms the logistic regression method, and also the Mantel-Haenszel method, especially in the presence of item impact, while it yields similar results with larger samples.