Detection of Differential Item Functioning Using the Lasso Approach

Abstract

This article 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 (Akaike information criterion, Bayesian information criterion, 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 LR 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 LR method, and also the Mantel-Haenszel method, especially in the presence of item impact, while it yields similar results with larger samples.

Regularized Structural Equation Modeling

“…A recent overview of using the lasso for regression (McNeish, 2015), along with applications in differential item functioning (Magis, Tuerlinckx, & Boeck, 2014;Tutz & Schauberger, 2015), highlight this movement. It is fitting that regularization will start its proliferation at the same time that we face a crisis of replication (e.g., Pashler & Wagenmakers, 2012).…”

Item-focussed Trees for the Identification of Items in Differential Item Functioning

“…The test scores are used as a proxy for the ability of a person. However, test scores as the number of solved items are sufficient statistics for ability parameters only if the Rasch model holds, that is, if no DIF is present (see also Magis et al 2015). Nevertheless, it provides a general method to investigate DIF.…”

“…For comparison, we also consider the logistic regression method that was proposed by Swaminathan and Rogers (1990) and, more recently, extended by Magis et al (2015). The basic concept is to fit a logistic model for answering an item correctly given the test score and the group membership.…”

“…If one has only two groups, there is only one parameter for each item. Following Magis et al (2015), the parameters β 0i can be seen as the counterparts of the item difficulties and the parameters β i as the counterparts of item discrimination parameters. The parameters of interest, however, are the parameters γ i1 , .…”

“…Alternatively, one may use boosting techniques to reduce the number of parameters . A regularization method that uses the logistic regression approach to DIF detection was proposed by Magis, Tuerlinckx, and De Boeck (2015). A further approach that is also able to handle several groups and continuous variables was proposed by Strobl, Kopf, and Zeileis (2015).…”