Differential item functioning detection with logistic regression

Logistic regression has been used as a method for identifying differential item functioning (DIF) in different contexts. Some studies have shown that DIF detection through this procedure may be affected by variables such as sample size ratio, and sample size. It also seems related to specific item parameters like certain ranges of difficulty and discrimination [Herrera, 2005 ; Santana 2009]. We made a simulation study with four partially crossed independent variables which resulted in 270 conditions and simulated 200 replications for each experimental condition. McFadden’s distance R2 between models (R2∆) was used as an effect size measure and as a dependent variable in order to minimize type I and II errors that the statistical test would not have been able to control. We used linear models to define which variables affected the effect size measures : R2∆ for detecting items with uniform DIF (DRU) and for detecting items with non uniform DIF (DRN). The results show that manipulated variables and some of their interactions affect DRU and DRN differently. We also obtained cut-off points, both for DRU and DRN, for several levels of the variables that affect the R2∆ measures.