Ramsay-Curve Differential Item Functioning

Differential item functioning (DIF) occurs when an item on a test, questionnaire, or interview has different measurement properties for one group of people versus another, irrespective of true group-mean differences on the constructs being measured. This article is focused on item response theory based likelihood ratio testing for DIF (IRT-LR or IRT-LR-DIF). Historically, the models have been fitted assuming the latent variables for both reference and focal groups are normal, but this is unnecessary. A new variation, called Ramsay-curve DIF (RC-DIF), is introduced here. In RC-DIF, the latent density for both groups is estimated simultaneously with the item parameters. Similar approaches in which the density for only one group is estimated, or the densities are estimated as empirical histograms (EHs), are also studied. Free software is available from the author to test each item individually for DIF with the latent densities estimated as EHs or RCs. A simulation study shows that these methods improve results compared with assuming normality mistakenly, and an empirical example illustrates the procedures.