Likelihood-ratio DIF testing: Effects of nonnormality

Differential item functioning (DIF) occurs when an item has different measurement properties for members of one group versus another. Likelihood-ratio (LR) tests for DIF based on item response theory (IRT) involve statistically comparing IRT models that vary with respect to their constraints. A simulation study evaluated how violation of the normality assumption about the random latent variable for one or both groups affected IRT-LR-DIF results. Item response data with or without DIF were generated from the two-parameter logistic model and fitted Under the assumption that the latent distribution was normal for both groups. Although the IRT-LR-DIF method performed well when latent distributions were normal for both groups, results were distorted when the distribution was skewed for one or both groups. Specifically, Type I error was inflated, differences between reference- and focal-group item parameter estimates were inaccurate, and group differences in the mean and variance of the latent distribution were overestimated.