DIF Testing With an Empirical-Histogram Approximation of the Latent Density for Each Group

This research introduces, illustrates, and tests a variation of IRT-LR-DIF, called EH-DIF-2, in which the latent density for each group is estimated simultaneously with the item parameters as an empirical histogram (EH). IRT-LR-DIF is used to evaluate the degree to which items have different measurement properties for one group of people versus another, irrespective of mean differences on the construct. Usually, the latent distribution is presumed normal for both groups, but results are biased if this assumption is violated. Simulations show that if the latent densities are nonnormal, Type I error and estimates of the item parameters and focal-group mean and SD are more accurate using EH-DIF-2 than standard methods. Free software for carrying out EH-DIF-2 is available on request.