How Item Residual Heterogeneity Affects Tests for Differential Item Functioning

Differential item functioning (DIF) occurs when people with the same proficiency have different probabilities of giving a certain response to an item. The present study focused on an assumption implicit in popular methods for DIF testing that has received little attention in published literature (item residual homogeneity). The assumption is explained, a strategy for detecting violations of it (i.e., item residual heterogeneity) is illustrated with empirical data, and simulations are carried out to evaluate the performance of binary logistic regression, two-group item response theory (IRT), and the Mantel-Haenszel (MH) test in the presence of item residual heterogeneity. Results indicated that heterogeneity inflated Type I error and attenuated power for logistic regression, and attenuated power and produced biased estimates of the latent focal group mean and standard deviation for two-group IRT. The MH test was robust to item residual heterogeneity, probably because it does not use the logistic function.