Item response theory–likelihood ratio–differential item functioning (IRT-LR-DIF) is used to evaluate the degree to which items on a test or questionnaire have different measurement properties for one group of people versus another, irrespective of group-mean differences on the construct. Usually, the latent distribution is presumed normal for both groups, but previous research shows that results are biased if the true distribution is not approximately normal. This article introduces a variation of IRT-LR-DIF, called empirical histogram–differential item functioning (EH-DIF), in which the focal-group latent density is estimated simultaneously with the item parameters as an empirical histogram (EH). A simulation study shows that if the focal-group density is nonnormal, Type I error rates and focal-group estimates of the item parameters, mean, and SD are more accurate using EH-DIF than standard IRT-LR-DIF methods that presume normality. A pseudoempirical example is analyzed to illustrate EH-DIF.
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