Differential Item Functioning: A Mixture Distribution Conceptualization

Differential item functioning (DIF) may be defined as an item that displays different statistical properties for different groups after matching the groups on an ability measure. For instance, with binary data, DIF exists when there is a difference in the conditional probabilities of a correct response for two manifest groups. This article argues that the occurrence of DIF can be explained by recognizing that the observed data do not reflect a homogeneous population of individuals, but are a mixture of data from multiple latent populations or classes. This conceptualization of DIF hypothesizes that when one observes DIF using the current conceptualization of DIF it is only to the degree that the manifest groups are represented in the latent classes in different proportions. A Monte Carlo study was conducted to compare various approaches to detecting DIF under this formulation of DIF. Results showed that as the latent class proportions became more equal the DIF detection methods identification rates approached null condition levels. An empirical data set was used to demonstrate the utility of the approach.