Differential Item Functioning, Part 2: Measure Classifications
There are a number of types of DIF measures, which can be categorized into eight octants, based on three dichotomous classifications: whether it focuses on observed scores vs. latent variables, whether it uses parametric vs. nonparametric methods, and whether it is designed for dichotomous vs. polytomous items.
The first category by which measures of DIF are defined is whether they focus on observed scores vs. latent variables. With regards to DIF, observed scores refer to the examinees' actual test scores. Conversely, latent variables refer to the abstract trait (e.g. personality, and IQ) the test is intended to measure, but which cannot be observed directly. For instance, since we cannot directly measure personality, we must estimate based on the results of personality tests. Observed score measures are simpler than latent trait approaches, but are often incapable of detecting the more subtle manifestations of DIF.
Parametric approaches tend to be more powerful than their nonparametric counterparts, but require stronger assumptions (for instance that examinee scores follow a normal distribution). As a result, parametric procedures can be tricky to implement, and may not be applicable in every situation.