Different kinds of DIF: A distinction between absolute and relative forms of measurement invariance and bias

In this article, a distinction is made between absolute and relative measurement. Absolute measurement refers to the measurement of traits on a group-invariant scale, and relative measurement refers to the within-group measurement of traits, where the scale of measurement is expressed in terms of the within-group position on a trait. Relative measurement occurs, for example, if an item induces a within-group comparison in respondents. These distinctions are discussed within the framework of measurement invariance, differentiating between absolute and relative forms of measurement invariance and bias. It is shown that items for relative measurement will produce bias as classically defined if the mean and/or variance of the trait distribution differ between groups. This form of bias, however, does not result from multidimensionality but from the fact that measurement is on a relative scale. A logistic regression procedure for the detection of relative measurement invariance and bias is proposed, as well as a model that allows for the incorporation of items for relative measurement in test analysis. Implications of the distinction between absolute and relative measurement are discussed and prove to be especially relevant for the domain of personality research.