Measurement Invariance: Dealing with the Uncertainty in Anchor Item Choice by Model Averaging

Abstract

ABSTRACT A core challenge in modeling partial measurement invariance (MI) is choosing reference items as anchors for which MI indeed holds. Many approaches dealing with this issue have been proposed, each making a different assumption about MI and yielding a single set of anchor items. Here, we consider the case where i) partial MI modeling is used for estimating effects, e.g., a group mean difference, and ii) there is no straightforward theoretical reason to choose specific items as anchors. We argue that in this situation the uncertainty of anchor item choice should be considered and propose to use model averaging with a priori defined model weights. The approach allows not only to depict uncertainty in the anchor items choice but also allows to include prior knowledge and beliefs of the researcher. We derive the properties of the approach and illustrate its use with an example on the assessment of obsessive-compulsive disorder.