How to detect which variables are causing differences in component structure among different groups

When comparing the component structures of a multitude of variables across different groups, the conclusion often is that the component structures are very similar in general and differ in a few variables only. Detecting such "outlying variables" is substantively interesting. Conversely, it can help to determine what is common across the groups. This article proposes and evaluates two formal detection heuristics to determine which variables are outlying, in a systematic and objective way. The heuristics are based on clusterwise simultaneous component analysis, which was recently presented as a useful tool for capturing the similarities and differences in component structures across groups. The heuristics are evaluated in a simulation study and illustrated using cross-cultural data on values.