I'm investigating the measurement invariance of perceived relationship dimensions across parent-child and teacher-child relationship; do children perceive dimensions such as control equally in parent-child and teacher-child relationships. My question is whether I may considered the relationship dimensions in their relationships with parents and teachers as two groups and thus conduct multi-group confirmatory factor analyses, since the same children rate the different relationships (1 sample of children, 2 'groups', dependent samples). If not, how would you go about it?
You would run a single-group analysis where you compare the parent-child versus the teacher-child factor loadings and intercepts. See the Topic 6 course handout under multiple indicator growth where we show how to do this for multiple time points. The issues are the same.