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.
2. Question: Assuming that the syntax is correct are there any ways to get any information regarding specific parameters? As far as I can see it, this way it is only possible to evaluate the global fit and not differences like different factor means or different correlation coefficients?
3. Question: Assuming that the syntax is correct, would you still call that a growth modell?
1. Yes, correct. No need for the growth model part.
2. You can estimate factor mean differences if you apply scalar invariance instead of the metric invariance you use (add intercept invariance). Any parameter difference for fathers vs mothers can be expressed as NEW parameter in Model Constraint and thereby get tested.