Dear forum,

I am currently working on a project where I have two groups (A and B), and I want to compare if a relationship between an IV and a DV significantly differs across the two groups.

Using a structural invariance technique, I compare a constrained model to an unconstrained mode.l In the constrained model, the factor loadings, intercepts and path strengths were set equal across the two groups. In the unconstrained model, only the path strengths were allowed to vary between the models.

By comparing the structural coefficients, the difference between the groups was assessed.

My question is, if this approach also takes into account the difference in lines if the intercepts are different (see attached)? In this example, the line strengths are similar to me (same steepness), and the intercept differs. Would the structural invariance technique also capture these difference in lines between A and B. My first guess is yes, as it also constraints the mean of the IV.

Thanks in advance.