Context: I am using SEM (in lavaan) on a sample of about 1000 children between 6-16 years who solved several cognitive tasks. The goal was to establish a model for how different cognitive domains predict reasoning abilities; which has worked very well for the complete sample. The measurement model showed a good fit, and so did my structural model. Here's a picture of my structural model for some background: The next thing I'm interested in is how age groups differ regarding these structural relations. I expect them to differ because cognitive processes might vary depending on developmental stage. I have split my sample into five age groups of n = 200 each. The splits are based on a theory, and my hypotheses are that in specific age groups, the connection between WM and Gf is higher / lower than in others.
Questions: I've established weak measurement invariance in my measurement model - when I constrain the indicator variables' loadings to be the same over all age groups, the model still shows a good fit compared to an unconstrained model. However, when constrain loadings and intercepts to be the same, the AFIs for the measurement model get significantly worse.
- How do I interpret the scalar non-invariance? In other words, what does it mean that intercepts differ across age groups? I'm new to SEM and struggle with understanding the concept of intercepts here.
- Which parameters can I compare between the age groups? My main interest lies in comparing the regression parameters in the SEM (e.g., "in age group 1, the path coefficient between WM and Gf is higher compared to age group 2"), but I'm not sure if that is "allowed" given the weak measurement invariance in the measurement model.
I'd be eternally grateful for help with this and can provide more information if my description wasn't clear enough!