There is no difference, but in the one-dimensional model in AMOS you can make MIMIC SEM model where you can include your SEM model as predictors the variables of age categories, sex, etc, if there is significant effect indicates lack of equivalence otherwise evidence that there is invariance, also allows you to determine evaluate the effect on each element, determining whether there is the differential analysis of the item (DIF)

https://www.youtube.com/watch?v=9j68Q4T7jGI

Thank you very much for your help.

Hi folks,

if you allow some "fine tuning": In the MIMIC model, you have causal predictors (not outcomes) of your latent variable(s) and potential direct effects resemble lack of scalar invariance (observed means differ across groups beyond what would be expected from latent mean differences. What you cannot test is for metric invariance --and this is far more essential. Beyond that, a direct effect in the MIMIC model would lead me to question whether the common factor model holds at all. And finally, MIMIC models of course can be applied to several latent variable models (why not?). In such situation, you would have external variables having effect of all or several latent variables and potentially indicators. But as I have said above, direct effects probably have more severe interpretations than just mean differences.

This paper is interesting in this regard:

Cadogan, J. W., Lee, N., & Chamberlain, L. (2013). Formative variables are unreal variables: Why the formative MIMIC model is invalid. AMS Review, 3(1), 38-49. doi:10.1007/s13162-013-0038-9

With regard to your question about differences between a single factor model and multiple factor model: Firstly, the latter provides a more challenging test for your structure (beyond the invariance issue). Secondly, testing invariances can include the covariances among the latent variables or structural effects (if you have a full SEM instead of mere CFA). This provides either further evidence for the important question whether you measure the same thing or evidence for a moderation. Note that moderation requires equality of constructs and measurement (equal loadings). Otherwise you have no moderation but simply relationships among different things.

Best,

Holger