Hello. I am proposing a model to predict a student-level (within) outcome that is binary.
At the student-level, I have some observed demographic covariates and 2 latent variables predicting this outcome.
At the school-level (between), I have some school variables (not indicators of latent variables) and then the same two latent variables as in the within-level, but one of them is going to be measured a little differently by using between variables + a within variable, whereas the other is measured by the same 3 within indicators as the latent variable in the within-level.
In the between-level, the observed school variables affect one of the 2 school latent variables, and both school latent variables will predict the within-level student outcome. In other words, one of the latent variables is hypothesized to mediate the effect between those observed school variables and the student-level outcome.
In a lot of examples, I have seen people using the same exact same measurement and structural models at both levels, but mine will have some same but also some different variables in either level. Is there a similar example out there that I can reference?
I think it is likely that models on within and between differ particularly the number of factors. See the following paper that is available on the website:
Muthén, B. & Asparouhov, T. (2011). Beyond multilevel regression modeling: Multilevel analysis in a general latent variable framework. In J. Hox & J.K. Roberts (eds), Handbook of Advanced Multilevel Analysis, pp. 15-40. New York: Taylor and Francis.