If I understand anything about Luedtke et al 2008 'The Multilevel Latent Covariate Model' then it would mean that we should take account of the variance of contextual variables which are derived from (function of) aggregate of individual level variables.
In my context, the multilevel structure is individual nested in area.
Now, I may have a 'similar' situation where the contextual variables are not aggregated from the same sample but imported from another sample (about the same area or context). Thus there are area/contextual level variables WITH their variances known.
If I haven't read Luedtke et al, I would just use the imported area/contextual level variables as they come. However, I'm not innocent anymore, so how do I specify a multilevel model where the variance of the area/contextual level are also accounted for? In other words, how do I specify the known variance of area level variables?
The Mplus decomposition into level1 and level 2 components that Ludtke et al discuss need the individuals' raw data to actually create the latent predictor variables on the two levels. The variances on the different levels are not sufficient.