

Endogenous factor intercepts vary acr... 

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Dear Mplus Team and User Colleagues We are working on an introductory text for Multilevel SEM, using Mplus, and came across a question: latent variables defined at the within level cannot have an intercept varying across groups. However, we are able to include a random slope for the regression of a withinlevel latent variable on a withinlevel covariate. If this works like nonSEM multilevel models, however, we understand that a random slope model should also have a random intercept, or estimates of the effect of a betweenlevel covariate on the random slope would be biased. An example model syntax of this model (which we are able to run) is below: MODEL: %within% fw1 by y1y3; fw2 by y4y6; s  fw2 on xw; fw2 on fw1; %between% fb1 by y1y3; fb2 by y4y6; fb2 on xb fb1; s on xb; We sense that either this is not interpretable, or there should be also a "fw2 on xb" on the %between% part, which returns an error message that withinlevel variable cannot be used at the betweenlevel (fw2). 


You can modify the model as follows MODEL: %within% fw1 by y1 y2y3 (l1l2); fw2 by y4 y5y6 (l3l4); s  fw2 on xw; fw2 on fw1; %between% fb1 by y1 y2y3 (l1l2); fb2 by y4 y5y6 (l3l4); fb2 on xb fb1; s on xb; In this setup the random intercepts are fb1 and fb2. Some basic algebra happens when you put the twolevels together to see this. If the loadings are not equal between the two levels a random intercepts could be identified on its own but A. they are probably not super well identified B. You need more than 3 indicators because with 3 it is just saturated Further you can add a covariate XW=1 (using an option variance=nocheck) in the data command to allow you no variance covariate. Also factors with random loadings are allowed on the between level. 

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