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Mplus Discussion > Multilevel Data/Complex Sample >
 Lesa Hoffman posted on Thursday, December 26, 2013 - 11:48 am
Greetings, I am trying to estimate a three-level model that includes a latent variable interaction at level 3 between an observed level-3 predictor (varA) and a latent level-3 predictor (i.e., a level-3 random intercept, called varB).

In using this syntax in the level-3 model:

intX | varA XWITH varB;
y ON intX;

It tells me "random effect variables cannot be declared at level 3". I have also tried creating a latent factor for varA and varB and interacting those instead, but I get the same error. Any suggestions you can provide would be greatly appreciated!

Thank you,
Lesa Hoffman
 Tihomir Asparouhov posted on Friday, December 27, 2013 - 10:04 am

Just to make sure the model is as you describe. You need a good measurement model for VarB (the above interaction portion would not be good enough to identify VarB in most cases). Also you should have Y on VarA VarB in the model as well I think.

Currently you can do this model in two steps only. Estimate the model without the interaction using Bayes or ML and get imputed estimates for the factor(Bayes) or factor scores(ML). Then form the interaction with those factor score using the factor score estimates and with the define command. This will give you a clue about the significance of the interaction. The method is imperfect because it doesn't account for the error in the factor score estimate but it looks like the best possibility at this point.
 Lesa Hoffman posted on Saturday, December 28, 2013 - 6:29 am
Hi Tihomir,

Thanks for your help! Btw, I did have the other syntax you referred to as well, I just didn't include it so as to keep my post as brief as possible. I will try your suggestion for the interaction.

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