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Mplus Discussion > Multilevel Data/Complex Sample >
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 Michael Covell posted on Saturday, June 08, 2019 - 3:20 pm
Below is copied from Preacher, Zyphur, & Zhang's supplement. How is this multilevel SEM when there are no latent variables specified?

I. 1-1-1 model with fixed slopes (MSEM)
VARIABLE: NAMES ARE id x m y;
USEVARIABLES ARE id x m y;
CLUSTER IS id;
ANALYSIS: TYPE IS TWOLEVEL RANDOM;
MODEL:
%WITHIN%
m ON x(aw);
y ON m(bw);
y ON x;
%BETWEEN%
x m y;
m ON x(ab);
y ON m(bb);
y ON x;
MODEL CONSTRAINT:
NEW(indb indw);
indw=aw*bw;
indb=ab*bb;
 Bengt O. Muthen posted on Saturday, June 08, 2019 - 3:47 pm
There are latent variables involved because of the Mplus latent variable decomposition of x and m into within and between parts. See the paper on our website:

Asparouhov, T. & Muthén, B. (2018). Latent variable centering of predictors and mediators in multilevel and time-series models. Structural Equation Modeling: A Multidisciplinary Journal, DOI: 10.1080/10705511.2018.1511375 (Download scripts).
 Michael Covell posted on Monday, June 10, 2019 - 8:27 pm
Shouldn't multilevel SEM include BY statements? Like, are BY statements excluded from the syntax above as a shorthand?
 Bengt O. Muthen posted on Tuesday, June 11, 2019 - 1:56 pm
One definition of SEM is that it has relationships involving latent variables. That is fulfilled here. Latent variables don't have to be factors using measured BY but can be any latent quantity such as a between-level part of a variable, a random effect, etc.
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