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Mplus Discussion > Structural Equation Modeling >
 Lia Smith posted on Sunday, February 18, 2018 - 7:52 pm
Hello Drs. Muthen,

I am working on a SEM model with 2 latent variables (PTSD, SLEEP) and their Interaction (PTSDxSLP) predicting two latent variables (ALC, COPE).

When I run the model without the XWITH interaction defined (i.e. the main effects model), I get higher R-Squared values than when I add in the Interaction term (i.e. the interaction model). Despite the lower R-Squared values in the interaction model, the interaction term for both outcomes (ALC and COPE) is statistically significant. I am confused by this as 1) I would have expected the amount of explained variance to increase with the addition of the interaction term and 2) there is statistical significance without an increase in explained variance (per my current output).

I have reviewed the Latent Variable Interactions FAQ (, but was confused as to whether the computation of R-Squared detailed in that document is used in M-Plus 8 and included in the STDYX output or if I need to do all those computations separately?

If they are included in the STDYX output already, could you help me to understand the theory as to how the R-Squared would decrease when adding in the interaction term?

Thank you in advance for your time and consideration!

Warm regards,
 Bengt O. Muthen posted on Monday, February 19, 2018 - 4:48 pm
Because you have a significant effect of the interaction on your DV factor, the model without it is misfitting and should not be interpreted, including its R-square.

The R-square expressions shown in that document are indeed used in the Mplus V8 output.
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