Interactions with latent continuous v... PreviousNext
Mplus Discussion > Structural Equation Modeling >
 Karen S. Mitchell posted on Friday, April 11, 2008 - 2:10 pm

I am testing an interaction with latent continuous variables. I have two questions: first, the coefficient for the interaction term was significant. However, statistical comparison of this model to one without the interaction term (following the equations in the technical appendices for computing a chi-square difference test for MLR estimation) yielded a non-significant chi square value. Does this mean that I should not interpret the interaction?

Second, concerning interpretation of latent interactions, it seems that following the Aiken and West approach is recommended. From reading threads on this website, it appears that I would plot lines for equations with the path coefficients (b1, b2, and b3) for low and high values of the predictor and moderator, as factor means are 0. What is the best way to obtain high and low factor values--is calculating the standard deviation from the variance obtained in the measurement model acceptable?
 Bengt O. Muthen posted on Friday, April 11, 2008 - 3:36 pm
Your first paragraph concerns differences in results using Wald testing and using Likelihood ratio testing. That can happen in cases with either not large enough samples or not large enough effects. Typically the two tests agree.

Second, high and low factor values can be computed using the factor mean and variance estimates. Use e.g. + and - 1 SD from the mean. For an example in a growth model context, see handout for Topic 2 on our web site, slides 125-132.
 Bengt O. Muthen posted on Friday, April 11, 2008 - 3:45 pm
I meant to say Topic 3.
 Jeremiah Schumm posted on Wednesday, July 16, 2008 - 11:49 am
Prof Muthen:

I am having difficulty bridging the example presented in Topic 3 slides 125-132 regarding the interpretation of latent continuous interactions in a non-growth model.

Could you please indicate where the latent variable means would be listed in the Mplus output (i.e., what is the label of the row and column heading in the output)? Also could you please point out where the variance estimate of the of the latent variables would listed in the output? I want to make sure that I am understanding the correct location to obtain this information in the output for the purposes of graphing this interaction.
 Linda K. Muthen posted on Wednesday, July 16, 2008 - 3:15 pm
That information would be in TECH4 of the OUTPUT command.
 Jeremiah Schumm posted on Thursday, July 17, 2008 - 10:46 am
Thank you. I did not request the tech 4 output, which led to the confusion.
 Gregory Stevens posted on Monday, April 16, 2012 - 9:00 am
Hello Drs. Muthen,

Following up on the question above, I have defined interactions between latent factors using XWITH, which requires ANALYSIS: TYPE IS RANDOM. Under these settings, TECH4 is not an available output. Is there anywhere else to get the factor means so as to plot the interactions?

 Linda K. Muthen posted on Monday, April 16, 2012 - 1:36 pm
You would need to use MODEL CONSTRAINT to define the factor means using the intercepts and other model parameters. See the user's guide for more information on how to use MODEL CONSTRAINT.
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