Plotting interactions
Message/Author
 Luke Brooks-Shesler posted on Thursday, October 27, 2011 - 7:27 am
Hi everyone,
I'd like to plot an interaction so that I can understand the nature of the interaction...but I can't figure out how to do this.
Using xwith, I created an interaction term, based on 2 latent continuous variables, that predicts a latent continuous outcome variable. The interaction term is significant.
Now how do I plot this interaction?
Thanks for any help with this!
Luke
 Linda K. Muthen posted on Thursday, October 27, 2011 - 12:15 pm
See if Slides 170-171 of the Topic 3 course handout can help you determine the values to plot. You will need to plot them outside of Mplus with R or Excel.
 Luke Brooks-Shesler posted on Tuesday, November 01, 2011 - 10:53 am
Hi Linda,

I wasn't able to figure out the values to plot based on Slides 170 - 171 of Topic 3.

Is there any way to calculate the standardized parameter estimates based on the Mplus output when "xwith" is used?

Luke
 Luke Brooks-Shesler posted on Tuesday, November 01, 2011 - 4:57 pm
Here's an email response from a friend:

"The parameter estimates for the interaction are unstandardized, but they're unstandardized relative to a standardized, latent variable. So the interpretation of the latent interaction is actually in terms of a standardized variable. The gamma weight for the interaction is the rate of change of the XY relationship over Z. To put it a little differently, for every unit increase in Z (i.e., for every SD change in Z) the XY gamma weight changes by the magnitude of the interaction gamma weight.

Although the output suggests that its unstandardized (and it is), the variables it's computed on are standardized (like running a regression using Z-scores) so, in the end, its interpretable as a standardized weight."
 Bengt O. Muthen posted on Tuesday, November 01, 2011 - 5:49 pm
Say that you have the regression

y = b1*x + b2*z + b3*x*z,

where y, x, z are continuous latent variables and x and z have means zero and variances 1. What the Topic 3 slides tell you is that you can rewrite this as a moderated relation, for instance as

y = b1*x + (b2+b3*x)*z

where the second right-hand side terms shows that x moderates the influence of z on y. This means that you can draw a picture with y on the y axis and z on the x axis, where there is a line for each different x value. You can for instance use plus and minus 1 SD from the mean of x. Remember that we have the x SD=1 and mean=0. The z values can vary from say -3SD to +3SD. That's what you plot.