SEM latent variable interaction indir...
Message/Author
 Rebecca A Ferrer posted on Thursday, February 06, 2014 - 12:03 pm
I am trying to calculate indirect effects in structural equation modeling with continuous factor indicators and an interaction between two latent variables.

The model is roughly:
f1 by y1-y9;
f2 by y10-y19;
f3 by y20-y29;
f3 on f1 f2;
f1xf2 | f1 xwith x2;
f3 on f1xf2;

The model indirect command is not available on analysis type = random/ algorithm = integration.

My general understanding from sorting through the discussion boards is that indirect paths for this type of model cannot be estimated using Mplus, but that it might be possible to calculate the indirect effects by hand using information from the output. Is that correct? If so, if you know of any references for these calculations, I would be very appreciative. Thank you in advance.
 Bengt O. Muthen posted on Thursday, February 06, 2014 - 2:20 pm
What is the indirect effect you consider here? I see only one regression equation:

f3 on f1 f2 f1xf2;

Or do you consider your factor indicators as the distal outcomes?
 Rebecca A Ferrer posted on Saturday, February 08, 2014 - 8:10 am
I'm sorry, I completely omitted that line of the model!

The model is roughly:
f1 by y1-y9;
f2 by y10-y19;
f3 by y20-y29;
f3 on f1 f2;
y30 on f3;
f1xf2 | f1 xwith x2;
f3 on f1xf2;

I'm trying to estimate the indirect effects of f1/ f2/ f1xf2 to y30 (a measured outcome) via f3.

Thanks!
 Bengt O. Muthen posted on Monday, February 10, 2014 - 10:29 am
I would take the same approach as for observed variable mediation with an interaction. See our UG ex 3.18. The interaction implies moderation in line with regular moderated mediation modeling.

To make the interpretation easier, set the metric of f1 and f2 by fixing their variances at one instead of the first loading so you get those factors in standardized metric (mean zero, var zero). Pick one of them as the moderator based on substantive interest. You then get the moderated mediation plot using the Model Constraint setup. As a first step, you may want to run UG ex3.18 using the data and setup on our website to see what it looks like.
 Rebecca A Ferrer posted on Thursday, February 13, 2014 - 6:08 am
Thank you! That response is greatly appreciated.
 Amber Williams posted on Monday, April 21, 2014 - 9:01 pm
Hi Drs. Muthen,

I am also wondering if I can do a model indirect (or check for significant mediation) with latent variable interactions (xwith), given that type=RANDOM for such an interaction, which is not allowed. I found this on the MPlus forum, but am not sure how to carry this out.

"In this case you replace Model Indirect with Model Constraint where you define your indirect effect using labels given to your slope parameters in the Model command."

Any guidance/sample syntax would be greatly appreciated. Thank you
 Linda K. Muthen posted on Tuesday, April 22, 2014 - 10:10 am
See the following two FAQ's on the website:

Latent variable interactions
Latent variable interaction LOOP plot
 Florian Kaiser posted on Thursday, September 15, 2016 - 6:16 am
I am estimating a longitudinal SEM with continuous factor indicators and an interaction between two LVs (one is the mediator). My DV is a count variable. The IV is binary.

The model (without mean structure):
f11 by y1-y3* (1-3);
f12 by y4-y6* (4-6);
f21 by y7-y9* (1-3);
f22 by y10-y12* (4-6);
f12xf22 | f12 xwith f22;

f11@1; f21@1;
f12*; f22*;

c on f12 f22 f12xf22;
f22 on u;

f12 on f11;
f22 on f21;

Using the xtwith command with a count DV, Mplus does not provide stand coeff and indirect effects (u -> f22 -> c).

My questions are:
1) How is it possible to calculate the indirect effect from u to c considering thereby the latent interaction? (The indirect effect may vary depending on the level of f12.)
2) How is it possible to calculate stand coefficients from the unstand model results? What is with standard errors and CIs?
3) With a count DV, would you recommend to calulate STDX or use the raw solution for the regression coefficients concerning the count DV? Is it correct to use STDY for "f2 on u"?
4) Estimating this model with two different samples (with slightly different measures), would you recommend me to compare the standardized or unstandardized results?
 Florian Kaiser posted on Thursday, September 15, 2016 - 6:19 am
Sry the equality constraints have to be:

The model (without mean structure):
f11 by y1-y3* (1-3);
f12 by y4-y6* (1-3);
f21 by y7-y9* (4-6);
f22 by y10-y12* (4-6);
 Bengt O. Muthen posted on Thursday, September 15, 2016 - 10:34 am
Indirect effects for a count outcome needs special computations. See our new book at

http://www.statmodel.com/Mplus_Book.shtml