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 Steffen Nestler posted on Tuesday, April 23, 2013 - 10:34 am
Dear Dr. Muthén's,

in a forthcoming paper we want to test a theory that - on a more abstract level - assumes that the relation between latent variables X and Y is mediated by the latent interaction of M1 and M2.

If I am correct that Mplus does not support the estimation of such a model as it does not allow the latent interaction to be an endogenous variable? Is this due to the fact that Mplus uses the LMS approach to estimate latent interactions?

Do you come across an approach that allows to model endogenous latent interaction? I have searched the Internet and Web of Science but have not found any useful references. Or is there a mathematical reason to not model nonlinear effects as dependent variables?

Thanks for your help!
Steffen Nestler
 Bengt O. Muthen posted on Tuesday, April 23, 2013 - 12:29 pm
I don't know how to think about an interaction being a dependent variable. Can you enlighten me?
 Steffen Nestler posted on Wednesday, May 29, 2013 - 8:08 am
Dear Dr. Muthén,

Consider the following case: In a longitudinal study, participants have been measured at two time-points on the same psychological construct, e.g. extraversion (X = extraversion at T1, Y = extraversion at T2 - about one year later). To examine the rank-order stability of the participants on the construct, Y is regressed on X.

During the two time-points subjects have also repeately filled out two scales assumed to measure two state variables, e.g., well-being and affect. For each state variable we use a latent growth model to depict the change in the variable across the occassions. We have thus a slope reflecting the change in well-being and a slope that reflects the change in affect.

What we are interested in is whether the change in well-being and affect mediate the decrease in the stability of the construct measured at the two time-points (the slopes are the mediators; this is a simple multiple mediator model). However, what we also want to examine is whether the interaction of the two slopes mediate the decrease in stability. The idea, for instance is, that high rates of change in well-being AND affect go along with more stronger decreases in stability.

This sounds like a mediation model where the interaction serves as a mediator. But perhaps I am wrong here and there is another analysis strategy that one can use. Many thanks in advance for your answer.

Sincerely,
Steffen Nestler
 Bengt O. Muthen posted on Wednesday, May 29, 2013 - 12:19 pm
You talk about a growth model for each state variable with a slope reflecting change. Is that also from 2 timepoints? I don't see how you can get a random slope from only 2 timepoints.
 Steffen Nestler posted on Wednesday, May 29, 2013 - 2:23 pm
Dear Dr. Muthén,

this seems to be a misunderstanding. X refers to extraversion at T1 (e.g. January 2012) and Y to extraversion measured at T2 (with a 1 year delay, e.g. January 2013).

During the year, subjects have ten times filled in two state variable measures(e.g., at march, june, and so on). The first slope refers to the change in well-being across the 10 time-points and and the second slope to the change in affect during the ten time-points. The idea is to the test for a mediation of the X-Y path via slope1, slope2 and their interaction.

Sincerely,
Steffen Nestler
 Bengt O. Muthen posted on Thursday, May 30, 2013 - 5:06 pm
I see. So then you want an interaction between the 2 slopes and the X variable in its influence on Y. You would use XWITH for this interaction term since a latent variable is involved.
 Steffen Nestler posted on Friday, May 31, 2013 - 1:29 pm
Dear Dr. Muthén,


Thanks for the hint. Let me get this right, you are suggesting that one should test the effect of the interaction of X x slope1 x slope2 on Y to test whether the effect of X on Y is mediated by slope1 x slope2 interaction (of what my question refered to)?

Thanks again for your help!
Sincerely,
Steffen Nestler
 Bengt O. Muthen posted on Friday, May 31, 2013 - 2:26 pm
Right. Or, X x slope1 and X x slope2.
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