Latent growth model with moderation
Message/Author
 Curtis Chen posted on Tuesday, June 24, 2014 - 12:45 am
Hello ,

I have a problem about latent growth model with moderation. Here are 7 main variable which are all latent variables: outcome variable-Y1, Y2, Y3, Y4; predictor-X1, X2 which are indicators of X3 (second-order). I want to test whether the path X3 to Y1, Y2, Y3, Y4 is moderated by M (latent). Y1 to Y4 are outcomes at 4 time points. Syntax I would try is as below. Could you please see if it is correct. Thank you so much.

VARIABLE: NAMES = Y1 Y2 Y3 Y4 X1 X2 M b1 b2 c1 c2 a1 a2;
ANALYSIS: TYPE = RANDOM;
ALGORITHM = INTEGRATION;
MODEL: X1 BY b1 b2;
X2 BY c1 c2;
X3 BY X1 X2;
M BY a1 a2;
Y1 Y2 Y3 Y4 ON X3;
Y1 Y2 Y3 Y4 ON M;
inter| X3 xwith M;
I S | Y1@0 Y2 Y3 Y4 @1;
I S on inter X3;
OUTPUT: TECH1 TECH8;
PLOT:TYPE = plot3;
SERIES = Y1 Y2 Y3 Y4 (*);

Best regards.

Curtis
 Bengt O. Muthen posted on Tuesday, June 24, 2014 - 11:32 am
The syntax looks ok, but that's a very complex model, having X3 and M influence both the growth factors and the growth factor indicators directly. I am not sure how that model is identified. Also, your model has a "treatment-mediator" interaction so the indirect effect estimation has to be done using counterfactually-defined "causal" effects - see the paper on our website:

Muthén, B. & Asparouhov T. (2014). Causal effects in mediation modeling: An introduction with applications to latent variables. Forthcoming in Structural Equation Modeling.
 Curtis Chen posted on Wednesday, June 25, 2014 - 8:43 am
Hello,

Thank you so much for your response, Dr. Muthen. But I have some more questions. The syntax is written according to my model, which is built based on theory from literatures. I do not respect the model as complex as you say.

The main hypothesis I want to test is simply that 4 waves outcome variable are influenced by a predict variable, which is moderated by a moderator. All variables are latent and predict variable is second-order. I want to see if the moderation effect would affect the intercept and shape(slope) of the 4 waves outcome.

I am afraid that I am not able to interpret such complex model (treatment mediator, causal effect and so forth). Is there any probability to simplify my model? For example, transform the latent moderator to observed variable ( I know this is not a good method). Thank you!

Best regards,

Curtis
 Bengt O. Muthen posted on Wednesday, June 25, 2014 - 5:57 pm
You may want to ask this type of general modeling question on SEMNET.

Note that predictors that influence your growth factors as in your statement

I S on inter X3;

also influence the growth outcomes Y1-Y4 indirectly. My point was that you cannot also identify direct effects of the predictors onto Y1-Y4. These are basic growth modeling issues that we discuss in short course Topics 3-4 on our website.
 Curtis Chen posted on Thursday, June 26, 2014 - 3:09 am
Hello,

Thank you, Dr. Muthen. I got your point. I will modify my model as you suggested.

Best regards,

Curtis
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