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| Model indirect for residual variances |
 
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Hi Drs Muthen,
I'm aiming to tease apart the general versus specific effects of a categorical predictor u1 on a continuous variable x1 using MODEL INDIRECT. Specifically, I want to see whether (and how much) of the total effect is at the level of the residual variance of x1.
My current syntax is:
variable:
...
usevariable are x1-x3 u1;
weight is weights;
analysis:
estimator = mlr;
model:
f1 by x1* x2 x3;
f1@1;
[f1@0];
f1 on u1;
x1 on u1;
model indirect:
x1 IND u1;
output: stand cint tech1;
The STDY model output looks sensible, and shows that while the total effect is significant, the direct effect is not (80% of the effect is mediated by f1).
The thing I want to clarify is whether the direct effect is based on u1 predicting the residual variance of x1 (after partialling out its shared variance in f1) because the TECH1 output shows x1 in the ALPHA, BETA, and PSI matrices not in the NU, LAMBDA, and THETA matrices. The output lists x1 as a continuous observed dependent variable, but just wanted to double check I'm not missing something in the parameterization of the model.
Thanks for your help!
Miri |
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| Your model does not show any mediation so I don't know why you use Model Indirect. |
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Thanks for your response.
My understanding was that the output from model indirect allows me to see how much of the relationship between u1 and x1 is accounted for by f1.
So the total effect is x1 on u1; the direct effect is x1 on u1, net of f1; and the indirect effect is the proportion of the relationship accounted for by f1.
Is that not right? |
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| My mistake, I didn't see that you have f1 as a mediator by virtue of x1 being one of its indicators. To answer your initial question, because x1 is directly influenced by u1, a factor is put behind x1 and the regression carried out by that factor regressed on u1. That's why Alpha, Beta, Psi get activated. So it is just trivial parameter organization matters to be ignored. In other words, you are right to say that the direct effect is based on u1 predicting the residual variance of x1 (after partialling out its shared variance in f1). |
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Excellent - thanks for the clarification.
Can I also extend this framework to look at the unique prediction of u1, net of a second latent variable?
For example:
model:
f1 by x1* x2 x3;
f1@1;
[f1@0];
f2 by u1* u2 u3;
f2@1;
[f2@0];
f1 on u1;
x1 on u1;
model indirect:
x1 IND u1;
Since theta parameterization is not an option with montecarlo integration, it doesn't seem that the direct effect for u1 to x1 would be interpretable in the way I would like since the residual of u1 isn't a parameter in the model, and f2 isn't included in the indirect effects paths.
Is there a way to model the total, direct, and indirect effects for u1 to x1 net of f1 and f2?
Thanks again for your help. |
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I think the way you set up the model is fine. Although I don't know why your model does not have f1 on f2.
You don't need montecarlo integration for this model if you use WLSMV (or Bayes) estimation; that's only for ML. Also, even though the residual variance for u1 is not a parameter to be estimated, the u1 residual still exists in the model - and for both Theta and Delta parameterizations. |
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Ah yep thank you for pointing out I should have f1 on f2 in the model.
When I use WLSMV with theta parameterization and include f1 on f2, f2 still isn't included in the indirect effects paths. It seems like this is because f2 is reflective, so there is no path via f2 to x1. Is the u1 to x1 path still being modeled net of f1 and f2 (i.e., based on their residuals) in this set-up?
Also, to clarify that I'm understanding your point above - if I use MLR and delta parameterization, the u1 to x1 direct effect would be between their residuals even though the u1 residual is not estimated?
Finally, is it right to still use the STDY output to interpret the u1 to x1 direct effect (between the residuals)?
Thanks again for your help with this! |
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Q1: I need to see the full output - send to Support along with your license number.
Q2: Yes. But note that it is not correct to say that the residual isn't estimated - the residual variance is not estimated but the residual still exists in the model.
Q3: Yes. |
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