Correlated dependent latent variables PreviousNext
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 Loren Post posted on Monday, May 14, 2012 - 6:25 pm

I have a basic question. Does Mplus automatically correlate dependent latent variables even if it is not written as a command? If so, does that mean the model then includes a disturbance correlation between the latent variables? ( I thought disturbance correlations were something to be avoided)

 Linda K. Muthen posted on Tuesday, May 15, 2012 - 10:23 am
Mplus covaries as the default the residuals of final outcomes but not mediating outcomes. I am not sure where you heard disturbance correlations are something to be avoided. If they are large and not included, the model is misspecified. It is desirable for them to be small because if they are not, there are covariates that have been left out.
 Loren Post posted on Tuesday, May 15, 2012 - 12:28 pm
Thank you!
 Loren Post posted on Tuesday, May 15, 2012 - 2:01 pm
I'm sorry, I have yet another question. If I received a message that the latent variable covariance matrix is not positive definite and I want to report the problem do I refer to the y2 WITH y1 standardized model results (estimate = 1.047) or the TECH 4 estimated correlation between y2 and y1 (.985)?
What is the difference between the two?

Thank you so much for your help!
 Linda K. Muthen posted on Tuesday, May 15, 2012 - 5:21 pm
You would look at TECH4. TECH4 is the model estimated variances and covariances for the latent variables in the model. The standardized results are the raw results standardized.
 Loren Post posted on Tuesday, May 15, 2012 - 6:20 pm
Is there a way to get significance tests for the estimated correlations in tech4?
 Bengt O. Muthen posted on Tuesday, May 15, 2012 - 6:34 pm
Only if you express the correlation in Model Constraint.
 Loren Post posted on Tuesday, May 15, 2012 - 6:56 pm
I'm sorry, I'm new to SEM and am not sure how to do that. Is there a reference you can refer me to?

Thank you!
 Linda K. Muthen posted on Wednesday, May 16, 2012 - 11:59 am
You can read about how MODEL CONSTRAINT works in the user's guide. You would have to see a book on SEM to understand how to create correlations from the parameters in your model.
 Emil Coman posted on Wednesday, May 16, 2012 - 12:23 pm
Loren, luckily Phillip Wood took the time to set these straight, and he posted them online, I guess waiting for a book would have taken too much time...
How to Use Tracing Rules to Express Correlations: Standardized Coefficients
See also:
As for a book, there are a few great ones, I recommend:
Loehlin, J. C. (2004). Latent variable models: An introduction to factor, path, and structural equation analysis: Lawrence Erlbaum.
cheers, emil
 Loren Post posted on Wednesday, May 16, 2012 - 12:53 pm
Fantastic! Thanks so much!
 Steve posted on Wednesday, August 28, 2013 - 3:10 pm

It was my understanding SEM models only include the correlation of exogenous latent variables - however it seems that Mplus is estimating correlation between dependent latent variables as well.

F1 by X1 X2 X3;
F2 by X4 X5 X6;
F3 by X7 X8 X9;
F4 by X10 X11 X12;
F3 on F1 F2;
F4 on F1 F2;

The STDYX output lists correlation F3 with F4 (and they are theoretically correlated). So:

1) is this really a correlation as traditionally defined - or is this some kind of 'disturbance correlation'?
2) if 'disturbance correlation' - could yo please explain what that is?
3) does the inclusion of this estimate then somehow make this a feedback loop and the model non-recursive?

Many thanks.
 Bengt O. Muthen posted on Wednesday, August 28, 2013 - 6:26 pm
The User's Guide says that for dependent variables Y1 and Y2, saying


refers to their residual covariance (disturbance covariance), not their covariance.

3) No.
 Steve posted on Thursday, August 29, 2013 - 1:55 am
Dear Bengt,

Thanks for your response. As a point of clarification, I did not specify


(covariance between dependent latent variables) in the model. However, F3 WITH F4 still is listed as an estimated parameter in the output.

So, if I understand, this is a default estimate for dependent latent variables, and the output F3 WITH F4 still refers to their residual covariance (disturbance covariance), not their covariance.

Correct? Thanks so much.
 Linda K. Muthen posted on Thursday, August 29, 2013 - 6:20 am
 Steve posted on Friday, August 30, 2013 - 8:09 am
Thanks Linda!
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