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 Maurits Masselink posted on Thursday, January 24, 2019 - 3:58 am

I am using DSEM to analyse time-series data of multiple participants. I look at the lagged associations, and the momentary associations (correlations between the residuals). I want to test whether the momentary association between X and Z differs significantly from X with Y.

Is the following (simplified) approach correct?
X with Z (a);
X with Y (b);

model constraint:
new (test); test = a-b;

Does the significance of the "test" variable indeed indicate whether the association between x-z is significantly different from x-y?


 Bengt O. Muthen posted on Friday, January 25, 2019 - 10:44 am
It indicates the difference for the residual covariance, not the total covariance.
 Maurits Masselink posted on Monday, January 28, 2019 - 12:30 am
How would I test the difference of the total covariance?

 Bengt O. Muthen posted on Monday, January 28, 2019 - 1:18 pm
You have to express the total variance and covariance in formulas based on your model using Model Constraint.
 Maurits Masselink posted on Tuesday, January 29, 2019 - 2:09 am
I suspect that I may have specified the model correctly after all. To clarify:
I specified a model with cross-lagged effects and autocorrelation. The
Within-Level Standardized Estimates output also gives the output X WITH Y and X WITH Z. To my understanding they indicate the residual covariance. This residual covariance indicates the covariance after the lagged covoriances has been taken out (=estimate of momentary/contemporaneous covariance).

If the above is correct, then shouldn't the following be correct to test whether the momentary covariances differ between X-Z and X-Y?
X with Z (a); !this indicates the residual covariance right?
X with Y (b);

model constraint:
new (test); test = a-b; !using absolute values

I am having difficulties understanding why I would need the total covariance.
 Tihomir Asparouhov posted on Tuesday, January 29, 2019 - 12:43 pm
The above test is for the residual covariance. If you want to test the total covariance you would need to use the formulas in Appendix D
These formulas are used in the computation of output:residual;
 Maurits Masselink posted on Wednesday, January 30, 2019 - 8:17 am
Thank you for your reply. I do have a follow-up question. For the residual covariance, I report the within-person standardized result. So I am interested in testing the difference in standardized coefficients instead of the unstandardized coefficients. For the newly created variable in model constraint, I only get unstandardized output. Is there a way to test the the difference between standardized coeffficients or would the test result be identical to the test for the unstandardized coefficients as I specified above?
 Tihomir Asparouhov posted on Wednesday, January 30, 2019 - 3:20 pm
For the standardized test use this

X with Z (a);
X with Y (b);
X (v1); Y (v2); Z (v3);

model constraint:
new (test); test = a/sqrt(v1*v3)-b/sqrt(v1*v2);
 Maurits Masselink posted on Thursday, January 31, 2019 - 1:47 am
Thank you very much for your help, it is much appreciated!

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