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? Model: %within% 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?
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? Model: %within% 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.
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 http://www.statmodel.com/download/DSEM.pdf These formulas are used in the computation of output:residual;
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?