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Mplus Discussion > Structural Equation Modeling >
 Anonymous posted on Friday, September 17, 2004 - 1:01 pm
In an autoregressive path model with no latent variables, When does a WITH statement refer to the correlation between two variables and when does it refer to the residuals of those variables?
 Linda K. Muthen posted on Wednesday, September 29, 2004 - 3:53 pm
It refers to the covariance between two variables when the two variables are exogenous. It refers to the residual covariance when the two variables are endogenous.
 Michael posted on Thursday, September 29, 2005 - 4:16 am
Since a WITH statement for endogenous variables refers to their residual covariance: how can I get the covariance of two endogenous variables (e.g. in a cross-lagged panel design)?
 bmuthen posted on Thursday, September 29, 2005 - 5:43 am
Uset TECH4.
 Michael posted on Thursday, September 29, 2005 - 6:03 am
Thanks for the quick answer! Is there also a possibility to get the standard error of a covariance of two endogenous variables?
 bmuthen posted on Thursday, September 29, 2005 - 6:54 am
That is not straighforward currently. This covariance is a function of several parameters and therefore the "Delta" method has to be applied to get the standard error. If you have a simple model you can use Model Constraint to define a new parameter as this function and thereby get the SE. Perhaps we should add automatic SEs for TECH4.
 Richard E. Zinbarg posted on Thursday, September 15, 2011 - 12:45 pm
In testing for measurement invariance over time, it seems to me standard and reasonable to account for the association of a factor with itself over time and for the residual of an indicator with itself over time. My intuition was that it should not make a difference for model whether I model those associations as regression paths (e.g., t2 factor regressed on t1 factor) or as correlations (t1 factor with t2 factor). Yet, I am clearly wrong about that as I just tried this and see that it does impact model fit. Can you recommend a reading that might help to explain why this should make a difference? Also, I am assuming that on theoretical grounds it would be more appropriate to go with the On statements rather than With statements given the temporal ordering but not sure that is the conventional choice. Any thoughts? Thanks as always!
 Bengt O. Muthen posted on Thursday, September 15, 2011 - 5:59 pm
There must be more in the model to produce that difference in fit.
 Richard E. Zinbarg posted on Thursday, September 15, 2011 - 6:21 pm
yes, the full model consists of 3 indicators of a factor measured at two time points. So, we have one factor at time 1 with 3 indicators and one factor at time 2 with 3 indicators. For one of the 3 indicators, its correlated residual with itself over time is notsignificant. Thus, we have in addition to the six factor loadings, one correlated residual (or regression path) from the time 1 factor to itself at time 2 and two additional correlated residuals (or regression paths) from two of the time 1 indicators to themselves at time 2. I am not sure that I follow why these other parts of the model make a difference though.
 Bengt O. Muthen posted on Saturday, September 17, 2011 - 10:37 am
If you like you can send your two outputs to support.
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