I would imagine that the researchers first get a well-fitting measurement model (BY statements in Mplus) and report the fit from that analysis. It would not make sense to have a structural model using latent variables that are not well-fitting. Then add the structural part (ON statements in Mplus) and report the fit for that part of the model.
I am using SEM and tested a measurement model and then structural model. Once I applied one modification to my structural model, the model fit for the measurement model and the structural model matched exactly. This seems very strange to me, but I've checked my work and it matches. Can this be an error? I appreciate your help.
AMN posted on Monday, November 04, 2019 - 10:35 am
Hello, I am running a SEM and first tested a measurement model and then the structural model. My model includes 4 latent variables. Upon running the structural model, the modification indices suggest that I allow two of the latent variables to co-vary. Doesn't the Mplus assume correlations between latent variables? Thus, I should not include the new "WITH" statement in my syntax. Thanks!
Mplus correlates latent variables by default if they are exogenous or the final endogenous. You see from the output which ones are correlated. If you get a non-zero modindex, then the correlations was not included.
At the top of my output page under "Sample Statistics", I see a Correlation Matrix of the individual items used to create the latent variables. Additionally, under "Technical 4 Output", I see "Estimated Correlation Matrix for the Latent Variables" and these scores are non-zeros. Besides these two sections, I do not see any correlation output under "Model Results". Also, when I request the diagram, there are no visible co-varying arrows between my latent variables.
Considering this, were my latent variables not correlated?
Whenever two latent variables f1 and f2 don't have a f1 WITH f2 statement, they don't have a factor covariance (correlation) parameter. They can still correlate in TECH4, for example due to both being influenced by another variable.