Measurement model fit vs Structural m... PreviousNext
Mplus Discussion > Structural Equation Modeling >
 Kostas Papadopoulos posted on Tuesday, October 07, 2008 - 12:42 pm

As most papers suggest there should be a two-step approach for SEM

a) Measurement model
b) Structural model

I have read many papers that mention two times the measures of fit (RMSEA,etc) -> one for (a) and one for (b) (with different values)

1)Is that mentioning correct? Aren't measures of fit appropriate only for the overall model? Are they different in values each time?

2)In MPLUS i can only see overall model measures of fit. Where can i find the measures of fit for (a) and (b) for my SEM model?

Thank you
 Linda K. Muthen posted on Tuesday, October 07, 2008 - 1:21 pm
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.
 AMN posted on Friday, November 01, 2019 - 2:03 pm
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.
 Bengt O. Muthen posted on Friday, November 01, 2019 - 5:25 pm
We need to see your two outputs - send to along with your license number.
 AMN posted on Monday, November 04, 2019 - 10:35 am
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!
 Bengt O. Muthen posted on Monday, November 04, 2019 - 2:13 pm
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.
 AMN posted on Monday, November 04, 2019 - 3:08 pm
Thank you for your quick response.

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?
 Bengt O. Muthen posted on Monday, November 04, 2019 - 5:09 pm
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.
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