Correlation structure
Message/Author
 Anonymous posted on Wednesday, August 18, 2004 - 6:02 am
Hi,

I want to know if Mplus 2 or 3 is capable of analyzing correlation structure with correlation matrix and its asymptotic covariance matrix only.
I know that LISREL and Mx can handle correlation structure with WLS estimation method while EQS cannot.

Thanks!
 Linda K. Muthen posted on Wednesday, August 18, 2004 - 7:10 am
This type of analysis can be handled in Mplus. See the MATRIX option of the ANALYSIS command. Raw data must be used.
 ehsan malek posted on Sunday, April 20, 2008 - 7:47 pm
Hi,

There is a warning in the results report:
WARNING: THE RESIDUAL COVARIANCE MATRIX (PSI) IS NOT POSITIVE DEFINITE. PROBLEM INVOLVING VARIABLE OR.

I calculated determinant of correlation and covariance matrix in Splus:
> det(var(t))
[1] 7.234943e-008
> det(cor(t))
[1] 0.000666757

Am I facing an ill-conditioned matrix?
Which matrix does Mplus use in analysis and how can we change it? (Like Lisrel that asks which matrix to use?)
 Linda K. Muthen posted on Monday, April 21, 2008 - 7:42 am
The covariance matrix that is referred to is the model estimated covariance matrix not the sample matrix. You can look at the standardized solution to see if you see a residual covariance related to OR is one. If you cannot see the problem using the suggestions in the error message, please send the input, data, output, and your license number to support@statmodel.com.
 Steve posted on Tuesday, July 02, 2013 - 11:41 am
Hello,

1) I am wondering if it is appropriate to specify single-item demographic variables (e.g., Age) to correlate with all of the latent variables (Age WITH F1 F2 F3) and obtain values for a measurement model correlation matrix (I have done this and the output is provided in the STDYX section). I am wanting to do this because a) I need to assess nomological validity of a latent construct and include Age in correlation matrix, and b) because I will be needing to include Age in structural model (so it seems it should also be part of measurement model).

2) Related to this, I have followed what many others have done in the literature previously and used mean scores of the latent variables and obtained a correlation matrix in SPSS. While I was expecting differences in correlation levels due to measurement error – I was very surprised that they could be SO different. For example, my model has some latent contructs with discriminant validity concerns – which have correlations of approximately .85 in measurement model, but only .65 when using mean scores (with reliabilities >.8). While the mean score approach provides support for discriminant validity, it does not seem feasible that I can present these two very different correlation tables without being able to more adequately explain such large discrepancies.

Any information and guidance you could give would be much appreciated. Thanks!
 Bengt O. Muthen posted on Tuesday, July 02, 2013 - 5:44 pm
1) You can do this, but you can also use regression F1-F3 ON Age.

2) It sounds like you are comparing model-estimated and factor score-based factor correlations. I would use the former.
 Steve posted on Wednesday, July 03, 2013 - 8:58 am
Dear Bengt,

Thank you so much for your quick response. I will proceed as you suggest. If may ask a quick follow-up question:

Would you be able to tell me how to explain why when I correlate only two latent constructs in Mplus their correlation is .584, but their correlation in the full measurement model (with other latent constructs) changes slightly to .586 (e.g., one rounds to .59 and the other to .58!)? I have to do this and need to be able to explain why they are slightly different.

Thank you.
 Bengt O. Muthen posted on Wednesday, July 03, 2013 - 2:57 pm
So the two models have different number of observed and latent variables? If so, the correlations would be the same only if the fit is absolutely perfect.
 Steve posted on Thursday, July 04, 2013 - 9:20 am
Okay - got it. Thank you very much Bengt.
 Svetlana Migunova posted on Wednesday, April 25, 2018 - 12:59 am
Dear Bengt and Linda!

I am doing a cross-lagged panel model with latent constructs for EF at three time points.
The last model with a better model fit included correlations between observed variables of EF accross all time points (not between each other). I am wondering what does it mean and how the results can be interpreted.