Correlation between latent variables
Message/Author
 Yuan-Pang Wang posted on Tuesday, December 02, 2008 - 6:20 am
Dear Linda, Bengst:

We are trying a MIMIC model with dichotomic data SRQ1-SRQ20 (20 observed variables)with 25 observed covariates. The following warning message appears in the output:

THE MODEL ESTIMATION TERMINATED NORMALLY

WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE
DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR A
LATENT VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO LATENT
VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO LATENT VARIABLES.
PROBLEM INVOLVING VARIABLE F3.

THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE
COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL.
PROBLEM INVOLVING PARAMETER 113.

THE CONDITION NUMBER IS 0.587D-17.

Checking TECH4 option for output, two latent variables were found to be correlated at 1.011.

What do you suggest to overcome this problem?

Kind regards,

Y.-P. Wang
Institute of Psychiatry
Sao Paulo University, Brazil
 Linda K. Muthen posted on Tuesday, December 02, 2008 - 6:26 am
You would need to change your model. I would suggest starting with an EFA.
 Derek Kosty posted on Tuesday, August 18, 2009 - 10:34 am
I would like to regress a variable (Z) on two correlated latent factors (X & Y). Is there a way to separate out the effects of a) the shared variance between X and Y, b) the unique variance of X, and c) the unique variance of Y on the dependent variable (Z)?

This is how the model is currently setup and I believe the estimates for 'Z on X Y' reflect the effect of a) the total variance of X and b) the total variance of Y on Z. Is that correct?

MODEL: X by var1 var2;
Y by var1 var2 var3 var4 var5 var6 var7;
Z on X Y;

 Bengt O. Muthen posted on Tuesday, August 18, 2009 - 4:46 pm
With correlated predictors (X & Y) I don't think one can separate out the effects.
 Masih Shafiei posted on Thursday, January 15, 2015 - 11:08 pm
A silly questions, I don't know how to constrain correlation between latent variables to those of interest.
I have a four-factor model in which based on EFA, F1 is uncorrelated with F3 and F4. How can I make Mplus understand this. I tried the following syntax, but in the output, Mplus calculate all the possible correlation between latent variables, no matter I use the "WITH" option (as in the below syntax) or not, I get the same values for all the possible correlation between the latent variables.

MODEL:
F1 by item4 item6 item14;
F2 by item3 item8 item12 item13;
F3 by item9 item11 item22;
F4 by item20 item21 item24;
F1 with F2;
F2 with F3 F4;
F3 with F4;
 Linda K. Muthen posted on Friday, January 16, 2015 - 5:27 am
Covarying all of the exogenous factors is the default. To set a covariance to zero, say f1 WITH f2@0;
 Steven John posted on Monday, October 26, 2015 - 1:39 am
Dear Linda, dear Bengt,

I'm trying to replicate Marsh's I/E frame of reference model and found that Mplus correlates the residuals of my latent (DV's) Self-concept vars. As I want to estimate the correlation between the latent factors, should I set the residual correlation @0 and look at TECH4 for the correlation between the latent factors?

Thanks for a great forum.
Steve
 Linda K. Muthen posted on Monday, October 26, 2015 - 9:16 am
You should not set the residual correlation at zero. You can find the correlation in TECH4.
 Brittany Rudd posted on Tuesday, February 21, 2017 - 9:41 am
Dear Linda and Bengt,

In running a CFA of a longitudinal latent factor, I have a latent correlation greater than 1 between two time points. I would expect longitudinal measures of the same construct to be significantly correlated; however, it is strange that the correlation is greater than one. What would you suggest in this case?

Thank you,
Brittany
 Linda K. Muthen posted on Tuesday, February 21, 2017 - 9:50 am
This makes the results inadmissible. You need to change the model. You can try correlating residuals at adjacent time points.
 Brittany Rudd posted on Tuesday, February 21, 2017 - 12:02 pm
Thank you for your quick response!

I correlated the residuals at adjacent time points as you suggested, and T1 and T2 are still correlated at greater than 1.

I'm using these latent variables in a longitudinal panel model. More specifically, they are the "Y" in my mediation model:

X ->M ->Y

I have 3 waves of data for X, M, and Y. X and Y are quantified as observed variables and Y is quantified as a latent variable. I will be predicting Y at wave 3, controlling for previous levels of Y. It is Y at wave 1 and 2 that is correlated greater than 1.

Is it admissible to run this analyses with Y1 and Y2 correlating greater than 1, since they are only covariates in the model?

Thanks!
 Linda K. Muthen posted on Wednesday, February 22, 2017 - 11:21 am
No. This message should not be ignored. you should change the model.
 Brittany Rudd posted on Thursday, February 23, 2017 - 11:26 am