Warning meassage in CFA
Message/Author
 Noa Cohen posted on Saturday, May 09, 2015 - 5:52 am
I was trying to run a CFA with two latent variables and this message came up:

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.CHECK THE TECH4 OUTPUT FOR MORE INFORMATION.
PROBLEM INVOLVING VARIABLE F2.

TECHNICAL 4 OUTPUT:

ESTIMATES DERIVED FROM THE MODEL

ESTIMATED MEANS FOR THE LATENT VARIABLES
F1 F2
________ ________
1 0.000 0.000

ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
F1 F2
________ ________
F1 0.652
F2 0.610 0.536

ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES
F1 F2
________ ________
F1 1.000
F2 1.032 1.000

Could you please tell me what the problem is and how do I fix it?
 Linda K. Muthen posted on Saturday, May 09, 2015 - 6:48 am
F1 and f2 correlate greater than one. They are not statistically distinguishable. You need to change your model.
 Noa Cohen posted on Saturday, May 09, 2015 - 9:10 am
Thank you! Is there any way that I can fix this still using these two factors, or do I have to completely change the model?
 Linda K. Muthen posted on Saturday, May 09, 2015 - 9:23 am
You need to change the model. Perhaps there is only one factor. Do an EFA to see how many factors are found in the data.
 Olli Kiviruusu posted on Thursday, September 03, 2015 - 3:57 am
I'd like to compare CFA-models with one, two or three factors. There are alltogether six indicator variables and they are all binary. When I spesify the three factor model (with two indicators in each factor) I get the "LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE DEFINITE" error message and it turns out that one of the correlations between the factors is >1.

My questions are:
Can I still compare this three-factor model (despite the error message) using DIFFTEST option with two-factor model (where the two highly correlated factor are combined) - i.e. is the chi-square value trust worthy in the presence of that error message?

Or can I use ML estimator (instead of WLSMV), then I would get "error free" models with comparable BIC values, but is it okay to use ML estimator with binary factor indicators?
 Linda K. Muthen posted on Thursday, September 03, 2015 - 5:26 am
If you get that message, the results are inadmissible and further analysis is not appropriate.
 Olli Kiviruusu posted on Thursday, September 03, 2015 - 6:43 am
Okay, thank you.
I suppose I can report that correlation above 1.0 suggests that the two factors should be combined? I'd like to report this somehow, because there is a current debate on this (two vs. three factors) I'd like to contribute to.

What about ML estimator and comparisons using BIC? When I use ML, there aren't any errors and correlations are below 1. But I'm wondering whether I can use ML with categorical indicators.
 Linda K. Muthen posted on Thursday, September 03, 2015 - 6:52 am
You can use ML with the CATEGORICAL option. It gives logisitic regression as the default.
 Olli Kiviruusu posted on Thursday, September 03, 2015 - 7:09 am
Ok, thank you for your answer.
While ML with CATEGORICAL gives logistic regression as the default, I suppose the factor loadings and correlations between factors are to interpreted as usual (I'm reading STYDX output)?
 Linda K. Muthen posted on Thursday, September 03, 2015 - 7:38 am
If the factor indicators are categorical, the factor loadings are logistic regression coefficients. In a factor model, the factor indicators are regressed on the factors.
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