THE RESIDUAL COVARIANCE MATRIX (THETA... PreviousNext
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 Daniel Thompson posted on Friday, May 13, 2011 - 7:31 pm
I'm running a CFA of survey response items with two variables on one factor and three variables on another, and I'm correlating them. I'm often getting errors on the factor with two variables. Here is my error:

WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IS NOT POSITIVE DEFINITE.
THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR AN OBSERVED
VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO OBSERVED
VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO OBSERVED VARIABLES.
CHECK THE RESULTS SECTION FOR MORE INFORMATION.
PROBLEM INVOLVING VARIABLE HI4R.

The only possibility is a negative variance, so I set HI4R@0. Then I get this error:

*** ERROR in MODEL command
Variances for categorical outcomes can only be specified using
PARAMETERIZATION=THETA with estimators WLS, WLSM, or WLSMV.
Variance given for: HI4R

I set the parameterization to theta, and I get more errors. Any suggestions?? Thanks!
 Linda K. Muthen posted on Friday, May 13, 2011 - 8:06 pm
Residual variances for categorical variables are not parameters in a cross-sectional model. They can be specified only in multiple group and multiple time points models. I'm assuming that you see the negative residual variance with R-square. Here it is computed as a remainder. You need to change your model.
 Xu, Man posted on Wednesday, April 10, 2013 - 9:57 am
I have run into the same situation myself. I am comparing several nested models. It is the bi-factor model that gave this warning for one item.

Would it be unacceptable to ignore this warning? The model was converged and all estimates were given, apart from r-square of this item, of course.

Also, when I revert to theta parameterization, this warning went away but a different one pops up:
MINIMIZATION FAILED WHILE COMPUTING FACTOR SCORES FOR THE FOLLOWING
OBSERVATION(S) :
126 FOR VARIABLE GHQ0899

What's best way for me to proceed? Thanks!
 Linda K. Muthen posted on Wednesday, April 10, 2013 - 12:49 pm
This message cannot be ignored. Please send the output with the not positive difference message and your license number to support@statmodel.com. Changing to the Theta parametrization is not a solution.
 Xu, Man posted on Wednesday, April 10, 2013 - 2:34 pm
Thank you very much. I have sent relevant information to you at this email address.

It seems that this is at least related to sample size. Another point is that I need to look at the results based on listwise complete data including some observed external predictors. This substantially reduces sample size and probably leads to problems in the estimation of the latent model.

In this situation, would it be a reasonable compromise if I export factor scores from the FIML analysis model based on complete sample, then defined the complete sample on the factor scores and external predictors?

Thank you very much!
 Linda K. Muthen posted on Thursday, April 11, 2013 - 4:48 pm
I would not use factor scores from a full sample in an analysis using a listwise sample.
 Claudia Bernhard posted on Tuesday, March 24, 2015 - 11:08 am
Hi,

I have a similar problem.

I have run a multiple group model. After that I have established metric invariance, I have run a path model, first of all, with free paths.

However, I get this warning:

WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IN GROUP TEMP IS NOT
POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL
VARIANCE FOR AN OBSERVED VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE
BETWEEN TWO OBSERVED VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO
OBSERVED VARIABLES. CHECK THE RESULTS SECTION FOR MORE INFORMATION.
PROBLEM INVOLVING VARIABLE KONTR6_2.


I have checked for multicollinearity, but that was not the problem.

the item does not correlate more than .662 with another observed variable.

However, the item is one of two items in one factor (all other factors have at least three items, only this factor has only two). The item has a residual variance that is almost 0 (I have checked in the CFA and invariance tests again).

Now my colleague suggested to set the residual variance of that particular item to zero, which I have done, and that works fine.

However, my question is what you would suggest as a solution.

PS: By the way, when I run a model with constrained paths, the problem does not appear.
 Bengt O. Muthen posted on Tuesday, March 24, 2015 - 4:40 pm
Check the STDYX solution to see if a residual correlation is greater than 1. It is not a matter of correlation among observed variables but among residuals.

One approach is to delete this residual covariance., so fixing it at zero.
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