COVARIANCE MATRIX NOT POSITIVE DEFINITE
Message/Author
 Arne Floh posted on Thursday, August 30, 2007 - 11:20 am
Linda & Bengt,

I wanna run a unconditional LGM with 7 data points. The outcome is a cumulative profit variable: y1= profit t1, y2= profit t1 + t2, y3 = profit t1 - t3.

Unfortunately, I got the following error message.

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 P2001.

Help appreciated.
 Linda K. Muthen posted on Thursday, August 30, 2007 - 12:17 pm
I would look to see if p2001 has a negative residual variance or one of the other issues outlined in the warning. If you can't figure this out, please send your input, data, output, and license number to support@statmodel.com.
 Luca Mariotti posted on Wednesday, September 05, 2007 - 7:01 am
dear Linda,

I´ve just seen this post and I have the same problem. The variable specified in the warning does have a negative residual variance!!! what I should do in this case, or better, is there anything i can do?

thanks a lot in advance

luca
 Linda K. Muthen posted on Tuesday, September 18, 2007 - 5:18 am
This means you need to change your model or if it is very small and not significant, you may want to fix it at zero.
 Lea Dipper posted on Wednesday, January 27, 2016 - 8:21 am
Dear Linda and Bengt,

I'm running a CFA of items with four variables on one factor, three variables on a second and five on a third. I'm getting errors on the factor with three 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 FEL_POS.

The variable specified in the warning has a negative residual variance (and keeps it if I reanalyze the data with the recoded problematic variable). You recommend a model change or, if the residual variance is small, I may fix the problematic variable to zero, is this correct?
The residual variance in my MODEL RESULT section is -0.391 and it is not significant (p = 0.148). Is this a small residual variance? And if so, is it correct to set the problematic variable to zero by writing this in the model = ...-section: fel_pos@0;? And my last question: What does this imply for my CFA?
 Linda K. Muthen posted on Wednesday, January 27, 2016 - 11:59 am
Please send the output and your license number to support@statmodel.com.
 Miguel Freitas posted on Thursday, March 03, 2016 - 8:05 am
Dear Drs. Muthén,

I am trying to run a Growth Mixture Modeling on my data.
A 3-class solution seems to present the best fit.
However, after including my predictor covariates, the model presents different trajectory patterns than those in the unconditional model.
Also, I get the following warning messages:

WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IN CLASS 1
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 SLP.

The warnings also refer classes 2 and 3.
Can you help me identifying what went wrong, please?
Thank you
 Linda K. Muthen posted on Thursday, March 03, 2016 - 5:14 pm
Please send the output and your license number to support@statmodel.com. Include TECH4.
 H Feng posted on Saturday, March 05, 2016 - 10:49 am
Dear Dear Drs. Muthén,
I also got the WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IN CLASS...

Is there a way that I can get Tech4 output without re-run the model? as I have a large dataset (25k individuals, it took 24hrs). (I have 9 groups, with Q and cubic constrained@0, the variance of S in only one group <0, the cov is copied here-sorry about the format)

Variances
I 1.202 0.094 12.762 0.000
S -0.350 0.027 -13.196 0.000
Q 0.000 0.000 999.000 999.000
CUBIC 0.000 0.000 999.000 999.000

Covariances
I S Q CUBIC C_I
________ ________ ________ ________ ________
I 19.128
S -22.758 38.323
Q 41.893 -68.831 129.328
CUBIC -17.340 29.616 -56.854 25.609
C_I 19.197 -22.953 42.204 -17.472 19.328
C_S -22.900 39.340 -70.490 30.391 -23.492
C_Q 41.869 -70.283 131.828 -58.127 42.800
C_CUBIC -17.252 30.217 -57.956 26.210 -17.643

......
 Linda K. Muthen posted on Saturday, March 05, 2016 - 12:48 pm
There is no way to get TECH4 without rerunning the model.
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