Message/Author 

Phil Rodkin posted on Tuesday, March 01, 2011  9:48 am



When we run a CFA to test for configural invariance, we receive the following 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 ATAGGB." When we ran this model in Lisrel, we did not encounter this problem. We also checked the correlation matrix for values of 1.0; there were none. We are welcome to any suggestions to help us move forward. Thank you. 


This is usually due to a negative residual variance. Check this for ATAGGB. I think some programs fix these to zero as the default. If you can't see the problem, please send your full output and license number to support@statmodel.com. 


Hi Dr Muthen, I run a CFA and I have the following message : 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 F3 But I don't have a negative variance nor a correlation greater or equal to one. What else could it be ? Is it possible that the model is good despite this message ? Thank you 


Then there must be a linear dependence between f3 and two or more variables. 

Elan Cohen posted on Thursday, October 13, 2011  10:14 am



Dr. Muthen, I'm running a CFA with 16 factors and 84 items. I'm receiving the following warning: 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 F2A11. I have not been able to identify the root of this problem. Do you have any practical advice as to how to go about this? If it is a linear dependence between this factor and other variables, how can I identify which are the problematic variables? Thank you. 


Please send the full output and your license number to support@statmodel.com. 

Ivenfield posted on Monday, March 12, 2012  10:23 am



Dear Dr Muthen, We're running a multigroup CFA to test for latent correlation matrix invariance. We have 5 observed factor scores from 5 latent factors. The observed and latent factors are on the same metric. Our syntax is as follows: MODEL: F1 BY V1*; F2 BY V2*; F3 BY V3*; F4 BY V4*; F5 BY V5*; F1F5@1; MODEL GROUP1: F1 WITH F2* (1); F1 WITH F3* (2); F1 WITH F4* (3); F1 WITH F5* (4); F2 WITH F3* (5); F2 WITH F4* (6); F2 WITH F5* (7); F3 WITH F4* (8); F3 WITH F5* (9); F4 WITH F5* (10); MODEL GROUP2: F1 WITH F2* (1); F1 WITH F3* (2); ... F4 WITH F5* (10); This model specification follows the same logic as the one that runs fine in EQS but we get the below warning: THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL. PROBLEM INVOLVING PARAMETER 626. THE CONDITION NUMBER IS 0.337D06. Any suggestions on what we have done wrong would be very much appreciated. Many thanks! 


What are you trying to do with the following: F1 BY V1*; F2 BY V2*; F3 BY V3*; F4 BY V4*; F5 BY V5*; F1F5@1; If you are trying to create a oneindicator factor, the specification is: f BY v1@1; v1@0; 

Ivenfield posted on Tuesday, March 13, 2012  4:49 am



Thank you very much for replying quickly Dr Muthen. We're indeed trying to create oneindicator factors and fixing latent factor variances to 1, which is what we have done in EQS. Your suggestion gets rid of the warning message nicely, although we're still getting vastly different fit indices compared to EQS. We also tried fixing factor variances to 1 instead of fixing factor loading to 1 for identification to match EQS better (f BY v*; f@1; v@0;), but results deviate even further. Any ideas on what we're missing here? Many thanks! 


You will get the same or very similar results if you have the same sample size, the same model, and the same estimator. If you can't see your problem, send the Mplus and EQS outputs and your license number to support@statmodel.com. 


Dear Dr. Muthen, I'm running a CFA with 4 factors and 22 items. The output gives me the following error message: 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 DZ. DZ is one of the defined latent factors. There are negative residual variances, but these are also when running other analysis based on the same data set. Any suggestions on what I have done wrong would be very much appreciated. Many thanks! Simone 


The results of any analysis with negative residual variances are inadmissible. The model should be changed. 

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