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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! 


Residual variances for categorical variables are not parameters in a crosssectional 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 Rsquare. Here it is computed as a remainder. You need to change your model. 

Xu, Man posted on Wednesday, April 10, 2013  3:57 am



I have run into the same situation myself. I am comparing several nested models. It is the bifactor 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 rsquare 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! 


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  8:34 am



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! 


I would not use factor scores from a full sample in an analysis using a listwise sample. 


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. 


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. 

Daisy1 posted on Tuesday, October 06, 2015  12:48 pm



Dear Dr. Muthen, I am testing the measurement invariance of a bifactor model with a general factor and 3 specific factors across three groups. When I test configural invariance, I get the following message: WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IN GROUP AFR 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 X1. The residual variance of X1 is negative for one of the groups. How can I remedy this problem? 


If it is small and insignificant, fix it at zero. Or, hold residual variances equal to other groups. If it is big, it can be a sign of a poor model. 


Hello, I am running a longitudinal measurement invariance model with the personality dimension of agreeableness. There are three time points, and three items at each time point. When running the configural model with MLR estimation, I 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 T3PER13. I have checked the data, and the tech 1 and tech 4 output, but I don't see any problems nor anything that would correspond to the suggestions in the error message of what to look for. Any suggestions? What can I try? What should I look for? I have used the same code and data for the other 4 personality dimensions with no problems. Thank you! 


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


Hi, I'm running a multigroup CFA model (Grade 6 vs. Grade 8). I've established metric invariance, and now I'm testing for structural invariance by testing a model where the latent variances are constrained equal across my two groups. When I do this I get this error message: WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IN GROUP GRADE6 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 MEAC. I have checked for multicollinearity, but that was not the problem. The residual variance of MEAC is statistically significant. Setting the residual variance to 0 does not solve the problem. What do you advise? Thanks! 


I should have mentioned that, in the same model, I'm constraining the latent covariances to be equal across groups. The error message occurs regardless of whether or not I'm just constraining the latent variances, the latent covariances, or both at the same time. Thanks again! 


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

Dennis Reidy posted on Wednesday, September 04, 2019  1:53 pm



I am attempting to run a monte carlo simulation to do a power analysis for a LGC regressed on a binary predictor. I get the following message for every replication: 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. I cannot figure out why I am getting this message 


Please send your output to Support along with your license number. 

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