# Bifactor-model in Mplus - warning message: PSI is not positive-definite

This question is about: When does the warning massage appear?

I have a rather complicated model in Mplus that consists of three individual models. Each model consists of several manifest variables modeled in the bifactor model: there is one g-factor per model as well as specific ability factors. The individual models fit well and without error message.

For the overall model (Estimator = MLR) I get 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.
PROBLEM INVOLVING VARIABLE XY.


If I exclude the individuals that have some missing values, the error message disappears in the model.

I looked at the covariance matrix of the latent variables in the Tech4 output in both cases. These differ only numerically, but not in content. Both matrices contain negative values - even looking at the associated p-values shows that they do not differ. In both cases the covariance between V2.1 and V3.2 is negative (both: p < .05) but once I get an error message and the other time I do not.

Latent variable covariance matrix WITH warning message

           ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
V1.1          V1.2          V1_g          V2.1          V2.2
________      ________      ________      ________      ________
V1.1           1.000
V1.2           0.000         1.000
V1_g           0.000         0.000         1.000
V2.1           0.473         0.276         0.000         1.000
V2.2           0.251         0.763         0.000         0.000         1.000
V2.3           0.530         0.005         0.000         0.000         0.000
V2_g           0.000         0.000         0.760         0.000         0.000
V3.1           0.244         0.230         0.000         0.568         0.193
V3.2           0.018         0.229         0.000        -0.313         0.755
V3.3           0.115         0.214         0.000         0.089         0.212
V3_g           0.000         0.000         0.213         0.000         0.000


Latent variable covariance matrix WITHOUT warning message

           ESTIMATED COVARIANCE MATRIX FOR THE LATENT VARIABLES
V1.1          V1.2          V1_g          V2.1          V2.2
________      ________      ________      ________      ________
V1.1           1.000
V1.2           0.000         1.000
V1_g           0.000         0.000         1.000
V2.1           0.444         0.263         0.000         1.000
V2.2           0.229         0.746         0.000         0.000         1.000
V2.3           0.489         0.003         0.000         0.000         0.000
V2_g           0.000         0.000         0.764         0.000         0.000
V3.1           0.272         0.244         0.000         0.627         0.200
V3.2          -0.005         0.229         0.000        -0.294         0.713
V3.3           0.101         0.207         0.000         0.106         0.197
V3_g           0.000         0.000         0.239         0.000         0.000


My question is therefore:
Why does the warning message appear in the first case, but not in the second case?

Am I making a mistake when looking at the matrix? If yes, which one?
Thank you very much for your support and help!