Between Level Covariance Matrix is NPD
Message/Author
 Anonymous posted on Tuesday, March 29, 2005 - 8:38 am
First, let me congratulate you all on keeping this great resource up and running. I realize it requires a substantial time investment on your part and it is greatly appreciated!

I am a relative novice at multi-level SEM and wanted to get your thoughts on an error message that I am getting when running a model in Mplus.

The model I am running is as follows (Type=twolevel; estimator=muml):

Within level: 3 constructs each measured by 3 continuous indicators (the 3 constructs are allowed to covary but no directional relationships are specified).

Between level: No between-level factors are specified—3 observed independent variables are utilized to predict the between level random intercepts (my focus is on testing the relationship between the observed independent variables and the cluster means).

Number of level 2 (between) units=30 (unbalanced groups)
Number of level 1 (within) units=300

After running the model, it converges and I get the needed parameter estimates. The problem is that I am also getting an error message which reads” WARNING: THE RESIDUAL COVARIANCE MATRIX (PSI) ON THE BETWEEN LEVEL IS NOT POSITIVE DEFINITE.”

So, my questions are:

1. Is this NPD error message a result of my small between level sample size (n=30)?
2. What are the implications of this message as it pertains to the validity of the parameter estimates I get? (In other words, what statistically valid conclusions can I reach if I do nothing to correct this problem?).
3.Is there anyway of correcting this problem that does not involve constraining my between level covariances to 0?

I’ve run multiple variations of the model and cannot seem to circumvent this problem. Any help you could offer would be greatly appreciated.

Thanks.
 Linda K. Muthen posted on Saturday, April 02, 2005 - 8:40 pm
It does not sound like you are using the most recent version of Mplus. If you were, you would be getting an error message that would point you more directly to the problem. You should check for negative residual variances of your factors. If you do not have these, you should ask for TECH4 to see if you have variables with correlations greater than one. You need to take this message seriously as it points to a problem with your model. It is often the case that there is less variation on the between level and that you may be able to obtain fewer factors on the betweem level. 30 clusters should be sufficient although the minimum.