Hello Dr. Muthen: I have estimated a growth model in which I know that my covariance matrix is singular because I am including a person mean in the presence of a time-varying covariate. Other SEM programs will not estimate the model because of this singularity; I must instead invoke some form of ridge estimator. However, in Mplus I get the message:
WARNING: THE SAMPLE COVARIANCE OF THE INDEPENDENT VARIABLES IS SINGULAR. PROBLEM INVOLVING VARIABLE XBAR.
THE MODEL ESTIMATION TERMINATED NORMALLY
Could you please briefly clarify what Mplus is doing to get a solution here? Does this involve a ridge estimator? Or some other sandwich-type approach?
Dr. Muthen: Thank you for your kind reply. Very briefly, can results of ML with gentle ridging be treated as true ML estimates, or are there some limitations due to the adding of an artificial constant to the diagonal of sigma?
Thank you yet again. You are most kind. One final question, if I may.
Even if the model is estimated conditioned on the independent variables, would the addition of an artificial value to the variance of the exogenous variables potentially change the correlation structure of the entire set of measures? And might this in turn bias other model estimates relative to their population counterparts?
No, this would not happen. Only the diagonal of the xx covariance matrix is affected, not the yx or yy covariance matrices.
csulliva posted on Thursday, October 08, 2009 - 9:25 am
I posted a similar question in another thread last week:
"Is it possible to include both a time stable [mean] and time varying [deviation score] component of the same covariate in a GMM or LCGA model?"
Linda K. Muthen posted on Saturday, October 03, 2009 - 8:56 am
I don't think this will work because of singularity among the covariates. You can try it out. You may have to exclude some deviations.
I did in fact get a warning that the covariance of the independent variables was singular. My question--given the discussion in this thread--is whether the estimates are useable? It sounds like the same problem and the previous responses seem to suggest that the ridge process helps to deal with this issue
csulliva posted on Friday, October 09, 2009 - 10:23 am
Thank you very much. If you might permit one more brief question...is the situation I'm posing qualitatively different from the one posted at the top of this thread? The premise and the warning message seem the same, so I am slightly confused about where the ridging process fits into the estimation and the viability of the estimates. I couldn't find anything in the technical appendices on this.
It is the same situation. Ridging may lead to poor estimates in some cases. We allow ridging for users who are sure that the estimates are good for their situation. The safest approach is to avoid singularity in the first place.
You should not go on without having resolved this problem. It sounds like some of your variables have a linear dependency among them. This would for instance happen if you use both the sum and each variable in the sum, or if you use 3 dummy variables for a 3-category variable.