I am currently running both latent change models and autoregressive latent trajectory models with structured residuals. The models are often quite complex - large samples over four years, but a lot of missing data (and ideally four different variables acting reciprocally).
I am having a problem with some of the models (even simpler ones with less variables), in that I am often getting the error message lots of others get: "WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE DEFINITE."
The most common solution to this problem from the board is to set slope variances to 0. This changes the estimates and is inappropriate for our model, however (where slope variance is significant and theorised about).
Another option that we can take it to relax convergence to somewhere between CONVERGENCE = .00001 to CONVERGENCE =.1 - this gets rid of the error and produces estimates that seem more sensible. Is there a problem with doing this? Or any more information about what this is doing? In particular, is there a problem with setting it at something as high as 0.1?
If you don't have negative variances, the cause for this error message should be explored. Often, you have to simplify the model or estimate parts of it separately to see when and why the message occurs.
I would not recommend the option in your last paragraph.