I am analyzing (in SPSS 19) the data from a field experiment using a Linear Mixed Model with Repeated Measures. When checking the model, I always obtain negative values in the information criteria table. I know the rule of thumb “smaller is better”, but how should these negative values be interpreted? As example, when I select a type of covariance “Unstructured” the Bayesian information criterion (BIC) reads $-642.868$ and with a “Compound symmetry” covariance it reads $-497.270$. So, which type of covariance, “Unstructured” or “Compound symmetry”, is better?
The second question is that I receive the following warning message: "The Final Hessian matrix is not positive definite although all convergence criteria are satisfied. The MIXED procedure continues despite the warning. Validity of subsequent cannot be ascertained". May I ignore it or I have a real trouble? Is there some way to fix it?