Even better: If E is symmetric you can solve the linear equations more efficiently! Yes, there are times when you get negative estimates for the variance (?!?!). There are many reasons that this can occur. It is usually a signal that your model is misspecified, although Gary King gives other reasons: http://gking.harvard.edu/files/help.pdf I like Figure 1 of the paper, which show WHY the covariance matrix misbehaves. There is also a short, easy, article about how this can arise in mixed models: When the Hessian Matrix goes Wacky
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