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The phase rule also reveals that no more than three phases can stably coexist in a one-component system because additional phases would lead to negative variance.
I fully stand by this 90 mile claim although a 10% positive or negative variance is appropriate.
In many cases, such negative variance components can be translated as negative within-unit correlations.
It is established that such negative variance components in generalized linear mixed models can occur in practice and that they can be estimated using standard statistical software.
It is shown that negative variance components, with corresponding negative associations, can occur in hierarchical models for non-Gaussian outcomes as well, such as repeated binary data or counts.
It is shown that for the same computational requirements, the derivation of the PMM is more coherent and resolves the problem of the negative variance which can occur when using other PEMs derived from the Taylor Series Expansion.
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To do this, one constructs an earnings model incorporating all positive and negative variances you can imagine.
Negative variances often result from immoderate multicollinearity [54]; that is, they indicate that some indicators for the same factor "are sufficiently different, but nevertheless similar enough to measure the same concept" [55] (p. 99).
However, such subtraction may generate negative transition probabilities or negative variances in emission probabilities.
Such estimates are not only meaningless, but also inappropriate since negative variances are inadmissible.
Then, negative entries along the diagonal of the Hessian matrix led to negative variances in the variance-covariance matrix, making uncertainty estimation impossible using the present framework.
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