Standard errors of variances; negative variance

Regarding standard errors for variance components: Will, I'm not sure if
you were asking about lme4::lmer() or nlme::lme(). If you're not familiar
with the latter, you might find it interesting. It is in some respects more
flexible than lmer(), such as providing model components for different
level-1 error structures and correlation structures, and so you might find
it more comparable to SAS. If you're using nlme::lme(), the lmeInfo package
provides a variance-covariance matrix for the variance component parameters
(based on the inverse expected information or average information):
https://jepusto.github.io/lmeInfo/
That said, I agree with the other folks who've suggested that likelihood
ratio tests and profile likelihood CIs might be a better choice for
inference on variance components.

Regarding negative variances, Ben's post is instructive. In addition, in
some specific problems related to meta-analysis, we've found that allowing
for negative variance components can improve the performance of score and
likelihood ratio tests involving other model parameters. My working theory
here is that bounding variances at zero means that the log likelihood is no
longer smooth, which seems to  muck up the behavior or tests that involve
the first and second derivatives of the log likelihood.

James

Standard errors of variances; negative variance

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