[R-sig-ME] Negative Variance

[Ben Bolker]

John Maindonald <john.maindonald at ...> writes:

> 
> Negative variance estimates can be very useful in alerting that the
> variance-covariance structure is not what one expects.  Or they may
> allow the simplest way of specifying the overall variance-covariance
> structure, short of specifying the variance-covariance structure in
> some detail.
> 
> I was told of an experiment where the experimenters had chosen 
> blocks to be at right angles to the river bank, accordingly maximising
> between plot variance.  This came to light, in data analysed away
> from the scene of the original trial, when the block variance was
> estimated as negative -- a very useful diagnostic.  Certainly, one can 
> check on such a possibility by specifying a suitable variance-covariance 
> structure, but how many analysts will take that trouble?

  I don't quite get the geometry you're talking about, but
I take the general point that diagnostics are good and that
one wouldn't necessarily think to consider negative correlation.
  
> Or one has results from each of two eyes per person.  After allowing
> for any systematic left/right difference, are two eyes from the same
> individual more or less different than two eyes from different 
> individuals?  I doubt that there is a general answer that applies to all
> types of eye measurements.

  I find this one a little bit less convincing -- here it would
seem to be perfectly natural to fit a model that allowed for
positive or negative correlation.

  The fact remains that, whether or not it's a good idea,
 this is very hard to do in nlme/lme4 for
structural reasons. Luckily people are suggesting alternative
packages.  (Anyone who would like to edit 
http://glmm.wikidot.com/pkg-comparison accordingly is welcome
to do so ...)

  I don't think "how do I estimate negative variances?" has quite
risen to the level of a FAQ yet, so I won't bother adding it
to http://glmm.wikidot.com/faq (although again, if anyone wants
to take the initiative to do so I wouldn't complain).

    Ben Bolker