Negative Variance

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?

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.

The job of computer output, in my view, is to be as informative as
possible while keeping the output as terse as possible.

John Maindonald             email: john.maindonald at anu.edu.au
phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
Centre for Mathematics & Its Applications, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.
http://www.maths.anu.edu.au/~johnm

Callie Baird <calliebaird at ...> writes:

I am trying to fit multilevel models, allowing negative variance estimates.
Is there a way to allow negative variance estimates as in nobound in SAS?

Thanks,

Rachel Baird

 I don't know of one.  This is typically a 'feature' of 
method-of-moments estimators; most of the approaches I know of
that are implemented in R use Bayesian or (restricted) maximum
likelihood approaches for which negative variances would be
completely nonsensical ...

 Just out of curiosity, why would you _want_ negative variance
estimates ... ?  The only reason I can think of would be to
match previous estimates ...

 Ben Bolker

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