[R-sig-ME] Why am I getting a Variance of 0 for my random effect

[Andrew Robinson]

On Wed, Aug 11, 2010 at 03:05:06PM -0500, Douglas Bates wrote:
> > Thanks Doug. ?Your response is helpful, as always. ?If RN does not
> > contribute a random effect, would it be appropriate to revert to a
> > standard regression model, or is it best to leave the unimportant
> > random effect? ?In the case of ordinary regression, dropping
> > variables based on their p-values compromises inference. ?Does the
> > same apply with dropping a random effect with no variance?
> 
> When the random effects variance is zero the model reverts to the
> linear regression model in the sense that the two models give the same
> predicted values, the same log-likelihood, coefficient estimates for
> the fixed effects and standard errors.  That is, there is no need to
> continue to represent the model as a linear mixed model if the only
> variance component parameter's estimated value is zero.

It's worth noting that this behaviour will not always be what you want
to happen.  There are times when you may want the inference and
estimation that arise from a model to reflect the inclusion of random
effects, even if the mode of the density of those effects is zero.

This is true, for example, in design-based inference.  For example,
you may feel strongly that the experimental design (or sample design)
has elements of clustering, and that to fit a model that ignores the
clustering will result in negatively biased estimates of the standard
errors of the fixed effects.

If your inference is model based, then this behaviour should be
perfectly fine.

Best wishes,

Andrew

-- 
Andrew Robinson  
Program Manager, ACERA 
Department of Mathematics and Statistics            Tel: +61-3-8344-6410
University of Melbourne, VIC 3010 Australia               (prefer email)
http://www.ms.unimelb.edu.au/~andrewpr              Fax: +61-3-8344-4599
http://www.acera.unimelb.edu.au/