[R] ANOVA vs REML approach to variance component estimation

[Adaikalavan Ramasamy]

Thank you.

On Sun, 2005-06-12 at 18:54 -0500, Douglas Bates wrote:
> On 6/12/05, Adaikalavan Ramasamy <ramasamy at cancer.org.uk> wrote:
> > Thank you for confirming this and introducing me to varcomp().
> > 
> > I have another question that I hope you or someone else can help me
> > with. I was trying to generalise my codes for variable measurement
> > levels and discovered that lme() was estimating the within group
> > variance even with a single measure per subject for all subjects !
> > 
> > Here is an example where we have 12 animals but with single measurement.
> > 
> >   y  <- c(2.2, -1.4, -0.5, -0.3, -2.1, 1.5,
> >           1.3, -0.3, 0.5, -1.4, -0.2, 1.8)
> >   ID <- factor( 1:12 )
> > 
> > 
> > Analysis of variance method correctly says that there is no residual
> > variance and it equals to total variance.
> > 
> > summary(aov(y ~ ID))
> >             Df  Sum Sq Mean Sq
> > ID          11 20.9692  1.9063
> > 
> > 
> > However the REML method is giving me a within animal variance when there
> > is no replication at animal level. It seems like I can get components of
> > variance for factors that are not replicated.
> > 
> > library(ape)
> > varcomp(lme(y ~ 1, random = ~ 1 | ID))
> >        ID    Within
> > 1.6712661 0.2350218
> > 
> > Am I reading this correct and can someone kindly explain this to me ?
> 
> It's a spurious convergence in lme.  There is no check in lme for the
> number of observations exceeding the number of groups.  There should
> be.  I'll add this to the bug reports list.
>