[R] variance estimates in lme biased?

[Thomas Lumley]

On Tue, 16 Dec 2003, Gary Allison wrote:

> Hi all,
> I didn't get a response to my post of this issue a week ago, so I've
> tried to clarify:
>
> When I use lme to analyze a model of nested random effects, the variance
> estimates of levels higher in the hierarchy appear to have much more
> variance than they should.
>
> In the example below with 4 levels, I simulate variance in level 2
> (sd=1.0) and level 4 (sd=0.1), but levels 1 and 3 do not vary.  Although
> I expected to see a small amount of variability in the lme estimates of
> levels 1 and 3, I am confused by what happens in the level 1 estimates:
>   more than 10% of the runs produce stdDev of >0.4 and in many cases the
> level 1 estimate is close to level 2's. Nothing like that happens in
> level 3.
>

While I haven't seen any literature on this precise problem I would not be
particularly surprised by it.  Your model says that there is a lot of
variability at level two but that it all averages out to zero within a
level 1 unit.  It would not be particularly surprising if some of the
level 2 variability leaked up to level one, since it is only being
averaged over 5 level 2 units per level 1 unit.

Given sufficient data this will eventually stop happening, but you don't
have very many level 1 replicates either.

I think that if you really need to estimate a small variance component
with large variances nested within it, you need a lot more data or a
prior.


	-thomas