[R] within group variance of the coeficients in LME

[J.R. Lockwood]

> I would appreciate your reflection on the following. I need a quantitative
> figure to evaluate weather the covariate varies across second level units in
> the process of simulation. Of course I will be running thousands of them and
> would need to program the condition in code. In one of the previous
> questions to the group dr. Bates suggested to use the CI estmates, however
> he warned me about their very conservative nature (I got the same tip from
> the book). I thought about using the lower bound of the CI as an estimate
> with the rule "if above 0 then the covariate varies". Would that be a sound
> think to do? Do you have any other suggestions? I would really appreciate
> the feedback.

I somehow missed Dr. Bates useful clarification regarding the apVar
component of the lme object (I had forgotten that the optimization and
apVar used different transformations).  I agree with him that even
though it is possible to obtain standard errors for your variance
components using an appropriate transformation of the apVar component,
you probably don't want to use that because the Wald statistics on
this scale will be ill-behaved. I would second the notion that the CIs
obtained from intervals() on your lme object (using a more
well-behaved scale) during the simulation is the best way to get at
what you want, even if they are conservative.  I think what you want
to do is think about why you are simulating -- presumably to
understand the properties of some operation on real data.  If you had
real data and wanted to test the variance components, you would
probably use the CIs from intervals().

J.R. Lockwood
412-683-2300 x4941
lockwood at rand.org
http://www.rand.org/methodology/stat/members/lockwood/