lmer stand dev of coefficients

On Sun, Dec 21, 2008 at 2:12 PM, Andrew Robinson
<A.Robinson at ms.unimelb.edu.au> wrote:

Hi all,

This article might help:

The BLUPs are not "best" when it comes to bootstrapping

Jeffrey S. Morris

Statistics & Probability Letters 56 (2002) 425-430

In the setting of mixed models, some researchers may construct a
semiparametric bootstrap by sampling from the best linear unbiased
predictor residuals.  This paper demonstrates both mathematically and
by simulation that such a bootstrap will consistently underestimate
the variation in the data in finite samples.

Cheers,

Andrew

Thanks, Andrew.

It occurred to me after I wrote my response that simulation would be a
good way of seeing this effect.  In other words, simulate data from a
simple model with a known variance for the random effects and the
noise then check what the mle and REML estimates of the variance are
and what the variance or standard deviation of the conditional modes
are.

Also, are there formulas for the BLUPs in the case of a simple
one-factor balanced design like the Dyestuff data?  Can these be used
to show that the BLUPs will tend to have an empirical standard
deviation whose expectation is less than the standard deviation of the
random effects?