[R-sig-ME] Fwd: lmer stand dev of coefficients

[Andrew Robinson]

On Sun, Dec 21, 2008 at 02:35:20PM -0600, Douglas Bates wrote:
> 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?

Yes indeed - this is how I believe Morris proceeds.

Andrew
 
-- 
Andrew Robinson  
Department of Mathematics and Statistics            Tel: +61-3-8344-6410
University of Melbourne, VIC 3010 Australia         Fax: +61-3-8344-4599
http://www.ms.unimelb.edu.au/~andrewpr
http://blogs.mbs.edu/fishing-in-the-bay/