Hi Joyce,
 
If you want to simulate from the model parameters, including simulating from the variance component distribution you can get pretty exact distributions (all beit Bayesian ...) using Havad Rue's INLA package which can be found in http://www.r-inla.org/.  You had to use your wits to simulate from the posterior distributions last time i looked (abt 4 months ago), but he is always working on it so it may be more user freindly now. 
 
Its strength is structured random effects, however it will also do iid random effects so is a Bayesian alternative in R to lme4.  Its definately worth a reccy.
 
Hope this helps,
Colin

________________________________

From: r-sig-mixed-models-bounces@r-project.org on behalf of Douglas Bates
Sent: Wed 03/03/2010 18:21
To: Yuan Yuan
Cc: r-sig-mixed-models@r-project.org
Subject: Re: [R-sig-ME] var estimates of the random effects variance in lme4



On Wed, Mar 3, 2010 at 11:57 AM, Yuan Yuan <joyce@mcs.st-and.ac.uk> wrote:
> Hi, all
> For an estimate of the parameter, we have a variance estimate associated with
> the parameter estimate.

Usually called the standard error of a parameter estimate.

> Say, let beta denote the fixed effect in linear regresssion, we have an estimate
> given the data,\hat{beta} and its variance estimate \hat{var}[\hat{beta}].
> My question is, for the random effects, denoted by b, sd(b) is our parameter of
> interest, but I can not find the estimated sd[sd(b)]. There is \hat{sd(b)} in
> the summary list, but not \hat{sd}{\hat{sd(b)}}.

> I was told that you can find estimted var[var(random effect)] in SAS
> Is there anyone can tell me whether or not I can find var[var(random effect)] in
> the output given by glmer in package lme4?

It is true that SAS does provide a standard error of a variance
estimate from SAS PROC MIXED.  If you check the book by West, Welch
and Galecki (ISBN 1-58488-480-0) you will see that all of the software
systems they use to fit mixed-effects models provide such standard
errors, except for the nlme package in R and the lme4 package for R.
This is intentional.  Standard errors of variance estimates are
nonsensical because the estimators are highly skewed.  This is
discussed and illustrated in chapters 1 and 2 of the book I am writing
for which the chapter drafts are available at
http://lme4.R-forge.R-project.org/book/

> Thank you very much.
>
> Cheers,
> Joyce
> --
> Yuan(Joyce) Yuan
> PhD student in Statistics
>
> CREEM - Centre for Research into Ecological and Environmental Modelling
> University of St Andrews
> The Observatory
> Buchanan Gardens
> St Andrews
> Fife
> KY16 9LZ
> Scotland
>
> Tel: +44 (0)1334 461826
> Fax: +44 (0)1334 461800
>
>
> ------------------------------------------------------------------
> University of St Andrews Webmail: https://webmail.st-andrews.ac.uk <https://webmail.st-andrews.ac.uk/> 
>
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