[R-sig-ME] var estimates of the random effects variance in lme4

[Douglas Bates]

On Wed, Mar 3, 2010 at 11:57 AM, Yuan Yuan <joyce at 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
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> St Andrews
> Fife
> KY16 9LZ
> Scotland
>
> Tel: +44 (0)1334 461826
> Fax: +44 (0)1334 461800
>
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