From: Douglas Bates <bates_at_stat.wisc.edu>

Date: Tue 18 Jul 2006 - 05:42:11 EST

R-help@stat.math.ethz.ch mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Tue Jul 18 05:49:26 2006

Date: Tue 18 Jul 2006 - 05:42:11 EST

On 7/17/06, Göran Broström <goran.brostrom@gmail.com> wrote:

> On 7/15/06, Douglas Bates <bates@stat.wisc.edu> wrote:

*> [....]
**> > <rant>
**> > Some software, notably SAS PROC MIXED, does produce standard errors
**> > for the estimates of variances and covariances of random effects. In
**> > my opinion this is more harmful than helpful. The only use I can
**> > imagine for such standard errors is to form confidence intervals or to
**> > evaluate a z-statistic or something like that to be used in a
**> > hypothesis test. However, those uses require that the distribution of
**> > the parameter estimate be symmetric, or at least approximately
**> > symmetric, and we know that the distribution of the estimate of a
**> > variance component is more like a scaled chi-squared distribution
**> > which is anything but symmetric.
**>
**> You should add ..."when the true value of the variance is (close to)
**> zero", I guess. Or does not standard asymptotic ML theory apply to
**> these models? BTW, what is a
**> "scaled chi-squared distribution"?
*

Consider a simple case of an iid sample from a normal distribution with mean $\mu$ and variance $\sigma^2$. In that case the sample variance $s^2$ has a $\sigma^2\chi^2$ distribution with n-1 degrees of freedom. (Either that or I have been seriously misinforming my intro statistics classes for several years now.) That's all I meant by a "scaled chi-squared distribution".

All I am claiming here is that estimates of other variance components in more complicated models have a similar behavior, not exactly this behavior. The point is that they would not be expected to have nice, symmetric distributions that can be characterized by the estimate and a standard error of the estimate. If you create a Markov chain Monte Carlo sample from a fitted lmer object you generally find that the logarithm of a variance component has a posterior distribution that is close to symmetric. Depending on how precisely the variance component is estimated, the distribution of the variance component itself can be far from symmetric.

If it still seems that I am stating things too loosely then perhaps we could correspond off-list and I could try to explain more clearly what I am claiming.

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https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html Received on Tue Jul 18 05:49:26 2006

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