[R-SIG-Mac] [R] storing the estimates from lmer

Martin Henry H. Stevens HStevens at MUOhio.edu
Mon Jul 17 21:52:24 CEST 2006

Hi Doug,
I, for one, am learning a lot of theoretical and applied statistics  
by following these threads. I would love to continue to be able to  
eavesdrop, either on r-help, or elsewhere.
Hank Stevens
On Jul 17, 2006, at 3:42 PM, Douglas Bates wrote:

> On 7/17/06, Göran Broström <goran.brostrom at gmail.com> wrote:
>> On 7/15/06, Douglas Bates <bates at 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.
> ______________________________________________
> R-help at 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

Dr. M. Hank H. Stevens, Assistant Professor
338 Pearson Hall
Botany Department
Miami University
Oxford, OH 45056

Office: (513) 529-4206
Lab: (513) 529-4262
FAX: (513) 529-4243
"E Pluribus Unum"

More information about the R-SIG-Mac mailing list