# [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.
Regards,
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.
>
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Dr. M. Hank H. Stevens, Assistant Professor
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