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 <[EMAIL PROTECTED]> wrote: >> On 7/15/06, Douglas Bates <[EMAIL PROTECTED]> 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. > > ______________________________________________ > [email protected] 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 http://www.cas.muohio.edu/~stevenmh/ http://www.muohio.edu/ecology/ http://www.muohio.edu/botany/ "E Pluribus Unum" _______________________________________________ R-SIG-Mac mailing list [email protected] https://stat.ethz.ch/mailman/listinfo/r-sig-mac
