# [R] standard error of variances and covariances of the random effects with LME

Roel de Jong dejongroel at gmail.com
Fri Sep 30 01:10:33 CEST 2005

```Well I finally figured it out. If you use the delta method with
transformations exp(x) for the standard deviations and
((exp(y)-1)/(exp(y)+1) for the correlation elements of the apVar
structure, which is btw *not* the inverse of a fisher transformation,
you get the standard errors.

Douglas Bates wrote:
> With lme you could but it would take a while to work it out.  There is
> an approximate Hessian matrix for the parameters that determine the
> variance-covariance matrix in there somewhere and if you were
> sufficiently persistent you could convert that apVar component to the
> scale of the variances and covariances.  I believe it is in the scale
> of the logarithm of the standard deviation and Fisher's z
> transformation (i.e. the hyperbolic arc tangent) of the correlation.
>
> On 9/29/05, Doran, Harold <HDoran at air.org> wrote:
>
>>You cannot. Also, it's not that the distribution of the random effects
>>is not symmetric, but that it *may* not be symmetric, and this is an
>>assumption that should be checked.
>>
>>-----Original Message-----
>>From: r-help-bounces at stat.math.ethz.ch
>>[mailto:r-help-bounces at stat.math.ethz.ch] On Behalf Of Roel de Jong
>>Sent: Thursday, September 29, 2005 9:20 AM
>>To: r-help at stat.math.ethz.ch
>>Subject: [R] standard error of variances and covariances of the random
>>effects with LME
>>
>>Hello,
>>
>>how do I obtain standard errors of variances and covariances of the
>>random effects with LME comparable to those of for example MlWin? I know
>>you shouldn't use them because the distribution of the estimator isn't
>>symmetric blablabla, but I need a measure of the variance of those
>>estimates for pooling my multiple imputation results.
>>
>>Regards,
>>   Roel.
>>
>>______________________________________________
>>R-help at stat.math.ethz.ch mailing list
>>https://stat.ethz.ch/mailman/listinfo/r-help
>>http://www.R-project.org/posting-guide.html
>>
>>______________________________________________
>>R-help at stat.math.ethz.ch mailing list
>>https://stat.ethz.ch/mailman/listinfo/r-help