I am trying to obtain the asymptotic covariance matrix of the covariance parameters of a mixed-effects model using SAS and R
In SAS, this matrix can easily be obtained by using the 'asycov' option in PROC MIXED.
For example, suppose we fit a random intercept model to the Orthodont dataset (which is available in the nlme package or can be downloaded here: https://dl.dropboxusercontent.com/u/8416806/Orthodont.txt ) using the following syntaxis:
proc mixed data=WORK.Ortho method=reml covtest asycov; class sex ; model distance = age sex / SOLUTION ddfm=kr ; random intercept /type=un subject=Subject ; run;
Then we get:
Asymptotic Covariance Matrix of Estimates Row Cov Parm CovP1 CovP2 1 UN(1,1) 1.1491 -0.02625 2 Residual -0.02625 0.1050
Now a similar model is fitted in R using the nlme package:
library(nlme) model <- lme(distance ~ age + Sex, data = Orthodont, random = ~ 1)
As far as I understand, "model$apVar" provides the estimated asymptotic covariance matrix of a particular transformation of the variance components.
For example, model$apVar
reStruct.Subject lSigma reStruct.Subject 0.0269251707 -0.0009807458 lSigma -0.0009807458 0.0062498946 attr(,"Pars") reStruct.Subject lSigma 0.5919030 0.3587872 attr(,"natural")  TRUE
It is not clear to me which particular transformation is used, and how I can obtain the 'untransformed' estimates (similar to what is provided by the asycov option in proc MIXED)?
Any help would be greatly appreciated,