# Asymptotic covariance matrix of the covariance parameters SAS versus lme

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")
[1] 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,

Regards Willem