Extract the covariance matrix for estimates covariance parameters in R?

Question

I'm trying to run a simulation on pattern mixture model and I need to "Asymptotic Covariance Matrix of Estimates or Covariance matrix for estimates covariance parameter" in R (under unstructured).
I know this will be achieved by AsyCov in SAS and by mixed model in SPSS.
But I don't know why the results of asyCov (metaSEM package) are not consistent with SAS and SPSS output.

Here is my SAS code:

proc Mixed data=OutcomeSort method=reml asycov covtest;
  class Subject Rep; 
  model Y= x / s covb; 
  repeated Rep / subject=Subject type=UN r; 
run;

and my SAS output:

                               Covariance Parameter Estimates

                                              Standard         Z
           Cov Parm    Subject    Estimate       Error     Value        Pr Z

           UN(1,1)     Subject     50.6700      5.2325      9.68      <.0001
           UN(2,1)     Subject     38.9197      6.1316      6.35      <.0001
           UN(2,2)     Subject      109.57     11.3113      9.69      <.0001
           UN(3,1)     Subject     37.8759      7.1731      5.28      <.0001
           UN(3,2)     Subject     83.7478     11.5030      7.28      <.0001
           UN(3,3)     Subject      162.44     16.7682      9.69      <.0001
           UN(4,1)     Subject     32.3689      8.6577      3.74      0.0002
           UN(4,2)     Subject     85.1421     13.6659      6.23      <.0001
           UN(4,3)     Subject      149.65     18.3647      8.15      <.0001
           UN(4,4)     Subject      247.16     25.7446      9.60      <.0001


                  Asymptotic Covariance Matrix of Estimates

Row  Cov Parm     CovP1     CovP2     CovP3     CovP4     CovP5     CovP6     CovP7     CovP8

  1  UN(1,1)    27.3790   20.9481   15.9859   20.3577   15.5259   15.0775   17.0100   12.8662
  2  UN(2,1)    20.9481   37.5971   45.4151   30.4336   39.4733   33.8181   29.8290   36.7129
  3  UN(2,2)    15.9859   45.4151    127.95   34.7757   97.8981   74.9444   36.0516    100.22
  4  UN(3,1)    20.3577   30.4336   34.7757   51.4533   50.6228   65.5963   47.2107   45.8363
  5  UN(3,2)    15.5259   39.4733   97.8981   50.6228    132.32    145.12   49.1089    126.34
  6  UN(3,3)    15.0775   33.8181   74.9444   65.5963    145.12    281.17   61.4499    134.74
  7  UN(4,1)    17.0100   29.8290   36.0516   47.2107   49.1089   61.4499   74.9564   69.2153
  8  UN(4,2)    12.8662   36.7129    100.22   45.8363    126.34    134.74   69.2153    186.76
  9  UN(4,3)    12.4790   31.8059   76.8862   58.5769    141.49    260.08   79.1265    182.24
 10  UN(4,4)    10.2027   29.7120   78.8488   52.3062    137.66    240.73   91.0933    231.19

                               Row     CovP9      CovP10

                                 1   12.4790     10.2027
                                 2   31.8059     29.7120
                                 3   76.8862     78.8488
                                 4   58.5769     52.3062
                                 5    141.49      137.66
                                 6    260.08      240.73
                                 7   79.1265     91.0933
                                 8    182.24      231.19
                                 9    337.26      401.18
                                10    401.18      662.78

and here my R code:

Std.Err.Cov.par <- matrix (c(5.2325,6.1316,7.1731,8.6577,6.1316, 11.3113,11.5030,13.6659,7.1731,11.5030,16.7682,18.3647,8.6577,13.6659,18.3647,25.7446),4)) 
Std.Err.Cov.parasyCov
       [,1]    [,2]    [,3]    [,4]
[1,] 5.2325  6.1316  7.1731  8.6577
[2,] 6.1316 11.3113 11.5030 13.6659
[3,] 7.1731 11.5030 16.7682 18.3647
[4,] 8.6577 13.6659 18.3647 25.7446

asyCov(Std.Err.Cov.par,n=100,cor.analysis = F)

      x1x1      x2x1      x3x1      x4x1      x2x2      x3x2     x4x2
x1x1 0.5366875 0.6289067 0.7357319 0.8880043 0.7369721 0.8621534 1.040591
x2x1 0.6289067 0.9485741 1.0209965 1.2211370 1.3595297 1.4865150 1.781083
x3x1 0.7357319 1.0209965 1.3642389 1.5504870 1.3825724 1.8164115 2.079731
x4x1 0.8880043 1.2211370 1.5504870 2.0549314 1.6425356 2.0644151 2.706764
x2x2 0.7369721 1.3595297 1.3825724 1.6425356 2.5079958 2.5505029 3.030071
x3x2 0.8621534 1.4865150 1.8164115 2.0644151 2.5505029 3.1558301 3.576670
x4x2 1.0405908 1.7810828 2.0797308 2.7067640 3.0300707 3.5766699 4.684520
x3x3 1.0085977 1.6174143 2.3577429 2.5822236 2.5937308 3.7809433 4.140927
x4x3 1.2173439 1.9368496 2.7139703 3.3682746 3.0814257 4.3163971 5.362250
x4x4 1.4692936 2.3192276 3.1166576 4.3690889 3.6608210 4.9195376 6.896459

     x3x3     x4x3      x4x4
x1x1 1.008598 1.217344  1.469294
x2x1 1.617414 1.936850  2.319228
x3x1 2.357743 2.713970  3.116658
x4x1 2.582224 3.368275  4.369089
x2x2 2.593731 3.081426  3.660821
x3x2 3.780943 4.316397  4.919538
x4x2 4.140927 5.362250  6.896459
x3x3 5.511570 6.036326  6.611043
x4x3 6.036326 7.536536  9.267696
x4x4 6.611043 9.267696 12.991931

Answer 1

We really need a reproducible example, but based on this SAS code:

proc Mixed data=OutcomeSort method=reml asycov covtest;
  class Subject Rep; 
  model Y= x / s covb; 
  * options: covb displays fixed-effect var-cov matrix
  *          s (solution) displays fixed-effect estimates
  repeated Rep / subject=Subject type=UN r; 
  * repeated: "R-side" (residual) effects
  * Rep governs order? of obs (I think this is 
  *    irrelevant for unstructured var-cov matrices?)
  * Subject is grouping variable
  * unstructured var-cov matrix (this is R's default)
  * r: display blocks of R matrix
run;

I would suggest that the corresponding R code is something like:

library(nlme)
Orthodont$fAge <- factor(Orthodont$age)
Orthodont$nAge <- as.numeric(Orthodont$fAge)
fit1 <- gls(distance~Sex,
    correlation=corSymm(form=~nAge|Subject),
    weights=varIdent(form=~1|fAge),
    data=Orthodont)

However, this gives Wald variances on the correlation parameters ( corStruct* ), ratios of variances 2-4 to variance 1 ( varStruct* ), and residual variance ( lSigma ); furthermore, these are the variances of the parameters on the natural scale.

From Pinheiro and Bates 2000 p. 93 Google books :

The approach used in lme [and gls ] is to consider a different parameterization when calculating confidence intervals. This parameterization, which we call the natural parameterization, uses the logarithm of standard deviations and the generalized logits of the correlations. For a given correlation parameter $-1 < \\rho < 1$, its generalized logit is $\\log[(1+\\rho)/(1-\\rho)]$ which can take any value on the real line

The inverse transformations for these transformations are exp(lSigma) and (exp(logitRho)-1)/(exp(logitRho)+1) .

From here, you have to use the delta method to put these pieces and transformations back together ...

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