[R-sig-ME] [R] coef se in lme

[dave fournier]

The AD Model Builder method I posted earlier takes into account the
uncertainty in the mean and both std deviations in Harold's simple model.

        Y_ij - mu + u_i +eps_ij

To illustrate this
I built a little model and simulated a data set with 1<=i<=10, 1<=j<=5 
observations.  Below are the parameter estiamtes tigether with their
estimated std devs.  The true values were mu=3.0 sigma_u=2.0 and sigma=3.0



>     1   mu           2.4091e+00 7.4307e-01
>     2   log_sigma_u  6.3908e-01 3.4913e-01
>     3   log_sigma    1.1354e+00 1.1180e-01
>     4   u           -3.1695e-01 6.4561e-01
>     5   u            2.0441e-01 6.4496e-01
>     6   u            5.1996e-01 6.4748e-01
>     7   u            4.3754e-01 6.4661e-01
>     8   u            4.8381e-01 6.4708e-01
>     9   u            1.2214e+00 6.6075e-01
>    10   u           -1.7631e+00 6.7793e-01
>    11   u            3.3987e-01 6.4578e-01
>    12   u           -1.7663e-01 6.4485e-01
>    13   u           -9.5030e-01 6.5439e-01

then I fixed log_sigma_u and log_sigma at their
estimated values and obtained.
> # fixed sd's
>  index   name   value      std dev
>      1   mu  2.4093e+00 7.4307e-01
>      2   u  -3.1736e-01 6.4407e-01
>      3   u   2.0456e-01 6.4407e-01
>      4   u   5.2045e-01 6.4407e-01
>      5   u   4.3794e-01 6.4407e-01
>      6   u   4.8426e-01 6.4407e-01
>      7   u   1.2226e+00 6.4407e-01
>      8   u  -1.7650e+00 6.4407e-01
>      9   u   3.4016e-01 6.4407e-01
>     10   u  -1.7689e-01 6.4407e-01
>     11   u  -9.5138e-01 6.4407e-01
and finally I almost fixed mu
(can't fix it completley because then there would be
no "fixed" effects and the model thinks there is
nothing to do.) and obtained

> # all fixed
>  index   name   value      std dev
>      1   mu  2.4093e+00 2.2361e-03
>      2   u  -3.1736e-01 5.9145e-01
>      3   u   2.0456e-01 5.9145e-01
>      4   u   5.2045e-01 5.9145e-01
>      5   u   4.3794e-01 5.9145e-01
>      6   u   4.8426e-01 5.9145e-01
>      7   u   1.2226e+00 5.9145e-01
>      8   u  -1.7650e+00 5.9145e-01
>      9   u   3.4016e-01 5.9145e-01
>     10   u  -1.7689e-01 5.9145e-01
>     11   u  -9.5138e-01 5.9145e-01
So for example u(1) the first random effect has estimated std devs

  6.4561e-01, 6.4407e-01, and 5.9145e-01


under the three models. It appears that most of the "extra" uncertainty 
in u(1) comes from the uncertainty in mu.

-- 
David A. Fournier
P.O. Box 2040,
Sidney, B.C. V8l 3S3
Canada
Phone/FAX 250-655-3364
http://otter-rsch.com